Using Neural Networks to Determine the Significance of Aggregate Characteristics Affecting the Mechanical Properties of Recycled Aggregate Concrete
Using Neural Networks to Determine the Significance of Aggregate Characteristics Affecting the...
Duan, Zhenhua;Hou, Shaodan;Poon, Chi-Sun;Xiao, Jianzhuang;Liu, Yun
2018-11-06 00:00:00
applied sciences Article Using Neural Networks to Determine the Significance of Aggregate Characteristics Affecting the Mechanical Properties of Recycled Aggregate Concrete 1 , 2 1 2 , 1 1 , Zhenhua Duan , Shaodan Hou , Chi-Sun Poon *, Jianzhuang Xiao and Yun Liu * Department of Structural Engineering, Tongji University, Shanghai 200092, China; zhduan@tongji.edu.cn (Z.D.); hsd2017@tongji.edu.cn (S.H.); jzx@tongji.edu.cn (J.X.) Department of Civil and Environmental Engineering, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong, China * Correspondence: cecspoon@polyu.edu.hk (C.-S.P.); liuyun@tongji.edu.cn (Y.L.); Tel.: +852-2766-6024 (C.-S.P.); +86-21-6598-3320 (Y.L.) Received: 29 September 2018; Accepted: 1 November 2018; Published: 6 November 2018 Abstract: It has been proved that artificial neural networks (ANN) can be used to predict the compressive strength and elastic modulus of recycled aggregate concrete (RAC) made with recycled aggregates from different sources. This paper is a further study of the use of ANN to analyze the significance of each aggregate characteristic and determine the best combinations of factors that would affect the compressive strength and elastic modulus of RAC. The experiments were carried out with 46 mixes with several types of recycled aggregates. The experimental results were used to build ANN models for compressive strength and elastic modulus, respectively. Different combinations of factors were selected as input variables until the minimum error was reached. The results show that water absorption has the most important effect on aggregate characteristics, further affecting the compressive strength of RAC, and that combined factors including concrete mixes, curing age, specific gravity, water absorption and impurity content can reduce the prediction error of ANN to 5.43%. Moreover, for elastic modulus, water absorption and specific gravity are the most influential, and the network error with a combination of mixes, curing age, specific gravity and water absorption is only 3.89%. Keywords: recycled aggregate; recycled aggregate concrete; artificial neural networks; aggregate characteristic; input variable 1. Introduction There is no doubt that the utilization of recycled aggregate concrete (RAC) has been the best way to resolve the problem of the increasing amount of construction and demolition (C&D) waste and further attain sustainable development. The improved environmental performance of recycled aggregate concrete (RAC) [1–3] has led to research on recycled aggregate (RA) and RAC, a popular topic in the last decades [4–7]. Recycled coarse aggregate and recycled fine aggregate were both used in concrete to make full use of C&D wastes; meanwhile, the cementitious materials supplied, such as fly ash and silica fume, were used together with RA for high-performance RAC [8–11]. Though there has been a large amount of research on the properties of RAC, the results have been varied because the properties of RAs from different sources (such as the demolition of bridges, buildings and airport pavements) and produced using different recycling methods (e.g., the type and effort of the crushers used) vary greatly [12]. It is generally accepted that the properties of RA and the hardened properties of RAC made with such RA are both largely affected by the nature of the attached old mortar [13–17]. However, it is difficult to establish an accurate relationship between the two, since at present there is Appl. Sci. 2018, 8, 2171; doi:10.3390/app8112171 www.mdpi.com/journal/applsci Appl. Sci. 2018, 8, 2171 2 of 14 no established method for accurately measuring the quantity and quality of the attached mortar in RA. On the other hand, RAs may also contain impurities, such as bricks, glass, tiles, asphalt, plastics, gypsum, wood and clay, etc. In small amounts, however, their presence may seriously deteriorate the quality of RA. The presence of other impurities makes it more complicated to predict the properties of RAC. Therefore, there are at least two major difficulties in building a model that can predict the performance of hardened RAC made with RAs from different sources: (1) the model should act as an expert system covering the factors that may affect the properties of RAC, such as cement content, water to cement ratio, aggregate to cement ratio, cement type and particle size of aggregates, etc.; (2) an optimal combination of RA characteristics should be included in the model so that it can be applicable to the majority of RAs from different sources. A previous study [18] used regression analysis to propose a number of equations relating the hardened properties (compressive strength) of RAC with the water absorption or density of different types and combinations of aggregates obtained from different sources. However, the accuracy of the prediction is limited since the properties of RA cannot be completely represented by the density or water absorption values of RA. Tam and Tam [19] suggested that there were six main factors that characterize the properties of RA: (1) particle size distribution; (2) particle density; (3) porosity and absorption; (4) particle shape; (5) strength and toughness; and (6) chloride and sulphate contents. Through a comparison and analysis of ten sources of RAs and one type of natural aggregate (NA), they constructed relationships among these factors and indicated that the RA properties could be assessed by only measuring three of the six parameters mentioned. However, whether the model is suitable for RAs obtained from other sources has not been verified. As a modeling tool, artificial neural networks (ANN) have been widely used since the mid-1980s, and have also been demonstrated to have superior capacities in modeling more complex relationships. Among all the ANN structures, the back-propagation network (BPN) is generally regarded as one of the simplest and most applicable networks used in simulating concrete properties. As shown in Figure 1, a typical BPN model consists of an input layer, one or more hidden layers and an output layer, and each layer consists of numerous neurons. During the training set, feed-forward propagation and back-propagation propagation run in turn to reach the required criteria. The former propagation can first transform the input mode onto the hidden layer, and then pass the weighted sum of inputs to the output layer through an activation function, resulting in one output value. In this stage, the sigmoidal function (f (.)) is generally used, and the output can be calculated according to Equation (1). Immediately after that, the back-propagation propagation works by passing the error of network backwards from the output layer to the input layer, with the weights adjusted based on some learning strategies to reduce the network error. f = (1) 1 + exp( w o + b) ji i where w is the connection weight from neuron i in the lower layer to neuron j in the upper layer and ji an initially small random value, o is the output of neuron i, and b is the bias value. i Appl. Sci. 2018, 8, 2171 3 of 14 Appl. Sci. 2018, 8, x FOR PEER REVIEW 3 of 15 Figure 1. A typical artificial neural networks (ANN) model. Figure 1. A typical artificial neural networks (ANN) model. Duan et al. [20] carried out a study on predicting the compressive strength of RAC at the curing Duan et al. [20] carried out a study on predicting the compressive strength of RAC at the curing time of 28 days using an ANN model. The authors collected a large amount of published data on the time of 28 days using an ANN model. The authors collected a large amount of published data on the 28-day compressive strength of RAC, which came from previous research. The RA used was derived 28-day compressive strength of RAC, which came from previous research. The RA used was derived from different countries and sources. The data were used for the construction of the ANN model, from different countries and sources. The data were used for the construction of the ANN model, and and the predicted results of the ANN model were quite accurate. Moreover, the same author also the predicted results of the ANN model were quite accurate. Moreover, the same author also established another ANN model for predicting the elastic modulus of RAC [21]. This model was built established another ANN model for predicting the elastic modulus of RAC [21]. This model was built based on regression analysis and performed better predictions. Sensitivity analysis, an uncertainty based on regression analysis and performed better predictions. Sensitivity analysis, an uncertainty analysis technique in relation to quantitative analysis, is a study to assess the sensitivity of the analysis technique in relation to quantitative analysis, is a study to assess the sensitivity of the prediction results of the model to the change in the selected input variables [22]. It also determines prediction results of the model to the change in the selected input variables [22]. It also determines the significance of these uncertain factors on the results [23–25]. Therefore, it is of interest to apply the significance of these uncertain factors on the results [23–25]. Therefore, it is of interest to apply the sensitivity analysis to the constructed ANN model to further study the influence of each input the sensitivity analysis to the constructed ANN model to further study the influence of each input variable on the output. By conducting a sensitivity analysis, Jain et al. [26] determined the effect of the variable on the output. By conducting a sensitivity analysis, Jain et al. [26] determined the effect of constituents of concrete mixes on the desired workability. the constituents of concrete mixes on the desired workability. To predict the compressive strength of NAC (natural aggregate concrete) using ANN, the concrete To predict the compressive strength of NAC (natural aggregate concrete) using ANN, the mix proportions used [27–30] and the time of testing of the compressive strength [31–33] were generally concrete mix proportions used [27–30] and the time of testing of the compressive strength [31–33] selected as the input variables. For concrete made with RAs from different sources, the difference were generally selected as the input variables. For concrete made with RAs from different sources, between the properties of different RAs should be taken into account. The aggregate characteristics, the difference between the properties of different RAs should be taken into account. The aggregate such as water absorption, specific gravity, and aggregate crush value are closely related to the properties characteristics, such as water absorption, specific gravity, and aggregate crush value are closely of the old mortar attached, which can affect the properties of RAC by different levels. In theory, related to the properties of the old mortar attached, which can affect the properties of RAC by the more factors are taken into consideration, the more accurate the model is. However, in practice different levels. In theory, the more factors are taken into consideration, the more accurate the model it is unsuitable to use all the affected factors due to the complicated calculation and the measuring is. However, in practice it is unsuitable to use all the affected factors due to the complicated error. Therefore, it is important to determine the significance of each RA characteristic and the optimal calculation and the measuring error. Therefore, it is important to determine the significance of each combination of factors, which aims to ensure the factors can be applicable to the majority of RAs from RA characteristic and the optimal combination of factors, which aims to ensure the factors can be different sources. In other words, how to fully represent the aggregate properties in the ANN model is applicable to the majority of RAs from different sources. In other words, how to fully represent the an important issue. aggregate properties in the ANN model is an important issue. The purpose of this study is to examine the relative importance of the different characteristics The purpose of this study is to examine the relative importance of the different characteristics of of RA in affecting RAC properties. Moreover, it also aims to determine which factor or combination RA in affecting RAC properties. Moreover, it also aims to determine which factor or combination of of factors is most suitable for representing RA properties when used in ANN model for compressive factors is most suitable for representing RA properties when used in ANN model for compressive strength and elastic modulus prediction. In this study, the following steps were used for this purpose. strength and elastic modulus prediction. In this study, the following steps were used for this purpose. 2. Methodologies 2. Methodologies 2.1. Building the ANN Models and the Sensitivity Analysis 2.1. Building the ANN Models and the Sensitivity Analysis First, experiments on the mechanical properties of RAC with different RAs were carried out in the First, experiments on the mechanical properties of RAC with different RAs were carried out in laboratory, which had 46 concrete mixes and were divided into 3 groups. The RAs were categorized the laboratory, which had 46 concrete mixes and were divided into 3 groups. The RAs were into 3 groups according to their sources: (1) RAs derived from 3 different sources and crushed categorized into 3 groups according to their sources: (1) RAs derived from 3 different sources and crushed using different methods; (2) RAs derived from concrete cubes made in the laboratory with Appl. Sci. 2018, 8, 2171 4 of 14 using different methods; (2) RAs derived from concrete cubes made in the laboratory with different compressive strengths (35–85 MPa); (3) RAs contained different amounts of masonry added (clay bricks or tiles). As many sources of natural and recycled aggregates were used in these mixes, 8 aggregate characteristics, including fineness modulus of the fine aggregate (FM), residual mortar content (M ), 10% fines value (TFV), aggregate crushing value (ACV), water absorption value (W ), specific gravity (SG ), impurity content () and masonry content (m) of the coarse aggregate, were comprehensively SSD measured and quantified. These factors, together with the mix proportions and concrete curing time, were selected as the input variables of the ANN for modeling the compressive strength and elastic modulus. To facilitate the analysis, factors including the mix proportions (5 variables) and curing time (1 variable) were designated as “certainties”, while the other factors (8 variables) were named “uncertainties”. The experimental results obtained from the above mixes at different ages were divided into three groups, acting as: (i) the training set; (ii) the validation set; and (iii) the testing set, respectively. The corresponding ANN model could be established using the procedures described previously [20]. For each model, the ANN network parameters were determined when the error values reached the minimum. Based on the comparison of the error of integral testing set after a series of trials, the initial network architecture and parameters used in this study were as follows: Number of input layer units = 14 Number of hidden layers = 1 Number of hidden layer units = 40 Number of output layer units = 1 Momentum rate = 0.9 Learning rate = 0.01 Learning cycle = 15,000 In this study, the mean absolute percentage error (MAPE), root-mean-squared error (RMS) and absolute fraction of variance (R ) computed using Equations (2)–(4) were used to access the accuracy of the ANN model developed. o t j j MAPE = (2) RMS = t o (3) å j j 0 1 å t o j j @ A R = 1 (4) (o ) j j where t: the predicted output of the network; o: the actual output of the network; p: the total number of training and testing patterns; t : the predicted output of jth pattern of the network; o : the actual j j output of jth pattern of the network. After the construction of the ANN models, the sensitivity analysis was then conducted according to Figure 2. Appl. Sci. 2018, 8, x FOR PEER REVIEW 5 of 15 Appl. Sci. 2018, 8, 2171 5 of 14 Appl. Sci. 2018, 8, x FOR PEER REVIEW 5 of 15 Figure 2. Flow chart of the sensitivity analysis Figure 2. Flow chart of the sensitivity analysis Figure 2. Flow chart of the sensitivity analysis Step 1: A comparison of the performance between the models (ANN14) with all variables (14 Step 1: A comparison of the performance between the models (ANN ) with all variables variableStep 1: A s) and that co (AN mparison N6) wi of th certa the perform inties (only 6 ance between variables)the models ( was first made, ANN while keepi 14) with aln l v g the ariab other les (14 (14 variables) and that (ANN ) with certainties (only 6 variables) was first made, while keeping networks parameters constant. variables) and that (ANN6) with certainties (only 6 variables) was first made, while keeping the other the other networks parameters constant. networks p Step 2: Va ara riou meters consta s combinations of nt. the uncertainties (aggregate characteristics) together with the Step 2: Various combinations of the uncertainties (aggregate characteristics) together with the “certainties” were used as the inputs of each model to find the best model with the minimum error. Step 2: Various combinations of the uncertainties (aggregate characteristics) together with the “certainties” were used as the inputs of each model to find the best model with the minimum error. However, it “certainties” would t were a used a ke a huge amo s the inputs untof of t eaich me if mode all t l to f he combinat ind the best model ions were wi trth ied out the mi one nimum by one. error. However, it would take a huge amount of time if all the combinations were tried out one by one. Considering the interaction and constraints among the aggregate characteristics, a simple method However, it would take a huge amount of time if all the combinations were tried out one by one. Considering the interaction and constraints among the aggregate characteristics, a simple method developed t Considering o det th ee int rmine t eract he best ion and combin const at raint ion o s am f vaon riag bles the ag is shown gregat in F e char iguact re 3. er istics, a simple method developed to determine the best combination of variables is shown in Figure 3. developed to determine the best combination of variables is shown in Figure 3. Figure 3. The determination of the best combination of input variables. Figure 3. The determination of the best combination of input variables. Figure 3. The determination of the best combination of input variables. At Stage a, the resulted error of ANN was compared with that of the networks (ANN ) when 6 7 • At Stage a, the resulted error of ANN6 was compared with that of the networks (ANN7) when each “uncertainty” was sequentially added as an input variable. If the error could not be reduced, each “uncertainty” was sequentially added as an input variable. If the error could not be • At Stage a, the resulted error of ANN6 was compared with that of the networks (ANN7) when then the “uncertainty” added was regarded as negative for the output and would not be further reduced, then the “ each “uncertainty” was uncertainty” sequ aent dded ially wa added as s regarded a an input va s negative ria for the output a ble. If the error coul nd woul d not d not be studied in the next stages. The larger the reduction in the error value, the more important the be further studied in the next stages. The larger the reduction in the error value, the more reduced, then the “uncertainty” added was regarded as negative for the output and would not respective “uncertainty”, and vice versa. imbe further st portant the respecti udied in ve “uncerta the next stage inty”, s and vi . The larg ce versa er the red . uction in the error value, the more At Stage b, the variables that could reduce the error of ANN were retained. Sequentially, each • At Stage b, the variables that could reduce the error of ANN6 were retained. Sequentially, each important the respective “uncertainty”, and vice versa. variable was paired with the others as the added inputs of ANN to build a new model (ANN ), 6 8 • varia At Stage b, the var ble was paired wi iab th the others as the a les that could reduce the error dded inputs of of ANN ANN 6 6were to build retaine a new d. Se model ( quentially, ANN8eac ), h and the resulted error values were compared with those of the networks (ANN ) when only and the resulted error values were compared with those of the networks (ANN7) when only one variable was paired with the others as the added inputs of ANN6 to build a new model (ANN8), one variable was added to ANN . If the resulted error of the ANN was not less than that of 6 8 vari and the re able wassulted error v added to AN aN lues were comp 6. If the resulted ared w error ith those of the netw of the ANN8 was not less tha orks (ANN7n ) tha when only on t of each e each ANN , the pair of variables was not further studied. For example, as shown in Figure 3, ANN7, the pair of variables was not further studied. For example, as shown in Figure 3, in the variable was added to ANN6. If the resulted error of the ANN8 was not less than that of each ANN7, the pair of variables was not further studied. For example, as shown in Figure 3, in the Appl. Sci. 2018, 8, 2171 6 of 14 in the further right column, items 3 and 4 represent two aggregate characteristics, respectively. Accordingly, C3 and C4 (in the second right column) represent a combination of “certainty” variables with items 3 and 4, respectively. Assuming that the addition of either item 3 or item 4 to the certainties could reduce the network error of ANN , C3 and C4 would be both retained and used to form a new combination C34, which contained 8 input variables (items 3, 4 and certainties). When comparing the MAPE values of the networks using C34, C3 and C4 as inputs, respectively, and if the first one was lower than both the latter two values, C34 would be retained for the next stage. Otherwise, it would be discarded. This above approach was continued until the networks error could not be further reduced. In this way, after trying out all the possible combinations, the most influential factor or a combination of factors to the compressive strength and elastic modulus of RAC could be identified. Considering that the predicted results of the networks would change slightly even when using the same model, each of the networks was trained 5 times and the average value of the MAPEs of the testing set and validation set was used as the final indicator of the network error. 2.2. Experimental Program It is not necessary to use ANN to model the effect of RA on the properties of RAC when only one type of RA is used, since in this case the complexity of RA cannot be reflected and the predictive ability of ANN is generally no better than that of traditional methods like regression analysis. When RAs from different sources were used, ANN models, which are more capable of modeling complex non-linear relationships, may be more suitable for predicting the hardened properties of RAC. The published data of RAs used can be divided into two cases: (1) several types of RAs used by a single researcher; (2) the data of RAs from different literature sources. The factors that influence the properties of RAC and used as the input variables of the networks in the two cases are quite different. For the former case, the types of materials other than aggregate, specimen size and operator error are essentially the same, so only the mix proportions and RA characteristics are chosen as the input variables; for the latter case, on the other hand, in addition to the mix proportions and RA characteristics, more factors such as cement type, specimen size, etc. should be included to establish a generalized model. In this paper, only the first case is considered. The second case will be dealt with in a separate paper. (1) The source of the data As introduced above, experiments on the mechanical properties of RAC with different RAs were carried out in the laboratory, which had 46 concrete mixes and were divided into 3 groups. The properties of these aggregates are shown in Table 1. Except for the chosen aggregate characteristics, the particle size was also listed in Table 1 for different aggregate types. The details of the mixes and the corresponding hardened properties of the concrete prepared are shown in Tables 2 and 3, respectively. Table 1. Properties of aggregates. Aggregate Particle Size SG W M ACV (%) TFV (KN) m SSD a c Sources FM Type mm % % 10–14 mm 10–14 mm % % g/cm NA1 20 2.6 1.01 0 21.7 155 0 0 / RA1 20 2.48 3.36 21 22.5 143 1.4 0.4 / RA2 20 2.36 6.14 35.1 23.4 133 2.9 1.1 / Source 1 RA3 20 2.36 6.44 62 23.9 127 1 0 / FNA1 5 2.63 0.94 0 / / 0 0 2.19 Appl. Sci. 2018, 8, 2171 7 of 14 Table 1. Cont. Aggregate Particle Size SG W M ACV (%) TFV (KN) m SSD a c FM Sources Type mm g/cm % % 10–14 mm 10–14 mm % % NA2 20 2.66 0.71 0 15.8 259 0 0 / RA4 20 2.41 6.38 0 19.3 131 0 0 / RA5 20 2.42 5.18 0 19.7 154 0 0 / Source 2 RA6 20 2.44 5.36 0 19.5 151 0 0 / RA7 20 2.45 5.3 0 20.3 147 0 0 / RA8 20 2.46 5.36 0 20.4 155 0 0 / FNA2 5 2.62 0.76 0 / / 0 0 3.28 NA1 20 2.6 1.01 0 21.7 155 0 0 / NA2 20 2.66 0.71 0 15.8 259 0 0 / RA9 20 2.49 3.85 22 21.5 149 2 1.1 / Source 3 brick 20 1.99 21.74 0 27.1 44 100 100 / tile 10 2.03 14.82 0 19.1 105 100 100 / FNA2 5 2.62 0.76 0 / / 0 0 3.28 FNA3 5 2.61 0.44 0 / / 0 0 2.94 NA1-NA2, RA1-RA9, FNA1-FNA3 represent natural coarse aggregate, recycled coarse aggregate, and natural fine aggregate from different sources or batches, respectively. SGSSD: specific gravity; W : water absorption value; M : a c residual mortar content; ACV: aggregate crushing value; TFV: 10% fines value; FM: fineness modulus. Table 2. Mix proportions of recycled aggregate concrete (RAC) made with aggregates from different sources (kg/m ). Sources Mixes W Cement Sand NA RA Aggregate Used NA30 205 300 697 1143 0 NA1 RC30-1 205 300 697 0 1075 RA1 RC30-2 205 300 697 0 1027 RA2 RC30-3 205 300 697 0 1027 RA3 NC45 180 350 706 1158 0 NA1 RC45-1 180 350 706 0 1089 RA1 RC45-2 180 350 706 0 1041 RA2 RC45-3 180 350 706 0 1041 RA3 NA60 185 425 696 1092 0 NA1 RC60-1 185 425 696 0 1028 RA1 Source 1 RC60-2 185 425 696 0 982 RA2 RC60-3 185 425 696 0 982 RA3 NA80 165 485 685 1089 0 NA1 RC80-1 165 485 685 0 1039 RA1 RC80-2 165 485 685 0 979 RA2 RC80-3 165 485 685 0 982 RA3 MC45-2 180 350 675 0 1089 RA2 MC45-3 180 350 654 0 1041 RA3 MC60-2 185 425 637 0 1028 RA2 MC60-3 185 425 618 0 982 RA3 NAC 155 440 666 1166 0 NA2 R30 155 440 666 0 1070 RA4 R45 155 440 666 0 1077 RA5 Source 2 R60 155 440 666 0 1083 RA6 R80 155 440 666 0 1090 RA7 R100 155 440 666 0 1094 RA8 Control 190 380 710 1110 0 NA2 + FNA3 T5 190 380 710 1055 44 NA2 + FNA3 + tile T10 190 380 710 999 88 NA2 + FNA3 + tile T15 190 380 710 944 132 NA2 + FNA3 + tile b5 190 380 710 1055 43 NA2 + FNA3 + brick Source 3 b10 190 380 710 999 86 NA2 + FNA3 + brick b15 190 380 710 944 129 NA2 + FNA3 + brick b5r50 185 370 732 545 481 NA1 + RA9 + FNA2 + brick b5r100 185 370 732 0 961 RA9 + FNA2 + brick b10r50 185 370 732 545 475 NA1 + RA9 + FNA2 + brick b10r100 185 370 732 0 948 RA9 + FNA2 + brick Appl. Sci. 2018, 8, 2171 8 of 14 Table 2. Cont. Sources Mixes W Cement Sand NA RA Aggregate Used b15r50 185 370 732 545 526 NA1 + RA9 + FNA2 + brick b15r100 185 370 732 0 1049 RA9 + FNA2 + brick T5r50 185 370 732 545 486 NA1 + RA9 + FNA2 + tile T5r100 185 370 732 0 970 RA9 + FNA2 + tile T10r50 185 370 732 545 511 NA1 + RA9 + FNA2 + tile T10r100 185 370 732 0 1018 RA9 + FNA2 + tile ro 185 370 732 1090 0 NA1 + FNA2 r50 185 370 732 545 463 NA1 + RA9 + FNA2 r100 185 370 732 0 924 RA9 + FNA2 NA: natural aggregate; RA: recycled aggregate. Table 3. Mechanical properties of RAC. f (MPa) E (GPa) c c Sources Mixes 1 Day 4 Days 7 Days 28 Days 90 Days 28 Days 90 Days NA30 34.5 39.4 25.1 26.6 RC30-1 35 39.8 20.85 25.18 RC30-2 29.2 34 21.9 22.83 RC30-3 27.7 28.4 20.49 21.5 NC45 48.3 53 30.68 31.1 RC45-1 47.6 51.3 28.86 30.68 RC45-2 42 47 24.46 25.91 RC45-3 42.9 46.3 26.55 27.22 NA60 61.6 69.6 32.36 34.5 RC60-1 60 67.7 29.42 33.42 Source 1 RC60-2 53.7 55.5 24.61 26.3 RC60-3 53.2 58.6 28.5 27.94 NA80 80.5 88.3 35.43 36.88 RC80-1 78.2 84.1 34.76 35.49 RC80-2 71.2 74.3 29.52 29.92 RC80-3 65.4 73.3 30.62 30.74 RC45-1 49.2 51.5 29.5 31.2 RC45-2 43.6 50.1 25.48 26.35 RC60-1 60.4 68 30.7 33.6 RC60-2 57.3 62.7 26.99 27.3 NAC 29.3 54.8 59.7 69.6 75.3 32.3 36.1 R30 24 50.7 54.1 59.4 63 27.43 28.67 R45 31 56 60.2 69.8 76.3 27.26 30.9 Source 2 R60 22.9 50.1 57.6 67.8 74.8 27.02 30.98 R80 24.8 52.6 59.4 68.7 72.7 26.85 30 R100 20.1 46.5 55.2 62.1 66.3 26.79 28.48 Control 54.4 60.5 29.85 31.51 T5 54.4 59.9 28.42 30.94 T10 54.9 60 27.44 29.14 T15 52.5 57.6 27.09 28.08 b5 54.2 59.4 27.49 30.27 b10 52.3 57.6 25.46 28.05 b15 46.9 54.8 23.18 24.24 b5r50 18.6 38.2 41.7 48.4 54.1 29.03 30 b5r100 15.9 34.7 35 44 45.9 27.1 27.9 b10r50 39.1 47.5 54 27 28.26 25.3 Source 3 b10r100 34.6 42.4 45.4 26.69 27.85 23.9 b15r50 21.6 37.5 38.8 46.7 50.5 24.42 26.14 b15r100 17.5 31.5 33.9 41.1 42.1 24.15 25.58 Appl. Sci. 2018, 8, 2171 9 of 14 Table 3. Cont. Appl. Sci. 2018, 8, x FOR PEER REVIEW 9 of 15 f (MPa) E (GPa) c c Sources Mixes b15r50 21.6 37.5 38.8 46.7 50.5 24.42 26.14 1 Day 4 Days 7 Days 28 Days 90 Days 28 Days 90 Days b15r100 17.5 31.5 33.9 41.1 42.1 24.15 25.58 T5r50 20 34.9 41.4 49.1 54 27.39 30.13 T5r50 20 34.9 41.4 49.1 54 27.39 30.13 T5r100 18.5 36.5 44.7 47.4 25.69 26.15 T10r50 19.2 37.6 42.5 50.7 52.8 26.72 28.87 T5r100 18.5 36.5 44.7 47.4 25.69 26.15 T10r100 14.4 28.6 34.4 39.9 42 24.55 25.55 T10r50 19.2 37.6 42.5 50.7 52.8 26.72 28.87 r0 21.3 42.1 48.2 51.3 30.45 33.86 T10r100 14.4 28.6 34.4 39.9 42 24.55 25.55 r50 20 40.2 44.1 50.3 53.6 29.58 30.35 r100 18 40.1 43 49.2 51.3 26.78 27.86 r0 21.3 42.1 48.2 51.3 30.45 33.86 a b c , , measured at the age of 5 days, 2 days and 3 days, respectively. r50 20 40.2 44.1 50.3 53.6 29.58 30.35 r100 18 40.1 43 49.2 51.3 26.78 27.86 a b c , , measured at the age of 5 days, 2 days and 3 days, respectively. (2) Construction of the ANN models As shown in Table 3, the experiment had a total of 145 and 92 results for compressive strength (2) Construction of the ANN models and elastic modulus, respectively, which were divided randomly into 3 groups used to construct As shown in Table 3, the experiment had a total of 145 and 92 results for compressive strength the ANN models. The 3 groups were used as the training, testing and validation sets, respectively. and elastic modulus, respectively, which were divided randomly into 3 groups used to construct the The testing and validation sets were intended to establish the model with the generalization ability. ANN models. The 3 groups were used as the training, testing and validation sets, respectively. The After training, the optimal models for simulating the compressive strength (ANN -f ) and elastic 14 c testing and validation sets were intended to establish the model with the generalization ability. After modulus (ANN -E ) using all 14 variables were constructed (Figure 4), and the network architecture training, the optimal models for simulating the compressive strength (ANN14-fc) and elastic modulus and parameters selected were as follows, in line with the similar procedure previously established [15]. (ANN14-Ec) using all 14 variables were constructed (Figure 4), and the network architecture and parameters selected were as follows, in line with the similar procedure previously established [15]. Number of input layer units = 16 Number of hidden layers = 1 • Number of input layer units = 16 Number of hidden layer units = 40 • Number of hidden layers = 1 Number of output layer units = 1 • Number of hidden layer units = 40 • Momentum Number of ou rate tpu =t0.9 layer units = 1 • Learning Momentum ra rate =te = 0.9 0.01 • Learning rate = 0.01 Learning cycle = 10,000 • Learning cycle = 10,000 Figure 4. ANN model constructed for compressive strength or elastic modulus. Figure 4. ANN model constructed for compressive strength or elastic modulus. 3. Results and Discussion 3. Results and Discussion The performance of the constructed ANN models (ANN -f , ANN -E ) in predicting the c c 14 14 The performance of the constructed ANN models (ANN14-fc, ANN14-Ec) in predicting the compressive strength and elastic modulus of RAC with all 14 variables and compared to the models compressive strength and elastic modulus of RAC with all 14 variables and compared to the models (ANN -f , ANN -E ) using only the “certainties” as input variables is shown in Table 4 and Figure 5. c c 6 6 (ANN6-fc, ANN6-Ec) using only the “certainties” as input variables is shown in Table 4 and Figure 5. Appl. Sci. 2018, 8, x FOR PEER REVIEW 10 of 15 Appl. Sci. 2018, 8, 2171 10 of 14 Table 4. Performance of ANN models. MAPE: the mean absolute percentage error; RMS: root-mean- Table 4. Performance of ANN models. MAPE: the mean absolute percentage error; RMS: root-mean- squared error. squared error. 2 2 Sets Model R RMS MAPE (%) Model R RMS MAPE (%) 2 2 Sets Model RMS MAPE (%) Model RMS MAPE (%) R R Training 0.9984 2.067 3.531 0.9999 0.2825 0.73 Training 0.9984 2.067 3.531 0.9999 0.2825 0.73 Testing 0 ANN14-fc .9952 3.445 5.859 ANN14-Ec 0.9965 1.6986 4.72 Testing ANN -f 0.9952 3.445 5.859 ANN -E 0.9965 1.6986 4.72 14 14 c Validation 0.9949 3.562 6.032 0.9968 1.563 4.399 Validation 0.9949 3.562 6.032 0.9968 1.563 4.399 Training 0.997 2.764 4.743 0.9941 0.9558 2.641 Training 0.997 2.764 4.743 0.9941 0.9558 2.641 Testing ANN -f 0.987 5.234 8.67 ANN -E 0.9931 2.3066 6.437 Testing 0 ANN 6 c 6-fc .987 5.234 8.67 ANN 66-E c c 0.9931 2.3066 6.437 Validation 0.992 4.41 7.557 0.9913 2.5234 7.264 Validation 0.992 4.41 7.557 0.9913 2.5234 7.264 Figure 5. Figure 5. Perfo Performance rmance of the ANN mode of the ANN models ls constructed. constructed. MAP MAPE E: the mean : the mean absolute percentage error; absolute percentage error; RMS: root-mean-squared error. RMS: root-mean-squared error. The correlation coefficient R of the networks in modeling the compressive strength and The correlation coefficient R of the networks in modeling the compressive strength and elastic elastic modulus reached 0.9984 and 0.9999, respectively, indicating that the correlations between modulus reached 0.9984 and 0.9999, respectively, indicating that the correlations between the the predictions and the true results were very good. The R values of both models were all above 0.994 predictions and the true results were very good. The R values of both models were all above 0.994 in the testing and validation sets and these further proved that the constructed models, ANN -f and in the testing and validation sets and these further proved that the constructed models, ANN14-fc c and ANN -E , had not only good simulating abilities, but also good generalization capabilities. ANN14 14-Ecc , had not only good simulating abilities, but also good generalization capabilities. When only the mix proportions and the curing ages were used as the inputs of the networks, When only the mix proportions and the curing ages were used as the inputs of the networks, the the R values of ANN -f and ANN -E in the training sets were still up to 0.997 and 0.9941. However, R values of ANN6-fc and 6 c ANN6-Ec i6 n the trai c ning sets were still up to 0.997 and 0.9941. However, the the generalization performance (testing and validation sets) of both networks were significantly poorer, generalization performance (testing and validation sets) of both networks were significantly poorer, with the R values reduced to the range of 0.987–0.9931 and the predicted errors MAPE increased by with the R values reduced to the range of 0.987–0.9931 and the predicted errors MAPE increased by about 50% in both the validation and testing sets. This might explain why many established formulae about 50% in both the validation and testing sets. This might explain why many established formulae (based on regression analysis) could not be used for practical applications although they had good (based on regression analysis) could not be used for practical applications although they had good correlation coefficients. correlation coefficients. For compressive strength, Figure 6 shows that the predicted error of the networks (ANN -f ) using For compressive strength, Figure 6 shows that the predicted error of the networks 6(ANN c 6-fc) only “certainties” as inputs was about 8.11%, and the performance of the networks could be enhanced using only “certainties” as inputs was about 8.11%, and the performance of the networks could be with the addition of each aggregate characteristic to the inputs. It can be found that the predicted enhanced with the addition of each aggregate characteristic to the inputs. It can be found that the error of compressive strength was lower when the water absorption or masonry content of the coarse predicted error of compressive strength was lower when the water absorption or masonry content of aggregate were taken into consideration, which was almost close to the model (ANN -f ) with all the coarse aggregate were taken into consideration, which was almost close to the model ( 14 cANN14-fc) variables as inputs. with all variables as inputs. Appl. Sci. 2018, 8, 2171 11 of 14 Appl. Sci. 2018, 8, x FOR PEER REVIEW 11 of 15 Figure 6. Influence of each uncertainty on the properties of RAC relative to models (ANN ) with only Figure 6. Influence of each uncertainty on the properties of RAC relative to models (ANN6) with only “certainties” as inputs—Stage a. “certainties” as inputs—Stage a. As shown in Table 5, the performance of the networks (ANN ) with the combinations of two As shown in Table 5, the performance of the networks (ANN8) with the combinations of two aggregate characteristics added as inputs of ANN -f was not necessarily better than those with only aggregate characteristics added as inputs of ANN6-fc was not necessarily better than those with only one aggregate characteristic added to the inputs. This was mainly due to the fact that the degrees one aggregate characteristic added to the inputs. This was mainly due to the fact that the degrees of of influence related to these aggregate characteristics were inconsistent, which may have misled influence related to these aggregate characteristics were inconsistent, which may have misled the the correlation of the inputs and outputs. However, the results demonstrated that the use of seven correlation of the inputs and outputs. However, the results demonstrated that the use of seven combinations (italics) of aggregate characteristics as inputs to ANN -f could improve the predicted combinations (italics) of aggregate characteristics as inputs to ANN6-fc could improve the predicted capability of the networks; these combinations were SG and W , SG and TFV, W and , W and SSD a SSD a a capability of the networks; these combinations were SGSSD and Wa, SGSSD and TFV, Wa and δ, Wa and TFV, FM and TFV, m and , and m and M . TFV, FM and TFV, m and δ, and m and Mc. Table 5. The errors of networks for compressive strength with different input variables—Stage b (%). Table 5. The errors of networks for compressive strength with different input variables—Stage b (%). Factors SG W FM M m TFV ACV SSD a c Factors SGSSD Wa FM Mc δ m TFV ACV SG 6.44 5.94 6.95 7.12 6.8 7.63 6.11 6.54 SGSSD SSD 6.44 5.94 6.95 7.12 6.8 7.63 6.11 6.54 W 6.03 6.6 6.99 5.76 6.89 5.92 6.55 Wa 6.03 6.6 6.99 5.76 6.89 5.92 6.55 FM 7.36 7.34 7.48 6.91 6.55 8.02 FM 7.36 7.34 7.48 6.91 6.55 8.02 M 7.7 5.84 5.99 6.99 7.25 Mc 7.7 5.84 5.99 6.99 7.25 7.07 6.88 8.09 7.23 m 6.16 8.32 6.64 δ 7.07 6.88 8.09 7.23 TFV 6.94 6.87 m 6.16 8.32 6.64 ACV 6.42 TFV 6.94 6.87 For Tables 5–8, each figure represents the mean absolute percentage error (MAPE) value of the networks with ACV 6.42 “certainties” and the uncertain factors indicated in the 1st row and 1st column as inputs; the bold figures represent For Tables 5–8 the MAPE value , ea of the ch figure r networks with epresents “certainties” the mean absolute and the uncertain percentage er factors indicated ror ( either MAPE in the ) va 1st lure ow ofor th 1st e column as inputs; the underlined figures are MAPE values lower than those of the corresponding bold letters. networks with “certainties” and the uncertain factors indicated in the 1st row and 1st column as inputs; the bold figures represent the MAPE value of the networks with “certainties” and the Then, these combinations of two characteristics were used to examine whether they could form uncertain factors indicated either in the 1st row or 1st column as inputs; the underlined figures are newMAPE combinations values lower than those of th of three or four characteristics e corresponding that boldcould letters. further improve the prediction of the networks. The results listed in Table 6 show that the error of networks could be reduced to 5.43–5.91 Then, these combinations of two characteristics were used to examine whether they could form when the following combinations of aggregate characteristics, together with “certainties”, were adopted new combinations of three or four characteristics that could further improve the prediction of the as the inputs of networks: SG + W + , SG + m + TFV + M , SG + W + TFV and FM + m + SSD a SSD c SSD a networks. The results listed in Table 6 show that the error of networks could be reduced to 5.43–5.91 TFV + M . Moreover, the further combinations of these factors was no longer useful to reduce the error when the following combinations of aggregate characteristics, together with “certainties”, were of prediction of the networks (Table 7). adopted as the inputs of networks: SGSSD + Wa + δ, SGSSD + m + TFV + Mc, SGSSD + Wa + TFV and FM + m + TFV + Mc. Moreover, the further combinations of these factors was no longer useful to reduce the error of prediction of the networks (Table 7). Appl. Sci. 2018, 8, 2171 12 of 14 Table 6. The errors of networks for compressive strength with different input variables—Stage c (%). Factors SG + W SG + TFV W + W + TFV FM + TFV m + m + M a a a c SSD SSD SG + W 5.94 5.61 5.43 5.61 6.26 6.93 6.55 SSD SG + TFV 6.11 6.4 5.61 6.67 6.85 5.53 SSD W + 5.76 5.81 6.33 6.52 6.16 W + TFV 5.92 5.96 5.96 7.87 FM + TFV 6.55 6.8 5.91 m + 5.84 6.95 m + M 5.99 Table 7. The errors of networks for compressive strength with different input variables—Stage d (%). Factors SG + W + TFV SG + W + SG + m + TFV + M FM + m + TFV + M SSD a SSD a SSD c C SG + W + TFV 5.61 5.91 5.93 6.07 SSD SG + W + 5.43 5.94 6.28 SSD a SG + m + TFV + M 5.53 6.19 SSD c FM + m + TFV + M 5.91 To sum up, the addition of any one of the eight aggregate characteristics to ANN -f could help 6 c achieve a better prediction of the compressive strength of RAC. When these characteristics were added to the input variables of ANN -f alone, water absorption contributed to the largest reduction 6 c in the error of networks, from about 8.11% to only 6.03%. The use of some combinations of these eight characteristics could further decrease the error of networks, even lower than that of ANN -f . 14 c The network error was only 5.43% when a combination of SG , W , , and the “certainties” (mix SSD a proportions and curing ages) were used as the input variables. The case was slightly different for the elastic modulus. As shown in Figure 5, the error of the networks (ANN -E ) with only the mix proportions and the curing ages as inputs was about 6.73%. 6 c When each one of the eight aggregate characteristics was added to the input variables alone, the results showed that three characteristics (viz mortar content, aggregate crushing value and 10% fines value) could not improve the prediction, while the other five characteristics could help to optimize the model; among the eight aggregate characteristics, the SG and W played the most significant influence, SSD being capable of reducing the error to about 4.84% and 4.83%, respectively. However, only the combination of SG and W could further decrease the network error to SSD about 3.89%, as shown in Table 8. Therefore, in this study the best combination of parameters for modeling the elastic modulus of RAC was mix proportions, curing ages, and the specific gravity and water absorption values of the RA. Table 8. The errors of networks for elastic modulus with different input variables—Stage b (%). Factors M FM SG W c a SSD M 6.43 6.93 6.76 5.5 5.15 FM 6.35 6.98 5.01 4.94 5.58 5.76 5.52 SG 4.84 3.89 SSD W 4.83 4. Conclusions The purpose of this paper was to analyze the significance of each aggregate characteristic and determine the best combinations of factors which further influence the compressive strength and elastic modulus of RAC using the ANN model. The ANN model was trained and built on the basis of a series of experimental results including 46 concrete mixes. The research took eight factors into consideration as the inputs of the ANN model. The results are as follows. Appl. Sci. 2018, 8, 2171 13 of 14 (1) The predicted results of RAC prepared with different sources of RAs were not satisfactory using the ANN models (ANN -f and ANN -E ), although the learning abilities of these models were c c 6 6 still good. This was because these ANN models only adopted the mix proportions and curing age as the input variables, without considering the aggregate characteristics of RA, which were quite different from the natural aggregate. (2) The water absorption of RA played a most important role in affecting the compressive strength of RAC, the addition of which could reduce the error of ANN -f from 8.11% to 6.03%. 6 c The combination of specific gravity, water absorption and impurity content could further decrease the error to only about 5.43%. (3) As regards elastic modulus, characteristics like mortar content, aggregate crushing value and 10% fines value were proved to be not important in affecting the prediction. In addition to the mix proportions and curing ages, water absorption and specific gravity were the most significant aggregate characteristics. The addition of each of them as networks inputs could decrease the error to less than 4.85%, and the network error could even be reduced to only about 3.89% when the inputs were a combination of mix proportions, curing time, specific gravity and water absorption of the coarse aggregate. Author Contributions: Funding acquisition, C.-S.P. and Y.L.; Investigation, S.H. and J.X.; Methodology, Z.D. and C.-S.P.; Software, Y.L.; Writing—original draft, Z.D. Funding: This research was funded by the National Natural Science Foundation of China (grant number 51708419) and Shanghai Pujiang Talent Fund (grant number 17PJ1409500). Acknowledgments: The authors wish to acknowledge the financial support of the Hong Kong Polytechnic University and Sun Hung Kai Properties Ltd. Conflicts of Interest: The authors declare no conflict of interest. References 1. Kurda, R.; Silvestre, J.D.; Brito, J.D. Life cycle assessment of concrete made with high volume of recycled concrete aggregates and fly ash. 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