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Prediction of compressive strength of concrete containing construction and demolition waste using artificial neural networks
Construction and Building Materials 38 (2013) 717–722
Contents lists available at SciVerse ScienceDirect
Construction and Building Materials journal homepage: www.elsevier.com/locate/conbuildmat
Prediction of compressive strength of concrete containing construction and demolition waste using artificial neural networks Adriana Trocoli Abdon Dantas, Mônica Batista Leite, Koji de Jesus Nagahama ⇑ Department of Technology, State University of Feira de Santana, 44.036-900 Bahia, Brazil
h i g h l i g h t s " The concrete uses aggregates from construction and demolition waste. " The ANN was used to construct an equation for predicting the compressive strength. " The compressive strength is predicted at 3, 7, 28 and 91 days. " The results show the potential of using ANN for predicting the compressive strength.
a r t i c l e
i n f o
Article history: Received 6 February 2012 Received in revised form 3 September 2012 Accepted 23 September 2012 Available online 24 October 2012 Keywords: Recycled concrete Compressive strength Artificial neural networks
a b s t r a c t In this study Artificial Neural Networks (ANNs) models were developed for predicting the compressive strength, at the age of 3, 7, 28 and 91 days, of concretes containing Construction and Demolition Waste (CDW). The experimental results used to construct the models were gathered from literature. A total of 1178 data was used for modeling ANN, 77.76% in the training phase, and 22.24% in the testing phase. To construct the model, 17 input parameters were used to achieve one output parameter, referred to as the compressive strength of concrete containing CDW. The results obtained in both, the training and testing phases strongly show the potential use of ANN to predict 3, 7, 28 and 91 days compressive strength of concretes containing CDW. Ó 2012 Elsevier Ltd. All rights reserved.
1. Introduction Currently, there is an environmental concern in relation to the scarcity of natural resources, and an emerging tendency to reduce this impact. The use of construction and demolition waste (CDW), as replacement of natural resources, can decrease the extraction of natural materials and thus preserve the environment. The use of CDW in the production of concrete for building and infrastructure construction and other engineering works is a way of recycling this material. This waste represents a significant percentage of the solid waste generated in urban areas and its destination must be properly determined, according to Conama Resolution 307 (Brazilian Law) [1]. Several researches have been developed with the aim of studying the influence of CDW on concrete properties such as compressive strength [2–6]. However, recycled aggregates have a very heterogeneous composition, since they are made of mortar,
⇑ Corresponding author. Tel.: +55 75 31618310; fax: +55 75 31618056. E-mail addresses: [email protected] (A.T.A. Dantas), mleite.uefs@gmail. com (M. Batista Leite), [email protected] (K. de Jesus Nagahama). 0950-0618/$ - see front matter Ó 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.conbuildmat.2012.09.026
concrete, ceramic brick and blocks, natural stone and other materials. According to Lima [7], the CDW’s variability represents a limitation to its use in construction, because the composition varies for each region, and the same studies cannot be applied. In order to improve these studies, reducing the amount of material, testing, time and cost, models based on experimental data can predict with an acceptable error range, the influence of CDW aggregate in the concrete behavior. Some of these models are based on artificial neural networks (ANN), which is an artificial intelligence technique that can be applied to tasks where there is a database of a problem and the ANN model learns by example. According to Braga [8], modeling is performed through the use of input and output variables, without many restrictions on the amount of input. The ANN model is a powerful tool that gives viable solutions to problems which are difficult to solve by through conventional techniques such as multiple regression models, not invalidating these existing techniques [9]. Some studies have been published, showing that ANN can model complex and nonlinear relationships between parameters affecting the compressive strength of concrete [10–17], the compressive strength of high strength concrete [18], the compressive strength
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of concrete containing fly ash and/or silica [19–22], the compressive strength of concrete containing granulated blast furnace slag [23], and the compressive strength of high performance concrete [24]. As Snell, apud Hong-Guang and Ji-Zong [10], conventional methods for predicting the compressive strength of concrete are mainly based on statistical analysis, through which the linear and nonlinear regression equations are built for forecasting. However, the choice of an appropriate regression equation involves technique and experience, besides not being a simple task. The purpose of this study is to evaluate the potential of artificial neural networks to concatenate a large amount of experimental data obtained from literature and predict the compressive strength of concrete containing CDW. 2. Artificial neural networks
yk ¼ f ðuk þ bk Þ ¼ tgh½a ðuk þ bk Þ
– A signal xm in a synapse’s input m connected to neuron k is multiplied by synaptic weights wkm. – An adder to sum the inputs, weighted by the respective neuron’s synapses, in which the transactions constitute a linear combiner. – An activation function f(), to restrict the amplitude of the output of a neuron. The range of normalized output amplitude can be [0, 1] or alternatively [1, 1]. – Bias, applied externally, represented by bk, whose function is to increase or decrease the influence of the activation function. Fig. 1 illustrates how information is processed through a single neuron. Mathematically, a neuron k can be described by the following equation:
ð1Þ
and
ð3Þ
where a is the constant used to control the slope of the semi-linear curve. The hyperbolic tangent function represented by Eq. (3) adjusts results on the interval [1, 1]. There is also a linear function, which, according to Nascimento Jr. and Yoneyama [27], is the simplest computational unit, where the bias can be interpreted as another weight coming from a unit whose output is always 1, represented by the following equation:
yk ¼ f ðuk þ bk Þ ¼ a ðuk þ bk Þ
The study of artificial neural networks was inspired on the study of biological neural networks, and the ANN model resulted in a powerful tool for applications in data mining [20]. Artificial neural networks are parallel and distributed systems, composed of simple processing units, the artificial neurons, which calculate specific mathematical functions, similar to the structure of the human brain, allowing a performance superior to that of conventional models [8]. According to Haykin [25], in an artificial neural network, the neuron is the unit of information processing, which consists of:
uk ¼ Rwkm xm
According to Topçu [20], the activation function is a function that processes input obtained with the sum function and determines the output of the neuron. In general, in multilayer models, the hyperbolic tangent function is the most used activation function. Using this, the output neuron is calculated with the aid of Eq. (3).
ð4Þ
The network architecture and the information flow are defined in the modeling of ANN. Neural networks might be single layer or multilayer [16]. ANN architecture presents an input layer, showing or not hidden layers, and an output layer. Regarding the information flow, it is known that the network structure corresponds to a feed forward network, i.e. outputs depend only on current inputs [8]. The neural network model that uses multilayer architecture and presents feed forward information flow is one of the neural network models most commonly used. Its application might be extended to almost all areas [10,28]. The neural network has two processing stages: training and testing, which represent very different times of operation and are applied at different moments of the analyses [9]. A modification of the weights is obtained using an appropriate method of training [28]. The most popular methods of training are supervised methods, which use, as an algorithm, the delta rule and its generalization to multilayer networks, which is the back propagation algorithm [8]. The back propagation algorithm is a gradient descent technique to minimize the error for a specific training pattern, through adjustments of the weights by a small amount at a time [18,19,22,28]. The weights before training are random and have no meaning, but after training might contain significant information [28]. They represent the degree of influence that each input variable shows with respect to the output variable. The testing process is the way the network answers to an input without changes in the structure [9]. 3. Neural network model
yk ¼ f ðuk þ bk Þ
ð2Þ
where x1, x2, . . . xm are inputs; wk1, wk2, . . . wkm are synaptic weights of euron k; uk is the linear combiner output due to inputs; bk is the bias; f(uk + bk) is the activation function; yk is the output.
Fig. 1. Schematic Artificial Neuron as described by Haykin [25].
The experimental data used in this work were collected in researches from Leite [2], Vieira [3], Cabral [4], Lovato [5] and Lima [6]. These studies were chosen because they present a complete set of information about materials properties, as well as, mix design parameters. At the beginning, 24 input variables were divided into four groups, as can be seen in Table 1. After performing a Principal Component Analysis (PCA), the input variables were chosen based on the cumulated explained variance. Then, 24 input variables were limited to 17. This procedure is known as dimensionality reduction of the ANN input vector. In this procedure, the amount of input variables can be limited to the amount of variables associated with a cumulated explained variance immediately above 70%. In this case, even when some variables explained small variance, they were considered in order to obtain approximately 98% of cumulated explained variance. It should be considered that some variables with small variance were chosen considering technical aspects not only statistical ones.
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A.T.A. Dantas et al. / Construction and Building Materials 38 (2013) 717–722 Table 1 Principal components analysis results.
a b
Initial input variables
Explained variancea (%)
Used? (y/n)
Explained varianceb (%)
Mix design parameters WCR – Water/Cement Ratio CEM – Cement Content CDM – Ratio of Dry Mortar CDA – Content of Total Dry Aggregate, by mass PFA – Substitution Ratio of Recycled Fine Aggregate (RFA) PCA – Substitution Ratio of Recycled Coarse Aggregate (RCA) ADD – Chemical Admixture Rate
0.040 0.000 1.557 0.000 1.023 2.619 0.093
y y y y y y y
0.0598 0.0002 1.4393 30.6284 4.0069 3.6048 0.1359
CDW composition PRM – Ratio of Recycled Mortar PRC – Ratio of Recycled Concrete PRR – Ratio of Recycled Red Ceramic POR – Ratio of Other Recycled Materials
3.905 8.263 4.764 3.070
y y y n
5.1749 2.3349 5.3804 –
Physical characteristics FNF – Fineness Modulus of Natural Fine Aggregate FRF – Fineness Modulus of RFA FNC – Fineness Modulus of Natural Coarse Aggregate FRC – Fineness Modulus of RCA SNF – Maximum Aggregate Size of Natural Fine Aggregate SRF – Maximum Aggregate Size of RFA SNC – Maximum Aggregate Size of Natural Coarse Aggregate SRC – Maximum Aggregate Size of RCA CRF – Compensation Rate of the water absorption rate of RFA CRC – Compensation Rate of the water absorption rate of RCA ARF – Water absorption rate of RFA ARC – Water absorption rate of RCA
12.855 0.000 33.656 0.000 0.002 0.000 5.263 0.000 0.248 0.010 21.491 0.604
y n y n y n y n n n y y
15.5248 – 0.5472 – 0.0022 – 8.9640 – – – 21.9109 0.0340
Age AGE – Age
0.489
y
0.2516
First principal components analysis results. Second principal components analysis results.
Statistical analysis was used as a tool for decision support. Considering only the statistical tool, it must be said that the vector of input ANN could be reduced to four variables (percentage of recycled concrete, fineness modulus of natural fine aggregate, fineness modulus of natural coarse aggregate and water absorption rate of recycled fine aggregate). But, the critique of the ‘‘physical model’’ resulted in a technical infeasibility. In this way, the PCA was performed twice. At first, it was used to support the choice of the variables to reduce the dimensionality of the input vector ANN. And, in the second time, it was used to confirm that the variables chosen, based on preliminary analysis, indeed explain some variance and must be used. Note that the variable ‘‘content of dry aggregate’’ explains a variance zero, at first PCA use. However, at second one, this variable explains a variance of approximately 31%. In concrete technology it is well established that compressive strengths vary with the content of total aggregate in relation to the content of cement, and the PCA was able to capture that. Moreover, Table 1 shows that fineness modulus of fine and coarse natural aggregate, ratio of recycled concrete and the absorption rate of fine recycled aggregate have great influence on the variance of compressive strength value (output). Type of recycled aggregate, water absorption ratio and substitution ratio of natural by recycled aggregate had also been reported as some variables influencing concrete behavior, as described by Etxeberria et al. [29], Eguchi et al. [30] and Poon et al. [31]. Thus, the 17 variables were kept and still separated into four groups: mix design parameters, CDW composition, physical characteristics of the materials and age. The limit values and units of input and output variables used in ANN to predict the compressive strength of concrete containing CDW are listed in Table 2. Furthermore, recycled concrete shows more variables than conventional concrete, e.g. variables related with composition of the CDW and substitution ratio of natural aggregate for recycled aggregate.
The neural network architecture chosen was a feed forward multilayer. The topology of the ANN is composed of 17 neurons in the input layer, one hidden layer and one neuron in the output referred to the value of the compressive strength of concrete containing CDW aggregates, as shown in Fig. 2. In the hidden layer, three neurons were used due to the minimum absolute percentage error values for training and testing sets. Hyperbolic tangent activation function was used in the hidden layer, while the linear function was used in the output layer. The neurons in adjacent layers were fully interconnected by weights. About 77.76% from 1178 data were used for training and 22.24% for testing. In the modeling of ANN, the back propagation learning algorithm was used, associated with the Levenberg–Marquardt training algorithm, which is the fastest algorithm for training neural networks of moderate size. Namely, this algorithm can use up a few hundred weights [26]. The training of the network was done through iterations until the total of 1000 times, calculating the errors to reach the estimated value of 108. Each ‘‘training stage’’ of the ANN was repeated 20 times, and the best result was selected. The network that showed the highest R2 is the one with the greatest accuracy. 4. Results and discussion All results, obtained from experimental studies [2–6] should be predicted using Eqs. (5)–(8). The experimental and predicted results using the training and testing ANN model, for 3, 7, 28 and 91 days FC, are shown in Figs. 4 and 3.
FC ¼
1122; 484 728; 641 100; 944 tan hðk1 Þ þ tanhðk2 Þ 6521 1109 139 113917 tan hðk3 Þ 1244
where kj is given by Eqs. (6)–(8).
ð5Þ
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Table 2 Limit values and units of input and output variables. Variables Input Mix design parameters
CDW composition
Physical characteristics
Age Output
k1 ¼
k2 ¼
Description
Limit values
Units
WCR – Water/Cement Ratio CEM – Cement Content CDM – Ratio of Dry Mortar CDA – Content of Total Dry Aggregate, by mass PFA – Substitution Ratio of Recycled Fine Aggregate (RFA) PCA – Substitution Ratio of Recycled Coarse Aggregate (RCA) ADD – Chemical Admixture Rate PRM – Ratio of Recycled Mortar PRC – Ratio of Recycled Concrete PRR – Ratio of Recycled Red Ceramic FNF – Fineness Modulus of Natural Fine Aggregate FNC – Fineness Modulus of Natural Coarse Aggregate SNF – Maximum Aggregate Size of Natural Fine Aggregate SNC – Maximum Aggregate Size of Natural Coarse Aggregate ARF – Water absorption rate of RFA ARC – Water absorption rate of RCA AGE – Age
0.4–0.8 205–511.44 47–62 3.24–9.57 0–100 0–100 0–3 0–100 0–100 0–100 2.17–3.49 5.43–7.00 2.4–4.8 9.5–19.00 4.13–21 4.3–15.62 3–91
– kg % – % % % % % % – – mm mm % % Days
FC – Compressive Strength of Concrete
6.5–57.35
MPa
44; 623 734 1661 2777 WCR þ PFA þ PCA þ PRM 16229 311807 521650 542650 3739 847 9311 23192 PRC þ PRR þ CDM CDA þ 514191 353226 131184 30229 15751 9828 14650 444145 FNF þ FNC SNF SNC 78723 3385 29971 1792 31903 821 1505 6325 CEM þ ADD ARF þ ARC 19395 625617 182309 135389 5468 1500961 AGE þ ð6Þ þ 79489 1200 83605 3723 1777 164 WCR þ PFA þ PCA PRM 24534 1594310 742531 49417 4589 176 13477 5720 þ PRC þ PRR þ CDM CDA 470952 195859 116102 13373 8599 31123 23486 288712 FNF þ FNC þ SNF SNC 32102 8698 59791 1509 28293 613 1205 9691 CEM þ ADD þ ARF þ ARC 22736 771309 272227 249301 14903 922873 þ AGE þ ð7Þ 444112 975
k3 ¼
45746 1538 24007 383 WCR þ PFA þ PCA PRM 14179 674459 9016811 217896 3571 4985 13951 12475 PRC PRR þ CDM CDA þ 376052 6480856 123812 23306 14441 67420 360853 320658 FNF þ FNC SNF SNC 57157 17443 1263233 1453 45445 1404 1274 8397 CEM þ ADD ARF þ ARC 32316 2006189 195693 225865 15189 1598196 AGE þ ð8Þ þ 327880 1453
Several studies [10–24] have used artificial intelligence techniques for predicting concrete properties successfully. However, none of them presents an equation that can be used in practice. In all cases, it is necessary to use specific software to run the ANN and to estimate the material properties. In this work, as the equation is showed above it can be used with simple computer tools, as a spreadsheet (ExcelÒ, e.g.), considering the ranges of the variables showed in Table 2, to calculate the concrete compressive strength. Fig. 3 shows the network performance for the training and testing data, respectively. In this study, the statistical parameter R2
Fig. 2. Architecture of the ANN used in this study.
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Fig. 3. Experimental versus predicted results of the ANN model: (a) training and (b) testing.
Fig. 4. Histogram of the absolute errors achieved with target and output values.
(absolute fraction variance) for the training and testing of the ANN model was obtained using the following equation:
R2 ¼ 1
P
K ðt k
P
2
yk Þ
2 K yk
ð9Þ
where t is the target value and y is the output value. As shown in Fig. 3, the values obtained through the training and testing of ANN model are very close for experimental results, indicating a strong correlation between the input and output parameters of the ANN model. The statistical value of R2 found from ANN training and testings are 0.928 and 0.971, respectively. The absolute error was calculated from the testing data using Eq. (10). Fig. 4 shows the histogram of the absolute error percentage rate of FC values predicted by testing in the ANN model. The max and min absolute errors found were 83.09% and 0.02%, respectively.
y t k 100 AE ¼ k tk where yk is the output value and tk is the target value.
ð10Þ
The results in Fig. 4 show that approximately 60% of the data have errors less than 7.5% and also that approximately 95% of the data have errors less than 20%. This is another indication of the high correlation between the results obtained by ANN and the experimental results. All statistical values prove that the proposed the ANN model is suitable to predict the FC values very close to the experimental results. 5. Conclusions This study shows an ANN model (Eq. (5)), which allows the prediction of compressive strength of recycled concrete, at different ages of hydration, with high level of confidence. Thus, using this prediction equation obtained by the ANN will not be necessary to produce and evaluate large amount of concrete samples in the lab. This makes the task to determine the mechanical behavior of the recycled concrete much easier. To achieve this it is just necessary to know the physical characteristics of aggregates, the composition of the CDW and to establish the minimum mixture design parameters (content of mortar, cement content, aggregate content
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and w/c ratio), within the ranges presented in this paper. Then, using a spreadsheet, as ExcelÒ e.g., it is simple to achieve the concrete strength result. In this study, ANN analysis indicates a good correlation between the input parameters and the response variable, which is 3, 7, 28 and 91 days compressive strength of concrete containing CDW. The statistical parameters R2, 0.928 and 0.971, for ANN training and testing, respectively, and the frequency of results with errors less than 7.5% (60%) and greater than 20% (5%), for ANN testing, demonstrate that the output values are very close to the experimental values. The Principal Component Analysis allowed establishing that ratio of recycled concrete and the absorption rate of fine recycled aggregate, and content of dry aggregate and finesses modulus of aggregates (fine and coarse) are the main variables influencing the variance of the compressive strength (output). It was concluded that the ANN model used indicates good accuracy of the prediction for the property of 3, 7, 28 and 91 days compressive strength of concrete containing CDW, considering the experimental data obtained by Leite [2], Vieira [3], Cabral [4], Lovato [5] and Lima [6] and the limit values used in this study.
Acknowledgment This research was funded by Grant No. PE170/2008 from CAPES and the scholarship funded by FAPESB.
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[9] Oliveira Junior HA, Caldeira AM, Machado MAS, Souza RC, Tanscheit R. Computational Intelligence Applied to the Administrative, Economics and Engineering in Matlab. New York: Thomson Learning; 2007. [10] Hong-Guang N, Ji-Zong W. Prediction of compressive strength of concrete by neural networks. Cem Concr Res 2000;30:1245–50. [11] Fazel Zarandi MH, Turksen IB, Sobhani J, Ramezanianpour AA. Fuzzy polynomial neural networks for approximation of the compressive strength of concrete. Appl Soft Computing 2008;8:488–98. [12] Lee JJ, Kim D, Chang SK, Nocete CFM. An improved application technique of the adaptive probabilistic neural network for predicting concrete strength. Comput Mater Sci 2009;44:988–98. [13] Sarıdemir M, Topçu IB, Ozcan F, Severcan MH. Prediction of long-term effects of GGBFS on compressive strength of concrete by artificial neural networks and fuzzy logic. Constr Build Mater 2009;23:1279–86. [14] Naderpour H, Kheyroddin A, Amiri GG. Prediction of FRP-confined compressive strength of concrete using artificial neural networks. Compos Struct 2010;92:2817–29. [15] Madandoust R, Ghavidel R, Nariman-Zadeh N. Evolutionary design of generalized GMDH-type neural network for prediction of concrete compressive strength using UPV. Comput Mater Sci 2010;49:556–67. [16] Kewalramani MA, Gupta R. Concrete compressive strength prediction using ultrasonic pulse velocity through artificial neural networks. Autom Constr 2006;15:374–9. [17] Sobhani J, Najimi M, Pourkhorshidi AR, Parhizkar T. Prediction of the compressive strength of no-slump concrete: a comparative study of regression, neural network and ANFIS models. Constr Build Mater 2010;24:709–18. [18] Öztas A, Pala M, Özbay E, Kanca E, Çaglar N, Bhatti MA. Predicting the compressive strength and slump of high strength concrete using neural network. Constr Build Mater 2006;20:769–75. [19] Pala M, Özbay E, Öztas A, Yuce MI. Appraisal of long-term effects of fly ash and silica fume on compressive strength of concrete by neural networks. Constr Build Mater 2007;21:384–94. [20] Topçu IB, Sarıdemir M. Prediction of compressive strength of concrete containing fly ash using artificial neural networks and fuzzy logic. Comput Mater Sci 2008;41:305–11. [21] Özcan F, Atis CD, Karahan O, Uncuoglu E, Tanyildizi H. Comparison of artificial neural network and fuzzy logic models for prediction of long-term compressive strength of silica fume concrete. Adv Eng Softw 2009;40:856–63. [22] Saridemir M. Prediction of compressive strength of concretes containing metakaolin and silica fume by artificial neural networks. Adv Eng Softw 2009;40:350–5. [23] Bilim C, Atis CD, Tanyildizi H, Karahan O. Predicting the compressive strength of ground granulated blast furnace slag concrete using artificial neural network. Adv Eng Softw 2009;40:334–40. [24] Słonski M. A comparison of model selection methods for compressive strength prediction of high-performance concrete using neural networks. Comput Struct 2010;88:1248–53. [25] Haykin S. Neural networks: principles and practice. Porto Alegre: Ed Bookman; 2001 [in Portuguese]. [26] Demuth H, Beale M. Neural network toolbox for use with MATLAB. Natick: The Math Works Inc.; 2002. [27] Nascimento CL, Yoneyama T. Artificial intelligence in control and automation. São Paulo: Edgard Blücher LTDA and FAPESP; 2000 [in Portuguese]. [28] Mata J. Interpretation of concrete dam behaviour with artificial neural network and multiple linear regression models. Eng Struct 2011;33:903–10. [29] Etxeberria M, Vázquez E, Marí A, Barra M. Influence of amount of recycled coarse aggregates and production process on properties of recycled aggregate concrete. Cem Concr Res 2007;37:735–42. [30] Eguchi K, Teranishi K, Nakagome A, Kishimoto H, Shinozaki K, Narikawa M. Application of recycled coarse aggregate by mixture to concrete construction. Const Build Mater 2007;21:1542–51. [31] Poon C, Shui Z, Lam L, Fok H, Kou S. Influence of moisture states of natural and recycled aggregates on the slump and compressive strength of concrete. Cem Concr Res 2004;34:31–6.
Contents lists available at SciVerse ScienceDirect
Construction and Building Materials journal homepage: www.elsevier.com/locate/conbuildmat
Prediction of compressive strength of concrete containing construction and demolition waste using artificial neural networks Adriana Trocoli Abdon Dantas, Mônica Batista Leite, Koji de Jesus Nagahama ⇑ Department of Technology, State University of Feira de Santana, 44.036-900 Bahia, Brazil
h i g h l i g h t s " The concrete uses aggregates from construction and demolition waste. " The ANN was used to construct an equation for predicting the compressive strength. " The compressive strength is predicted at 3, 7, 28 and 91 days. " The results show the potential of using ANN for predicting the compressive strength.
a r t i c l e
i n f o
Article history: Received 6 February 2012 Received in revised form 3 September 2012 Accepted 23 September 2012 Available online 24 October 2012 Keywords: Recycled concrete Compressive strength Artificial neural networks
a b s t r a c t In this study Artificial Neural Networks (ANNs) models were developed for predicting the compressive strength, at the age of 3, 7, 28 and 91 days, of concretes containing Construction and Demolition Waste (CDW). The experimental results used to construct the models were gathered from literature. A total of 1178 data was used for modeling ANN, 77.76% in the training phase, and 22.24% in the testing phase. To construct the model, 17 input parameters were used to achieve one output parameter, referred to as the compressive strength of concrete containing CDW. The results obtained in both, the training and testing phases strongly show the potential use of ANN to predict 3, 7, 28 and 91 days compressive strength of concretes containing CDW. Ó 2012 Elsevier Ltd. All rights reserved.
1. Introduction Currently, there is an environmental concern in relation to the scarcity of natural resources, and an emerging tendency to reduce this impact. The use of construction and demolition waste (CDW), as replacement of natural resources, can decrease the extraction of natural materials and thus preserve the environment. The use of CDW in the production of concrete for building and infrastructure construction and other engineering works is a way of recycling this material. This waste represents a significant percentage of the solid waste generated in urban areas and its destination must be properly determined, according to Conama Resolution 307 (Brazilian Law) [1]. Several researches have been developed with the aim of studying the influence of CDW on concrete properties such as compressive strength [2–6]. However, recycled aggregates have a very heterogeneous composition, since they are made of mortar,
⇑ Corresponding author. Tel.: +55 75 31618310; fax: +55 75 31618056. E-mail addresses: [email protected] (A.T.A. Dantas), mleite.uefs@gmail. com (M. Batista Leite), [email protected] (K. de Jesus Nagahama). 0950-0618/$ - see front matter Ó 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.conbuildmat.2012.09.026
concrete, ceramic brick and blocks, natural stone and other materials. According to Lima [7], the CDW’s variability represents a limitation to its use in construction, because the composition varies for each region, and the same studies cannot be applied. In order to improve these studies, reducing the amount of material, testing, time and cost, models based on experimental data can predict with an acceptable error range, the influence of CDW aggregate in the concrete behavior. Some of these models are based on artificial neural networks (ANN), which is an artificial intelligence technique that can be applied to tasks where there is a database of a problem and the ANN model learns by example. According to Braga [8], modeling is performed through the use of input and output variables, without many restrictions on the amount of input. The ANN model is a powerful tool that gives viable solutions to problems which are difficult to solve by through conventional techniques such as multiple regression models, not invalidating these existing techniques [9]. Some studies have been published, showing that ANN can model complex and nonlinear relationships between parameters affecting the compressive strength of concrete [10–17], the compressive strength of high strength concrete [18], the compressive strength
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of concrete containing fly ash and/or silica [19–22], the compressive strength of concrete containing granulated blast furnace slag [23], and the compressive strength of high performance concrete [24]. As Snell, apud Hong-Guang and Ji-Zong [10], conventional methods for predicting the compressive strength of concrete are mainly based on statistical analysis, through which the linear and nonlinear regression equations are built for forecasting. However, the choice of an appropriate regression equation involves technique and experience, besides not being a simple task. The purpose of this study is to evaluate the potential of artificial neural networks to concatenate a large amount of experimental data obtained from literature and predict the compressive strength of concrete containing CDW. 2. Artificial neural networks
yk ¼ f ðuk þ bk Þ ¼ tgh½a ðuk þ bk Þ
– A signal xm in a synapse’s input m connected to neuron k is multiplied by synaptic weights wkm. – An adder to sum the inputs, weighted by the respective neuron’s synapses, in which the transactions constitute a linear combiner. – An activation function f(), to restrict the amplitude of the output of a neuron. The range of normalized output amplitude can be [0, 1] or alternatively [1, 1]. – Bias, applied externally, represented by bk, whose function is to increase or decrease the influence of the activation function. Fig. 1 illustrates how information is processed through a single neuron. Mathematically, a neuron k can be described by the following equation:
ð1Þ
and
ð3Þ
where a is the constant used to control the slope of the semi-linear curve. The hyperbolic tangent function represented by Eq. (3) adjusts results on the interval [1, 1]. There is also a linear function, which, according to Nascimento Jr. and Yoneyama [27], is the simplest computational unit, where the bias can be interpreted as another weight coming from a unit whose output is always 1, represented by the following equation:
yk ¼ f ðuk þ bk Þ ¼ a ðuk þ bk Þ
The study of artificial neural networks was inspired on the study of biological neural networks, and the ANN model resulted in a powerful tool for applications in data mining [20]. Artificial neural networks are parallel and distributed systems, composed of simple processing units, the artificial neurons, which calculate specific mathematical functions, similar to the structure of the human brain, allowing a performance superior to that of conventional models [8]. According to Haykin [25], in an artificial neural network, the neuron is the unit of information processing, which consists of:
uk ¼ Rwkm xm
According to Topçu [20], the activation function is a function that processes input obtained with the sum function and determines the output of the neuron. In general, in multilayer models, the hyperbolic tangent function is the most used activation function. Using this, the output neuron is calculated with the aid of Eq. (3).
ð4Þ
The network architecture and the information flow are defined in the modeling of ANN. Neural networks might be single layer or multilayer [16]. ANN architecture presents an input layer, showing or not hidden layers, and an output layer. Regarding the information flow, it is known that the network structure corresponds to a feed forward network, i.e. outputs depend only on current inputs [8]. The neural network model that uses multilayer architecture and presents feed forward information flow is one of the neural network models most commonly used. Its application might be extended to almost all areas [10,28]. The neural network has two processing stages: training and testing, which represent very different times of operation and are applied at different moments of the analyses [9]. A modification of the weights is obtained using an appropriate method of training [28]. The most popular methods of training are supervised methods, which use, as an algorithm, the delta rule and its generalization to multilayer networks, which is the back propagation algorithm [8]. The back propagation algorithm is a gradient descent technique to minimize the error for a specific training pattern, through adjustments of the weights by a small amount at a time [18,19,22,28]. The weights before training are random and have no meaning, but after training might contain significant information [28]. They represent the degree of influence that each input variable shows with respect to the output variable. The testing process is the way the network answers to an input without changes in the structure [9]. 3. Neural network model
yk ¼ f ðuk þ bk Þ
ð2Þ
where x1, x2, . . . xm are inputs; wk1, wk2, . . . wkm are synaptic weights of euron k; uk is the linear combiner output due to inputs; bk is the bias; f(uk + bk) is the activation function; yk is the output.
Fig. 1. Schematic Artificial Neuron as described by Haykin [25].
The experimental data used in this work were collected in researches from Leite [2], Vieira [3], Cabral [4], Lovato [5] and Lima [6]. These studies were chosen because they present a complete set of information about materials properties, as well as, mix design parameters. At the beginning, 24 input variables were divided into four groups, as can be seen in Table 1. After performing a Principal Component Analysis (PCA), the input variables were chosen based on the cumulated explained variance. Then, 24 input variables were limited to 17. This procedure is known as dimensionality reduction of the ANN input vector. In this procedure, the amount of input variables can be limited to the amount of variables associated with a cumulated explained variance immediately above 70%. In this case, even when some variables explained small variance, they were considered in order to obtain approximately 98% of cumulated explained variance. It should be considered that some variables with small variance were chosen considering technical aspects not only statistical ones.
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a b
Initial input variables
Explained variancea (%)
Used? (y/n)
Explained varianceb (%)
Mix design parameters WCR – Water/Cement Ratio CEM – Cement Content CDM – Ratio of Dry Mortar CDA – Content of Total Dry Aggregate, by mass PFA – Substitution Ratio of Recycled Fine Aggregate (RFA) PCA – Substitution Ratio of Recycled Coarse Aggregate (RCA) ADD – Chemical Admixture Rate
0.040 0.000 1.557 0.000 1.023 2.619 0.093
y y y y y y y
0.0598 0.0002 1.4393 30.6284 4.0069 3.6048 0.1359
CDW composition PRM – Ratio of Recycled Mortar PRC – Ratio of Recycled Concrete PRR – Ratio of Recycled Red Ceramic POR – Ratio of Other Recycled Materials
3.905 8.263 4.764 3.070
y y y n
5.1749 2.3349 5.3804 –
Physical characteristics FNF – Fineness Modulus of Natural Fine Aggregate FRF – Fineness Modulus of RFA FNC – Fineness Modulus of Natural Coarse Aggregate FRC – Fineness Modulus of RCA SNF – Maximum Aggregate Size of Natural Fine Aggregate SRF – Maximum Aggregate Size of RFA SNC – Maximum Aggregate Size of Natural Coarse Aggregate SRC – Maximum Aggregate Size of RCA CRF – Compensation Rate of the water absorption rate of RFA CRC – Compensation Rate of the water absorption rate of RCA ARF – Water absorption rate of RFA ARC – Water absorption rate of RCA
12.855 0.000 33.656 0.000 0.002 0.000 5.263 0.000 0.248 0.010 21.491 0.604
y n y n y n y n n n y y
15.5248 – 0.5472 – 0.0022 – 8.9640 – – – 21.9109 0.0340
Age AGE – Age
0.489
y
0.2516
First principal components analysis results. Second principal components analysis results.
Statistical analysis was used as a tool for decision support. Considering only the statistical tool, it must be said that the vector of input ANN could be reduced to four variables (percentage of recycled concrete, fineness modulus of natural fine aggregate, fineness modulus of natural coarse aggregate and water absorption rate of recycled fine aggregate). But, the critique of the ‘‘physical model’’ resulted in a technical infeasibility. In this way, the PCA was performed twice. At first, it was used to support the choice of the variables to reduce the dimensionality of the input vector ANN. And, in the second time, it was used to confirm that the variables chosen, based on preliminary analysis, indeed explain some variance and must be used. Note that the variable ‘‘content of dry aggregate’’ explains a variance zero, at first PCA use. However, at second one, this variable explains a variance of approximately 31%. In concrete technology it is well established that compressive strengths vary with the content of total aggregate in relation to the content of cement, and the PCA was able to capture that. Moreover, Table 1 shows that fineness modulus of fine and coarse natural aggregate, ratio of recycled concrete and the absorption rate of fine recycled aggregate have great influence on the variance of compressive strength value (output). Type of recycled aggregate, water absorption ratio and substitution ratio of natural by recycled aggregate had also been reported as some variables influencing concrete behavior, as described by Etxeberria et al. [29], Eguchi et al. [30] and Poon et al. [31]. Thus, the 17 variables were kept and still separated into four groups: mix design parameters, CDW composition, physical characteristics of the materials and age. The limit values and units of input and output variables used in ANN to predict the compressive strength of concrete containing CDW are listed in Table 2. Furthermore, recycled concrete shows more variables than conventional concrete, e.g. variables related with composition of the CDW and substitution ratio of natural aggregate for recycled aggregate.
The neural network architecture chosen was a feed forward multilayer. The topology of the ANN is composed of 17 neurons in the input layer, one hidden layer and one neuron in the output referred to the value of the compressive strength of concrete containing CDW aggregates, as shown in Fig. 2. In the hidden layer, three neurons were used due to the minimum absolute percentage error values for training and testing sets. Hyperbolic tangent activation function was used in the hidden layer, while the linear function was used in the output layer. The neurons in adjacent layers were fully interconnected by weights. About 77.76% from 1178 data were used for training and 22.24% for testing. In the modeling of ANN, the back propagation learning algorithm was used, associated with the Levenberg–Marquardt training algorithm, which is the fastest algorithm for training neural networks of moderate size. Namely, this algorithm can use up a few hundred weights [26]. The training of the network was done through iterations until the total of 1000 times, calculating the errors to reach the estimated value of 108. Each ‘‘training stage’’ of the ANN was repeated 20 times, and the best result was selected. The network that showed the highest R2 is the one with the greatest accuracy. 4. Results and discussion All results, obtained from experimental studies [2–6] should be predicted using Eqs. (5)–(8). The experimental and predicted results using the training and testing ANN model, for 3, 7, 28 and 91 days FC, are shown in Figs. 4 and 3.
FC ¼
1122; 484 728; 641 100; 944 tan hðk1 Þ þ tanhðk2 Þ 6521 1109 139 113917 tan hðk3 Þ 1244
where kj is given by Eqs. (6)–(8).
ð5Þ
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Table 2 Limit values and units of input and output variables. Variables Input Mix design parameters
CDW composition
Physical characteristics
Age Output
k1 ¼
k2 ¼
Description
Limit values
Units
WCR – Water/Cement Ratio CEM – Cement Content CDM – Ratio of Dry Mortar CDA – Content of Total Dry Aggregate, by mass PFA – Substitution Ratio of Recycled Fine Aggregate (RFA) PCA – Substitution Ratio of Recycled Coarse Aggregate (RCA) ADD – Chemical Admixture Rate PRM – Ratio of Recycled Mortar PRC – Ratio of Recycled Concrete PRR – Ratio of Recycled Red Ceramic FNF – Fineness Modulus of Natural Fine Aggregate FNC – Fineness Modulus of Natural Coarse Aggregate SNF – Maximum Aggregate Size of Natural Fine Aggregate SNC – Maximum Aggregate Size of Natural Coarse Aggregate ARF – Water absorption rate of RFA ARC – Water absorption rate of RCA AGE – Age
0.4–0.8 205–511.44 47–62 3.24–9.57 0–100 0–100 0–3 0–100 0–100 0–100 2.17–3.49 5.43–7.00 2.4–4.8 9.5–19.00 4.13–21 4.3–15.62 3–91
– kg % – % % % % % % – – mm mm % % Days
FC – Compressive Strength of Concrete
6.5–57.35
MPa
44; 623 734 1661 2777 WCR þ PFA þ PCA þ PRM 16229 311807 521650 542650 3739 847 9311 23192 PRC þ PRR þ CDM CDA þ 514191 353226 131184 30229 15751 9828 14650 444145 FNF þ FNC SNF SNC 78723 3385 29971 1792 31903 821 1505 6325 CEM þ ADD ARF þ ARC 19395 625617 182309 135389 5468 1500961 AGE þ ð6Þ þ 79489 1200 83605 3723 1777 164 WCR þ PFA þ PCA PRM 24534 1594310 742531 49417 4589 176 13477 5720 þ PRC þ PRR þ CDM CDA 470952 195859 116102 13373 8599 31123 23486 288712 FNF þ FNC þ SNF SNC 32102 8698 59791 1509 28293 613 1205 9691 CEM þ ADD þ ARF þ ARC 22736 771309 272227 249301 14903 922873 þ AGE þ ð7Þ 444112 975
k3 ¼
45746 1538 24007 383 WCR þ PFA þ PCA PRM 14179 674459 9016811 217896 3571 4985 13951 12475 PRC PRR þ CDM CDA þ 376052 6480856 123812 23306 14441 67420 360853 320658 FNF þ FNC SNF SNC 57157 17443 1263233 1453 45445 1404 1274 8397 CEM þ ADD ARF þ ARC 32316 2006189 195693 225865 15189 1598196 AGE þ ð8Þ þ 327880 1453
Several studies [10–24] have used artificial intelligence techniques for predicting concrete properties successfully. However, none of them presents an equation that can be used in practice. In all cases, it is necessary to use specific software to run the ANN and to estimate the material properties. In this work, as the equation is showed above it can be used with simple computer tools, as a spreadsheet (ExcelÒ, e.g.), considering the ranges of the variables showed in Table 2, to calculate the concrete compressive strength. Fig. 3 shows the network performance for the training and testing data, respectively. In this study, the statistical parameter R2
Fig. 2. Architecture of the ANN used in this study.
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Fig. 3. Experimental versus predicted results of the ANN model: (a) training and (b) testing.
Fig. 4. Histogram of the absolute errors achieved with target and output values.
(absolute fraction variance) for the training and testing of the ANN model was obtained using the following equation:
R2 ¼ 1
P
K ðt k
P
2
yk Þ
2 K yk
ð9Þ
where t is the target value and y is the output value. As shown in Fig. 3, the values obtained through the training and testing of ANN model are very close for experimental results, indicating a strong correlation between the input and output parameters of the ANN model. The statistical value of R2 found from ANN training and testings are 0.928 and 0.971, respectively. The absolute error was calculated from the testing data using Eq. (10). Fig. 4 shows the histogram of the absolute error percentage rate of FC values predicted by testing in the ANN model. The max and min absolute errors found were 83.09% and 0.02%, respectively.
y t k 100 AE ¼ k tk where yk is the output value and tk is the target value.
ð10Þ
The results in Fig. 4 show that approximately 60% of the data have errors less than 7.5% and also that approximately 95% of the data have errors less than 20%. This is another indication of the high correlation between the results obtained by ANN and the experimental results. All statistical values prove that the proposed the ANN model is suitable to predict the FC values very close to the experimental results. 5. Conclusions This study shows an ANN model (Eq. (5)), which allows the prediction of compressive strength of recycled concrete, at different ages of hydration, with high level of confidence. Thus, using this prediction equation obtained by the ANN will not be necessary to produce and evaluate large amount of concrete samples in the lab. This makes the task to determine the mechanical behavior of the recycled concrete much easier. To achieve this it is just necessary to know the physical characteristics of aggregates, the composition of the CDW and to establish the minimum mixture design parameters (content of mortar, cement content, aggregate content
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and w/c ratio), within the ranges presented in this paper. Then, using a spreadsheet, as ExcelÒ e.g., it is simple to achieve the concrete strength result. In this study, ANN analysis indicates a good correlation between the input parameters and the response variable, which is 3, 7, 28 and 91 days compressive strength of concrete containing CDW. The statistical parameters R2, 0.928 and 0.971, for ANN training and testing, respectively, and the frequency of results with errors less than 7.5% (60%) and greater than 20% (5%), for ANN testing, demonstrate that the output values are very close to the experimental values. The Principal Component Analysis allowed establishing that ratio of recycled concrete and the absorption rate of fine recycled aggregate, and content of dry aggregate and finesses modulus of aggregates (fine and coarse) are the main variables influencing the variance of the compressive strength (output). It was concluded that the ANN model used indicates good accuracy of the prediction for the property of 3, 7, 28 and 91 days compressive strength of concrete containing CDW, considering the experimental data obtained by Leite [2], Vieira [3], Cabral [4], Lovato [5] and Lima [6] and the limit values used in this study.
Acknowledgment This research was funded by Grant No. PE170/2008 from CAPES and the scholarship funded by FAPESB.
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