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A New Procedure for Damage Assessment of Prestressed Concrete Beams Using Artificial Neural Network

A New Procedure for Damage Assessment of Prestressed Concrete Beams Using Artificial Neural Network Hindawi Publishing Corporation Advances in Artificial Neural Systems Volume 2011, Article ID 786535, 9 pages doi:10.1155/2011/786535 Research Article A New Procedure for Damage Assessment of Prestressed Concrete Beams Using Artificial Neural Network K. Sumangala and C. Antony Jeyasehar Department of Civil and Structural Engineering, Annamalai University, Tamilnadu, Annamalainagar 608 002, India Correspondence should be addressed to K. Sumangala, josuma@rediffmail.com Received 31 May 2011; Revised 24 August 2011; Accepted 24 August 2011 Academic Editor: Wilson Wang Copyright © 2011 K. Sumangala and C. Antony Jeyasehar. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. A damage assessment procedure has been developed using artificial neural network (ANN) for prestressed concrete beams. The methodology had been formulated using the results obtained from an experimental study conducted in the laboratory. Prestressed concrete (PSC) rectangular beams were cast, and pitting corrosion was introduced in the prestressing wires and was allowed to be snapped using accelerated corrosion process. Both static and dynamic tests were conducted to study the behaviour of perfect and damaged beams. The measured output from both static and dynamic tests was taken as input to train the neural network. Back propagation network was chosen for this purpose, which was written using the programming package MATLAB. The trained network was tested using separate test data obtained from the tests. A damage assessment procedure was developed using the trained network, it was validated using the data available in literature, and the outcome is presented in this paper. 1. Introduction quantify the damage with nondestructive tests and various analytical models [1]. Vibration-based damage detection Concrete structures are designed and constructed to suit methods seem to be effective at detecting and localizing the the requirements of its time. Damages may be unavoidable damage on full-scale structures [2]. during its design life time due to various reasons. A structure The easiest and simplest way to detect damage with which is said to be well designed may survive the damage but dynamic parameters is by noting the changes in the natural safety is not guaranteed. When the damage goes undetected frequency of the system. Cawley and Adams [3]formulateda and unrepaired, it will lead to failure or may demand costly scheme to detect damage in composite materials from natu- repair and huge loss of life. Therefore, the problem of ral frequency shifts. Abdel Wahab and Roeck [1]investigated maintenance and repair of existing structures involves dam- the application of the change in modal curvatures to detect age detection at an early stage. For massive structures like the damage in a prestressed concrete bridge. They modelled bridges which were constructed some 50 to 60 years ago, it is simply supported and continuous beams using finite ele- necessary to test their functionality under the present loading ments and introduced damage at different locations in terms condition and quantify damage, if any, since demolishing of reduced stiffness of the corresponding elements, and they and reconstructing them would involve huge expenditures. concluded that the natural frequencies of the damaged and Evaluating the residual life and remaining load-carrying undamaged beams indicated the presence of damage in a capacity of these structures is also important. Damage can be global sense. Abdul Razak and Choi [4] studied the effect defined as the change in performance of structures, which of general corrosion on the modal parameters of reinforced can be identified in terms of crack formation and a conse- concrete beams. Modal tests were performed and compared quent stiffness reduction. Damage recognition and location against that from a control beam. The changes were incon- are the key factors in the design of a structural health mon- sistent with the changes in natural frequencies, but a trend itoring system. When damage lies inside the structure and observed was mode dependent. The load carrying capacity is not visible to the naked eye, it is possible to locate and of the beams was determined through static load test, and 2 Advances in Artificial Neural Systems the results were correlated with the state of corrosion damage need user’s judgment. By using the proposed ANN-design and changes in the modal parameters. From the changes in method both location, and severity of damage could be natural frequencies, stiffness degradation was estimated and known. The method was employed in an example to demon- compared. strate their proposed methodology. Norhisham Bakhary et al. [11] in this study proposed a statistical approach to Carpinteri et al. [5] have discussed some aspects of the take into account the effect of uncertainties in developing NDE techniques in in situ damage assessment. They have an ANN model. By applying Rosenblueth’s point estimate taken up the study on assessing the stability of a historical method verified by Monte Carlo simulation, the statistics masonry tower using the NDE technique called thermogra- of the stiffness parameters were estimated. The probability phy and with nonlinear numerical simulations. According to of damage existence (PDE) is then calculated based on the the authors, the results of the analysis gave valuable hints probability density function of the existence of undamaged about how much damage had occurred and when the and damaged states. The developed approach is applied to restoration should take place. detect simulated damage in a numerical steel portal frame Wu et al. [6] illustrated the neural network-based meth- model and also in a laboratory-tested concrete slab. The odology to show that this approach could be used to identify effects of using different severity levels and noise levels on the member damage. The authors used the Fourier spectra of the damage detection results were discussed. computed relative acceleration, generated from a numerical de Lautour and Omenzetter [12] in this study present model of a simple three-storey frame, as an input to neural a general method for predicting seismic-induced damage network. According to their results, ANNs can learn about using artificialneuralnetworks(ANNs). Theapproach was the behaviour of undamaged and damaged structures to to describe both the structure and ground motion using a identify the damaged member and the extent of damage from large number of structural and ground motion properties. patterns in the frequency response of a structure. The class of structures analysed were 2D reinforced concrete According to Chen et al. [7], neural network can dis- (RC) frames that varied in topology, stiffness, strength, and tinguish small differences between the transmissibility func- damping and were subjected to a suite of ground motions. tions which carry the information of structural faults. The Dynamic structural responses were simulated using nonlin- transmissibility function is sensitive to structural faults and ear FEM analysis and damage indices describing the extent easy to measure in the situations where the excitations of the of damage calculated. Using the results of the numerical structural system are not available or immeasurable. They simulations, a mapping between the structural and ground had also suggested that transmissibility is a useful feature motion properties and the damage indices was than estab- for training neural network as a fault diagnosis model. Fang lished using an ANN. The performance of the ANN was et al. [8] referred the features of various training algorithms assessed using several examples, and the ANN was found to and with that as basis implemented the neural network to be capable of successfully predicting damage. the frequency-response-functions- (FRFs-) based structural Though more works have been done involving reinforced damage detection. The analysis results on a cantilever beam concrete and steel structures using ANN, not much work show that, in all considered damage cases (i.e., trained dam- has been done on PSC members. Modelling of damaged pre- age cases and unseen damage cases, single-damage cases and stressed concrete beam is complicated, and usage of conven- multiple-damage cases), the neural network can assess dam- tional methods for damage assessment of Prestressed Con- age conditions with very good accuracy. crete(PSC) beamsthusbecomes difficult. ANN is a possible Zapico et al. [9] in their paper described a procedure solution in this situation. Therefore, a well-designed neural for damage assessment in a two-storey steel frame and network is able to serve as a real time data processor for steel-concrete composite floors structure. The procedure is damage assessment. based on a multilayer perceptron (MLP). A simplified finite The main focus of this work was to train and test the element model was used to generate the training data. This network only with natural frequency and stiffness of dam- model was previously updated through another MLP using aged and perfect beams. Widely used feed forward ANN that two natural frequencies as inputs and the stiffness of the learns with back propagation algorithm was adopted, and beams and masses as updating parameters. The different details about network architecture are presented. Further, combinations of damage at the ends of the longitudinal it has been demonstrated that it is possible to predict the beams were used as damage scenarios. The training data for damage with acceptable accuracy by just feeding the current the MLP were generated by varying at random the stiffness of stiffness and natural frequency of the damaged structure the longitudinal beams. Two natural frequencies and mode [13] as inputs to the trained ANN. A novel in situ damage shapes were used as inputs, and three different definitions assessment procedure that needs only limited nondestructive of damage (sections, bars, and floors) were tried as outputs. measurements on the damaged structure is proposed. MLPs were trained through the error back-propagation algorithm. Finally, the performance of the procedure was The newness of this procedure is that it requires only evaluated through the experimental data. Only the approach minimum data collected from the damaged structure and of damage at floor level gives reasonable results. theoretical data developed for the original structure. So, with Yuen and Lam [10] had reviewed the works of many minimum number of inputs, the procedure is adopted. No researchers on damage detection using ANN. They have also further experiments are needed to get data in order to adopt developed an ANN based design method which does not procedure. Advances in Artificial Neural Systems 3 3. Experimental Study Output layer Fivepost tensioned concrete rectangular beams were used in this investigation. The beams were of uniform cross section, that is, 125 × 250 × 4200 mm. At each end, there were Direction Direction of of Hidden anchorage zones with enlarged section of size 350 × 230 × error activation layers propagation 250 mm and length of 230 mm. The overall length of the propagation beam was 4860 mm, out of which 4590 mm was consid- ered as the test zone. In order to achieve accessibility to prestressing tendons where the damage is introduced by Input layer corrosion, an opening 100× 120× 60 mm wide was provided in the middle bottom side of the beam. The beams were provided with nominal reinforcement in order to take up the Figure 1: Architecture of the back propagation network. handling stresses. The longitudinal reinforcement consists of two high yield strength deformed (HYSD) bars of 8 mm diameter at the top and the bottom. The stirrups were made using mild steel bars of 6 mm diameter and were 2. Feed Forward Artificial Neural Network and provided with a spacing of 175 mm. At the anchorage zone, Back Propagation Algorithm 12 bars of 6 mm diameter were provided between 25 and 250 mm from the edge. Reinforcement details were kept the Even though the ANN and back propagation algorithm are same for all the beams. The beams were cast with a mean well known, this section briefly revisits the concepts of feed concrete strength of 57 N/mm , posttensioned to a stress forward that learns by back propagation algorithm used level of 0.7 f . The ultimate strength of the high tensile pu in the damage assessment of prestressed concrete beams steel (HTS) wire is 1715.2 N/mm . Six HTS wires of 7 mm presented in this paper. The processing units in this artificial diameter were used for each beam. The first beam, designated neural network are arranged in layers, that is, input layer, as P7B1, was a perfect beam with absolutely no damage. an output layer, and a number of hidden layers as shown in The other four beams, namely, P7CB1, P7CB2, P7CB3, and Figure 1. The hidden units presented here allow the network P7CB4 were damaged to 33.33, 50, 66.67, and 83.33%, to represent and compute more complicated associations respectively. The damage percentage represents the percent- between patterns. The inputs are presented to the input layer. age of wires snapped. Snapping of wires was done using the Each neuron in the hidden layer receives the weighted sum accelerated electrochemical process. Through this process, from the input layer and transfers its result to the output pitting corrosion was induced and the wires were snapped. The setup made for inducing corrosion damage using ac- layer. The back propagation-learning algorithm calculates celerated electrochemical process is shown in Figure 3.After the error between the generated output and targeted output damaging the beams, static and dynamic tests were con- and uses the estimated error to modify the weight in response ducted on all five beams. to the errors. The back propagation algorithm learns by changing its weights to follow the steepest path towards the bottom of a bowl shaped error surface. This process contin- 3.1. Testing of Beams. All the beams were subjected to both ues until a set of weights, which processes data accurately static and dynamic tests. The beams were tested under for the application, is found out. The final weights represent repeated loading at an interval of 10 kN each (load stage). what the network has learnt and enable to infer for other Four cycles of repeated load were applied in each load stage. data. Processing element of this network with specified The beams were repeatedly loaded till the failure load is inputs is shown in Figure 2. reached. Deflections and strains were measured for a load increment of 2.5 kN up to failure. Crack width of five cracks Once the type of ANN and the learning algorithm are in the constant bending moment zone was also measured decided, it is necessary to generate the required training using a crack detection microscope of 0.02 mm precision. and test data. When the modeling of damaged PSC beam Static tests were conducted for determining the moment is difficult, one needs to depend upon the experimentally curvature, load deflection variations with loading in addition acquired data on the structure under study for training and to the evaluation of ultimate load carrying capacity of the test testing the ANN. From theory, it is well known that the beams. dynamic and/or static characteristics of the damaged PSC beams carry information about the damaged state of the Dynamic test was conducted at every 10 kN load interval structures. The ANN is made to recognize the damage and after four cycles of load application at each stage. The occurred in the structure under study by presenting the dynamic response was picked up by linear variable differential measured dynamic and/or static data of the damaged and transducer (LVDT) placed at mid span in the form of dis- undamaged beams obtained experimentally. The following placement history for the beams at all the chosen load stages. section presents the details of the experimental program car- It was utilised for the frequency analysis. The time history ried out to generate the necessary training and test data for records were analysed using the software DASYLAB for the ANN. obtaining the natural frequencies. 4 Advances in Artificial Neural Systems Summation Transfer function function Load Degree N. frequency of Sum Linear damage (inputs) w (output) Deflection Learning and recall schedule Supervised learning Learning cycle Figure 2: Processing element of this network with specified inputs. Anode ANN can be robust if large amount of training data is made available since training with large data can avoid the problem of over fitting and it can be fault tolerant with significant Cathode Container amount of redundancy and better learning algorithms. Over (corrosion fitting or over learning is indicated by the inability of a tank) Power network to perform better when unseen test data is presented source + − HT wire coated with to the network even though it is able to classify the training anticorrosive paint data. When large amount of data is used for training and the 2–8 mm φ structure and size of the network are chosen properly to han- dle the data, the problem of over fitting can be avoided. To 6-7 mm φ achieve this, the experimentally obtained results were linearly interpolated using the software ORIGIN to get the values All dimensions are in mm 2–8 mm φ at small regular intervals of load (1 kN) thus making the training and test database larger. Cross section of the beam The sample training data are given in Table 1. The data Figure 3: Corrosion induction setup. were normalized. The natural frequency, deflection, and crack width data obtained for the beam P7CB2 damaged to the extent of 50% in a similar manner were used as exclusive 4. Generation of Training and Test Data for test data (Table 2). This enables us to test the ability of ANN ANN and Its Architecture to generalize when presented with totally unseen data. In addition to these test data, the static and dynamic data for It was decided to use all the output obtained from the static 40% and 70% damage levels were also obtained by interpo- and dynamic tests such as stiffness (s), natural frequency ( f ), lation of the data acquired through experiments, and these deflection (δ), load at first crack (P ), crack width (w), and cr data were also used as test data. ultimate load (P ) from the perfect and damaged beams for training the neural network. It may be difficult to assess the 4.2. Architecture of the ANN. Feed forward neural network damage using the conventional methods since mathematical model is required to explain these behaviours. ANN does not learning by back propagation (BP) algorithm written in require prior mathematical model to solve a problem which MATLAB has been used, and its ability to predict damage just is a useful aspect of neural network. from the current natural frequency and postcrack stiffness obtained from the load-deflection characteristics of the dam- aged beam has been studied by training and testing the ANNs 4.1. Generation of Training and Test Data from Experiments. for various cases of input and comparing their performance The applied load and the corresponding stiffness, natural for various input conditions. Postcrack stiffness of the dam- frequency, deflection, and crack width values of damaged and undamaged beams (P7B1, P7CB1, P7CB3, and P7CB4) aged beam was also considered along with natural frequency were obtained at regular intervals from the static and since the frequency changes alone are insufficient to quantify dynamic tests. Even though two sets of beams were tested and the damage. To achieve this, the basic structure of the data collected for each case, only one data set was used for ANN was maintained and only the number of input nodes training. However, the ANN needs a larger volume of data in the input layer was changed. During training process, so that it learns better and predicts the damage accurately. different nodes were tried by trial and error for the hidden Advances in Artificial Neural Systems 5 Table 1: Sample training data. Natural frequency (Hz) at various damage levels Load kN 0% 33.33% 66.66% 83% P7B1 P7CB1 P7CB3 P7CB4 0 23.5 22.58 21.36 20.75 10 23.5 22.58 21.36 20.75 20 23.5 22.58 21.36 20.14 30 23.5 21.97 20.75 18.92 40 22.28 21.36 19.53 — 50 21.36 20.75 — — 60 16.48 — — — Table 2: Sample test data. having different cross sections, all the data were normalized before feeding into the network. The following were the cases Load kN Natural frequency (Hz) at 50% damage (P7CB2) studied in this work. 0 21.36 - Case i. ANN with applied load and natural frequency 10 21.36 as input. 20 21.36 - Case ii. ANN with postcrack stiffness and natural 30 20.75 frequency as input. 40 20.14 - Case iii. ANN with natural frequency (postcracking 50 19.53 preyielding) as input. - Case iv. ANN with applied load, natural frequency, layers to achieve the given performance accuracy, which is and deflection as input. user defined. After various trials, these nodes were finalized, - Case v. ANN with applied load, natural frequency, which gave the optimum output. So these numbers of nodes and crack width as input. were chosen based on the performance accuracy require- - Case vi. ANN with applied load, natural frequency, ment. The specifications of the ANN that gave the best deflection, and crack width as input. performance and are used in this study are as follows. - Case vii. ANN with applied load, natural frequency, (i) Number of input nodes in the input layer: 2–5 for deflection, crack width, and ultimate load as input. different cases. For the sake of practical application, only the first three (ii) Number of output nodes in the output layer: 1. cases are discussed in this paper. The remaining cases are (iii) Number of hidden layers: 2 with 7 and 5 nodes, re- explained elsewhere [14]. spectively. (iv) Training algorithm used: back propagation. Case i (ANN with applied load and natural frequency as inputs). This ANN is trained with applied load and natural (v) Learning method: supervised learning. frequencies obtained from the dynamic tests and aims at (vi) The output of the neural network is the predicted predicting the damage level from the average of possible extent of damage in the beam. solutions returned by the ANN for various test input data. The results obtained in this case are represented in a graph- ical form in Figure 4, which seems to be promising in the 5. ANN Training and Testing damage assessment process. This section presents the results of ANN training and test details for different cases and analyses the suitability of ANN Case ii (ANN with stiffness and natural frequency as inputs). for damage assessment of PSC beams. Mainly, the focus of Each training or test data has two inputs, that is, stiffness the study was to evaluate the effectiveness of ANN for dam- (postcracking-preyielding) and natural frequency. This ANN age assessment when trained only with natural frequency has been studied so that a damage assessment procedure can and stiffness of the damaged beam and with the mix of be evolved that is suitable in practical situation. In a field static and dynamic test data. Keeping this purpose in mind, beam, which is in the postcracking-preyielding stage, it is the training of the ANN has been carried out for a changing possible to obtain its current stiffness from its load deflection number of inputs. However, the structure of the ANN and characteristics measured over a portion of the service load. the training algorithm used were maintained as explained A dynamic test on the same beam can return its natural in the previous section for all the cases. In order to adopt frequency value. Therefore, these two parameters were the damage assessment procedure for various field beams selected for the ANN study and the network was trained, 6 Advances in Artificial Neural Systems 0 0 0 10 20 30 40 50 10 20 30 40 50 Test data set number Test data set number Predicted damage Predicted damage Expected damage Expected damage Average predicted damage Average predicted damage Figure 4: Input data set number versus damage predicted by ANN Figure 6: Input data set number versus damage predicted by ANN (Case i). (Case iii). network are summarised in Table 3.The performanceaccu- racy (user defined value) indicates how close the predicted output of the network is to the expected or targeted output. In our case, the targeted output is the expected damage. The performance accuracy is evaluated from the mean squared error where the error is the difference between the output of the network and the targeted output for a set of inputs. Epochs were not chosen for these cases, but only the performance accuracy was user defined. So when the accu- 10 racy level is obtained as expected, the training process stops. For making comparison, the number of epochs is mentioned. 10 20 30 When the network was provided with more number of Test data set number inputs, the prediction was better in terms of performance accuracy (user defined) and with fewer epochs. The perfor- Predicted damage mance accuracy becomes less with more number of epochs Expected damage required, when the number of inputs starts decreasing. Our Average predicted damage aim is to develop the procedure only with natural frequencies and stiffness from data obtained from the field. Therefore, Figure 5: Input data set number versus damage predicted by ANN only that particular network was used for developing the (Case ii). procedure. The table indicates that for all cases the error in the predicted damage can be very large when just one test input and the result is presented below in the form of graph and data obtained for a single applied load is used to predict the is shown in Figure 5. However, the average of the predicted damage level. Maximum error occurred when the ANN was damage levels for differenttestdatacould closelypredictthe trained with only frequency obtained from the dynamic test damage. as input to the network. This is justified by the fact that the Case iii (ANN with natural frequency (postcracking-prey- ANN can learn better and predict better when it is trained ielding) as input). Each training or test data has only one with more database. This error is still comparable with the input, that is, natural frequency. This ANN has been studied errors with which the other ANNs could predict the damage to check if it is possible to predict the damage only with levels. It is also found that the ANN trained with stiffness natural frequency obtained from dynamic tests. The network and frequency obtained over an applied load range within its was trained and the result is presented in Figure 6. From the service load limit could predict the damage very closely (with figure, it is observed that each set of the predicted damage is a maximum difference of 5% damage) thus paving the way closer to the expected value. for the development of a new practical method of damage assessment of prestressed concrete beams. The input test data for the damage levels of 40% and 70% were interpolated using ORIGIN software. From that 6. Damage Assessment Procedure observation, the minimum and the maximum deviations of the various cases and average predicted damage levels along It has been demonstrated that the ANN trained with natural with number of epochs and the performance accuracy of the frequency and stiffness can estimate the damage when tested Predicted damage (%) Predicted damage (%) Predicted damage (%) Advances in Artificial Neural Systems 7 Table 3: Summary of the results for various input cases. Input Number of Expected No. of epochs Performance Minimum predicted damage level Maximum predicted damage level Average predicted damage level parameter to inputs damage level Predicted Predicted Predicted taken for accuracy Difference Difference Difference the ANN (%) ED damage value damage value damage value training the (ED–OD) (ED–OD) (ED–OD) ANN (OD) (OD) (OD) 40 32.19 −7.81 47.98 +7.98 37.69 −2.31 p-f 2 50 33.37 −16.63 66.10 +16.10 57.56 +7.56 1203 1e − 5 70 68.09 −1.91 72.17 +2.17 70.40 +0.40 40 33.01 −6.99 52.95 +12.95 42.05 +2.05 s-f 2 50 31.77 −18.23 77.68 +27.68 48.63 −1.37 423 0.06 70 58.98 −11.02 77.68 +7.68 71.44 +1.44 40 20.13 −19.87 58.77 +18.77 35.82 −4.18 f1 50 52.59 +2.59 58.82 +8.82 56.09 +6.09 5000 0.25 70 57.60 −12.40 59.00 −11.00 59.00 −11.00 8 Advances in Artificial Neural Systems with the data obtained in situ. Also, it has been proved that Table 4: Comparison of predicted values with Ambrosini et al. [11]. the ANN trained just with natural frequency can also assess Degree of damage (%) the damage. Based on this concept, a damage assessment Serial no. Expected degree of damage procedure has been evolved and presented here. The steps Predicted damage (Ambrosini et al.) that should be followed for the damage assessment are 1 30 29.93 explained below. 2 40 41.61 (1) Evaluate the stiffness of the field beam, which is at 3 50 51.09 the postcracking-preyielding stage (service stage) by conducting a static test on the beam. A fraction of the service load is applied for this purpose. acquisition equipment consistent in a computer with a dif- ferential eight-channel card. Dynamic tests were performed (2) Measure the in situ natural frequency of the field by exciting the beam with a hammer blow in the central beam by conducting a dynamic test (free vibration section. The natural frequencies obtained in each one of the test) on the structure. test stages are tabulated and presented in the literature. These (3) Evaluate the stiffness ratio, (k/k ), as the ratio of the frequencies were normalized and modified based on the ratio measured stiffness of the field beam to the evaluated of sectional properties since the training is done for a beam, stiffness of the reference beam in the postcracking- which has different section. The modified frequencies are fed preyielding stage. as test input to the trained network, and the prediction of ANN gives the degree of damage. The ANN trained only with (4) Evaluate the frequency ratio, (f/ f ), as the ratio of natural frequencies has been used here to validate the ANN- the measured frequency of the field beam to the based theoretical approach for damage assessment since the evaluated frequency of the reference beam. stiffness data were not available in the literature. Table 4 (5) Normalised stiffnesses and the natural frequencies are explains how the damage assessment procedure developed in considered as input, and they are modified using a his study works. From Table 4, it is demonstrated that the ratio based on moment of inertia, mass, and length ANN approach can predict the damage very closely. of the field beam. Since the network is trained for a particular cross-section in this study, a ratio is 7. Conclusions arrived between the sectional properties (moment of inertia, mass, and length) of the field beam to that of A damage assessment procedure based on ANN for the the theoretical beam (beam considered in this study) prestressed concrete rectangular beams has been formulated, [15]. The normalised stiffness and the natural fre- and the procedure has been validated using the data available quency of the field beam are multiplied by the ratio, from the literature. From this study, it can be concluded that and the modified stiffness and the natural frequency are given as the test data in the already trained (i) an ANN trained with dynamic data obtained at dif- network. ferent loads of a prestressed concrete beam is suf- ficient to assess the damage level. An ANN trained (6) ANN trained with only natural frequency also can be with a mix of static and dynamic data can be used used in case if it is possible to carry out only free to confirm the prediction of an ANN trained with vibration test on the field beam. dynamic data, if needed. The average of the predicted (7) The output of the network gives the extent of damage damage levels for test data obtained at different loads suffered by the field beam. is the best method to assess the damage by ANN; (ii) an assessment technique leading to the quantitative 6.1. Validation of the Damage Assessment Procedure. The evaluation of degree of damage is possible by ANN above-mentioned procedure is validated using the experi- using the natural frequency and stiffness in the post- mental data presented by Ambrosini et al. [13]. It could be cracking-preyielding range as input data; well understood that the requirements of any validation (iii) ANN can be used as an effective tool in the damage procedure will rarely be available directly in the literature assessment of prestressed concrete beams; especially dealing with experiments. Ambrosini et al. [13], National University of Tucuman, ´ (iv) damage assessment procedure developed in this re- Argentina, had conducted static as well as dynamic tests search work can effectively be put in to use for dam- with simply supported conditions on laboratory PSC beam age assessment of field beams. with an I-section of 400 mm × 500 mm with a test span of 13.30 m. The beam had 20 prestressing bars. 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A New Procedure for Damage Assessment of Prestressed Concrete Beams Using Artificial Neural Network

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Hindawi Publishing Corporation
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Copyright © 2011 K. Sumangala and C. Antony Jeyasehar. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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1687-7594
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10.1155/2011/786535
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Hindawi Publishing Corporation Advances in Artificial Neural Systems Volume 2011, Article ID 786535, 9 pages doi:10.1155/2011/786535 Research Article A New Procedure for Damage Assessment of Prestressed Concrete Beams Using Artificial Neural Network K. Sumangala and C. Antony Jeyasehar Department of Civil and Structural Engineering, Annamalai University, Tamilnadu, Annamalainagar 608 002, India Correspondence should be addressed to K. Sumangala, josuma@rediffmail.com Received 31 May 2011; Revised 24 August 2011; Accepted 24 August 2011 Academic Editor: Wilson Wang Copyright © 2011 K. Sumangala and C. Antony Jeyasehar. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. A damage assessment procedure has been developed using artificial neural network (ANN) for prestressed concrete beams. The methodology had been formulated using the results obtained from an experimental study conducted in the laboratory. Prestressed concrete (PSC) rectangular beams were cast, and pitting corrosion was introduced in the prestressing wires and was allowed to be snapped using accelerated corrosion process. Both static and dynamic tests were conducted to study the behaviour of perfect and damaged beams. The measured output from both static and dynamic tests was taken as input to train the neural network. Back propagation network was chosen for this purpose, which was written using the programming package MATLAB. The trained network was tested using separate test data obtained from the tests. A damage assessment procedure was developed using the trained network, it was validated using the data available in literature, and the outcome is presented in this paper. 1. Introduction quantify the damage with nondestructive tests and various analytical models [1]. Vibration-based damage detection Concrete structures are designed and constructed to suit methods seem to be effective at detecting and localizing the the requirements of its time. Damages may be unavoidable damage on full-scale structures [2]. during its design life time due to various reasons. A structure The easiest and simplest way to detect damage with which is said to be well designed may survive the damage but dynamic parameters is by noting the changes in the natural safety is not guaranteed. When the damage goes undetected frequency of the system. Cawley and Adams [3]formulateda and unrepaired, it will lead to failure or may demand costly scheme to detect damage in composite materials from natu- repair and huge loss of life. Therefore, the problem of ral frequency shifts. Abdel Wahab and Roeck [1]investigated maintenance and repair of existing structures involves dam- the application of the change in modal curvatures to detect age detection at an early stage. For massive structures like the damage in a prestressed concrete bridge. They modelled bridges which were constructed some 50 to 60 years ago, it is simply supported and continuous beams using finite ele- necessary to test their functionality under the present loading ments and introduced damage at different locations in terms condition and quantify damage, if any, since demolishing of reduced stiffness of the corresponding elements, and they and reconstructing them would involve huge expenditures. concluded that the natural frequencies of the damaged and Evaluating the residual life and remaining load-carrying undamaged beams indicated the presence of damage in a capacity of these structures is also important. Damage can be global sense. Abdul Razak and Choi [4] studied the effect defined as the change in performance of structures, which of general corrosion on the modal parameters of reinforced can be identified in terms of crack formation and a conse- concrete beams. Modal tests were performed and compared quent stiffness reduction. Damage recognition and location against that from a control beam. The changes were incon- are the key factors in the design of a structural health mon- sistent with the changes in natural frequencies, but a trend itoring system. When damage lies inside the structure and observed was mode dependent. The load carrying capacity is not visible to the naked eye, it is possible to locate and of the beams was determined through static load test, and 2 Advances in Artificial Neural Systems the results were correlated with the state of corrosion damage need user’s judgment. By using the proposed ANN-design and changes in the modal parameters. From the changes in method both location, and severity of damage could be natural frequencies, stiffness degradation was estimated and known. The method was employed in an example to demon- compared. strate their proposed methodology. Norhisham Bakhary et al. [11] in this study proposed a statistical approach to Carpinteri et al. [5] have discussed some aspects of the take into account the effect of uncertainties in developing NDE techniques in in situ damage assessment. They have an ANN model. By applying Rosenblueth’s point estimate taken up the study on assessing the stability of a historical method verified by Monte Carlo simulation, the statistics masonry tower using the NDE technique called thermogra- of the stiffness parameters were estimated. The probability phy and with nonlinear numerical simulations. According to of damage existence (PDE) is then calculated based on the the authors, the results of the analysis gave valuable hints probability density function of the existence of undamaged about how much damage had occurred and when the and damaged states. The developed approach is applied to restoration should take place. detect simulated damage in a numerical steel portal frame Wu et al. [6] illustrated the neural network-based meth- model and also in a laboratory-tested concrete slab. The odology to show that this approach could be used to identify effects of using different severity levels and noise levels on the member damage. The authors used the Fourier spectra of the damage detection results were discussed. computed relative acceleration, generated from a numerical de Lautour and Omenzetter [12] in this study present model of a simple three-storey frame, as an input to neural a general method for predicting seismic-induced damage network. According to their results, ANNs can learn about using artificialneuralnetworks(ANNs). Theapproach was the behaviour of undamaged and damaged structures to to describe both the structure and ground motion using a identify the damaged member and the extent of damage from large number of structural and ground motion properties. patterns in the frequency response of a structure. The class of structures analysed were 2D reinforced concrete According to Chen et al. [7], neural network can dis- (RC) frames that varied in topology, stiffness, strength, and tinguish small differences between the transmissibility func- damping and were subjected to a suite of ground motions. tions which carry the information of structural faults. The Dynamic structural responses were simulated using nonlin- transmissibility function is sensitive to structural faults and ear FEM analysis and damage indices describing the extent easy to measure in the situations where the excitations of the of damage calculated. Using the results of the numerical structural system are not available or immeasurable. They simulations, a mapping between the structural and ground had also suggested that transmissibility is a useful feature motion properties and the damage indices was than estab- for training neural network as a fault diagnosis model. Fang lished using an ANN. The performance of the ANN was et al. [8] referred the features of various training algorithms assessed using several examples, and the ANN was found to and with that as basis implemented the neural network to be capable of successfully predicting damage. the frequency-response-functions- (FRFs-) based structural Though more works have been done involving reinforced damage detection. The analysis results on a cantilever beam concrete and steel structures using ANN, not much work show that, in all considered damage cases (i.e., trained dam- has been done on PSC members. Modelling of damaged pre- age cases and unseen damage cases, single-damage cases and stressed concrete beam is complicated, and usage of conven- multiple-damage cases), the neural network can assess dam- tional methods for damage assessment of Prestressed Con- age conditions with very good accuracy. crete(PSC) beamsthusbecomes difficult. ANN is a possible Zapico et al. [9] in their paper described a procedure solution in this situation. Therefore, a well-designed neural for damage assessment in a two-storey steel frame and network is able to serve as a real time data processor for steel-concrete composite floors structure. The procedure is damage assessment. based on a multilayer perceptron (MLP). A simplified finite The main focus of this work was to train and test the element model was used to generate the training data. This network only with natural frequency and stiffness of dam- model was previously updated through another MLP using aged and perfect beams. Widely used feed forward ANN that two natural frequencies as inputs and the stiffness of the learns with back propagation algorithm was adopted, and beams and masses as updating parameters. The different details about network architecture are presented. Further, combinations of damage at the ends of the longitudinal it has been demonstrated that it is possible to predict the beams were used as damage scenarios. The training data for damage with acceptable accuracy by just feeding the current the MLP were generated by varying at random the stiffness of stiffness and natural frequency of the damaged structure the longitudinal beams. Two natural frequencies and mode [13] as inputs to the trained ANN. A novel in situ damage shapes were used as inputs, and three different definitions assessment procedure that needs only limited nondestructive of damage (sections, bars, and floors) were tried as outputs. measurements on the damaged structure is proposed. MLPs were trained through the error back-propagation algorithm. Finally, the performance of the procedure was The newness of this procedure is that it requires only evaluated through the experimental data. Only the approach minimum data collected from the damaged structure and of damage at floor level gives reasonable results. theoretical data developed for the original structure. So, with Yuen and Lam [10] had reviewed the works of many minimum number of inputs, the procedure is adopted. No researchers on damage detection using ANN. They have also further experiments are needed to get data in order to adopt developed an ANN based design method which does not procedure. Advances in Artificial Neural Systems 3 3. Experimental Study Output layer Fivepost tensioned concrete rectangular beams were used in this investigation. The beams were of uniform cross section, that is, 125 × 250 × 4200 mm. At each end, there were Direction Direction of of Hidden anchorage zones with enlarged section of size 350 × 230 × error activation layers propagation 250 mm and length of 230 mm. The overall length of the propagation beam was 4860 mm, out of which 4590 mm was consid- ered as the test zone. In order to achieve accessibility to prestressing tendons where the damage is introduced by Input layer corrosion, an opening 100× 120× 60 mm wide was provided in the middle bottom side of the beam. The beams were provided with nominal reinforcement in order to take up the Figure 1: Architecture of the back propagation network. handling stresses. The longitudinal reinforcement consists of two high yield strength deformed (HYSD) bars of 8 mm diameter at the top and the bottom. The stirrups were made using mild steel bars of 6 mm diameter and were 2. Feed Forward Artificial Neural Network and provided with a spacing of 175 mm. At the anchorage zone, Back Propagation Algorithm 12 bars of 6 mm diameter were provided between 25 and 250 mm from the edge. Reinforcement details were kept the Even though the ANN and back propagation algorithm are same for all the beams. The beams were cast with a mean well known, this section briefly revisits the concepts of feed concrete strength of 57 N/mm , posttensioned to a stress forward that learns by back propagation algorithm used level of 0.7 f . The ultimate strength of the high tensile pu in the damage assessment of prestressed concrete beams steel (HTS) wire is 1715.2 N/mm . Six HTS wires of 7 mm presented in this paper. The processing units in this artificial diameter were used for each beam. The first beam, designated neural network are arranged in layers, that is, input layer, as P7B1, was a perfect beam with absolutely no damage. an output layer, and a number of hidden layers as shown in The other four beams, namely, P7CB1, P7CB2, P7CB3, and Figure 1. The hidden units presented here allow the network P7CB4 were damaged to 33.33, 50, 66.67, and 83.33%, to represent and compute more complicated associations respectively. The damage percentage represents the percent- between patterns. The inputs are presented to the input layer. age of wires snapped. Snapping of wires was done using the Each neuron in the hidden layer receives the weighted sum accelerated electrochemical process. Through this process, from the input layer and transfers its result to the output pitting corrosion was induced and the wires were snapped. The setup made for inducing corrosion damage using ac- layer. The back propagation-learning algorithm calculates celerated electrochemical process is shown in Figure 3.After the error between the generated output and targeted output damaging the beams, static and dynamic tests were con- and uses the estimated error to modify the weight in response ducted on all five beams. to the errors. The back propagation algorithm learns by changing its weights to follow the steepest path towards the bottom of a bowl shaped error surface. This process contin- 3.1. Testing of Beams. All the beams were subjected to both ues until a set of weights, which processes data accurately static and dynamic tests. The beams were tested under for the application, is found out. The final weights represent repeated loading at an interval of 10 kN each (load stage). what the network has learnt and enable to infer for other Four cycles of repeated load were applied in each load stage. data. Processing element of this network with specified The beams were repeatedly loaded till the failure load is inputs is shown in Figure 2. reached. Deflections and strains were measured for a load increment of 2.5 kN up to failure. Crack width of five cracks Once the type of ANN and the learning algorithm are in the constant bending moment zone was also measured decided, it is necessary to generate the required training using a crack detection microscope of 0.02 mm precision. and test data. When the modeling of damaged PSC beam Static tests were conducted for determining the moment is difficult, one needs to depend upon the experimentally curvature, load deflection variations with loading in addition acquired data on the structure under study for training and to the evaluation of ultimate load carrying capacity of the test testing the ANN. From theory, it is well known that the beams. dynamic and/or static characteristics of the damaged PSC beams carry information about the damaged state of the Dynamic test was conducted at every 10 kN load interval structures. The ANN is made to recognize the damage and after four cycles of load application at each stage. The occurred in the structure under study by presenting the dynamic response was picked up by linear variable differential measured dynamic and/or static data of the damaged and transducer (LVDT) placed at mid span in the form of dis- undamaged beams obtained experimentally. The following placement history for the beams at all the chosen load stages. section presents the details of the experimental program car- It was utilised for the frequency analysis. The time history ried out to generate the necessary training and test data for records were analysed using the software DASYLAB for the ANN. obtaining the natural frequencies. 4 Advances in Artificial Neural Systems Summation Transfer function function Load Degree N. frequency of Sum Linear damage (inputs) w (output) Deflection Learning and recall schedule Supervised learning Learning cycle Figure 2: Processing element of this network with specified inputs. Anode ANN can be robust if large amount of training data is made available since training with large data can avoid the problem of over fitting and it can be fault tolerant with significant Cathode Container amount of redundancy and better learning algorithms. Over (corrosion fitting or over learning is indicated by the inability of a tank) Power network to perform better when unseen test data is presented source + − HT wire coated with to the network even though it is able to classify the training anticorrosive paint data. When large amount of data is used for training and the 2–8 mm φ structure and size of the network are chosen properly to han- dle the data, the problem of over fitting can be avoided. To 6-7 mm φ achieve this, the experimentally obtained results were linearly interpolated using the software ORIGIN to get the values All dimensions are in mm 2–8 mm φ at small regular intervals of load (1 kN) thus making the training and test database larger. Cross section of the beam The sample training data are given in Table 1. The data Figure 3: Corrosion induction setup. were normalized. The natural frequency, deflection, and crack width data obtained for the beam P7CB2 damaged to the extent of 50% in a similar manner were used as exclusive 4. Generation of Training and Test Data for test data (Table 2). This enables us to test the ability of ANN ANN and Its Architecture to generalize when presented with totally unseen data. In addition to these test data, the static and dynamic data for It was decided to use all the output obtained from the static 40% and 70% damage levels were also obtained by interpo- and dynamic tests such as stiffness (s), natural frequency ( f ), lation of the data acquired through experiments, and these deflection (δ), load at first crack (P ), crack width (w), and cr data were also used as test data. ultimate load (P ) from the perfect and damaged beams for training the neural network. It may be difficult to assess the 4.2. Architecture of the ANN. Feed forward neural network damage using the conventional methods since mathematical model is required to explain these behaviours. ANN does not learning by back propagation (BP) algorithm written in require prior mathematical model to solve a problem which MATLAB has been used, and its ability to predict damage just is a useful aspect of neural network. from the current natural frequency and postcrack stiffness obtained from the load-deflection characteristics of the dam- aged beam has been studied by training and testing the ANNs 4.1. Generation of Training and Test Data from Experiments. for various cases of input and comparing their performance The applied load and the corresponding stiffness, natural for various input conditions. Postcrack stiffness of the dam- frequency, deflection, and crack width values of damaged and undamaged beams (P7B1, P7CB1, P7CB3, and P7CB4) aged beam was also considered along with natural frequency were obtained at regular intervals from the static and since the frequency changes alone are insufficient to quantify dynamic tests. Even though two sets of beams were tested and the damage. To achieve this, the basic structure of the data collected for each case, only one data set was used for ANN was maintained and only the number of input nodes training. However, the ANN needs a larger volume of data in the input layer was changed. During training process, so that it learns better and predicts the damage accurately. different nodes were tried by trial and error for the hidden Advances in Artificial Neural Systems 5 Table 1: Sample training data. Natural frequency (Hz) at various damage levels Load kN 0% 33.33% 66.66% 83% P7B1 P7CB1 P7CB3 P7CB4 0 23.5 22.58 21.36 20.75 10 23.5 22.58 21.36 20.75 20 23.5 22.58 21.36 20.14 30 23.5 21.97 20.75 18.92 40 22.28 21.36 19.53 — 50 21.36 20.75 — — 60 16.48 — — — Table 2: Sample test data. having different cross sections, all the data were normalized before feeding into the network. The following were the cases Load kN Natural frequency (Hz) at 50% damage (P7CB2) studied in this work. 0 21.36 - Case i. ANN with applied load and natural frequency 10 21.36 as input. 20 21.36 - Case ii. ANN with postcrack stiffness and natural 30 20.75 frequency as input. 40 20.14 - Case iii. ANN with natural frequency (postcracking 50 19.53 preyielding) as input. - Case iv. ANN with applied load, natural frequency, layers to achieve the given performance accuracy, which is and deflection as input. user defined. After various trials, these nodes were finalized, - Case v. ANN with applied load, natural frequency, which gave the optimum output. So these numbers of nodes and crack width as input. were chosen based on the performance accuracy require- - Case vi. ANN with applied load, natural frequency, ment. The specifications of the ANN that gave the best deflection, and crack width as input. performance and are used in this study are as follows. - Case vii. ANN with applied load, natural frequency, (i) Number of input nodes in the input layer: 2–5 for deflection, crack width, and ultimate load as input. different cases. For the sake of practical application, only the first three (ii) Number of output nodes in the output layer: 1. cases are discussed in this paper. The remaining cases are (iii) Number of hidden layers: 2 with 7 and 5 nodes, re- explained elsewhere [14]. spectively. (iv) Training algorithm used: back propagation. Case i (ANN with applied load and natural frequency as inputs). This ANN is trained with applied load and natural (v) Learning method: supervised learning. frequencies obtained from the dynamic tests and aims at (vi) The output of the neural network is the predicted predicting the damage level from the average of possible extent of damage in the beam. solutions returned by the ANN for various test input data. The results obtained in this case are represented in a graph- ical form in Figure 4, which seems to be promising in the 5. ANN Training and Testing damage assessment process. This section presents the results of ANN training and test details for different cases and analyses the suitability of ANN Case ii (ANN with stiffness and natural frequency as inputs). for damage assessment of PSC beams. Mainly, the focus of Each training or test data has two inputs, that is, stiffness the study was to evaluate the effectiveness of ANN for dam- (postcracking-preyielding) and natural frequency. This ANN age assessment when trained only with natural frequency has been studied so that a damage assessment procedure can and stiffness of the damaged beam and with the mix of be evolved that is suitable in practical situation. In a field static and dynamic test data. Keeping this purpose in mind, beam, which is in the postcracking-preyielding stage, it is the training of the ANN has been carried out for a changing possible to obtain its current stiffness from its load deflection number of inputs. However, the structure of the ANN and characteristics measured over a portion of the service load. the training algorithm used were maintained as explained A dynamic test on the same beam can return its natural in the previous section for all the cases. In order to adopt frequency value. Therefore, these two parameters were the damage assessment procedure for various field beams selected for the ANN study and the network was trained, 6 Advances in Artificial Neural Systems 0 0 0 10 20 30 40 50 10 20 30 40 50 Test data set number Test data set number Predicted damage Predicted damage Expected damage Expected damage Average predicted damage Average predicted damage Figure 4: Input data set number versus damage predicted by ANN Figure 6: Input data set number versus damage predicted by ANN (Case i). (Case iii). network are summarised in Table 3.The performanceaccu- racy (user defined value) indicates how close the predicted output of the network is to the expected or targeted output. In our case, the targeted output is the expected damage. The performance accuracy is evaluated from the mean squared error where the error is the difference between the output of the network and the targeted output for a set of inputs. Epochs were not chosen for these cases, but only the performance accuracy was user defined. So when the accu- 10 racy level is obtained as expected, the training process stops. For making comparison, the number of epochs is mentioned. 10 20 30 When the network was provided with more number of Test data set number inputs, the prediction was better in terms of performance accuracy (user defined) and with fewer epochs. The perfor- Predicted damage mance accuracy becomes less with more number of epochs Expected damage required, when the number of inputs starts decreasing. Our Average predicted damage aim is to develop the procedure only with natural frequencies and stiffness from data obtained from the field. Therefore, Figure 5: Input data set number versus damage predicted by ANN only that particular network was used for developing the (Case ii). procedure. The table indicates that for all cases the error in the predicted damage can be very large when just one test input and the result is presented below in the form of graph and data obtained for a single applied load is used to predict the is shown in Figure 5. However, the average of the predicted damage level. Maximum error occurred when the ANN was damage levels for differenttestdatacould closelypredictthe trained with only frequency obtained from the dynamic test damage. as input to the network. This is justified by the fact that the Case iii (ANN with natural frequency (postcracking-prey- ANN can learn better and predict better when it is trained ielding) as input). Each training or test data has only one with more database. This error is still comparable with the input, that is, natural frequency. This ANN has been studied errors with which the other ANNs could predict the damage to check if it is possible to predict the damage only with levels. It is also found that the ANN trained with stiffness natural frequency obtained from dynamic tests. The network and frequency obtained over an applied load range within its was trained and the result is presented in Figure 6. From the service load limit could predict the damage very closely (with figure, it is observed that each set of the predicted damage is a maximum difference of 5% damage) thus paving the way closer to the expected value. for the development of a new practical method of damage assessment of prestressed concrete beams. The input test data for the damage levels of 40% and 70% were interpolated using ORIGIN software. From that 6. Damage Assessment Procedure observation, the minimum and the maximum deviations of the various cases and average predicted damage levels along It has been demonstrated that the ANN trained with natural with number of epochs and the performance accuracy of the frequency and stiffness can estimate the damage when tested Predicted damage (%) Predicted damage (%) Predicted damage (%) Advances in Artificial Neural Systems 7 Table 3: Summary of the results for various input cases. Input Number of Expected No. of epochs Performance Minimum predicted damage level Maximum predicted damage level Average predicted damage level parameter to inputs damage level Predicted Predicted Predicted taken for accuracy Difference Difference Difference the ANN (%) ED damage value damage value damage value training the (ED–OD) (ED–OD) (ED–OD) ANN (OD) (OD) (OD) 40 32.19 −7.81 47.98 +7.98 37.69 −2.31 p-f 2 50 33.37 −16.63 66.10 +16.10 57.56 +7.56 1203 1e − 5 70 68.09 −1.91 72.17 +2.17 70.40 +0.40 40 33.01 −6.99 52.95 +12.95 42.05 +2.05 s-f 2 50 31.77 −18.23 77.68 +27.68 48.63 −1.37 423 0.06 70 58.98 −11.02 77.68 +7.68 71.44 +1.44 40 20.13 −19.87 58.77 +18.77 35.82 −4.18 f1 50 52.59 +2.59 58.82 +8.82 56.09 +6.09 5000 0.25 70 57.60 −12.40 59.00 −11.00 59.00 −11.00 8 Advances in Artificial Neural Systems with the data obtained in situ. Also, it has been proved that Table 4: Comparison of predicted values with Ambrosini et al. [11]. the ANN trained just with natural frequency can also assess Degree of damage (%) the damage. Based on this concept, a damage assessment Serial no. Expected degree of damage procedure has been evolved and presented here. The steps Predicted damage (Ambrosini et al.) that should be followed for the damage assessment are 1 30 29.93 explained below. 2 40 41.61 (1) Evaluate the stiffness of the field beam, which is at 3 50 51.09 the postcracking-preyielding stage (service stage) by conducting a static test on the beam. A fraction of the service load is applied for this purpose. acquisition equipment consistent in a computer with a dif- ferential eight-channel card. Dynamic tests were performed (2) Measure the in situ natural frequency of the field by exciting the beam with a hammer blow in the central beam by conducting a dynamic test (free vibration section. The natural frequencies obtained in each one of the test) on the structure. test stages are tabulated and presented in the literature. These (3) Evaluate the stiffness ratio, (k/k ), as the ratio of the frequencies were normalized and modified based on the ratio measured stiffness of the field beam to the evaluated of sectional properties since the training is done for a beam, stiffness of the reference beam in the postcracking- which has different section. The modified frequencies are fed preyielding stage. as test input to the trained network, and the prediction of ANN gives the degree of damage. The ANN trained only with (4) Evaluate the frequency ratio, (f/ f ), as the ratio of natural frequencies has been used here to validate the ANN- the measured frequency of the field beam to the based theoretical approach for damage assessment since the evaluated frequency of the reference beam. stiffness data were not available in the literature. Table 4 (5) Normalised stiffnesses and the natural frequencies are explains how the damage assessment procedure developed in considered as input, and they are modified using a his study works. From Table 4, it is demonstrated that the ratio based on moment of inertia, mass, and length ANN approach can predict the damage very closely. of the field beam. Since the network is trained for a particular cross-section in this study, a ratio is 7. Conclusions arrived between the sectional properties (moment of inertia, mass, and length) of the field beam to that of A damage assessment procedure based on ANN for the the theoretical beam (beam considered in this study) prestressed concrete rectangular beams has been formulated, [15]. The normalised stiffness and the natural fre- and the procedure has been validated using the data available quency of the field beam are multiplied by the ratio, from the literature. From this study, it can be concluded that and the modified stiffness and the natural frequency are given as the test data in the already trained (i) an ANN trained with dynamic data obtained at dif- network. ferent loads of a prestressed concrete beam is suf- ficient to assess the damage level. An ANN trained (6) ANN trained with only natural frequency also can be with a mix of static and dynamic data can be used used in case if it is possible to carry out only free to confirm the prediction of an ANN trained with vibration test on the field beam. dynamic data, if needed. The average of the predicted (7) The output of the network gives the extent of damage damage levels for test data obtained at different loads suffered by the field beam. is the best method to assess the damage by ANN; (ii) an assessment technique leading to the quantitative 6.1. Validation of the Damage Assessment Procedure. The evaluation of degree of damage is possible by ANN above-mentioned procedure is validated using the experi- using the natural frequency and stiffness in the post- mental data presented by Ambrosini et al. [13]. It could be cracking-preyielding range as input data; well understood that the requirements of any validation (iii) ANN can be used as an effective tool in the damage procedure will rarely be available directly in the literature assessment of prestressed concrete beams; especially dealing with experiments. Ambrosini et al. [13], National University of Tucuman, ´ (iv) damage assessment procedure developed in this re- Argentina, had conducted static as well as dynamic tests search work can effectively be put in to use for dam- with simply supported conditions on laboratory PSC beam age assessment of field beams. with an I-section of 400 mm × 500 mm with a test span of 13.30 m. The beam had 20 prestressing bars. 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