Deep Learning-Enriched Stress Level Identification of Pretensioned Rods via Guided Wave Approaches

Zi Zhang; Fujian Tang; Qi Cao; Hong Pan; Xingyu Wang; Zhibin Lin

doi:10.3390/buildings12111772

Deep Learning-Enriched Stress Level Identification of Pretensioned Rods via Guided Wave Approaches

Zhang, Zi;Tang, Fujian;Cao, Qi;Pan, Hong;Wang, Xingyu;Lin, Zhibin 2022-10-22 00:00:00 buildings Article Deep Learning-Enriched Stress Level Identiﬁcation of Pretensioned Rods via Guided Wave Approaches 1 2 2 1 1 1 , Zi Zhang , Fujian Tang , Qi Cao , Hong Pan , Xingyu Wang and Zhibin Lin * Department of Civil and Environmental Engineering, North Dakota State University, Fargo, ND 58018, USA School of Civil Engineering, Dalian University of Technology, Dalian 116024, China * Correspondence: zhibin.lin@ndsu.edu; Tel.: +1-701-231-7204 Abstract: By introducing pre-compression/inverse moment through prestressing tendons or rods, prestressed concrete (PC) structures could overcome conventional concrete weakness in tension, and thus, these tendons or rods are widely accepted in a variety of large-scale, long-span structures. Unfortunately, prestressing tendons or rods embedded in concrete are vulnerable to degradation due to corrosion. These embedded members are mostly inaccessible for visual or direct destructive assessments, posing challenges in determining the prestressing level and any corrosion-induced damage. As such, ultrasonic guided waves, as one of the non-destructive examination methods, could provide a solution to monitor and assess the health state of embedded prestressing tendons or rods. The complexity of the guided wave propagation and scattering in nature, as well as high variances stemming from the structural uncertainty and noise interference PC structures may experience under complicated operational and harsh environmental conditions, often make traditional physics- based methods invalid. Alternatively, the emerging machine learning approaches have potential for processing the guided wave signals with better capability of decoding structural uncertainty and noise. Therefore, this study aimed to tackle stress level prediction and the rod embedded conditions of prestressed rods in PC structures through guided waves. A deep learning approach, convolutional neural network (CNN), was used to process the guided wave dataset. CNN-based prestress level Citation: Zhang, Z.; Tang, F.; Cao, Q.; prediction and embedding condition identiﬁcation of rods were established by the ultrasonic guided Pan, H.; Wang, X.; Lin, Z. Deep wave technique. A total of ﬁfteen scenarios were designed to address the effectiveness of the stress Learning-Enriched Stress Level level prediction under different noise levels and grout materials. The results demonstrate that the Identiﬁcation of Pretensioned Rods via Guided Wave Approaches. deep learning approaches exhibited high accuracy for prestressing level prediction under structural Buildings 2022, 12, 1772. https:// uncertainty due to the varying surrounding grout materials. With different grout materials, accuracy doi.org/10.3390/buildings12111772 could reach up to 100% under the noise level of 90 dB, and still maintain the acceptable range of 75% when the noise level was as high as 70 dB. Moreover, the t-distributed stochastic neighbor embedding Academic Editor: Erwin Oh technology was utilized to visualize the feature maps obtained by the CNN and illustrated the Received: 24 September 2022 correlation among different categories. The results also revealed that the proposed CNN model Accepted: 20 October 2022 exhibited robustness with high accuracy for processing the data even under high noise interference. Published: 22 October 2022 Publisher’s Note: MDPI stays neutral Keywords: guided wave; convolutional neural network; structural health monitoring; stress level with regard to jurisdictional claims in prediction; t-distributed stochastic neighbor embedding published maps and institutional afﬁl- iations. 1. Introduction Conventional reinforced concrete, due to the weakness of the concrete in tension, Copyright: © 2022 by the authors. often shows cracking and corrosion at an early age [1,2]. PC has been proposed through Licensee MDPI, Basel, Switzerland. prestressing/post-tensioning tendons/rods to compensate this drawback [3]. PC structures This article is an open access article exhibit dramatically improved performance over conventional reinforced concrete ones, distributed under the terms and with the contribution of prestressing tendons or rods that enable them to cover a longer conditions of the Creative Commons span, thereby providing an effective solution in large-scale buildings, bridges, dams, and Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ nuclear power plant structures. It is known that PC structures often experience losses in 4.0/). prestress due to various factors, including shrinkage/creep of concrete and relaxation of Buildings 2022, 12, 1772. https://doi.org/10.3390/buildings12111772 https://www.mdpi.com/journal/buildings Buildings 2022, 12, 1772 2 of 19 tendons/rods, which in turn potentially lead to excessive deﬂection or cracking. As such, being able to quantify the stress level of these prestressing tendons/rods in service condi- tions is critical to ensure structural integrity and achieve successful performance. However, conventional visual or direct destructive examination tools are not valid, as the embedded prestressing tendons or rods with or without grout materials are often inaccessible. There- fore, non-destructive examination (NDE) methods and tools, including vibration-based sensors [4], distributed sensors [5], ultrasonic guided waves [6,7], or acoustic emission [8], could capture information of those far-reaching, inaccessible locations, while maintaining high-quality monitoring and assessing of structural health. For instance, Bartoli et al. [4] em- ployed dynamic identiﬁcation techniques to investigate the correlation between PC beam prestressing forces. Their results demonstrated that the vibration frequency could assist in identifying the prestress level. Chen et al. [5] used distributed sensor, long-gauge ﬁber Bragg grating to detect the damage of a bridge under stochastic trafﬁc ﬂow. In addition, the existence of anomalies is an important issue in monitoring data; hence, Zhang et al. [9] employed Bayesian dynamic regression to reconstruct missing data. Despite the merits of different sensing techniques, vibration-based methods are often limited in low frequency, while distributed sensors are often vulnerable to damage and anomalies. Alternatively, as stated in the literature [6,10–13], ultrasonic guided waves could be a better solution to tackle such situations, with the advantages of far-reaching, long-distance measurement and high accuracy in detecting small changes in material discontinuity. Additionally, as an active method, ultrasonic guided wave testing can judge the sensitivity and accuracy of a sensor by receiving the excitations, reducing the possibility of receiving abnormal data. Guided waves are widely used to evaluate the health of beams, plates, and pipes, owing to the potential of long-distance propagation and sensitivity to mechanical damage. Three modes, namely longitudinal, ﬂexural, and torsional modes, are generated when guided waves are propagated in a medium. Among them, longitudinal modes are more sensitive to tensile stress and easy to excite by piezoelectric actuators [14], and are used for the inspection of steel bars for corrosion, fracture, and stress reduction. Bread et al. [10] used the pulse-echo technique to detect the corrosion and fracture of grouted tendon anchors and rock bolts by ultrasonic guided waves. Lanza di Scalea et al. [15] applied guided waves through magnetostrictive transducers to monitor the stress in seven-wire strands. Their results demonstrated the feasibility of determining the prestress level using the guided wave method. Ervin et al. [16] created an embeddable ultrasonic sensor network to localize and monitor the corrosion of rebar embedded by mortar. They studied the characteristics of guided wave propagated in rebar and the effect forms for corrosion detection, and showed that the waves were sensitive to corrosion through scattering, mode conversions, and reﬂections. Chaki and Bourse [17] detected the stress level of the seven-wire steel strands by ultrasonic guided waves with L (0,1) mode. The typical calibration curves were plotted, which showed that the stress level corresponded to the phase velocity change in the guided waves. More recently, Treyssède and Laguerre [18] employed the semi-analytical ﬁnite element approach to study the guided wave propagation in multi-wire strands. In addition, high-order longitudinal modes were indicated to solve the leakage problem of fundamental mode L (0,1) by Dubuc et al. [19]. They used the acoustoelastic theory to propose an approximate theory for predicting the effect of stress on higher modes. Shoji Masanari [20] employed 60 kHz L (0,1) mode as the guided wave to inspect anchor rods embedded in soil, and unveiled the capability of the ultrasonic guided waves for stress identiﬁcation in rods. While physics-based approaches have been used for the signal process of guided waves to identify stress changes in stressed rods, these methods still face challenges in handling the wave signals with a variety of structural uncertainties, signal attenuation, and environmental noises during testing. In this way, recently emerging machine learning, particularly deep learning, could provide potential solutions to improve the signal process of guided waves [6,7,21,22]. Deep learning algorithms have been employed in time series [21,23–26] and image processing [27–30]. Guo et al. [31] utilized a sparse coding-based deep learning algorithm to process wireless Buildings 2022, 12, 1772 3 of 19 sensory data of a three-span bridge. The features of the dataset were learned by sparse coding and then trained by the network. Cha et al. [27] proposed a vision-based method by a deep learning network to detect concrete cracks without calculating the features. The comparative study indicated that the deep learning-based technique had better performance than the conventional physics-based methods. Furthermore, Cha et al. [28] investigated the fast region-based convolutional neural network to detect ﬁve types of damage in real time. Zhang et al. [32] proposed a CNN framework with some convolutional kernels to identify vibration signals. Harsh et al. [33] applied high-frequency guided waves to detect damages in railheads, generated the data by experiment and simulation study, and then set up a framework to detect damage of railheads by a machine learning method. The error rate was from 2% to 16.67%. Tabian et al. [34] used guided waves to detect impact energy, localization, and characterization of complex composite structures. The waves transferred into 2D images and were identiﬁed by a CNN algorithm. The results showed that the accuracy was above 95%. Zargar and Yuan [35] used a uniﬁed CNN-RNN network to extract the information of aluminum plates. This research focused on the wave propagation in both spatial and temporal domains. While deep learning approaches have been successfully used in many aspects of structural health monitoring, less research is involved in deep learning-based ultrasonic guided wave diagnoses. Therefore, we aimed to develop and implement the deep learning-enriched guided wave technique to quantify the stress level of prestressed rods used in PC structures. The CNN framework was utilized for processing guided wave signals to predict the stress level of the rods with varying grout materials. t-distributed stochastic neighbor embedding (t-SNE) was employed to visualize the features extracted by the CNN model. Moreover, different noise levels were considered to examine the robustness of the CNN classiﬁer. 2. Guided Waves as NDE Approach for Prestressed Rods 2.1. Governing Equations and Simulation of Guided Waves along a Rod Guided waves were ﬁrst introduced in cylinder structures in the 19th century [36]. The governing equation of the wave propagating in isotropic cylinders is expressed as [37] ¶ u (l + 2m)r(r u) + mr u + f = r (1) ¶x where u represents the displacement vector, x is the time, r is the three-dimensional Laplace operator, l and m indicate Lame’s constants, r is the mass density, and the body force f is equal to zero. Then, the Helmholtz decomposition is used in Equation (1) to simplify the problem as u = r' +r H (2) r H = 0 (3) where ' and H represent the scalar and vector potentials. Three types of guided waves, namely longitudinal mode (L (0, m)), torsional mode (T (0, m)), and ﬂexural mode (F (n, m)), were generated to propagate through a cylindrical structure. In the modes, n and m denote the circumferential order and modulus, respectively. When n = 0, the waves are symmetrical, such as L (0, m) and T (0, m). Otherwise, the waves are asymmetrical. Stress affects the phase velocity of the guided wave. The change in the phase velocity DC is expressed as " # (C ) DC = Dt (4) where C is the unstressed velocity, l represents the length of the wave propagation in the stress area, and Dt is the time change. Buildings 2022, 12, x FOR PEER REVIEW 4 of 19 spectively. When n = 0, the waves are symmetrical, such as L (0, m) and T (0, m). Other- wise, the waves are asymmetrical. Stress affects the phase velocity of the guided wave. The change in the phase veloci- ty is expressed as (𝐶 ) = − 𝛥𝑡 (4) Buildings 2022, 12, 1772 4 of 19 where 𝐶 is the unstressed velocity, l represents the length of the wave propagation in the stress area, and is the time change. Figure 1 shows the phase velocity and group velocity derived by MATLAB PCDisp Figure 1 shows the phase velocity and group velocity derived by MATLAB PCDisp [38,39]. [38,39]. The lower frequency of the excitation waves, less than 50 kHz, was used to re- The lower frequency of the excitation waves, less than 50 kHz, was used to reduce the duce the dispersion of the guided waves. dispersion of the guided waves. Figure 1. Phase velocities and group velocities. Figure 1. Phase velocities and group velocities. As such, the ultrasonic guided waves used in this study were numerically simulated As such, the ultrasonic guided waves used in this study were numerically simulat- by Multiphysics Finite Element (FE) software COMSOL, and their propagation charac- ed by Multiphysics Finite Element (FE) software COMSOL, and their propagation char- teristics along the prestressed rod under different conditions, including under varying acteristics along the prestressed rod under different conditions, including under varying grout materials and different stress levels, were then modeled and extracted using machine grout materials and different stress levels, were then modeled and extracted using ma- learning to assist in data classiﬁcation, as discussed in Section 3. chine learning to assist in data classification, as discussed in Section 3. 2.2. Calibration of the FE Analysis of the Ultrasonic Guided Waves through the Rod 2.2. Calibration of the FE Analysis of the Ultrasonic Guided Waves through the Rod We sought to ensure that proper parameters were used for the rod simulation and We sought to ensure that proper parameters were used for the rod simulation and calibrate the effectiveness of FE-based simulation for capturing the characteristics of the calibrate the effectiveness of FE-based simulation for capturing the characteristics of the wave propagation along rods. One case of the characterization of ultrasonic guided waves wave propagation along rods. One case of the characterization of ultrasonic guided along an anchor rod was selected from the literature [40], in which the rod had a diameter of waves along an anchor rod was selected from the literature [40], in which the rod had a 21 mm and was 2.3 m in length, and was embedded in a concrete block with a cross-section diameter of 21 mm and was 2.3 m in length, and was embedded in a concrete block with of 1.0 m by 1.0 m and a depth of 2.0 m, as shown in the FE meshed model in Figure 2a. The a cross-section of 1.0 m by 1.0 m and a depth of 2.0 m, as shown in the FE meshed model excitation of the ultrasonic guided waves was a six-cycle tone burst with a frequency of in Figure 2a. The excitation of the ultrasonic guided waves was a six-cycle tone burst 35 kHz. A pulse-echo test was set up on the rod where the actuators and receivers were with a frequency of 35 kHz. A pulse-echo test was set up on the rod where the actuators on the same side. Excitations were generated by Wavemaker 16 equipment, which is used and receivers were on the same side. Excitations were generated by Wavemaker 16 for long-range inspection of pipes. The rod was embedded in the concrete block along 2 equipment, which is used for long-range inspection of pipes. The rod was embedded in m and the remaining length of the rod from both ends of the block [40]. The comparison the concrete block along 2 m and the remaining length of the rod from both ends of the results are shown in Figure 2b, where signals in the literature are marked with red lines and block [40]. The comparison results are shown in Figure 2b, where signals in the literature the black ones were generated from this study, and the three circled wave packets denote are marked with red lines and the black ones were generated from this study, and the the excitation signals, the ﬁrst right boundary reﬂection, and the second right boundary three circled wave packets denote the excitation signals, the first right boundary reflec- reﬂection. As shown in Figure 2b, the simulated guided waves in this study matched well tion, and the second right boundary reflection. As shown in Figure 2b, the simulated with the experimental data collected from the literature in most cases, where three wave guided waves in this study matched well with the experimental data collected from the packets were captured well. The ﬁrst boundary wave reﬂections from simulated signals literature in most cases, where three wave packets were captured well. The first bounda- occurred at 0.001 s, identical to the experimental data with comparable amplitudes. Note that some deviations occurred after the excitation, and a potential reason could partially result from the attenuation of the concrete block where the simulation did not capture well. However, the entire trend and amplitudes in most cases were in agreement with the literature, suggesting that the simulation used in this study was appropriate to ensure capturing of the characteristics of the ultrasonic guided waves through the rods. 𝛥𝑡 𝛥𝐶 𝛥𝐶 Buildings 2022, 12, x FOR PEER REVIEW 5 of 19 ry wave reflections from simulated signals occurred at 0.001 s, identical to the experi- mental data with comparable amplitudes. Note that some deviations occurred after the excitation, and a potential reason could partially result from the attenuation of the con- crete block where the simulation did not capture well. However, the entire trend and amplitudes in most cases were in agreement with the literature, suggesting that the sim- ulation used in this study was appropriate to ensure capturing of the characteristics of Buildings 2022, 12, 1772 5 of 19 the ultrasonic guided waves through the rods. 2nd (a) (b) Figure 2. Calibration of the FE model. (a) Meshing of the rod embedded in concrete. (b) Compari- Figure 2. Calibration of the FE model. (a) Meshing of the rod embedded in concrete. (b) Comparison son of signals with the literature. of signals with the literature. 2.3. Design of Scenarios 2.3. Design of Scenarios Followed by the calibration in Section 2.2, this section details the design of different Followed by the calibration in Section 2.2, this section details the design of different scenarios to generate datasets that helped to elucidate the critical factors affecting the scenarios to generate datasets that helped to elucidate the critical factors affecting the characteristics of ultrasonic guided wave propagation along stressed rods, thus paving characteristics of ultrasonic guided wave propagation along stressed rods, thus paving the the way for stress level prediction using machine learning in Section 3. As such, the pro- way for stress level prediction using machine learning in Section 3. As such, the prototype totype of the stressed ro of the stressed rods was ds derived was der from ived from the literatur the literature [41]. The e [41]. The rod was rod was 31.75 mm 31.75 mm in in diameter diam with et a er length withof a 3657.6 length of mm. 36The 57.6 mm. T material he material p properties ofroperties o the rod wer f t ehdensity e rod were of 7800 density of kg/m , 3 5 7 Y 800 oung’s kg/m modulus , Young’s mod of 2 10 ulus MPa, of 2 and × 10 Poisson MPa, and ratioPo of i0.3. sson Arclamp atio of 0. served 3. A cl as am the p serv anchorage ed as of the rod, which was located 50.8 mm away from the free end. Besides the reference where the anchorage of the rod, which was located 50.8 mm away from the free end. Besides the ref the rod erence where the rod had no had no grout, two grout materials, grout, tw namely o grout ma greaseteri and als, cement, namely grease a were selected nd ce- to unveil their effects on the effectiveness of the proposed methods. The density of the cement ment, were selected to unveil their effects on the effectiveness of the proposed methods. 3 4 3 4 was 1440 kg/m , the Young’s modulus was 2.5 10 MPa, and the Poisson ratio was 0.25. The density of the cement was 1440 kg/m , the Young’s modulus was 2.5 × 10 MPa, and The density of the grease was 2600 kg/m . The detailed information of the rod models is the Poisson ratio was 0.25. The density of the grease was 2600 kg/m . The detailed in- shown in Figure 3. The entire rod with the clamp is illustrated in Figure 3a (note that the formation of the rod models is shown in Figure 3. The entire rod with the clamp is illus- meshing ﬁgure is a schematic diagram; the actual meshing unit is much smaller), and the trated in Figure 3a (note that the meshing figure is a schematic diagram; the actual embedded rod is shown in Figure 3b. Speciﬁcally, the rod passed through the plastic pipe meshing unit is much smaller), and the embedded rod is shown in Figure 3b. Specifical- and then added grease and cement to ﬁll the gap between the pipe and the rod. The outer ly, the rod passed through the plastic pipe and then added grease and cement to fill the diameter of the plastic pipe was 52.07 mm, and the thickness was 2.54 mm. In ﬁnite element gap between the pipe and the rod. The outer diameter of the plastic pipe was 52.07 mm, studies, meshing is one of the critical parts in simulation. Free triangular element was and the thickness was 2.54 mm. In finite element studies, meshing is one of the critical selected in this model. Guided wave simulation requires a high-quality meshing system parts in simulation. Free triangular element was selected in this model. Guided wave to minimize the propagation error of guided waves. Thus, a wavelength needs to contain simulation requires a high-quality meshing system to minimize the propagation error of at least eight elements. In this study, the maximum element size in the model was 2 mm guided waves. Thus, a wavelength needs to contain at least eight elements. In this study, and time steps were 5 10 s. Guided waves could be excited in the rod by adding -6 the maximum element size in the model was 2 mm and time steps were 5× 10 s. Guided displacement loads in all nodes of the left boundary in the model. The excitation waves waves could be excited in the rod by adding displacement loads in all nodes of the left were 35 kHz ﬁve-cycle sinusoidal waves modulated by the Hanning window. Four points, boundary in the model. The excitation waves were 35 kHz five-cycle sinusoidal waves as received points, distributed the circumferential surface of the rod. Positions of received modulated by the Hanning window. Four points, as received points, distributed the cir- nodes were 5 mm away from the left side. Received signals were time series data, which cumferential surface of the rod. Positions of received nodes were 5 mm away from the intercept the ﬁrst 1000 data points as results for further study. Buildings 2022, 12, x FOR PEER REVIEW 6 of 19 Buildings 2022, 12, 1772 6 of 19 left side. Received signals were time series data, which intercept the first 1000 data points as results for further study. Figure 3. Rod models. Figure 3. Rod models. To simulate the stress reduction in prestressed components, ﬁve different pressure To simulate the stress reduction in prestressed components, five different pressure levels were loaded into each rod: no prestress (State #1), 20% ultimate tensile strength (UTS) levels were loaded into each rod: no prestress (State #1), 20% ultimate tensile strength (State #2), 40% UTS (State #3), 60% UTS (State #4), and 80% UTS (State #5). In total, 15 cases (UTS) (State #2), 40% UTS (State #3), 60% UTS (State #4), and 80% UTS (State #5). In total, were designed in this section, which are shown in Table 1. Noise was added into the data 15 cases were designed in this section, which are shown in Table 1. Noise was added in- to increase the uncertainty of the dataset. to the data to increase the uncertainty of the dataset. Table 1. Test matrix for computation modeling. Table 1. Test matrix for computation modeling. Prestressing Level Case State Grout Material Noise Level (UTS) Prestressing Level Case State Grout Material Noise Level # 1 zero n (UTS) # 2 20% n # 1 zero \ # 3 40% n # 2 20% \ (no grout) # 4 60% n # 3 40% \ (no grout) # 5 80% n # 4 60% \ # 6 zero Grease # 5 80% \ # 6 # 7 20%zero GreaseGrease 100 dB–60 dB # 7 # 8 40%20% GreaseGrease (grease) # 8 # 9 60%40% GreaseGrease 100 dB–60 dB (grease) # 9 60% Grease # 10 80% Grease # 10 80% Grease # 11 zero Cement # 11 zero Cement # 12 20% Cement # 12 20% Cement # 13 40% Cement (cement) # 13 40% Cement # 14 60% Cement (cement) # 14 60% Cement # 15 80% Cement # 15 80% Cement 2.4. Data Collection and Augmentation Figure 4 shows the time records with five different prestress levels derived from the finite element simulation in Case 1 from Table 1. The received point was located 5 mm Buildings 2022, 12, 1772 7 of 19 Buildings 2022, 12, x FOR PEER REVIEW 7 of 19 2.4. Data Collection and Augmentation away from the left side of the rod. To ensure the input wave had similar energy, all the Figure 4 shows the time records with ﬁve different prestress levels derived from the received signal ﬁnite s were nor element m simulation alized, and in tCase he m1axim fromuT m able am1p . lit The udreeceived of the first point p was acket located was 5 mm away from the left side of the rod. To ensure the input wave had similar energy, all the equal to 1. The time series were from 0 s to 0.005 s; the guided wave can propagate and received signals were normalized, and the maximum amplitude of the ﬁrst packet was reflect at least twice throughout the rod. Figure 4a–e illustrates the received signals of equal to 1. The time series were from 0 s to 0.005 s; the guided wave can propagate and the steel with prestress levels equal to 0% UTS, 20% UTS, 40% UTS, 60% UTS, and 80% reﬂect at least twice throughout the rod. Figure 4a–e illustrates the received signals of UTS. Specifically, at low prestress level states (0–40% UTS), the results clearly exhibit the steel with prestress levels equal to 0% UTS, 20% UTS, 40% UTS, 60% UTS, and 80% three main wave packets that represent the initial excitation and the first and second re- UTS. Speciﬁcally, at low prestress level states (0–40% UTS), the results clearly exhibit three flections from the boundary. Following the first packet, fluctuations with small ampli- main wave packets that represent the initial excitation and the ﬁrst and second reﬂections tude were echoes from the clamp. With the stress level increased, the amplitude of this from the boundary. Following the ﬁrst packet, ﬂuctuations with small amplitude were part was smaller, and it was hard to detect at 80% UTS. In addition, the velocity of guid- echoes from the clamp. With the stress level increased, the amplitude of this part was smaller, and it was hard to detect at 80% UTS. In addition, the velocity of guided waves ed waves reduced with increasing the stress of the rod. The first reflection from the right reduced with increasing the stress of the rod. The ﬁrst reﬂection from the right boundary boundary was around 0.0018 s in the base state. The value was raised to 0.0019 s and was around 0.0018 s in the base state. The value was raised to 0.0019 s and 0.002 s when 0.002 s when stresses were 40% UTS and 80% UTS. At 60% and 80% UTS (shown in Fig- stresses were 40% UTS and 80% UTS. At 60% and 80% UTS (shown in Figure 4d,e), only ure 4d,e), only two main packets existed in the signals, where one was initial input two main packets existed in the signals, where one was initial input waves, and the other waves, and the other was the boundary reflection. The energy of guided waves was dis- was the boundary reﬂection. The energy of guided waves was dissipated when waves sipated when waves propagated in the second cycle. Thus, it was difficult to detect the propagated in the second cycle. Thus, it was difﬁcult to detect the second echo from the second echo from the boundary. boundary. 2nd Figure 4. Received signals at different stress levels: (a) zero; (b) 20% UST; (c) 40% UTS; (d) 60% Figure 4. Received signals at different stress levels: (a) zero; (b) 20% UST; (c) 40% UTS; (d) 60% UTS; UTS; (e) 80% UTS. (e) 80% UTS. As illustrated in Fi As illustrated gure 5, tin he collect Figure 5ed , the gu collected ided wave guided s of the rod ex waves of the hibited d rod exhibited ifferent different patterns from different grout materials. Figure 5 illustrates the signals collected from patterns from different grout materials. Figure 5 illustrates the signals collected from States #1, #6, and #11 (without stress) in the time domain and frequency domain. It was States #1, #6, and #11 (without stress) in the time domain and frequency domain. It was observed from the time domain that with long distance propagation, the energy of the observed from the time domain that with long distance propagation, the energy of the reflection waves was reduced progressively. However, comparing these three states, the rod embedded in cement had the highest attenuation, where the peak value of reflec- tions was reduced from 0.2588 to 0.1075. After propagating to the second cycle, the peak value of the second boundary echo was reduced to 0.0897 in the unembedded state, and the value of the rod in cement was the lowest, 0.0113. On the contrary, grease had less of Buildings 2022, 12, 1772 8 of 19 reﬂection waves was reduced progressively. However, comparing these three states, the Buildings 2022, 12, x FOR PEER REVIEW 8 of 19 rod embedded in cement had the highest attenuation, where the peak value of reﬂections was reduced from 0.2588 to 0.1075. After propagating to the second cycle, the peak value of the second boundary echo was reduced to 0.0897 in the unembedded state, and the value an effect on guided waves. With 1463.04 mm of propagation, the peak value of the re- of the rod in cement was the lowest, 0.0113. On the contrary, grease had less of an effect flected waves was 0.0455, which was close to the unembedded state. In the frequency on guided waves. With 1463.04 mm of propagation, the peak value of the reﬂected waves domain, it was clear that the main frequency of waves was 35 kHz. Some weak peaks was 0.0455, which was close to the unembedded state. In the frequency domain, it was occurred at the low frequency and the high frequency due to reflections from the clamp clear that the main frequency of waves was 35 kHz. Some weak peaks occurred at the low and the boundary. frequency and the high frequency due to reﬂections from the clamp and the boundary. 0.03 Unembedded Unembedded 0.02 Envelop 0.01 -1 0.000 0.001 0.002 0.003 0.004 0.005 Time (s) 0.00 0 50 100 Frequency (kHz) (a) 0.03 Grease Grease 0.02 Envelop 0.01 -1 0.000 0.001 0.002 0.003 0.004 0.005 0.00 Time (s) 0 50 100 Frequency (kHz) (b) 0.03 Cement Cement 0.02 Envelop 0.01 -1 0.000 0.001 0.002 0.003 0.004 0.005 0.00 Time (s) 0 50 100 Frequency (kHz) (c) Figure 5. Received signals for rods with different grout methods: (a) no grout; (b) grease; (c) ce- Figure 5. Received signals for rods with different grout methods: (a) no grout; (b) grease; (c) cement. ment. A total of 15 states were designed to simulate the actual situation of the rod. In each A total of 15 states were designed to simulate the actual situation of the rod. In each state, four received nodes were distributed around the circumference and were located 5 state, four received nodes were distributed around the circumference and were located 5 mm away from the left side. Since the received waves were easily contaminated by noise, mm away from the left side. Since the received waves were easily contaminated by ﬁve noise levels based on the signal to noise ratio (SNR) were added into the received noise, five noise levels based on the signal to noise ratio (SNR) were added into the re- signals. In addition, noise involved in the signals could increase the uncertainties of the ceived signals. In addition, noise involved in the signals could increase the uncertainties data, so we attempted to investigate the robustness of the deep learning methods. Figure 6 of the data, so we attempted to investigate the robustness of the deep learning methods. illustrates the collected signals at ﬁve different noise levels. When SNR exceeded 80 Db, the Figure 6 illustrates the collected signals at five different noise levels. When SNR exceed- interference from noise was obvious and covered some original features of the initial signals. ed 80 Db, the interference from noise was obvious and covered some original features of Especially, at 60 dB, the amplitude of the noise was greater than the signal amplitude, which the initial signals. Especially, at 60 dB, the amplitude of the noise was greater than the was not conductive for further study. signal amplitude, which was not conductive for further study. Figure 6. Received signals at different noise levels. Amplitude Amplitude Amplitude Amplitude Amplitude A m plitude Buildings 2022, 12, x FOR PEER REVIEW 8 of 19 an effect on guided waves. With 1463.04 mm of propagation, the peak value of the re- flected waves was 0.0455, which was close to the unembedded state. In the frequency domain, it was clear that the main frequency of waves was 35 kHz. Some weak peaks occurred at the low frequency and the high frequency due to reflections from the clamp and the boundary. 0.03 Unembedded Unembedded 0.02 Envelop 0.01 -1 0.000 0.001 0.002 0.003 0.004 0.005 Time (s) 0.00 0 50 100 Frequency (kHz) (a) 0.03 Grease Grease 0.02 Envelop 0.01 -1 0.000 0.001 0.002 0.003 0.004 0.005 0.00 Time (s) 0 50 100 Frequency (kHz) (b) 0.03 Cement Cement 0.02 Envelop 0.01 -1 0.000 0.001 0.002 0.003 0.004 0.005 0.00 Time (s) 0 50 100 Frequency (kHz) (c) Figure 5. Received signals for rods with different grout methods: (a) no grout; (b) grease; (c) ce- ment. A total of 15 states were designed to simulate the actual situation of the rod. In each state, four received nodes were distributed around the circumference and were located 5 mm away from the left side. Since the received waves were easily contaminated by noise, five noise levels based on the signal to noise ratio (SNR) were added into the re- ceived signals. In addition, noise involved in the signals could increase the uncertainties of the data, so we attempted to investigate the robustness of the deep learning methods. Figure 6 illustrates the collected signals at five different noise levels. When SNR exceed- ed 80 Db, the interference from noise was obvious and covered some original features of the initial signals. Especially, at 60 dB, the amplitude of the noise was greater than the Buildings 2022, 12, 1772 9 of 19 signal amplitude, which was not conductive for further study. Figure 6. Received signals at different noise levels. Figure 6. Received signals at different noise levels. 3. Deep Learning Framework CNN has been widely adopted in many application domains, such as image clas- siﬁcation and segmentation, speech recognition, and computer vision tasks. The CNN framework contains multiple layers, including a convolutional layer, pooling layer, fully connected layer, and ReLU layer. These layers help to decode the input data into high- dimensional slices, extract the intricate features, and then encode them into the target values. In this study, CNN was used to identify the complicated guided wave signals. The architecture of the CNN trained by guided wave signals is described. The model of the CNN was changed from LeNet-5. 3.1. Introductions of CNN The input data consisted of a series of signals with m detection points and n time steps. Thus, the size of the input layer was n m. The convolutional layer is one of the most crucial layers in a CNN. In this layer, each element from the kernel is multiplied with the data in the previous layer. The size of the kernel determines the operation area, and the number of kernels decides the third dimension of the output. The kernel size is much smaller than the input layer, so the kernel moves step by step to implement. The stride deﬁnes the length of each step, which causes the output data reduction. The size of the stride is an essential value which affects the efﬁciency and performance of the layer. A bigger size may cause the loss of some important features, and a small size may cause an increase in calculation. The initial kernels are generated randomly, and they update by learning from each iterator. A bias is added after summing all the multiplication results in the operation area. When all the kernels ﬁnish the multiplication with the input data and summarize, the result is the output in this layer. The pooling layer is used to reduce the size of the previous layer. Two pooling layers can be selected, namely max pooling and mean pooling. In max pooling, the maximum values in the operation area are taken as the result. In mean pooling, the average values are the result. The operation area is also moved by setting the values of stride. After adding a pooling layer to a CNN framework, the output of the convolutional bands has a dramatic decrease. In this CNN, all the pooling layers were set as max pooling layers. The activation layer adds nonlinearity into the CNN. In this model, ReLU was chosen as the activation layer in the CNN trained by guided wave signals. ReLU changes some of the neurons to zero, which will thin the network, reduce the interdependence between parameters, and avoid overﬁtting to some extent. In addition, it also saves computation and improves the efﬁciency of deep learning models, compared with other activation functions. After the cooperation of several layers, the initial data are changed into a series of feature maps, and the size is deformed. To transfer these feature maps into their own category, a fully connected layer is necessary. The result of this layer is the probability that the data belong to each label. The entire process is shown in Figure 7. Amplitude Amplitude Amplitude Amplitude Amplitude A m plitude Buildings 2022, 12, x FOR PEER REVIEW 9 of 19 3. Deep Learning Framework CNN has been widely adopted in many application domains, such as image classi- fication and segmentation, speech recognition, and computer vision tasks. The CNN framework contains multiple layers, including a convolutional layer, pooling layer, fully connected layer, and ReLU layer. These layers help to decode the input data into high- dimensional slices, extract the intricate features, and then encode them into the target values. In this study, CNN was used to identify the complicated guided wave signals. The architecture of the CNN trained by guided wave signals is described. The model of the CNN was changed from LeNet-5. 3.1. Introductions of CNN The input data consisted of a series of signals with m detection points and n time steps. Thus, the size of the input layer was n × m. The convolutional layer is one of the most crucial layers in a CNN. In this layer, each element from the kernel is multiplied with the data in the previous layer. The size of the kernel determines the operation area, and the number of kernels decides the third dimension of the output. The kernel size is much smaller than the input layer, so the kernel moves step by step to implement. The stride defines the length of each step, which causes the output data reduction. The size of the stride is an essential value which affects the efficiency and performance of the layer. A bigger size may cause the loss of some important features, and a small size may cause an increase in calculation. The ini- tial kernels are generated randomly, and they update by learning from each iterator. A bias is added after summing all the multiplication results in the operation area. When all the kernels finish the multiplication with the input data and summarize, the result is the output in this layer. The pooling layer is used to reduce the size of the previous layer. Two pooling lay- ers can be selected, namely max pooling and mean pooling. In max pooling, the maxi- mum values in the operation area are taken as the result. In mean pooling, the average values are the result. The operation area is also moved by setting the values of stride. Af- ter adding a pooling layer to a CNN framework, the output of the convolutional bands has a dramatic decrease. In this CNN, all the pooling layers were set as max pooling lay- ers. The activation layer adds nonlinearity into the CNN. In this model, ReLU was cho- sen as the activation layer in the CNN trained by guided wave signals. ReLU changes some of the neurons to zero, which will thin the network, reduce the interdependence between parameters, and avoid overfitting to some extent. In addition, it also saves computation and improves the efficiency of deep learning models, compared with other activation functions. After the cooperation of several layers, the initial data are changed into a series of feature maps, and the size is deformed. To transfer these feature maps into their own Buildings 2022, 12, 1772 category, a fully connected layer is necessary. The result of this layer is the pr 10 of 19 obability that the data belong to each label. The entire process is shown in Figure 7. Figure 7. Flowchart of CNN. 3.2. CNN Architecture The proposed CNN in this study was an eight-layer network, including three con- volutional layers, two max pooling layers, a ReLU layer, a fully connected layer, and a softmax layer. The selection of hyperparameters affects the performance of the neural network. Different methods [27,42,43] have been proposed to select these parameters. For instance, the learning rate is to adjust the gradient update, the kernel number size is to adjust the receptive ﬁled; in addition, stride step and batch size are critical in parameter design [26,41]. In this study, the hyperparameter selection stems from previous studies, maintaining the basic network architecture of LeNet-5. Note that several studies revealed that the introduction of Bayesian optimization [44,45] in determining the hyperparame- ters could further enhance the architecture of the CNN with less trial and error, and thus improve the accuracy. As part of the ongoing investigation of the applications of deep learning in civil structures, we consider advances in hyperparameter design, including using Bayesian optimization, for optimizing the CNN architecture. The detailed information of each CNN layer is given in Table 2. The input data are a matrix sized 1000 4, representing four collected signals in a rod sample. A total of 1000 data points were intercepted from received signals, which included the excitation and the reﬂection from the right boundary. Four is the number of received signals. In the ﬁrst convolutional layer, 20 ﬁlters sized 25 2 were generated and operated the input data into 976 3 20. The following was a max pooling layer with the stride equal to 5. The layer captured the maximum value in the response ﬁeld and signiﬁcantly cut down the size of the input. After that, the output of the data was 195 3 20. Then, the data experienced cooperation from the convolutional layer and the max pooling layer, involving 40 ﬁlters, and the pooling size was 5 1. At this moment, the output was 34 1, a dramatic decline compared with the initial input. The third convolutional layer had a small size, 5 1, and a ReLU was implemented to increase the nonlinearity. Finally, the fully connected layer and softmax layer transferred the data into several probabilities in each label. Table 2. Details of the proposed CNN. Name Filters Filter Size Stride Bias Output Layer Size Input layer – – – – 1000 4 Convolutional layer (C ) 20 25 2 1 20 976 3 Max pooling layer (P ) 20 5 1 5 – 195 3 Convolutional layer (C ) 40 25 3 1 40 171 1 Max pooling layer (P ) 40 5 1 5 – 34 1 Convolutional layer (C ) 20 5 1 1 20 30 1 ReLU – – – – 30 1 Fully connected layer (F ) 5 30 1 1 5 5 Softmax – – – – 5 Buildings 2022, 12, 1772 11 of 19 3.3. Feature Visualization with t-SNE The CNN classiﬁer achieves better performance since it automatically extracts features from the training data. It expands the data into high-dimensional matrices by multiple ﬁlters. Thus, these features are usually high-dimensional, which is not conductive to understanding. However, stochastic neighbor embedding (SNE) was introduced to reduce Buildings 2022, 12, x FOR PEER REVIEW 11 of 19 the dimensions of the features, making it possible to visualize the feature. SNE aims to convert the high-dimensional Euclidean distance between data samples into conditional probabilities. The t-distributed stochastic neighbor embedding (t-SNE) [46] proposed by similarity matrix and minimizes the gap between the distribution in two spaces. This Maaten and Hinton transforms a high-dimensional dataset into a pairwise similarity matrix and meth m od is po inimizes pula ther f gap or feat between ure vithe suadistribution lization in mach in two ine le spaces. arning This algmethod orithms.is popular for feature visualization in machine learning algorithms. 4. Results and Discussion 4. Results and Discussion 4.1. Feature Visualization 4.1. Feature Visualization In this study, 500 data points in each state emerged by adding white Gaussian In this study, 500 data points in each state emerged by adding white Gaussian noise, noise, including 60% data for training, 20% for validation, and 20% for testing. The CNN including 60% data for training, 20% for validation, and 20% for testing. The CNN model model was well trained after studying the features from the training data. The feature was well trained after studying the features from the training data. The feature maps maps can estimate the efficiency of the proposed method. The following figures show can estimate the efﬁciency of the proposed method. The following ﬁgures show the high- the high-dimensional feature maps in two-dimensional space by t-SNE. dimensional feature maps in two-dimensional space by t-SNE. Figure 8 depicts the features in Case 1, where the prestress level of the unembedded Figure 8 depicts the features in Case 1, where the prestress level of the unembedded rod is 80 dB. States #1–5 represent the rod with the prestress level equal to 0% (base rod is 80 dB. States #1–5 represent the rod with the prestress level equal to 0% (base state), state), 20% UTS, 40% UTS, 60% UTS, and 80% UTS. In total, 2500 samples comprised the 20% UTS, 40% UTS, 60% UTS, and 80% UTS. In total, 2500 samples comprised the dataset, dataset, where 1500 were used to train the model, 500 for validation, and the remaining where 1500 were used to train the model, 500 for validation, and the remaining 500 for 500 for testing. Figure 8a displays the feature maps of the test set after the first convolu- testing. Figure 8a displays the feature maps of the test set after the ﬁrst convolutional layer. tional layer. Through the distribution of features, data labeled as 40% UTS (green upper Through the distribution of features, data labeled as 40% UTS (green upper triangle) were triangle) were isolated from the entire dataset. This indicates that the features in this la- isolated from the entire dataset. This indicates that the features in this label extracted from bel extracted from the first layer of the CNN model were much easier to separate than the ﬁrst layer of the CNN model were much easier to separate than others because the others because the Euclidean distance is larger. However, the clusters in the red dia- Euclidean distance is larger. However, the clusters in the red diamond (base state) and mond (base state) and yellow circle (20% UTS) located on the right side overlapped. At yellow circle (20% UTS) located on the right side overlapped. At least one-quarter of the least one-quarter of the data were mixed and difficult to separate, which means errors data were mixed and difﬁcult to separate, which means errors will occur. In addition, the will occur. In addition, the rod samples prestressed in 60% UTS (blue lower triangle) and rod samples prestressed in 60% UTS (blue lower triangle) and 80% UTS (purple star) were 80% UTS (purple star) were tangled together. Figure 8b represents the feature maps tangled together. Figure 8b represents the feature maps from the last layer of the CNN. from the last layer of the CNN. After eight layers’ processing, most of the samples were After eight layers’ processing, most of the samples were separated, except one outlier in separated, except one outlier in the base class clustered in 20% UTS and a small overlap the base class clustered in 20% UTS and a small overlap appeared between the samples in appeared between the samples in 60% UTS and 80% UTS. The results demonstrate that 60% UTS and 80% UTS. The results demonstrate that the features became more sensitive the features became more sensitive after operating the whole CNN process. after operating the whole CNN process. Base 20% UTS 40% UTS 60% UTS 80% UTS Base 20% UTS -10 40% UTS −-20 60% UTS 80% UTS −-40 −-20 0 20 -10 0 10 20 (a) (b) Figure 8. Feature visualization by t-SNE. (a) Feature maps in the first convolutional layer; (b) fea- Figure 8. Feature visualization by t-SNE. (a) Feature maps in the ﬁrst convolutional layer; (b) feature ture maps in the last layer. maps in the last layer. The CNN model sliced input signals into several small pieces, which enlarged the sensitive features and cut off the excess. Figure 9 plots the feature maps from five differ- ent prestress levels after three convolutional layers. The data are signals from five differ- ent prestress levels in Case 1 when SNR is equal to 100 dB. The differences between the five figures are clear. The shape and peak values of lines characterize signals from dif- ferent groups. However, with the increasing noise level, extracting features became harder. Y Buildings 2022, 12, 1772 12 of 19 The CNN model sliced input signals into several small pieces, which enlarged the sensitive features and cut off the excess. Figure 9 plots the feature maps from ﬁve different prestress levels after three convolutional layers. The data are signals from ﬁve different Buildings 2022, 12, x FOR PEER REVIEW 12 of 19 prestress levels in Case 1 when SNR is equal to 100 dB. The differences between the ﬁve ﬁgures are clear. The shape and peak values of lines characterize signals from different groups. However, with the increasing noise level, extracting features became harder. Feature maps Feature maps Feature maps 50 50 0 0 015 30 015 30 015 30 (a) (b) (c) Feature maps 20 Feature maps -10 −-20 015 30 015 30 (d) (e) Figure 9. Feature maps: (a) 0% UTS; (b) 20% UTS; (c) 40% UTS; (d) 60% UTS; (e) 80% UTS. Figure 9. Feature maps: (a) 0% UTS; (b) 20% UTS; (c) 40% UTS; (d) 60% UTS; (e) 80% UTS. Figure 10 illustrates the feature visualization in Case 1 when SNRs were equal to Figure 10 illustrates the feature visualization in Case 1 when SNRs were equal to 100 dB, 70 dB, and 60 dB. At 100 dB (in Figure 10a), the ﬁve clusters were far from each 100 dB, 70 dB, and 60 dB. At 100 dB (in Figure 10a), the five clusters were far from each other, and each cluster of data is relatively concentrated, with an average standard deviation other, and each cluster of data is relatively concentrated, with an average standard devi- close to 2.53. With the noise level increased to 80 dB (shown in Figure 10b), a small overlap ation close to 2.53. With the noise level increased to 80 dB (shown in Figure 10b), a small appeared between the 60% UTS and 80% UTS data, but the other three groups were clearly overlap appeared between the 60% UTS and 80% UTS data, but the other three groups separated. The standard deviation in this situation was large, 2.83. However, when SNR were clearly separated. The standard deviation in this situation was large, 2.83. Howev- was lower than 80 dB, the distributions of features changed dramatically. At 70 dB, features er, when SNR was lower than 80 dB, the distributions of features changed dramatically. in either the base state and 20% UTS or 60% UTS and 80% UTS were blended into each At 70 other dB, f , and eatures i only the n ei data ther inthe thebase state green upper antriangles d 20% UTS wereor 60 independently % UTS and 8 located 0% UTS below were the graph, demonstrated in Figure 10b. In Figure 10c, feature maps at 60 dB had a worse blended into each other, and only the data in the green upper triangles were inde- situation, as all the data interwove together entirely. It is hard to ascertain the boundaries of pendently located below the graph, demonstrated in Figure 10b. In Figure 10c, feature each group. Therefore, this proved that noise had an adverse effect on the feature extraction maps at 60 dB had a worse situation, as all the data interwove together entirely. It is of the CNN. hard to ascertain the boundaries of each group. Therefore, this proved that noise had an adverse effect on the feature extraction of the CNN. Base Base 20% UTS 20% UTS 40% UTS 40% UTS 60% UTS 60% UTS 80% UTS 80% UTS Base 20% UTS 40% UTS −-10 -20 -20 60% UTS 80% UTS −-30 0 30 −-8 0 8 −-30 0 X X (a) (b) (c) Figure 10. Feature visualization by t-SNE. (a) SNR = 100 dB; (b) SNR = 70 dB; (c) SNR = 60 dB. Y Buildings 2022, 12, x FOR PEER REVIEW 12 of 19 Feature maps Feature maps Feature maps 0 0 015 30 015 30 015 30 X X (a) (b) (c) Feature maps 20 Feature maps -10 −-20 015 30 015 30 X X (d) (e) Figure 9. Feature maps: (a) 0% UTS; (b) 20% UTS; (c) 40% UTS; (d) 60% UTS; (e) 80% UTS. Figure 10 illustrates the feature visualization in Case 1 when SNRs were equal to 100 dB, 70 dB, and 60 dB. At 100 dB (in Figure 10a), the five clusters were far from each other, and each cluster of data is relatively concentrated, with an average standard devi- ation close to 2.53. With the noise level increased to 80 dB (shown in Figure 10b), a small overlap appeared between the 60% UTS and 80% UTS data, but the other three groups were clearly separated. The standard deviation in this situation was large, 2.83. Howev- er, when SNR was lower than 80 dB, the distributions of features changed dramatically. At 70 dB, features in either the base state and 20% UTS or 60% UTS and 80% UTS were blended into each other, and only the data in the green upper triangles were inde- pendently located below the graph, demonstrated in Figure 10b. In Figure 10c, feature maps at 60 dB had a worse situation, as all the data interwove together entirely. It is Buildings 2022, 12, 1772 13 of 19 hard to ascertain the boundaries of each group. Therefore, this proved that noise had an adverse effect on the feature extraction of the CNN. Base Base 40 20% UTS 20% UTS 40% UTS 40% UTS 60% UTS 60% UTS 80% UTS 80% UTS 0 Base 20% UTS Buildings 2022, 12, x FOR PEER REVIEW 40% UTS 13 of 19 −-10 −-20 -20 60% UTS 80% UTS −-30 0 30 -8 0 8 −-30 0 4.2. Classification for Prestress Levels of the Rod by CNN (a) (b) (c) The performance of CNN trained by the data under various noise levels is shown in Figure 10. Feature visualization by t-SNE. (a) SNR = 100 dB; (b) SNR = 70 dB; (c) SNR = 60 dB. Figure 10. Feature visualization by t-SNE. (a) SNR = 100 dB; (b) SNR = 70 dB; (c) SNR = 60 dB. Figure 11, which classified the prestress levels of the rod in Case 1. Of the 2500 data points, 1500 were used for training the CNN model, and the training curves are illustrat- 4.2. Classiﬁcation for Prestress Levels of the Rod by CNN ed in Figure 11a. Specifically, these training curves started near 20%, and then converged The performance of CNN trained by the data under various noise levels is shown to 10 in Figur 0%. When the noi e 11, which classiﬁed se level wa the prs 100 dB, th estress levelse model of the rod onl iny Case spent 1. seven epochs to Of the 2500 data im- points, 1500 were used for training the CNN model, and the training curves are illustrated prove the accuracy to 100%. That epoch number was enlarged to 25 at 90 dB. With SNR in Figure 11a. Speciﬁcally, these training curves started near 20%, and then converged to increased, more epochs were spent on converging, and the error reduced to 0 with 34 100%. When the noise level was 100 dB, the model only spent seven epochs to improve the epochs at 80 dB. The slope of training curves from 100 dB to 80 dB were much larger accuracy to 100%. That epoch number was enlarged to 25 at 90 dB. With SNR increased, than the curves at 70 dB and 60 dB. In detail, the accuracy of classification was raised more epochs were spent on converging, and the error reduced to 0 with 34 epochs at 80 dB. from 20% to 31% by 15 epochs at 60 dB and then close to 100% after the 30th epoch. The The slope of training curves from 100 dB to 80 dB were much larger than the curves at validation set included 500 data points for modifying the parameters in CNN. The vali- 70 dB and 60 dB. In detail, the accuracy of classiﬁcation was raised from 20% to 31% by dation curves for 40 epochs showed that the accuracy of CNN started at 20% and in- 15 epochs at 60 dB and then close to 100% after the 30th epoch. The validation set included creased with the epochs. At 100 dB and 90 dB, the accuracies reached 100% after training 500 data points for modifying the parameters in CNN. The validation curves for 40 epochs showed that the accuracy of CNN started at 20% and increased with the epochs. At 100 dB 6 and 20 epochs, respectively. When SNR was 80 dB, the curve was close to 0.98 after the and 90 dB, the accuracies reached 100% after training 6 and 20 epochs, respectively. When 28th epoch and would not improve as the epoch increased. However, the accuracies SNR was 80 dB, the curve was close to 0.98 after the 28th epoch and would not improve as were lower at 70 dB and 60 dB, where the curve converged to 0.78 and 0.34 after training the epoch increased. However, the accuracies were lower at 70 dB and 60 dB, where the 40 epochs. Approximately 32% of the data were misjudged as the incorrect category at curve converged to 0.78 and 0.34 after training 40 epochs. Approximately 32% of the data 70 dB. The situation at 60 dB was much worse, as most of the data could not be classified were misjudged as the incorrect category at 70 dB. The situation at 60 dB was much worse, into the right category. as most of the data could not be classiﬁed into the right category. 1.0 1.0 0.8 0.8 0.6 0.6 0.4 0.4 100 dB 100 dB 90 dB 90 dB 0.2 0.2 80 dB 80 dB 70 dB 70 dB 60 dB 60 dB 0.0 0.0 0 5 10 15 20 25 30 35 40 0 5 10 15 20 25 30 35 40 Epochs Epochs (a) (b) Figure 11. Learning results of CNN at various noise levels. (a) Training curve; (b) test curve. Figure 11. Learning results of CNN at various noise levels. (a) Training curve; (b) test curve. The test results at various noise levels are shown in Table 3. When SNR was no less than 90 dB, the CNN model classified the test data correctly into the corresponding cate- gories because the training curves and the validation curves reached 100% after training. At 80 dB, the accuracy of test data was 98%, and some misjudgments appeared in the base state and the 80% UTS state. The results of the feature map visualization show that some data in the base state were dropped into the 20% UTS group, and the 60% UTS and 80% UTS clusters overlapped (shown in Figure 11b). The mixed features caused the mis- judgments in the test. At 70 dB, only 74% of the data were identified correctly, and 25% of the data in the first category were misclassified into the second category. On the con- trary, 27% of the data that belonged to the second category were placed into the first cat- egory. The accuracies of the fourth and fifth categories were both equal to 63%. The con- clusion is consistent with the previous analysis in feature visualization and accurate curves. At 60 dB, the CNN model was not suitable in this situation because the noise covered the signals entirely and all the analysis focused on the noise. Thus, all results had low accuracy. Performance Performance Y Buildings 2022, 12, 1772 14 of 19 The test results at various noise levels are shown in Table 3. When SNR was no less than 90 dB, the CNN model classiﬁed the test data correctly into the corresponding categories because the training curves and the validation curves reached 100% after training. At 80 dB, the accuracy of test data was 98%, and some misjudgments appeared in the base state and the 80% UTS state. The results of the feature map visualization show that some data in the base state were dropped into the 20% UTS group, and the 60% UTS and 80% UTS clusters overlapped (shown in Figure 11b). The mixed features caused the misjudgments in the test. At 70 dB, only 74% of the data were identiﬁed correctly, and 25% of the data in the ﬁrst category were misclassiﬁed into the second category. On the contrary, 27% of the data that belonged to the second category were placed into the ﬁrst category. The accuracies of the fourth and ﬁfth categories were both equal to 63%. The conclusion is consistent with the previous analysis in feature visualization and accurate curves. At 60 dB, the CNN model was not suitable in this situation because the noise covered the signals entirely and all the analysis focused on the noise. Thus, all results had low accuracy. Table 3. Confusion matrices at various noise levels. 90 dB (100%) 80 dB (98%) Base 20% 40% 60% 80% Base 20% 40% 60% 80% Base 100.0% 0.0% 0.0% 0.0% 0.0% 99.0% 0.0% 0.0% 0.0% 0.0% 20% 0.0% 100.0% 0.0% 0.0% 0.0% 1.0% 100% 0.0% 0.0% 0.0% 40% 0.0% 0.0% 100.0% 0.0% 0.0% 0.0% 0.0% 100% 0.0% 0.0% 60% 0.0% 0.0% 0.0% 100.0% 0.0% 0.0% 0.0% 0.0% 98% 7.0% 80% 0.0% 0.0% 0.0% 0.0% 100.0% 0.0% 0.0% 0.0% 2.0% 93.0% 70 dB (74%) 60 dB (26.8%) Base 75% 27.0% 0.0% 0.0% 0.0% 28.0% 27.0% 20.0% 12.0% 15.0% 20% 25.0% 71.0% 1.0% 0.0% 0.0% 28.0% 22.0% 17.0% 15.0% 12.0% 40% 0.0% 0.0% 98% 0.0% 0.0% 20.0% 16.0% 34.0% 17.0% 22.0% 60% 0.0% 1.0% 1.0% 63.0% 37.0% 14.0% 14.0% 12.0% 23.0% 15.0% 80% 0.0% 1.0% 0.0% 37.0% 63.0% 10.0% 21.0% 17.0% 33.0% 36.0% The performance of the CNN classiﬁer in Cases 2 and 3 is shown in Figure 12. In Case 2, rods were embedded in cement. The training and validation results at ﬁve noise levels are illustrated in Figure 12a. The training and validation curves had better results when SNRs were higher than 70 dB. All the curves ﬂuctuated during the ﬁrst ﬁve epochs and then quickly converged to 0. Nearly 10 epochs were spent to increase the accuracies to 100%. At 70 dB, although the training curve took about 20 epochs to converge to 100%, the validation curve only reached 0.78. However, the performance of the CNN dropped sharply at 60 dB. In Case 3, the error occurred at 80 dB, where the training accuracy and validation accuracy were close to 0.99 and 0.94, respectively. The error rate increased at 70 dB, where the validation curve reached 0.77 at the 20th epoch and then ﬂattened out. The results in Case 3 were similar to those of Case 1 because the grease had less of an effect on guided wave propagation. The test results of Cases 2 and 3 are shown in Table 4 when SNRs were from 90 dB to 60 dB. In Case 2, all the test data were identiﬁed correctly at 90 dB and 80 dB. At 70 dB, only the base state had a classiﬁcation rate of 98%, and the other four groups had lower rates. Among them, 12 of 100 data samples in the second category were misclassiﬁed into the third and fourth categories. The accuracy of the third category was 74% with 26% misjudgment. In addition, the error rates in the fourth and ﬁfth categories were 66% and 64%, respectively. When the noise level increased to 60 dB, the accuracy of prestress identiﬁcation was the lowest (46.6%). Most of the data could not be identiﬁed, except the data in the base condition (at 99%). Compared with Case 2, the approach exhibited a slightly lower accuracy for Case 3, where 100% of data in 90 dB were classiﬁed, 94.4% were identiﬁed at 80 dB, 76% at 70 dB, and 41.6% at 60 dB. At 80 dB and 70 dB, most of the errors occurred between the fourth and ﬁfth categories. Speciﬁcally, the predictions of the fourth and ﬁfth categories reached 78% and 94% at 80 dB. At 70 dB, the proportions were reduced Buildings 2022, 12, x FOR PEER REVIEW 14 of 19 Table 3. Confusion matrices at various noise levels. 90 dB (100%) 80 dB (98%) Base 20% 40% 60% 80% Base 20% 40% 60% 80% Base 100.0% 0.0% 0.0% 0.0% 0.0% 99.0% 0.0% 0.0% 0.0% 0.0% 20% 0.0% 100.0% 0.0% 0.0% 0.0% 1.0% 100% 0.0% 0.0% 0.0% 40% 0.0% 0.0% 100.0% 0.0% 0.0% 0.0% 0.0% 100% 0.0% 0.0% 60% 0.0% 0.0% 0.0% 100.0% 0.0% 0.0% 0.0% 0.0% 98% 7.0% 80% 0.0% 0.0% 0.0% 0.0% 100.0% 0.0% 0.0% 0.0% 2.0% 93.0% 70 dB (74%) 60 dB (26.8%) Base 75% 27.0% 0.0% 0.0% 0.0% 28.0% 27.0% 20.0% 12.0% 15.0% 20% 25.0% 71.0% 1.0% 0.0% 0.0% 28.0% 22.0% 17.0% 15.0% 12.0% 40% 0.0% 0.0% 98% 0.0% 0.0% 20.0% 16.0% 34.0% 17.0% 22.0% 60% 0.0% 1.0% 1.0% 63.0% 37.0% 14.0% 14.0% 12.0% 23.0% 15.0% 80% 0.0% 1.0% 0.0% 37.0% 63.0% 10.0% 21.0% 17.0% 33.0% 36.0% The performance of the CNN classifier in Cases 2 and 3 is shown in Figure 12. In Case 2, rods were embedded in cement. The training and validation results at five noise levels are illustrated in Figure 12a. The training and validation curves had better results when SNRs were higher than 70 dB. All the curves fluctuated during the first five epochs and then quickly converged to 0. Nearly 10 epochs were spent to increase the ac- curacies to 100%. At 70 dB, although the training curve took about 20 epochs to converge to 100%, the validation curve only reached 0.78. However, the performance of the CNN dropped sharply at 60 dB. In Case 3, the error occurred at 80 dB, where the training ac- Buildings 2022, 12, 1772 15 of 19 curacy and validation accuracy were close to 0.99 and 0.94, respectively. The error rate increased at 70 dB, where the validation curve reached 0.77 at the 20th epoch and then flattened out. The results in Case 3 were similar to those of Case 1 because the grease to 52% and 51%, respectively. At 60 dB, only the data under the base condition could be had less of an effect on guided wave propagation. identiﬁed, and it was hard to identify the data in other conditions. 1.0 1.0 0.8 0.8 Training(100 dB) Training(100 dB) Validation(100 dB) Validation(100 dB) 0.6 0.6 Training(90 dB) Training(90 dB) Validation(90 dB) Validation(90 dB) Training(80 dB) Training(80 dB) 0.4 0.4 Validation(80 dB) Validation(80 dB) Training(70 dB) Training(70 dB) Validation(70 dB) Validation(70 dB) 0.2 0.2 Training(60 dB) Training(60 dB) Validation(60 dB) Validation(60 dB) 0 102030 4050 60 0 102030405060 Epoch Epoch (a) (b) Figure 12. Results of CNN at various noise levels. (a) Case 2; (b) Case 3. Figure 12. Results of CNN at various noise levels. (a) Case 2; (b) Case 3. The test results of Cases 2 and 3 are shown in Table 4 when SNRs were from 90 dB Table 4. Confusion matrices in Case 2 and 3. to 60 dB. In Case 2, all the test data were identified correctly at 90 dB and 80 dB. At 70 dB, only the base state had a classification rate of 98%, and the other four groups had Case 2 (Grease as the Grout Material) lower rates. Among them, 12 of 100 data samples in the second category were misclassi- 90 dB (100%) 80 dB (100%) fied into the third and fourth categories. The accuracy of the third category was 74% Base 20% 40% 60% 80% Base 20% 40% 60% 80% with 26% misjudgment. In addition, the error rates in the fourth and fifth categories Base 100.0% 0.0% 0.0% 0.0% 0.0% 100.0% 0.0% 0.0% 0.0% 0.0% were 66% and 64%, respectively. When the noise level increased to 60 dB, the accuracy 20% 0.0% 100.0% 0.0% 0.0% 0.0% 0.0% 100.0% 2.0% 5.0% 4.0% 40% 0.0% 0.0% 100.0% 0.0% 0.0% 0.0% 8.0% 100.0% 15.0% 18.0% 60% 0.0% 0.0% 0.0% 100.0% 0.0% 0.0% 4.0% 14.0% 100.0% 14.0% 80% 0.0% 0.0% 0.0% 0.0% 100.0% 0.0% 0.0% 10.0% 14.0% 100.0% 70 dB (78%) 60 dB (46.6%) Base 98% 0.0% 0.0% 0.0% 0.0% 99% 1% 0% 1% 0% 20% 2.0% 88% 2.0% 5.0% 4.0% 0% 50% 16% 29% 8% 40% 0.0% 8.0% 74% 15.0% 18.0% 0% 13% 24% 16% 25% 60% 0.0% 4.0% 14.0% 66% 14.0% 1% 26% 31% 26% 33% 80% 0.0% 0.0% 10.0% 14.0% 64.0% 0% 10% 29% 28% 34% Case 3 (Cement as the grout material) 90 dB (100%) 80 dB (94.4%) Base 100.0% 0.0% 0.0% 0.0% 0.0% 100.0% 0.0% 0.0% 0.0% 0.0% 20% 0.0% 100.0% 0.0% 0.0% 0.0% 0.0% 100.0% 0.0% 0.0% 0.0% 40% 0.0% 0.0% 100.0% 0.0% 0.0% 0.0% 0.0% 100.0% 0.0% 0.0% 60% 0.0% 0.0% 0.0% 100.0% 0.0% 0.0% 0.0% 0.0% 78.0% 6.0% 80% 0.0% 0.0% 0.0% 0.0% 100.0% 0.0% 0.0% 0.0% 22.0% 94.0% 70 dB (76%) 60 dB (41.6%) Base 99.0% 1.0% 0.0% 0.0% 0.0% 79.0% 18.0% 2.0% 5.0% 3.0% 20% 0.0% 99.0% 0.0% 0.0% 0.0% 18.0% 38.0% 20.0% 9.0% 11.0% 40% 1.0% 0.0% 79.0% 13.0% 12.0% 1.0% 19.0% 29.0% 29.0% 23.0% 60% 0.0% 0.0% 11.0% 52.0% 37.0% 1.0% 15.0% 25.0% 27.0% 28.0% 80% 0.0% 0.0% 10.0% 35.0% 51.0% 1.0% 10.0% 24.0% 30.0% 35.0% 4.3. Classiﬁcation for Embedding Situation by CNN The embedding situation of the rod could also be predicted by the CNN classiﬁer. A total of 1500 data points were used for training the CNN, including unembedded rods, rods embedded with cement, and rods embedded with grease. The training and validation curves are shown in Figure 13. At a lower noise level, the classiﬁer entirely predicted the state of the rod. Until SNR was 70 dB, the validation curve was 0.956, training 40 epochs. Amplitude Performance Buildings 2022, 12, 1772 16 of 19 However, the accuracies at 60 dB dropped sharply. The test results are given in Table 5. Predictions were equal to 100% in each category when SNRs were from 100 dB to 80 dB. Buildings 2022, 12, x FOR PEER REVIEW 16 of 19 Several errors occurred at 70 dB and the accuracy was 92%. Speciﬁcally, the rod samples labeled as unembedded were much easier to confuse as rods embedded in grease, as 15% of the data in that category were misclassiﬁed into the grease state. On the other hand, 7% Only 1% of data in cement were predicted incorrectly. The worst results were the classi- of the data were misclassiﬁed into the unembedded state. Only 1% of data in cement were fication at 60 dB, where the total accuracy was only 35%, which means the model cannot predicted incorrectly. The worst results were the classiﬁcation at 60 dB, where the total identify the accuracy was signals. only 35%, which means the model cannot identify the signals. 1.0 0.8 Training(100 dB) Validation(100 dB) 0.6 Training(90 dB) Validation(90 dB) Training(80 dB) Validation(80 dB) 0.4 Training(70 dB) Validation(70 dB) Training(60 dB) Validation(60 dB) 0.2 0 10203040 Epoch Figure 13. Results of CNN at various noise levels. Figure 13. Results of CNN at various noise levels. Table 5. Confusion matrices in varying embedding conditions. Table 5. Confusion matrices in varying embedding conditions. 90 dB (100%) 80 dB (100%) 90 dB (100%) 80 dB (100%) Unembedded Cement Grease Unembedded Cement Grease Unembedded Cement Grease Unembedded Cement Grease Unembedded 100.0% 0.0% 0.0% 100.0% 0.0% 0.0% Unembedded 100.0% 0.0% 0.0% 100.0% 0.0% 0.0% Cement 0.0% 100.0% 0.0% 0.0% 100.0% 0.0% Cement 0.0% 100.0% 0.0% 0.0% 100.0% 0.0% Grease Grease 0.0% 0.0% 0.0% 0.0% 100.100.0%0% 0.0% 0.0% 0.0% 0.0% 100. 100.0% 0% 70 dB (92%) 60 dB (35%) 70 dB (92%) 60 dB (35%) Unembedded 84.0% 0.0% 7.0% 37.0% 24.0% 39.0% Unembedded 84.0% 0.0% 7.0% 37.0% 24.0% 39.0% Cement 1.0% 99.0% 0.0% 28.0% 43.0% 36.0% Cement 1.0% 99.0% 0.0% 28.0% 43.0% 36.0% Grease 15.0% 1.0% 93.0% 35.0% 33.0% 25.0% Grease 15.0% 1.0% 93.0% 35.0% 33.0% 25.0% 5. Conclusions 5. Conclusions We investigated the deep learning-based guided wave process for stress level predic- We investigated the deep learning-based guided wave process for stress level pre- tion of prestressed rods. The CNN model was established for automatically encoding the diction of prestressed rods. The CNN model was established for automatically encoding hidden information from complex signals that accounted for the impacts of different noise the hidden information from complex signals that accounted for the impacts of different levels and embedded grout materials. Some conclusions can be listed as follows: noise levels and embedded grout materials. Some conclusions can be listed as follows: (a) The deep learning method effectively encoded the guided waves under complex (a) The deep learning method effectively encoded the guided waves under complex uncertainties and assisted in stress level prediction and the embedded conditions uncertainties and assisted in stress level prediction and the embedded conditions of of the rods, thereby showing potential for signal processing of NDE methods in the rods, ther structural health eby show monitoring ing potential of PC str for uctur sign es. al processing of NDE methods in struc- tural health monitoring of PC structures. (b) The feature visualization method, t-SNE, provided an effective window that the (b) The feature visualization method, t-SNE, provided an effective window that the dif- different feature patterns could be clearly identiﬁed from visual two-dimensional ferent plots. fe The atur distances e patterns c between ould be c each featur learly e point identindicated ified from vis the corr ual elation two-dimens amongio data. nal plots. The In addition, distances betwe the impacts ofenoise n each interfer feature ence poin on t ithe ndica data ted the correl were observed ation a with mong the da use - of this approach. ta. In addition, the impacts of noise interference on the data were observed with the (c) The deep learning approach also exhibited high accuracy and robustness for data use of this approach. with high noise interference. The CNN classiﬁcation for most cases could reach up (c) The deep learning approach also exhibited high accuracy and robustness for data with high noise interference. The CNN classification for most cases could reach up to 100% when the noise levels were lower (80 dB–100 dB). However, with the ener- gy of the noise (SNR = 70 dB) close to the signals, data classification exhibited a cer- tain level of reduction, and the error rates were close to 80%. Particularly, when the Performance Buildings 2022, 12, 1772 17 of 19 to 100% when the noise levels were lower (80 dB–100 dB). However, with the energy of the noise (SNR = 70 dB) close to the signals, data classiﬁcation exhibited a certain level of reduction, and the error rates were close to 80%. Particularly, when the noise increased to a much higher level (60 dB), all the signals were contaminated, and the effectiveness of the classiﬁcation dropped. (d) The proposed method can also identify the embedding conditions. The identiﬁcation is no less than 92% when the noise level is lower than 60 dB. However, the accuracy drops to 35% at 60 dB, which means it is difﬁcult to distinguish the embedding conditions of rods. This study simulated the different levels of PC structure’s prestress loss by a deep learning method. To accommodate engineering concerns, noise interference was added. In future work, the methods will be explored on more large-scale structures in laboratory and ﬁeld conditions. As high levels of noise prevent the model from achieving high accuracy, future perspective will focus on this issue to improve the accuracy of identiﬁcation under higher noise levels (60 dB). In addition, different kinds of damage will occur at same time; thus, future study will investigate more complex situations. Furthermore, as the selection of hyperparameters is also critical, future research will also focus on deep learning with optimization methods (Bayesian optimization). 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Abstract

buildings Article Deep Learning-Enriched Stress Level Identiﬁcation of Pretensioned Rods via Guided Wave Approaches 1 2 2 1 1 1 , Zi Zhang , Fujian Tang , Qi Cao , Hong Pan , Xingyu Wang and Zhibin Lin * Department of Civil and Environmental Engineering, North Dakota State University, Fargo, ND 58018, USA School of Civil Engineering, Dalian University of Technology, Dalian 116024, China * Correspondence: zhibin.lin@ndsu.edu; Tel.: +1-701-231-7204 Abstract: By introducing pre-compression/inverse moment through prestressing tendons or rods, prestressed concrete (PC) structures could overcome conventional concrete weakness in tension, and thus, these tendons or rods are widely accepted in a variety of large-scale, long-span structures. Unfortunately, prestressing tendons or rods embedded in concrete are vulnerable to degradation due to corrosion. These embedded members are mostly inaccessible for visual or direct destructive assessments, posing challenges in determining the prestressing level and any corrosion-induced damage. As such, ultrasonic guided waves, as one of the non-destructive examination methods, could provide a solution to monitor and assess the health state of embedded prestressing tendons or rods. The complexity of the guided wave propagation and scattering in nature, as well as high variances stemming from the structural uncertainty and noise interference PC structures may experience under complicated operational and harsh environmental conditions, often make traditional physics- based methods invalid. Alternatively, the emerging machine learning approaches have potential for processing the guided wave signals with better capability of decoding structural uncertainty and noise. Therefore, this study aimed to tackle stress level prediction and the rod embedded conditions of prestressed rods in PC structures through guided waves. A deep learning approach, convolutional neural network (CNN), was used to process the guided wave dataset. CNN-based prestress level Citation: Zhang, Z.; Tang, F.; Cao, Q.; prediction and embedding condition identiﬁcation of rods were established by the ultrasonic guided Pan, H.; Wang, X.; Lin, Z. Deep wave technique. A total of ﬁfteen scenarios were designed to address the effectiveness of the stress Learning-Enriched Stress Level level prediction under different noise levels and grout materials. The results demonstrate that the Identiﬁcation of Pretensioned Rods via Guided Wave Approaches. deep learning approaches exhibited high accuracy for prestressing level prediction under structural Buildings 2022, 12, 1772. https:// uncertainty due to the varying surrounding grout materials. With different grout materials, accuracy doi.org/10.3390/buildings12111772 could reach up to 100% under the noise level of 90 dB, and still maintain the acceptable range of 75% when the noise level was as high as 70 dB. Moreover, the t-distributed stochastic neighbor embedding Academic Editor: Erwin Oh technology was utilized to visualize the feature maps obtained by the CNN and illustrated the Received: 24 September 2022 correlation among different categories. The results also revealed that the proposed CNN model Accepted: 20 October 2022 exhibited robustness with high accuracy for processing the data even under high noise interference. Published: 22 October 2022 Publisher’s Note: MDPI stays neutral Keywords: guided wave; convolutional neural network; structural health monitoring; stress level with regard to jurisdictional claims in prediction; t-distributed stochastic neighbor embedding published maps and institutional afﬁl- iations. 1. Introduction Conventional reinforced concrete, due to the weakness of the concrete in tension, Copyright: © 2022 by the authors. often shows cracking and corrosion at an early age [1,2]. PC has been proposed through Licensee MDPI, Basel, Switzerland. prestressing/post-tensioning tendons/rods to compensate this drawback [3]. PC structures This article is an open access article exhibit dramatically improved performance over conventional reinforced concrete ones, distributed under the terms and with the contribution of prestressing tendons or rods that enable them to cover a longer conditions of the Creative Commons span, thereby providing an effective solution in large-scale buildings, bridges, dams, and Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ nuclear power plant structures. It is known that PC structures often experience losses in 4.0/). prestress due to various factors, including shrinkage/creep of concrete and relaxation of Buildings 2022, 12, 1772. https://doi.org/10.3390/buildings12111772 https://www.mdpi.com/journal/buildings Buildings 2022, 12, 1772 2 of 19 tendons/rods, which in turn potentially lead to excessive deﬂection or cracking. As such, being able to quantify the stress level of these prestressing tendons/rods in service condi- tions is critical to ensure structural integrity and achieve successful performance. However, conventional visual or direct destructive examination tools are not valid, as the embedded prestressing tendons or rods with or without grout materials are often inaccessible. There- fore, non-destructive examination (NDE) methods and tools, including vibration-based sensors [4], distributed sensors [5], ultrasonic guided waves [6,7], or acoustic emission [8], could capture information of those far-reaching, inaccessible locations, while maintaining high-quality monitoring and assessing of structural health. For instance, Bartoli et al. [4] em- ployed dynamic identiﬁcation techniques to investigate the correlation between PC beam prestressing forces. Their results demonstrated that the vibration frequency could assist in identifying the prestress level. Chen et al. [5] used distributed sensor, long-gauge ﬁber Bragg grating to detect the damage of a bridge under stochastic trafﬁc ﬂow. In addition, the existence of anomalies is an important issue in monitoring data; hence, Zhang et al. [9] employed Bayesian dynamic regression to reconstruct missing data. Despite the merits of different sensing techniques, vibration-based methods are often limited in low frequency, while distributed sensors are often vulnerable to damage and anomalies. Alternatively, as stated in the literature [6,10–13], ultrasonic guided waves could be a better solution to tackle such situations, with the advantages of far-reaching, long-distance measurement and high accuracy in detecting small changes in material discontinuity. Additionally, as an active method, ultrasonic guided wave testing can judge the sensitivity and accuracy of a sensor by receiving the excitations, reducing the possibility of receiving abnormal data. Guided waves are widely used to evaluate the health of beams, plates, and pipes, owing to the potential of long-distance propagation and sensitivity to mechanical damage. Three modes, namely longitudinal, ﬂexural, and torsional modes, are generated when guided waves are propagated in a medium. Among them, longitudinal modes are more sensitive to tensile stress and easy to excite by piezoelectric actuators [14], and are used for the inspection of steel bars for corrosion, fracture, and stress reduction. Bread et al. [10] used the pulse-echo technique to detect the corrosion and fracture of grouted tendon anchors and rock bolts by ultrasonic guided waves. Lanza di Scalea et al. [15] applied guided waves through magnetostrictive transducers to monitor the stress in seven-wire strands. Their results demonstrated the feasibility of determining the prestress level using the guided wave method. Ervin et al. [16] created an embeddable ultrasonic sensor network to localize and monitor the corrosion of rebar embedded by mortar. They studied the characteristics of guided wave propagated in rebar and the effect forms for corrosion detection, and showed that the waves were sensitive to corrosion through scattering, mode conversions, and reﬂections. Chaki and Bourse [17] detected the stress level of the seven-wire steel strands by ultrasonic guided waves with L (0,1) mode. The typical calibration curves were plotted, which showed that the stress level corresponded to the phase velocity change in the guided waves. More recently, Treyssède and Laguerre [18] employed the semi-analytical ﬁnite element approach to study the guided wave propagation in multi-wire strands. In addition, high-order longitudinal modes were indicated to solve the leakage problem of fundamental mode L (0,1) by Dubuc et al. [19]. They used the acoustoelastic theory to propose an approximate theory for predicting the effect of stress on higher modes. Shoji Masanari [20] employed 60 kHz L (0,1) mode as the guided wave to inspect anchor rods embedded in soil, and unveiled the capability of the ultrasonic guided waves for stress identiﬁcation in rods. While physics-based approaches have been used for the signal process of guided waves to identify stress changes in stressed rods, these methods still face challenges in handling the wave signals with a variety of structural uncertainties, signal attenuation, and environmental noises during testing. In this way, recently emerging machine learning, particularly deep learning, could provide potential solutions to improve the signal process of guided waves [6,7,21,22]. Deep learning algorithms have been employed in time series [21,23–26] and image processing [27–30]. Guo et al. [31] utilized a sparse coding-based deep learning algorithm to process wireless Buildings 2022, 12, 1772 3 of 19 sensory data of a three-span bridge. The features of the dataset were learned by sparse coding and then trained by the network. Cha et al. [27] proposed a vision-based method by a deep learning network to detect concrete cracks without calculating the features. The comparative study indicated that the deep learning-based technique had better performance than the conventional physics-based methods. Furthermore, Cha et al. [28] investigated the fast region-based convolutional neural network to detect ﬁve types of damage in real time. Zhang et al. [32] proposed a CNN framework with some convolutional kernels to identify vibration signals. Harsh et al. [33] applied high-frequency guided waves to detect damages in railheads, generated the data by experiment and simulation study, and then set up a framework to detect damage of railheads by a machine learning method. The error rate was from 2% to 16.67%. Tabian et al. [34] used guided waves to detect impact energy, localization, and characterization of complex composite structures. The waves transferred into 2D images and were identiﬁed by a CNN algorithm. The results showed that the accuracy was above 95%. Zargar and Yuan [35] used a uniﬁed CNN-RNN network to extract the information of aluminum plates. This research focused on the wave propagation in both spatial and temporal domains. While deep learning approaches have been successfully used in many aspects of structural health monitoring, less research is involved in deep learning-based ultrasonic guided wave diagnoses. Therefore, we aimed to develop and implement the deep learning-enriched guided wave technique to quantify the stress level of prestressed rods used in PC structures. The CNN framework was utilized for processing guided wave signals to predict the stress level of the rods with varying grout materials. t-distributed stochastic neighbor embedding (t-SNE) was employed to visualize the features extracted by the CNN model. Moreover, different noise levels were considered to examine the robustness of the CNN classiﬁer. 2. Guided Waves as NDE Approach for Prestressed Rods 2.1. Governing Equations and Simulation of Guided Waves along a Rod Guided waves were ﬁrst introduced in cylinder structures in the 19th century [36]. The governing equation of the wave propagating in isotropic cylinders is expressed as [37] ¶ u (l + 2m)r(r u) + mr u + f = r (1) ¶x where u represents the displacement vector, x is the time, r is the three-dimensional Laplace operator, l and m indicate Lame’s constants, r is the mass density, and the body force f is equal to zero. Then, the Helmholtz decomposition is used in Equation (1) to simplify the problem as u = r' +r H (2) r H = 0 (3) where ' and H represent the scalar and vector potentials. Three types of guided waves, namely longitudinal mode (L (0, m)), torsional mode (T (0, m)), and ﬂexural mode (F (n, m)), were generated to propagate through a cylindrical structure. In the modes, n and m denote the circumferential order and modulus, respectively. When n = 0, the waves are symmetrical, such as L (0, m) and T (0, m). Otherwise, the waves are asymmetrical. Stress affects the phase velocity of the guided wave. The change in the phase velocity DC is expressed as " # (C ) DC = Dt (4) where C is the unstressed velocity, l represents the length of the wave propagation in the stress area, and Dt is the time change. Buildings 2022, 12, x FOR PEER REVIEW 4 of 19 spectively. When n = 0, the waves are symmetrical, such as L (0, m) and T (0, m). Other- wise, the waves are asymmetrical. Stress affects the phase velocity of the guided wave. The change in the phase veloci- ty is expressed as (𝐶 ) = − 𝛥𝑡 (4) Buildings 2022, 12, 1772 4 of 19 where 𝐶 is the unstressed velocity, l represents the length of the wave propagation in the stress area, and is the time change. Figure 1 shows the phase velocity and group velocity derived by MATLAB PCDisp Figure 1 shows the phase velocity and group velocity derived by MATLAB PCDisp [38,39]. [38,39]. The lower frequency of the excitation waves, less than 50 kHz, was used to re- The lower frequency of the excitation waves, less than 50 kHz, was used to reduce the duce the dispersion of the guided waves. dispersion of the guided waves. Figure 1. Phase velocities and group velocities. Figure 1. Phase velocities and group velocities. As such, the ultrasonic guided waves used in this study were numerically simulated As such, the ultrasonic guided waves used in this study were numerically simulat- by Multiphysics Finite Element (FE) software COMSOL, and their propagation charac- ed by Multiphysics Finite Element (FE) software COMSOL, and their propagation char- teristics along the prestressed rod under different conditions, including under varying acteristics along the prestressed rod under different conditions, including under varying grout materials and different stress levels, were then modeled and extracted using machine grout materials and different stress levels, were then modeled and extracted using ma- learning to assist in data classiﬁcation, as discussed in Section 3. chine learning to assist in data classification, as discussed in Section 3. 2.2. Calibration of the FE Analysis of the Ultrasonic Guided Waves through the Rod 2.2. Calibration of the FE Analysis of the Ultrasonic Guided Waves through the Rod We sought to ensure that proper parameters were used for the rod simulation and We sought to ensure that proper parameters were used for the rod simulation and calibrate the effectiveness of FE-based simulation for capturing the characteristics of the calibrate the effectiveness of FE-based simulation for capturing the characteristics of the wave propagation along rods. One case of the characterization of ultrasonic guided waves wave propagation along rods. One case of the characterization of ultrasonic guided along an anchor rod was selected from the literature [40], in which the rod had a diameter of waves along an anchor rod was selected from the literature [40], in which the rod had a 21 mm and was 2.3 m in length, and was embedded in a concrete block with a cross-section diameter of 21 mm and was 2.3 m in length, and was embedded in a concrete block with of 1.0 m by 1.0 m and a depth of 2.0 m, as shown in the FE meshed model in Figure 2a. The a cross-section of 1.0 m by 1.0 m and a depth of 2.0 m, as shown in the FE meshed model excitation of the ultrasonic guided waves was a six-cycle tone burst with a frequency of in Figure 2a. The excitation of the ultrasonic guided waves was a six-cycle tone burst 35 kHz. A pulse-echo test was set up on the rod where the actuators and receivers were with a frequency of 35 kHz. A pulse-echo test was set up on the rod where the actuators on the same side. Excitations were generated by Wavemaker 16 equipment, which is used and receivers were on the same side. Excitations were generated by Wavemaker 16 for long-range inspection of pipes. The rod was embedded in the concrete block along 2 equipment, which is used for long-range inspection of pipes. The rod was embedded in m and the remaining length of the rod from both ends of the block [40]. The comparison the concrete block along 2 m and the remaining length of the rod from both ends of the results are shown in Figure 2b, where signals in the literature are marked with red lines and block [40]. The comparison results are shown in Figure 2b, where signals in the literature the black ones were generated from this study, and the three circled wave packets denote are marked with red lines and the black ones were generated from this study, and the the excitation signals, the ﬁrst right boundary reﬂection, and the second right boundary three circled wave packets denote the excitation signals, the first right boundary reflec- reﬂection. As shown in Figure 2b, the simulated guided waves in this study matched well tion, and the second right boundary reflection. As shown in Figure 2b, the simulated with the experimental data collected from the literature in most cases, where three wave guided waves in this study matched well with the experimental data collected from the packets were captured well. The ﬁrst boundary wave reﬂections from simulated signals literature in most cases, where three wave packets were captured well. The first bounda- occurred at 0.001 s, identical to the experimental data with comparable amplitudes. Note that some deviations occurred after the excitation, and a potential reason could partially result from the attenuation of the concrete block where the simulation did not capture well. However, the entire trend and amplitudes in most cases were in agreement with the literature, suggesting that the simulation used in this study was appropriate to ensure capturing of the characteristics of the ultrasonic guided waves through the rods. 𝛥𝑡 𝛥𝐶 𝛥𝐶 Buildings 2022, 12, x FOR PEER REVIEW 5 of 19 ry wave reflections from simulated signals occurred at 0.001 s, identical to the experi- mental data with comparable amplitudes. Note that some deviations occurred after the excitation, and a potential reason could partially result from the attenuation of the con- crete block where the simulation did not capture well. However, the entire trend and amplitudes in most cases were in agreement with the literature, suggesting that the sim- ulation used in this study was appropriate to ensure capturing of the characteristics of Buildings 2022, 12, 1772 5 of 19 the ultrasonic guided waves through the rods. 2nd (a) (b) Figure 2. Calibration of the FE model. (a) Meshing of the rod embedded in concrete. (b) Compari- Figure 2. Calibration of the FE model. (a) Meshing of the rod embedded in concrete. (b) Comparison son of signals with the literature. of signals with the literature. 2.3. Design of Scenarios 2.3. Design of Scenarios Followed by the calibration in Section 2.2, this section details the design of different Followed by the calibration in Section 2.2, this section details the design of different scenarios to generate datasets that helped to elucidate the critical factors affecting the scenarios to generate datasets that helped to elucidate the critical factors affecting the characteristics of ultrasonic guided wave propagation along stressed rods, thus paving characteristics of ultrasonic guided wave propagation along stressed rods, thus paving the the way for stress level prediction using machine learning in Section 3. As such, the pro- way for stress level prediction using machine learning in Section 3. As such, the prototype totype of the stressed ro of the stressed rods was ds derived was der from ived from the literatur the literature [41]. The e [41]. The rod was rod was 31.75 mm 31.75 mm in in diameter diam with et a er length withof a 3657.6 length of mm. 36The 57.6 mm. T material he material p properties ofroperties o the rod wer f t ehdensity e rod were of 7800 density of kg/m , 3 5 7 Y 800 oung’s kg/m modulus , Young’s mod of 2 10 ulus MPa, of 2 and × 10 Poisson MPa, and ratioPo of i0.3. sson Arclamp atio of 0. served 3. A cl as am the p serv anchorage ed as of the rod, which was located 50.8 mm away from the free end. Besides the reference where the anchorage of the rod, which was located 50.8 mm away from the free end. Besides the ref the rod erence where the rod had no had no grout, two grout materials, grout, tw namely o grout ma greaseteri and als, cement, namely grease a were selected nd ce- to unveil their effects on the effectiveness of the proposed methods. The density of the cement ment, were selected to unveil their effects on the effectiveness of the proposed methods. 3 4 3 4 was 1440 kg/m , the Young’s modulus was 2.5 10 MPa, and the Poisson ratio was 0.25. The density of the cement was 1440 kg/m , the Young’s modulus was 2.5 × 10 MPa, and The density of the grease was 2600 kg/m . The detailed information of the rod models is the Poisson ratio was 0.25. The density of the grease was 2600 kg/m . The detailed in- shown in Figure 3. The entire rod with the clamp is illustrated in Figure 3a (note that the formation of the rod models is shown in Figure 3. The entire rod with the clamp is illus- meshing ﬁgure is a schematic diagram; the actual meshing unit is much smaller), and the trated in Figure 3a (note that the meshing figure is a schematic diagram; the actual embedded rod is shown in Figure 3b. Speciﬁcally, the rod passed through the plastic pipe meshing unit is much smaller), and the embedded rod is shown in Figure 3b. Specifical- and then added grease and cement to ﬁll the gap between the pipe and the rod. The outer ly, the rod passed through the plastic pipe and then added grease and cement to fill the diameter of the plastic pipe was 52.07 mm, and the thickness was 2.54 mm. In ﬁnite element gap between the pipe and the rod. The outer diameter of the plastic pipe was 52.07 mm, studies, meshing is one of the critical parts in simulation. Free triangular element was and the thickness was 2.54 mm. In finite element studies, meshing is one of the critical selected in this model. Guided wave simulation requires a high-quality meshing system parts in simulation. Free triangular element was selected in this model. Guided wave to minimize the propagation error of guided waves. Thus, a wavelength needs to contain simulation requires a high-quality meshing system to minimize the propagation error of at least eight elements. In this study, the maximum element size in the model was 2 mm guided waves. Thus, a wavelength needs to contain at least eight elements. In this study, and time steps were 5 10 s. Guided waves could be excited in the rod by adding -6 the maximum element size in the model was 2 mm and time steps were 5× 10 s. Guided displacement loads in all nodes of the left boundary in the model. The excitation waves waves could be excited in the rod by adding displacement loads in all nodes of the left were 35 kHz ﬁve-cycle sinusoidal waves modulated by the Hanning window. Four points, boundary in the model. The excitation waves were 35 kHz five-cycle sinusoidal waves as received points, distributed the circumferential surface of the rod. Positions of received modulated by the Hanning window. Four points, as received points, distributed the cir- nodes were 5 mm away from the left side. Received signals were time series data, which cumferential surface of the rod. Positions of received nodes were 5 mm away from the intercept the ﬁrst 1000 data points as results for further study. Buildings 2022, 12, x FOR PEER REVIEW 6 of 19 Buildings 2022, 12, 1772 6 of 19 left side. Received signals were time series data, which intercept the first 1000 data points as results for further study. Figure 3. Rod models. Figure 3. Rod models. To simulate the stress reduction in prestressed components, ﬁve different pressure To simulate the stress reduction in prestressed components, five different pressure levels were loaded into each rod: no prestress (State #1), 20% ultimate tensile strength (UTS) levels were loaded into each rod: no prestress (State #1), 20% ultimate tensile strength (State #2), 40% UTS (State #3), 60% UTS (State #4), and 80% UTS (State #5). In total, 15 cases (UTS) (State #2), 40% UTS (State #3), 60% UTS (State #4), and 80% UTS (State #5). In total, were designed in this section, which are shown in Table 1. Noise was added into the data 15 cases were designed in this section, which are shown in Table 1. Noise was added in- to increase the uncertainty of the dataset. to the data to increase the uncertainty of the dataset. Table 1. Test matrix for computation modeling. Table 1. Test matrix for computation modeling. Prestressing Level Case State Grout Material Noise Level (UTS) Prestressing Level Case State Grout Material Noise Level # 1 zero n (UTS) # 2 20% n # 1 zero \ # 3 40% n # 2 20% \ (no grout) # 4 60% n # 3 40% \ (no grout) # 5 80% n # 4 60% \ # 6 zero Grease # 5 80% \ # 6 # 7 20%zero GreaseGrease 100 dB–60 dB # 7 # 8 40%20% GreaseGrease (grease) # 8 # 9 60%40% GreaseGrease 100 dB–60 dB (grease) # 9 60% Grease # 10 80% Grease # 10 80% Grease # 11 zero Cement # 11 zero Cement # 12 20% Cement # 12 20% Cement # 13 40% Cement (cement) # 13 40% Cement # 14 60% Cement (cement) # 14 60% Cement # 15 80% Cement # 15 80% Cement 2.4. Data Collection and Augmentation Figure 4 shows the time records with five different prestress levels derived from the finite element simulation in Case 1 from Table 1. The received point was located 5 mm Buildings 2022, 12, 1772 7 of 19 Buildings 2022, 12, x FOR PEER REVIEW 7 of 19 2.4. Data Collection and Augmentation away from the left side of the rod. To ensure the input wave had similar energy, all the Figure 4 shows the time records with ﬁve different prestress levels derived from the received signal ﬁnite s were nor element m simulation alized, and in tCase he m1axim fromuT m able am1p . lit The udreeceived of the first point p was acket located was 5 mm away from the left side of the rod. To ensure the input wave had similar energy, all the equal to 1. The time series were from 0 s to 0.005 s; the guided wave can propagate and received signals were normalized, and the maximum amplitude of the ﬁrst packet was reflect at least twice throughout the rod. Figure 4a–e illustrates the received signals of equal to 1. The time series were from 0 s to 0.005 s; the guided wave can propagate and the steel with prestress levels equal to 0% UTS, 20% UTS, 40% UTS, 60% UTS, and 80% reﬂect at least twice throughout the rod. Figure 4a–e illustrates the received signals of UTS. Specifically, at low prestress level states (0–40% UTS), the results clearly exhibit the steel with prestress levels equal to 0% UTS, 20% UTS, 40% UTS, 60% UTS, and 80% three main wave packets that represent the initial excitation and the first and second re- UTS. Speciﬁcally, at low prestress level states (0–40% UTS), the results clearly exhibit three flections from the boundary. Following the first packet, fluctuations with small ampli- main wave packets that represent the initial excitation and the ﬁrst and second reﬂections tude were echoes from the clamp. With the stress level increased, the amplitude of this from the boundary. Following the ﬁrst packet, ﬂuctuations with small amplitude were part was smaller, and it was hard to detect at 80% UTS. In addition, the velocity of guid- echoes from the clamp. With the stress level increased, the amplitude of this part was smaller, and it was hard to detect at 80% UTS. In addition, the velocity of guided waves ed waves reduced with increasing the stress of the rod. The first reflection from the right reduced with increasing the stress of the rod. The ﬁrst reﬂection from the right boundary boundary was around 0.0018 s in the base state. The value was raised to 0.0019 s and was around 0.0018 s in the base state. The value was raised to 0.0019 s and 0.002 s when 0.002 s when stresses were 40% UTS and 80% UTS. At 60% and 80% UTS (shown in Fig- stresses were 40% UTS and 80% UTS. At 60% and 80% UTS (shown in Figure 4d,e), only ure 4d,e), only two main packets existed in the signals, where one was initial input two main packets existed in the signals, where one was initial input waves, and the other waves, and the other was the boundary reflection. The energy of guided waves was dis- was the boundary reﬂection. The energy of guided waves was dissipated when waves sipated when waves propagated in the second cycle. Thus, it was difficult to detect the propagated in the second cycle. Thus, it was difﬁcult to detect the second echo from the second echo from the boundary. boundary. 2nd Figure 4. Received signals at different stress levels: (a) zero; (b) 20% UST; (c) 40% UTS; (d) 60% Figure 4. Received signals at different stress levels: (a) zero; (b) 20% UST; (c) 40% UTS; (d) 60% UTS; UTS; (e) 80% UTS. (e) 80% UTS. As illustrated in Fi As illustrated gure 5, tin he collect Figure 5ed , the gu collected ided wave guided s of the rod ex waves of the hibited d rod exhibited ifferent different patterns from different grout materials. Figure 5 illustrates the signals collected from patterns from different grout materials. Figure 5 illustrates the signals collected from States #1, #6, and #11 (without stress) in the time domain and frequency domain. It was States #1, #6, and #11 (without stress) in the time domain and frequency domain. It was observed from the time domain that with long distance propagation, the energy of the observed from the time domain that with long distance propagation, the energy of the reflection waves was reduced progressively. However, comparing these three states, the rod embedded in cement had the highest attenuation, where the peak value of reflec- tions was reduced from 0.2588 to 0.1075. After propagating to the second cycle, the peak value of the second boundary echo was reduced to 0.0897 in the unembedded state, and the value of the rod in cement was the lowest, 0.0113. On the contrary, grease had less of Buildings 2022, 12, 1772 8 of 19 reﬂection waves was reduced progressively. However, comparing these three states, the Buildings 2022, 12, x FOR PEER REVIEW 8 of 19 rod embedded in cement had the highest attenuation, where the peak value of reﬂections was reduced from 0.2588 to 0.1075. After propagating to the second cycle, the peak value of the second boundary echo was reduced to 0.0897 in the unembedded state, and the value an effect on guided waves. With 1463.04 mm of propagation, the peak value of the re- of the rod in cement was the lowest, 0.0113. On the contrary, grease had less of an effect flected waves was 0.0455, which was close to the unembedded state. In the frequency on guided waves. With 1463.04 mm of propagation, the peak value of the reﬂected waves domain, it was clear that the main frequency of waves was 35 kHz. Some weak peaks was 0.0455, which was close to the unembedded state. In the frequency domain, it was occurred at the low frequency and the high frequency due to reflections from the clamp clear that the main frequency of waves was 35 kHz. Some weak peaks occurred at the low and the boundary. frequency and the high frequency due to reﬂections from the clamp and the boundary. 0.03 Unembedded Unembedded 0.02 Envelop 0.01 -1 0.000 0.001 0.002 0.003 0.004 0.005 Time (s) 0.00 0 50 100 Frequency (kHz) (a) 0.03 Grease Grease 0.02 Envelop 0.01 -1 0.000 0.001 0.002 0.003 0.004 0.005 0.00 Time (s) 0 50 100 Frequency (kHz) (b) 0.03 Cement Cement 0.02 Envelop 0.01 -1 0.000 0.001 0.002 0.003 0.004 0.005 0.00 Time (s) 0 50 100 Frequency (kHz) (c) Figure 5. Received signals for rods with different grout methods: (a) no grout; (b) grease; (c) ce- Figure 5. Received signals for rods with different grout methods: (a) no grout; (b) grease; (c) cement. ment. A total of 15 states were designed to simulate the actual situation of the rod. In each A total of 15 states were designed to simulate the actual situation of the rod. In each state, four received nodes were distributed around the circumference and were located 5 state, four received nodes were distributed around the circumference and were located 5 mm away from the left side. Since the received waves were easily contaminated by noise, mm away from the left side. Since the received waves were easily contaminated by ﬁve noise levels based on the signal to noise ratio (SNR) were added into the received noise, five noise levels based on the signal to noise ratio (SNR) were added into the re- signals. In addition, noise involved in the signals could increase the uncertainties of the ceived signals. In addition, noise involved in the signals could increase the uncertainties data, so we attempted to investigate the robustness of the deep learning methods. Figure 6 of the data, so we attempted to investigate the robustness of the deep learning methods. illustrates the collected signals at ﬁve different noise levels. When SNR exceeded 80 Db, the Figure 6 illustrates the collected signals at five different noise levels. When SNR exceed- interference from noise was obvious and covered some original features of the initial signals. ed 80 Db, the interference from noise was obvious and covered some original features of Especially, at 60 dB, the amplitude of the noise was greater than the signal amplitude, which the initial signals. Especially, at 60 dB, the amplitude of the noise was greater than the was not conductive for further study. signal amplitude, which was not conductive for further study. Figure 6. Received signals at different noise levels. Amplitude Amplitude Amplitude Amplitude Amplitude A m plitude Buildings 2022, 12, x FOR PEER REVIEW 8 of 19 an effect on guided waves. With 1463.04 mm of propagation, the peak value of the re- flected waves was 0.0455, which was close to the unembedded state. In the frequency domain, it was clear that the main frequency of waves was 35 kHz. Some weak peaks occurred at the low frequency and the high frequency due to reflections from the clamp and the boundary. 0.03 Unembedded Unembedded 0.02 Envelop 0.01 -1 0.000 0.001 0.002 0.003 0.004 0.005 Time (s) 0.00 0 50 100 Frequency (kHz) (a) 0.03 Grease Grease 0.02 Envelop 0.01 -1 0.000 0.001 0.002 0.003 0.004 0.005 0.00 Time (s) 0 50 100 Frequency (kHz) (b) 0.03 Cement Cement 0.02 Envelop 0.01 -1 0.000 0.001 0.002 0.003 0.004 0.005 0.00 Time (s) 0 50 100 Frequency (kHz) (c) Figure 5. Received signals for rods with different grout methods: (a) no grout; (b) grease; (c) ce- ment. A total of 15 states were designed to simulate the actual situation of the rod. In each state, four received nodes were distributed around the circumference and were located 5 mm away from the left side. Since the received waves were easily contaminated by noise, five noise levels based on the signal to noise ratio (SNR) were added into the re- ceived signals. In addition, noise involved in the signals could increase the uncertainties of the data, so we attempted to investigate the robustness of the deep learning methods. Figure 6 illustrates the collected signals at five different noise levels. When SNR exceed- ed 80 Db, the interference from noise was obvious and covered some original features of the initial signals. Especially, at 60 dB, the amplitude of the noise was greater than the Buildings 2022, 12, 1772 9 of 19 signal amplitude, which was not conductive for further study. Figure 6. Received signals at different noise levels. Figure 6. Received signals at different noise levels. 3. Deep Learning Framework CNN has been widely adopted in many application domains, such as image clas- siﬁcation and segmentation, speech recognition, and computer vision tasks. The CNN framework contains multiple layers, including a convolutional layer, pooling layer, fully connected layer, and ReLU layer. These layers help to decode the input data into high- dimensional slices, extract the intricate features, and then encode them into the target values. In this study, CNN was used to identify the complicated guided wave signals. The architecture of the CNN trained by guided wave signals is described. The model of the CNN was changed from LeNet-5. 3.1. Introductions of CNN The input data consisted of a series of signals with m detection points and n time steps. Thus, the size of the input layer was n m. The convolutional layer is one of the most crucial layers in a CNN. In this layer, each element from the kernel is multiplied with the data in the previous layer. The size of the kernel determines the operation area, and the number of kernels decides the third dimension of the output. The kernel size is much smaller than the input layer, so the kernel moves step by step to implement. The stride deﬁnes the length of each step, which causes the output data reduction. The size of the stride is an essential value which affects the efﬁciency and performance of the layer. A bigger size may cause the loss of some important features, and a small size may cause an increase in calculation. The initial kernels are generated randomly, and they update by learning from each iterator. A bias is added after summing all the multiplication results in the operation area. When all the kernels ﬁnish the multiplication with the input data and summarize, the result is the output in this layer. The pooling layer is used to reduce the size of the previous layer. Two pooling layers can be selected, namely max pooling and mean pooling. In max pooling, the maximum values in the operation area are taken as the result. In mean pooling, the average values are the result. The operation area is also moved by setting the values of stride. After adding a pooling layer to a CNN framework, the output of the convolutional bands has a dramatic decrease. In this CNN, all the pooling layers were set as max pooling layers. The activation layer adds nonlinearity into the CNN. In this model, ReLU was chosen as the activation layer in the CNN trained by guided wave signals. ReLU changes some of the neurons to zero, which will thin the network, reduce the interdependence between parameters, and avoid overﬁtting to some extent. In addition, it also saves computation and improves the efﬁciency of deep learning models, compared with other activation functions. After the cooperation of several layers, the initial data are changed into a series of feature maps, and the size is deformed. To transfer these feature maps into their own category, a fully connected layer is necessary. The result of this layer is the probability that the data belong to each label. The entire process is shown in Figure 7. Amplitude Amplitude Amplitude Amplitude Amplitude A m plitude Buildings 2022, 12, x FOR PEER REVIEW 9 of 19 3. Deep Learning Framework CNN has been widely adopted in many application domains, such as image classi- fication and segmentation, speech recognition, and computer vision tasks. The CNN framework contains multiple layers, including a convolutional layer, pooling layer, fully connected layer, and ReLU layer. These layers help to decode the input data into high- dimensional slices, extract the intricate features, and then encode them into the target values. In this study, CNN was used to identify the complicated guided wave signals. The architecture of the CNN trained by guided wave signals is described. The model of the CNN was changed from LeNet-5. 3.1. Introductions of CNN The input data consisted of a series of signals with m detection points and n time steps. Thus, the size of the input layer was n × m. The convolutional layer is one of the most crucial layers in a CNN. In this layer, each element from the kernel is multiplied with the data in the previous layer. The size of the kernel determines the operation area, and the number of kernels decides the third dimension of the output. The kernel size is much smaller than the input layer, so the kernel moves step by step to implement. The stride defines the length of each step, which causes the output data reduction. The size of the stride is an essential value which affects the efficiency and performance of the layer. A bigger size may cause the loss of some important features, and a small size may cause an increase in calculation. The ini- tial kernels are generated randomly, and they update by learning from each iterator. A bias is added after summing all the multiplication results in the operation area. When all the kernels finish the multiplication with the input data and summarize, the result is the output in this layer. The pooling layer is used to reduce the size of the previous layer. Two pooling lay- ers can be selected, namely max pooling and mean pooling. In max pooling, the maxi- mum values in the operation area are taken as the result. In mean pooling, the average values are the result. The operation area is also moved by setting the values of stride. Af- ter adding a pooling layer to a CNN framework, the output of the convolutional bands has a dramatic decrease. In this CNN, all the pooling layers were set as max pooling lay- ers. The activation layer adds nonlinearity into the CNN. In this model, ReLU was cho- sen as the activation layer in the CNN trained by guided wave signals. ReLU changes some of the neurons to zero, which will thin the network, reduce the interdependence between parameters, and avoid overfitting to some extent. In addition, it also saves computation and improves the efficiency of deep learning models, compared with other activation functions. After the cooperation of several layers, the initial data are changed into a series of feature maps, and the size is deformed. To transfer these feature maps into their own Buildings 2022, 12, 1772 category, a fully connected layer is necessary. The result of this layer is the pr 10 of 19 obability that the data belong to each label. The entire process is shown in Figure 7. Figure 7. Flowchart of CNN. 3.2. CNN Architecture The proposed CNN in this study was an eight-layer network, including three con- volutional layers, two max pooling layers, a ReLU layer, a fully connected layer, and a softmax layer. The selection of hyperparameters affects the performance of the neural network. Different methods [27,42,43] have been proposed to select these parameters. For instance, the learning rate is to adjust the gradient update, the kernel number size is to adjust the receptive ﬁled; in addition, stride step and batch size are critical in parameter design [26,41]. In this study, the hyperparameter selection stems from previous studies, maintaining the basic network architecture of LeNet-5. Note that several studies revealed that the introduction of Bayesian optimization [44,45] in determining the hyperparame- ters could further enhance the architecture of the CNN with less trial and error, and thus improve the accuracy. As part of the ongoing investigation of the applications of deep learning in civil structures, we consider advances in hyperparameter design, including using Bayesian optimization, for optimizing the CNN architecture. The detailed information of each CNN layer is given in Table 2. The input data are a matrix sized 1000 4, representing four collected signals in a rod sample. A total of 1000 data points were intercepted from received signals, which included the excitation and the reﬂection from the right boundary. Four is the number of received signals. In the ﬁrst convolutional layer, 20 ﬁlters sized 25 2 were generated and operated the input data into 976 3 20. The following was a max pooling layer with the stride equal to 5. The layer captured the maximum value in the response ﬁeld and signiﬁcantly cut down the size of the input. After that, the output of the data was 195 3 20. Then, the data experienced cooperation from the convolutional layer and the max pooling layer, involving 40 ﬁlters, and the pooling size was 5 1. At this moment, the output was 34 1, a dramatic decline compared with the initial input. The third convolutional layer had a small size, 5 1, and a ReLU was implemented to increase the nonlinearity. Finally, the fully connected layer and softmax layer transferred the data into several probabilities in each label. Table 2. Details of the proposed CNN. Name Filters Filter Size Stride Bias Output Layer Size Input layer – – – – 1000 4 Convolutional layer (C ) 20 25 2 1 20 976 3 Max pooling layer (P ) 20 5 1 5 – 195 3 Convolutional layer (C ) 40 25 3 1 40 171 1 Max pooling layer (P ) 40 5 1 5 – 34 1 Convolutional layer (C ) 20 5 1 1 20 30 1 ReLU – – – – 30 1 Fully connected layer (F ) 5 30 1 1 5 5 Softmax – – – – 5 Buildings 2022, 12, 1772 11 of 19 3.3. Feature Visualization with t-SNE The CNN classiﬁer achieves better performance since it automatically extracts features from the training data. It expands the data into high-dimensional matrices by multiple ﬁlters. Thus, these features are usually high-dimensional, which is not conductive to understanding. However, stochastic neighbor embedding (SNE) was introduced to reduce Buildings 2022, 12, x FOR PEER REVIEW 11 of 19 the dimensions of the features, making it possible to visualize the feature. SNE aims to convert the high-dimensional Euclidean distance between data samples into conditional probabilities. The t-distributed stochastic neighbor embedding (t-SNE) [46] proposed by similarity matrix and minimizes the gap between the distribution in two spaces. This Maaten and Hinton transforms a high-dimensional dataset into a pairwise similarity matrix and meth m od is po inimizes pula ther f gap or feat between ure vithe suadistribution lization in mach in two ine le spaces. arning This algmethod orithms.is popular for feature visualization in machine learning algorithms. 4. Results and Discussion 4. Results and Discussion 4.1. Feature Visualization 4.1. Feature Visualization In this study, 500 data points in each state emerged by adding white Gaussian In this study, 500 data points in each state emerged by adding white Gaussian noise, noise, including 60% data for training, 20% for validation, and 20% for testing. The CNN including 60% data for training, 20% for validation, and 20% for testing. The CNN model model was well trained after studying the features from the training data. The feature was well trained after studying the features from the training data. The feature maps maps can estimate the efficiency of the proposed method. The following figures show can estimate the efﬁciency of the proposed method. The following ﬁgures show the high- the high-dimensional feature maps in two-dimensional space by t-SNE. dimensional feature maps in two-dimensional space by t-SNE. Figure 8 depicts the features in Case 1, where the prestress level of the unembedded Figure 8 depicts the features in Case 1, where the prestress level of the unembedded rod is 80 dB. States #1–5 represent the rod with the prestress level equal to 0% (base rod is 80 dB. States #1–5 represent the rod with the prestress level equal to 0% (base state), state), 20% UTS, 40% UTS, 60% UTS, and 80% UTS. In total, 2500 samples comprised the 20% UTS, 40% UTS, 60% UTS, and 80% UTS. In total, 2500 samples comprised the dataset, dataset, where 1500 were used to train the model, 500 for validation, and the remaining where 1500 were used to train the model, 500 for validation, and the remaining 500 for 500 for testing. Figure 8a displays the feature maps of the test set after the first convolu- testing. Figure 8a displays the feature maps of the test set after the ﬁrst convolutional layer. tional layer. Through the distribution of features, data labeled as 40% UTS (green upper Through the distribution of features, data labeled as 40% UTS (green upper triangle) were triangle) were isolated from the entire dataset. This indicates that the features in this la- isolated from the entire dataset. This indicates that the features in this label extracted from bel extracted from the first layer of the CNN model were much easier to separate than the ﬁrst layer of the CNN model were much easier to separate than others because the others because the Euclidean distance is larger. However, the clusters in the red dia- Euclidean distance is larger. However, the clusters in the red diamond (base state) and mond (base state) and yellow circle (20% UTS) located on the right side overlapped. At yellow circle (20% UTS) located on the right side overlapped. At least one-quarter of the least one-quarter of the data were mixed and difficult to separate, which means errors data were mixed and difﬁcult to separate, which means errors will occur. In addition, the will occur. In addition, the rod samples prestressed in 60% UTS (blue lower triangle) and rod samples prestressed in 60% UTS (blue lower triangle) and 80% UTS (purple star) were 80% UTS (purple star) were tangled together. Figure 8b represents the feature maps tangled together. Figure 8b represents the feature maps from the last layer of the CNN. from the last layer of the CNN. After eight layers’ processing, most of the samples were After eight layers’ processing, most of the samples were separated, except one outlier in separated, except one outlier in the base class clustered in 20% UTS and a small overlap the base class clustered in 20% UTS and a small overlap appeared between the samples in appeared between the samples in 60% UTS and 80% UTS. The results demonstrate that 60% UTS and 80% UTS. The results demonstrate that the features became more sensitive the features became more sensitive after operating the whole CNN process. after operating the whole CNN process. Base 20% UTS 40% UTS 60% UTS 80% UTS Base 20% UTS -10 40% UTS −-20 60% UTS 80% UTS −-40 −-20 0 20 -10 0 10 20 (a) (b) Figure 8. Feature visualization by t-SNE. (a) Feature maps in the first convolutional layer; (b) fea- Figure 8. Feature visualization by t-SNE. (a) Feature maps in the ﬁrst convolutional layer; (b) feature ture maps in the last layer. maps in the last layer. The CNN model sliced input signals into several small pieces, which enlarged the sensitive features and cut off the excess. Figure 9 plots the feature maps from five differ- ent prestress levels after three convolutional layers. The data are signals from five differ- ent prestress levels in Case 1 when SNR is equal to 100 dB. The differences between the five figures are clear. The shape and peak values of lines characterize signals from dif- ferent groups. However, with the increasing noise level, extracting features became harder. Y Buildings 2022, 12, 1772 12 of 19 The CNN model sliced input signals into several small pieces, which enlarged the sensitive features and cut off the excess. Figure 9 plots the feature maps from ﬁve different prestress levels after three convolutional layers. The data are signals from ﬁve different Buildings 2022, 12, x FOR PEER REVIEW 12 of 19 prestress levels in Case 1 when SNR is equal to 100 dB. The differences between the ﬁve ﬁgures are clear. The shape and peak values of lines characterize signals from different groups. However, with the increasing noise level, extracting features became harder. Feature maps Feature maps Feature maps 50 50 0 0 015 30 015 30 015 30 (a) (b) (c) Feature maps 20 Feature maps -10 −-20 015 30 015 30 (d) (e) Figure 9. Feature maps: (a) 0% UTS; (b) 20% UTS; (c) 40% UTS; (d) 60% UTS; (e) 80% UTS. Figure 9. Feature maps: (a) 0% UTS; (b) 20% UTS; (c) 40% UTS; (d) 60% UTS; (e) 80% UTS. Figure 10 illustrates the feature visualization in Case 1 when SNRs were equal to Figure 10 illustrates the feature visualization in Case 1 when SNRs were equal to 100 dB, 70 dB, and 60 dB. At 100 dB (in Figure 10a), the ﬁve clusters were far from each 100 dB, 70 dB, and 60 dB. At 100 dB (in Figure 10a), the five clusters were far from each other, and each cluster of data is relatively concentrated, with an average standard deviation other, and each cluster of data is relatively concentrated, with an average standard devi- close to 2.53. With the noise level increased to 80 dB (shown in Figure 10b), a small overlap ation close to 2.53. With the noise level increased to 80 dB (shown in Figure 10b), a small appeared between the 60% UTS and 80% UTS data, but the other three groups were clearly overlap appeared between the 60% UTS and 80% UTS data, but the other three groups separated. The standard deviation in this situation was large, 2.83. However, when SNR were clearly separated. The standard deviation in this situation was large, 2.83. Howev- was lower than 80 dB, the distributions of features changed dramatically. At 70 dB, features er, when SNR was lower than 80 dB, the distributions of features changed dramatically. in either the base state and 20% UTS or 60% UTS and 80% UTS were blended into each At 70 other dB, f , and eatures i only the n ei data ther inthe thebase state green upper antriangles d 20% UTS wereor 60 independently % UTS and 8 located 0% UTS below were the graph, demonstrated in Figure 10b. In Figure 10c, feature maps at 60 dB had a worse blended into each other, and only the data in the green upper triangles were inde- situation, as all the data interwove together entirely. It is hard to ascertain the boundaries of pendently located below the graph, demonstrated in Figure 10b. In Figure 10c, feature each group. Therefore, this proved that noise had an adverse effect on the feature extraction maps at 60 dB had a worse situation, as all the data interwove together entirely. It is of the CNN. hard to ascertain the boundaries of each group. Therefore, this proved that noise had an adverse effect on the feature extraction of the CNN. Base Base 20% UTS 20% UTS 40% UTS 40% UTS 60% UTS 60% UTS 80% UTS 80% UTS Base 20% UTS 40% UTS −-10 -20 -20 60% UTS 80% UTS −-30 0 30 −-8 0 8 −-30 0 X X (a) (b) (c) Figure 10. Feature visualization by t-SNE. (a) SNR = 100 dB; (b) SNR = 70 dB; (c) SNR = 60 dB. Y Buildings 2022, 12, x FOR PEER REVIEW 12 of 19 Feature maps Feature maps Feature maps 0 0 015 30 015 30 015 30 X X (a) (b) (c) Feature maps 20 Feature maps -10 −-20 015 30 015 30 X X (d) (e) Figure 9. Feature maps: (a) 0% UTS; (b) 20% UTS; (c) 40% UTS; (d) 60% UTS; (e) 80% UTS. Figure 10 illustrates the feature visualization in Case 1 when SNRs were equal to 100 dB, 70 dB, and 60 dB. At 100 dB (in Figure 10a), the five clusters were far from each other, and each cluster of data is relatively concentrated, with an average standard devi- ation close to 2.53. With the noise level increased to 80 dB (shown in Figure 10b), a small overlap appeared between the 60% UTS and 80% UTS data, but the other three groups were clearly separated. The standard deviation in this situation was large, 2.83. Howev- er, when SNR was lower than 80 dB, the distributions of features changed dramatically. At 70 dB, features in either the base state and 20% UTS or 60% UTS and 80% UTS were blended into each other, and only the data in the green upper triangles were inde- pendently located below the graph, demonstrated in Figure 10b. In Figure 10c, feature maps at 60 dB had a worse situation, as all the data interwove together entirely. It is Buildings 2022, 12, 1772 13 of 19 hard to ascertain the boundaries of each group. Therefore, this proved that noise had an adverse effect on the feature extraction of the CNN. Base Base 40 20% UTS 20% UTS 40% UTS 40% UTS 60% UTS 60% UTS 80% UTS 80% UTS 0 Base 20% UTS Buildings 2022, 12, x FOR PEER REVIEW 40% UTS 13 of 19 −-10 −-20 -20 60% UTS 80% UTS −-30 0 30 -8 0 8 −-30 0 4.2. Classification for Prestress Levels of the Rod by CNN (a) (b) (c) The performance of CNN trained by the data under various noise levels is shown in Figure 10. Feature visualization by t-SNE. (a) SNR = 100 dB; (b) SNR = 70 dB; (c) SNR = 60 dB. Figure 10. Feature visualization by t-SNE. (a) SNR = 100 dB; (b) SNR = 70 dB; (c) SNR = 60 dB. Figure 11, which classified the prestress levels of the rod in Case 1. Of the 2500 data points, 1500 were used for training the CNN model, and the training curves are illustrat- 4.2. Classiﬁcation for Prestress Levels of the Rod by CNN ed in Figure 11a. Specifically, these training curves started near 20%, and then converged The performance of CNN trained by the data under various noise levels is shown to 10 in Figur 0%. When the noi e 11, which classiﬁed se level wa the prs 100 dB, th estress levelse model of the rod onl iny Case spent 1. seven epochs to Of the 2500 data im- points, 1500 were used for training the CNN model, and the training curves are illustrated prove the accuracy to 100%. That epoch number was enlarged to 25 at 90 dB. With SNR in Figure 11a. Speciﬁcally, these training curves started near 20%, and then converged to increased, more epochs were spent on converging, and the error reduced to 0 with 34 100%. When the noise level was 100 dB, the model only spent seven epochs to improve the epochs at 80 dB. The slope of training curves from 100 dB to 80 dB were much larger accuracy to 100%. That epoch number was enlarged to 25 at 90 dB. With SNR increased, than the curves at 70 dB and 60 dB. In detail, the accuracy of classification was raised more epochs were spent on converging, and the error reduced to 0 with 34 epochs at 80 dB. from 20% to 31% by 15 epochs at 60 dB and then close to 100% after the 30th epoch. The The slope of training curves from 100 dB to 80 dB were much larger than the curves at validation set included 500 data points for modifying the parameters in CNN. The vali- 70 dB and 60 dB. In detail, the accuracy of classiﬁcation was raised from 20% to 31% by dation curves for 40 epochs showed that the accuracy of CNN started at 20% and in- 15 epochs at 60 dB and then close to 100% after the 30th epoch. The validation set included creased with the epochs. At 100 dB and 90 dB, the accuracies reached 100% after training 500 data points for modifying the parameters in CNN. The validation curves for 40 epochs showed that the accuracy of CNN started at 20% and increased with the epochs. At 100 dB 6 and 20 epochs, respectively. When SNR was 80 dB, the curve was close to 0.98 after the and 90 dB, the accuracies reached 100% after training 6 and 20 epochs, respectively. When 28th epoch and would not improve as the epoch increased. However, the accuracies SNR was 80 dB, the curve was close to 0.98 after the 28th epoch and would not improve as were lower at 70 dB and 60 dB, where the curve converged to 0.78 and 0.34 after training the epoch increased. However, the accuracies were lower at 70 dB and 60 dB, where the 40 epochs. Approximately 32% of the data were misjudged as the incorrect category at curve converged to 0.78 and 0.34 after training 40 epochs. Approximately 32% of the data 70 dB. The situation at 60 dB was much worse, as most of the data could not be classified were misjudged as the incorrect category at 70 dB. The situation at 60 dB was much worse, into the right category. as most of the data could not be classiﬁed into the right category. 1.0 1.0 0.8 0.8 0.6 0.6 0.4 0.4 100 dB 100 dB 90 dB 90 dB 0.2 0.2 80 dB 80 dB 70 dB 70 dB 60 dB 60 dB 0.0 0.0 0 5 10 15 20 25 30 35 40 0 5 10 15 20 25 30 35 40 Epochs Epochs (a) (b) Figure 11. Learning results of CNN at various noise levels. (a) Training curve; (b) test curve. Figure 11. Learning results of CNN at various noise levels. (a) Training curve; (b) test curve. The test results at various noise levels are shown in Table 3. When SNR was no less than 90 dB, the CNN model classified the test data correctly into the corresponding cate- gories because the training curves and the validation curves reached 100% after training. At 80 dB, the accuracy of test data was 98%, and some misjudgments appeared in the base state and the 80% UTS state. The results of the feature map visualization show that some data in the base state were dropped into the 20% UTS group, and the 60% UTS and 80% UTS clusters overlapped (shown in Figure 11b). The mixed features caused the mis- judgments in the test. At 70 dB, only 74% of the data were identified correctly, and 25% of the data in the first category were misclassified into the second category. On the con- trary, 27% of the data that belonged to the second category were placed into the first cat- egory. The accuracies of the fourth and fifth categories were both equal to 63%. The con- clusion is consistent with the previous analysis in feature visualization and accurate curves. At 60 dB, the CNN model was not suitable in this situation because the noise covered the signals entirely and all the analysis focused on the noise. Thus, all results had low accuracy. Performance Performance Y Buildings 2022, 12, 1772 14 of 19 The test results at various noise levels are shown in Table 3. When SNR was no less than 90 dB, the CNN model classiﬁed the test data correctly into the corresponding categories because the training curves and the validation curves reached 100% after training. At 80 dB, the accuracy of test data was 98%, and some misjudgments appeared in the base state and the 80% UTS state. The results of the feature map visualization show that some data in the base state were dropped into the 20% UTS group, and the 60% UTS and 80% UTS clusters overlapped (shown in Figure 11b). The mixed features caused the misjudgments in the test. At 70 dB, only 74% of the data were identiﬁed correctly, and 25% of the data in the ﬁrst category were misclassiﬁed into the second category. On the contrary, 27% of the data that belonged to the second category were placed into the ﬁrst category. The accuracies of the fourth and ﬁfth categories were both equal to 63%. The conclusion is consistent with the previous analysis in feature visualization and accurate curves. At 60 dB, the CNN model was not suitable in this situation because the noise covered the signals entirely and all the analysis focused on the noise. Thus, all results had low accuracy. Table 3. Confusion matrices at various noise levels. 90 dB (100%) 80 dB (98%) Base 20% 40% 60% 80% Base 20% 40% 60% 80% Base 100.0% 0.0% 0.0% 0.0% 0.0% 99.0% 0.0% 0.0% 0.0% 0.0% 20% 0.0% 100.0% 0.0% 0.0% 0.0% 1.0% 100% 0.0% 0.0% 0.0% 40% 0.0% 0.0% 100.0% 0.0% 0.0% 0.0% 0.0% 100% 0.0% 0.0% 60% 0.0% 0.0% 0.0% 100.0% 0.0% 0.0% 0.0% 0.0% 98% 7.0% 80% 0.0% 0.0% 0.0% 0.0% 100.0% 0.0% 0.0% 0.0% 2.0% 93.0% 70 dB (74%) 60 dB (26.8%) Base 75% 27.0% 0.0% 0.0% 0.0% 28.0% 27.0% 20.0% 12.0% 15.0% 20% 25.0% 71.0% 1.0% 0.0% 0.0% 28.0% 22.0% 17.0% 15.0% 12.0% 40% 0.0% 0.0% 98% 0.0% 0.0% 20.0% 16.0% 34.0% 17.0% 22.0% 60% 0.0% 1.0% 1.0% 63.0% 37.0% 14.0% 14.0% 12.0% 23.0% 15.0% 80% 0.0% 1.0% 0.0% 37.0% 63.0% 10.0% 21.0% 17.0% 33.0% 36.0% The performance of the CNN classiﬁer in Cases 2 and 3 is shown in Figure 12. In Case 2, rods were embedded in cement. The training and validation results at ﬁve noise levels are illustrated in Figure 12a. The training and validation curves had better results when SNRs were higher than 70 dB. All the curves ﬂuctuated during the ﬁrst ﬁve epochs and then quickly converged to 0. Nearly 10 epochs were spent to increase the accuracies to 100%. At 70 dB, although the training curve took about 20 epochs to converge to 100%, the validation curve only reached 0.78. However, the performance of the CNN dropped sharply at 60 dB. In Case 3, the error occurred at 80 dB, where the training accuracy and validation accuracy were close to 0.99 and 0.94, respectively. The error rate increased at 70 dB, where the validation curve reached 0.77 at the 20th epoch and then ﬂattened out. The results in Case 3 were similar to those of Case 1 because the grease had less of an effect on guided wave propagation. The test results of Cases 2 and 3 are shown in Table 4 when SNRs were from 90 dB to 60 dB. In Case 2, all the test data were identiﬁed correctly at 90 dB and 80 dB. At 70 dB, only the base state had a classiﬁcation rate of 98%, and the other four groups had lower rates. Among them, 12 of 100 data samples in the second category were misclassiﬁed into the third and fourth categories. The accuracy of the third category was 74% with 26% misjudgment. In addition, the error rates in the fourth and ﬁfth categories were 66% and 64%, respectively. When the noise level increased to 60 dB, the accuracy of prestress identiﬁcation was the lowest (46.6%). Most of the data could not be identiﬁed, except the data in the base condition (at 99%). Compared with Case 2, the approach exhibited a slightly lower accuracy for Case 3, where 100% of data in 90 dB were classiﬁed, 94.4% were identiﬁed at 80 dB, 76% at 70 dB, and 41.6% at 60 dB. At 80 dB and 70 dB, most of the errors occurred between the fourth and ﬁfth categories. Speciﬁcally, the predictions of the fourth and ﬁfth categories reached 78% and 94% at 80 dB. At 70 dB, the proportions were reduced Buildings 2022, 12, x FOR PEER REVIEW 14 of 19 Table 3. Confusion matrices at various noise levels. 90 dB (100%) 80 dB (98%) Base 20% 40% 60% 80% Base 20% 40% 60% 80% Base 100.0% 0.0% 0.0% 0.0% 0.0% 99.0% 0.0% 0.0% 0.0% 0.0% 20% 0.0% 100.0% 0.0% 0.0% 0.0% 1.0% 100% 0.0% 0.0% 0.0% 40% 0.0% 0.0% 100.0% 0.0% 0.0% 0.0% 0.0% 100% 0.0% 0.0% 60% 0.0% 0.0% 0.0% 100.0% 0.0% 0.0% 0.0% 0.0% 98% 7.0% 80% 0.0% 0.0% 0.0% 0.0% 100.0% 0.0% 0.0% 0.0% 2.0% 93.0% 70 dB (74%) 60 dB (26.8%) Base 75% 27.0% 0.0% 0.0% 0.0% 28.0% 27.0% 20.0% 12.0% 15.0% 20% 25.0% 71.0% 1.0% 0.0% 0.0% 28.0% 22.0% 17.0% 15.0% 12.0% 40% 0.0% 0.0% 98% 0.0% 0.0% 20.0% 16.0% 34.0% 17.0% 22.0% 60% 0.0% 1.0% 1.0% 63.0% 37.0% 14.0% 14.0% 12.0% 23.0% 15.0% 80% 0.0% 1.0% 0.0% 37.0% 63.0% 10.0% 21.0% 17.0% 33.0% 36.0% The performance of the CNN classifier in Cases 2 and 3 is shown in Figure 12. In Case 2, rods were embedded in cement. The training and validation results at five noise levels are illustrated in Figure 12a. The training and validation curves had better results when SNRs were higher than 70 dB. All the curves fluctuated during the first five epochs and then quickly converged to 0. Nearly 10 epochs were spent to increase the ac- curacies to 100%. At 70 dB, although the training curve took about 20 epochs to converge to 100%, the validation curve only reached 0.78. However, the performance of the CNN dropped sharply at 60 dB. In Case 3, the error occurred at 80 dB, where the training ac- Buildings 2022, 12, 1772 15 of 19 curacy and validation accuracy were close to 0.99 and 0.94, respectively. The error rate increased at 70 dB, where the validation curve reached 0.77 at the 20th epoch and then flattened out. The results in Case 3 were similar to those of Case 1 because the grease to 52% and 51%, respectively. At 60 dB, only the data under the base condition could be had less of an effect on guided wave propagation. identiﬁed, and it was hard to identify the data in other conditions. 1.0 1.0 0.8 0.8 Training(100 dB) Training(100 dB) Validation(100 dB) Validation(100 dB) 0.6 0.6 Training(90 dB) Training(90 dB) Validation(90 dB) Validation(90 dB) Training(80 dB) Training(80 dB) 0.4 0.4 Validation(80 dB) Validation(80 dB) Training(70 dB) Training(70 dB) Validation(70 dB) Validation(70 dB) 0.2 0.2 Training(60 dB) Training(60 dB) Validation(60 dB) Validation(60 dB) 0 102030 4050 60 0 102030405060 Epoch Epoch (a) (b) Figure 12. Results of CNN at various noise levels. (a) Case 2; (b) Case 3. Figure 12. Results of CNN at various noise levels. (a) Case 2; (b) Case 3. The test results of Cases 2 and 3 are shown in Table 4 when SNRs were from 90 dB Table 4. Confusion matrices in Case 2 and 3. to 60 dB. In Case 2, all the test data were identified correctly at 90 dB and 80 dB. At 70 dB, only the base state had a classification rate of 98%, and the other four groups had Case 2 (Grease as the Grout Material) lower rates. Among them, 12 of 100 data samples in the second category were misclassi- 90 dB (100%) 80 dB (100%) fied into the third and fourth categories. The accuracy of the third category was 74% Base 20% 40% 60% 80% Base 20% 40% 60% 80% with 26% misjudgment. In addition, the error rates in the fourth and fifth categories Base 100.0% 0.0% 0.0% 0.0% 0.0% 100.0% 0.0% 0.0% 0.0% 0.0% were 66% and 64%, respectively. When the noise level increased to 60 dB, the accuracy 20% 0.0% 100.0% 0.0% 0.0% 0.0% 0.0% 100.0% 2.0% 5.0% 4.0% 40% 0.0% 0.0% 100.0% 0.0% 0.0% 0.0% 8.0% 100.0% 15.0% 18.0% 60% 0.0% 0.0% 0.0% 100.0% 0.0% 0.0% 4.0% 14.0% 100.0% 14.0% 80% 0.0% 0.0% 0.0% 0.0% 100.0% 0.0% 0.0% 10.0% 14.0% 100.0% 70 dB (78%) 60 dB (46.6%) Base 98% 0.0% 0.0% 0.0% 0.0% 99% 1% 0% 1% 0% 20% 2.0% 88% 2.0% 5.0% 4.0% 0% 50% 16% 29% 8% 40% 0.0% 8.0% 74% 15.0% 18.0% 0% 13% 24% 16% 25% 60% 0.0% 4.0% 14.0% 66% 14.0% 1% 26% 31% 26% 33% 80% 0.0% 0.0% 10.0% 14.0% 64.0% 0% 10% 29% 28% 34% Case 3 (Cement as the grout material) 90 dB (100%) 80 dB (94.4%) Base 100.0% 0.0% 0.0% 0.0% 0.0% 100.0% 0.0% 0.0% 0.0% 0.0% 20% 0.0% 100.0% 0.0% 0.0% 0.0% 0.0% 100.0% 0.0% 0.0% 0.0% 40% 0.0% 0.0% 100.0% 0.0% 0.0% 0.0% 0.0% 100.0% 0.0% 0.0% 60% 0.0% 0.0% 0.0% 100.0% 0.0% 0.0% 0.0% 0.0% 78.0% 6.0% 80% 0.0% 0.0% 0.0% 0.0% 100.0% 0.0% 0.0% 0.0% 22.0% 94.0% 70 dB (76%) 60 dB (41.6%) Base 99.0% 1.0% 0.0% 0.0% 0.0% 79.0% 18.0% 2.0% 5.0% 3.0% 20% 0.0% 99.0% 0.0% 0.0% 0.0% 18.0% 38.0% 20.0% 9.0% 11.0% 40% 1.0% 0.0% 79.0% 13.0% 12.0% 1.0% 19.0% 29.0% 29.0% 23.0% 60% 0.0% 0.0% 11.0% 52.0% 37.0% 1.0% 15.0% 25.0% 27.0% 28.0% 80% 0.0% 0.0% 10.0% 35.0% 51.0% 1.0% 10.0% 24.0% 30.0% 35.0% 4.3. Classiﬁcation for Embedding Situation by CNN The embedding situation of the rod could also be predicted by the CNN classiﬁer. A total of 1500 data points were used for training the CNN, including unembedded rods, rods embedded with cement, and rods embedded with grease. The training and validation curves are shown in Figure 13. At a lower noise level, the classiﬁer entirely predicted the state of the rod. Until SNR was 70 dB, the validation curve was 0.956, training 40 epochs. Amplitude Performance Buildings 2022, 12, 1772 16 of 19 However, the accuracies at 60 dB dropped sharply. The test results are given in Table 5. Predictions were equal to 100% in each category when SNRs were from 100 dB to 80 dB. Buildings 2022, 12, x FOR PEER REVIEW 16 of 19 Several errors occurred at 70 dB and the accuracy was 92%. Speciﬁcally, the rod samples labeled as unembedded were much easier to confuse as rods embedded in grease, as 15% of the data in that category were misclassiﬁed into the grease state. On the other hand, 7% Only 1% of data in cement were predicted incorrectly. The worst results were the classi- of the data were misclassiﬁed into the unembedded state. Only 1% of data in cement were fication at 60 dB, where the total accuracy was only 35%, which means the model cannot predicted incorrectly. The worst results were the classiﬁcation at 60 dB, where the total identify the accuracy was signals. only 35%, which means the model cannot identify the signals. 1.0 0.8 Training(100 dB) Validation(100 dB) 0.6 Training(90 dB) Validation(90 dB) Training(80 dB) Validation(80 dB) 0.4 Training(70 dB) Validation(70 dB) Training(60 dB) Validation(60 dB) 0.2 0 10203040 Epoch Figure 13. Results of CNN at various noise levels. Figure 13. Results of CNN at various noise levels. Table 5. Confusion matrices in varying embedding conditions. Table 5. Confusion matrices in varying embedding conditions. 90 dB (100%) 80 dB (100%) 90 dB (100%) 80 dB (100%) Unembedded Cement Grease Unembedded Cement Grease Unembedded Cement Grease Unembedded Cement Grease Unembedded 100.0% 0.0% 0.0% 100.0% 0.0% 0.0% Unembedded 100.0% 0.0% 0.0% 100.0% 0.0% 0.0% Cement 0.0% 100.0% 0.0% 0.0% 100.0% 0.0% Cement 0.0% 100.0% 0.0% 0.0% 100.0% 0.0% Grease Grease 0.0% 0.0% 0.0% 0.0% 100.100.0%0% 0.0% 0.0% 0.0% 0.0% 100. 100.0% 0% 70 dB (92%) 60 dB (35%) 70 dB (92%) 60 dB (35%) Unembedded 84.0% 0.0% 7.0% 37.0% 24.0% 39.0% Unembedded 84.0% 0.0% 7.0% 37.0% 24.0% 39.0% Cement 1.0% 99.0% 0.0% 28.0% 43.0% 36.0% Cement 1.0% 99.0% 0.0% 28.0% 43.0% 36.0% Grease 15.0% 1.0% 93.0% 35.0% 33.0% 25.0% Grease 15.0% 1.0% 93.0% 35.0% 33.0% 25.0% 5. Conclusions 5. Conclusions We investigated the deep learning-based guided wave process for stress level predic- We investigated the deep learning-based guided wave process for stress level pre- tion of prestressed rods. The CNN model was established for automatically encoding the diction of prestressed rods. The CNN model was established for automatically encoding hidden information from complex signals that accounted for the impacts of different noise the hidden information from complex signals that accounted for the impacts of different levels and embedded grout materials. Some conclusions can be listed as follows: noise levels and embedded grout materials. Some conclusions can be listed as follows: (a) The deep learning method effectively encoded the guided waves under complex (a) The deep learning method effectively encoded the guided waves under complex uncertainties and assisted in stress level prediction and the embedded conditions uncertainties and assisted in stress level prediction and the embedded conditions of of the rods, thereby showing potential for signal processing of NDE methods in the rods, ther structural health eby show monitoring ing potential of PC str for uctur sign es. al processing of NDE methods in struc- tural health monitoring of PC structures. (b) The feature visualization method, t-SNE, provided an effective window that the (b) The feature visualization method, t-SNE, provided an effective window that the dif- different feature patterns could be clearly identiﬁed from visual two-dimensional ferent plots. fe The atur distances e patterns c between ould be c each featur learly e point identindicated ified from vis the corr ual elation two-dimens amongio data. nal plots. The In addition, distances betwe the impacts ofenoise n each interfer feature ence poin on t ithe ndica data ted the correl were observed ation a with mong the da use - of this approach. ta. In addition, the impacts of noise interference on the data were observed with the (c) The deep learning approach also exhibited high accuracy and robustness for data use of this approach. with high noise interference. The CNN classiﬁcation for most cases could reach up (c) The deep learning approach also exhibited high accuracy and robustness for data with high noise interference. The CNN classification for most cases could reach up to 100% when the noise levels were lower (80 dB–100 dB). However, with the ener- gy of the noise (SNR = 70 dB) close to the signals, data classification exhibited a cer- tain level of reduction, and the error rates were close to 80%. Particularly, when the Performance Buildings 2022, 12, 1772 17 of 19 to 100% when the noise levels were lower (80 dB–100 dB). However, with the energy of the noise (SNR = 70 dB) close to the signals, data classiﬁcation exhibited a certain level of reduction, and the error rates were close to 80%. Particularly, when the noise increased to a much higher level (60 dB), all the signals were contaminated, and the effectiveness of the classiﬁcation dropped. (d) The proposed method can also identify the embedding conditions. The identiﬁcation is no less than 92% when the noise level is lower than 60 dB. However, the accuracy drops to 35% at 60 dB, which means it is difﬁcult to distinguish the embedding conditions of rods. This study simulated the different levels of PC structure’s prestress loss by a deep learning method. To accommodate engineering concerns, noise interference was added. In future work, the methods will be explored on more large-scale structures in laboratory and ﬁeld conditions. As high levels of noise prevent the model from achieving high accuracy, future perspective will focus on this issue to improve the accuracy of identiﬁcation under higher noise levels (60 dB). In addition, different kinds of damage will occur at same time; thus, future study will investigate more complex situations. Furthermore, as the selection of hyperparameters is also critical, future research will also focus on deep learning with optimization methods (Bayesian optimization). 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Buildings – Multidisciplinary Digital Publishing Institute

Published: Oct 22, 2022

Keywords: guided wave; convolutional neural network; structural health monitoring; stress level prediction; t-distributed stochastic neighbor embedding

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Deep Learning-Enriched Stress Level Identification of Pretensioned Rods via Guided Wave Approaches

Deep Learning-Enriched Stress Level Identification of Pretensioned Rods via Guided Wave Approaches

Get 20M+ Full-Text Papers For Less Than $1.50/day. Start a 14-Day Trial for You or Your Team.

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Deep Learning-Enriched Stress Level Identification of Pretensioned Rods via Guided Wave Approaches

Deep Learning-Enriched Stress Level Identification of Pretensioned Rods via Guided Wave Approaches

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