Development of articial intelligence based model for prediction of the compressive strebgth of self compacting concrete

Development of artificial intelligence-based model for prediction of the compressive strength of self-compacting concrete Hai-Bang Ly1,*, Binh Thai Pham1, Thuy-Anh Nguyen1, May Huu Nguyen 1,2,* Civil Engineering Department, University of Transport Technology, 54 Trieu Khuc, Thanh Xuan, Hanoi 100000, Vietnam Civil and Environmental Engineering Program, Graduate School of Advanced Science and Engineering, Hiroshima University, 1-4-1, Kagamiyama, Higashi-Hiroshima, Hiroshima 739-8527, Japan * Corresponding authors Email addresses: banglh@utt.edu.vn (H.-B Ly), binhpt@utt.edu.vn (B P Pham), anhnt@utt.edu.vn (T.-A Nguyen), and nguyenhuumay@hiroshima-u.ac.jp (M H Nguyen) Abstract: This study investigated the usability of an artificial neural network model (ANN) and the Grey Wolf Optimizer (GWO) method for predicting the compressive strength of selfcompacting concrete (SCC) The ANN-GWO model was developed using an experimental database of 115 samples obtained from various sources considering nine key factors of SCC The validation of the proposed model was evaluated via six indices including correlation coefficient, mean squared error, mean absolute error, IA, Slope, and mean Electronic copy available at: https://ssrn.com/abstract=3970696 absolute percentage error In addition, the importance of each parameter affecting the compressive strength of SCC was investigated utilizing partial dependence plots The findings demonstrated that the proposed ANN-GWO model is a reliable predictor of SCC compressive strength Following that, an examination of the parameters impacting the compressive strength of SCC was provided Keywords: Artificial Neural Network (ANN); Grey Wolf Optimizer (GWO) algorithm; compressive strength; self-compacting concrete; Introduction In the sphere of construction and building, concrete is the most often used material due to its ease of production, low cost, and valuable structure characteristics [1,2] It may be used in a broad variety of structures such as buildings, bridges, roads, and dams In line with the scientific growth path, the need for high-performance concrete is developing on a continuous basis As a result, several particular concrete types have been proposed with notable features in physicochemical properties and fresh state properties [3–5] The construction industry in Japan has quickly adopted the use of self-compacting concrete (SCC), a concrete type that can approach and fill the corners of formwork without the requirement for a compaction phase [6,7] Since then, various studies have been focused on developing the applications of this kind of concrete [8,9] On the one hand, SCC is listed as a kid of high-performance concrete, flexible deformability, good segregation resistance, and less blocking surrounding the reinforcement The exclusion of the compaction step Electronic copy available at: https://ssrn.com/abstract=3970696 brings several advantages of SCC, including economic efficiency (e.g., accelerated casting speed, saving labor, energy, and cost), enhances the working environment, and proposes a novel approach to automating the concrete construction [6,10–13] On the other hand, to achieve its desired flowable behaviors and proper mechanical properties, SCC requires a complex manipulation of several mixture variables [10,11] For instance, the water-to-binder (w/b) ratio of SCC is lower than conventional concrete, which is usually supported by special additives and superplasticizers to obtain the desired workability [14–17] Also, the grading of the aggregates, including aggregate shapes, texture, mineralogy, and strength, are always carefully considered to ensure workability and concrete strengths [18,19] These features lead to a significant challenge to establishing a universal correlation between the SCC properties and its constituent parameters [8,9,20] In other words, they bring out the need for predicting the properties of SCC in both the fresh and hardened stages The traditional applications of analytical models to represent the influence of each of these parameters on the properties of SCC, and then optimizing this model utilizing regression analysis However, so far, no explicit equations have been established due to these methods being less productive for nonlinearly separable data and complicated [21,22] In this regard, over the past few decades, various modeling methods utilizing artificial intelligence (AI) techniques have been adopted, such as artificial neural networks (ANNs), genetic algorithm (GA), and expert system (ES) for modeling a variety of current problems in the field of civil engineering [23–25] Among these, ANN is a more prevalent and efficient approach since its ability to classify to capture interrelationships among input3 Electronic copy available at: https://ssrn.com/abstract=3970696 output data pairs Numerous researchers have proposed their own ANN models for predicting the concrete strength [26–28] Regarding SCC, several models have also been presented for predicting the compressive strength [29–31] Yeh has soon demonstrated the opportunities of adapting ANN to predict high-performance concrete's compressive strength [29] The viability of utilizing ANNs to forecast the characteristics of SCC that uses fly ash as a cementitious substitute was examined by Douma et al [30] In these models, numerous experimental results were collected from the previous studies and employed for training and evaluating the proposed model Siddique et al presented the useability of neural network for predicting the compressive strength of SCC based on some input properties [31] Their proposed model could be easily extended to different input parameters of the experimental results, containing bottom ash as a replacement of sand Despite this, there has not been a detailed investigation into an improved ANN model for predicting the compressive strength of SCC The need for a novel, appropriate artificial neural network model to forecast the strength of SCC is developing on a continuous basis, in step with the advancement of scientific knowledge Therefore, in the present research, the artificial neural network (ANN) approach coupled with the Grey Wolf Optimizer (GWO) algorithm for forecasting the compressive strength of SCC is examined For this target, a variety of databases from different independent sources was gathered and employed to train and assess the proposed model The ANN model is established on the basis of two groups of input parameters, including concrete mixture components (i.e., the contents of binder, fine and coarse aggregates, superplasticizer and water-to-binder ratio), and the fresh properties SCC such as slump Electronic copy available at: https://ssrn.com/abstract=3970696 flow, V-funnel and L-box tests The output predicted parameter is the compressive strength of SCC The influence of the used parameters on the compressive strength of SCC was then discussed Materials and methods 2.1 Machine learning methods 2.1.1 Artificial Neural Network (ANN) Artificial Neural Network (ANN) is being widely used to solve prediction problems by drawing on biology's understanding of how the nervous system functions [32–35] ANN contains many simple processing elements, the so-called neurons An ANN is made up of nodes and linked parts that are divided into three layers: the input layer, hidden layer, and output layer Because of this training process, the neural network produces a model that can predict a target parameter from an input value that has been provided [36] In general, an ANN includes the minimum number of neurons that can simulate the training progress A linking between nodes carries a weighted representative of some earlier learning stage On the basis of the changes in weights, the input-output correlation could be established The system has to be educated to recreate the input-output correlation, which is called optimal weights [37,38] In an ANN model, the correlation between the input and output variables is determined by the collected data points Because they are very independent of one another, it is feasible to execute a large number of processes at the same time Electronic copy available at: https://ssrn.com/abstract=3970696 In order to take advantage of these benefits, most suggested models determine the number of hidden layers and the number of nodes by using a rule of thumb or by looking for random designs that meet specific criteria Furthermore, several appropriate numbers of parameters similar to learning speed and momentum are needed for chosen hidden layers and nodes [29–31,39] As a final point, all of the research stated that ANN is a reliable method for estimating the compressive strength of concrete 2.1.2 Grey Wolf Optimizer (GWO) algorithm Over two past decades, metaheuristic optimization algorithms have commonly been applied in most engineering fields For example, the Grey Wolf Optimizer (GWO) algorithm, one of the models developed by Mirjalili et al., was invented based on the leadership and hunting skills of the grey wolf pack's communal life [40] In order to simulate the order of management, each wolf pack comprises of four main forms of grey wolves, including alpha (α), beta (β), delta (δ), and omega (ω) In this structure, grey wolves follow strict rules which clearly divide their responsibilities Accordingly, α wolves work as the most responsible wolves, whereas ω wolves have the least responsibility (Fig 1) The following orders in the pack are β and δ wolves, respectively Each location of a grey wolf in the GWO algorithm might result in a viable solution to the optimization problem From a mathematical standpoint, the optimal option is chosen among α, β, and δ wolves with the closest proximity to the prey Every iteration follows the same method for the second and third-best answers The locations of all other wolves (i.e., ω ones) are meant to be determined by the positions of α, β and δ wolves On the basis of this Electronic copy available at: https://ssrn.com/abstract=3970696 technique, several works [41–43] focused on the reliability of the GWO model for estimating compressive strength Fig The categorized leadership structure of grey wolves 2.2 Database construction To realize the objective of the current study, the dataset containing 115 SCC compressive strength data is collected from 12 published experimental works [44–55] The ANN model is designed with nine inputs, such as the water/powder ratio (W/B), coarse aggregate (C), fly ash percentage (P), fine aggregate (F), slump flow (D), binder content (B), V-funnel test, superplasticizer dosage (SP), and L-box test In detail, the values of the W/B, P, F, D, B range between 0.26 -0.45, 590 - 935 kg, and 60%, 656 - 1038, 480 - 880 mm, and 370 733 kg, respectively The V-funnel test value ranges from 1.95 to 19.2, the superplasticizer dose is between 0.74 and 21.84, and the L-box test value is between 1.95 and 19.2 Besides, the compressive strength values are in the range of 10.2 to 86.8 MPa Specifically, statistical analysis of input and output variables is detailed in Table Electronic copy available at: https://ssrn.com/abstract=3970696 Table Statistical analysis of the inputs and output Unit Task Min Average Max St D1 Range - Input 0.26 0.37 0.45 16.5859 60 C kg Input 590 742.63 935 121.809 345 P % Input 28.7 60 0.06 0.19 F kg Input 656 852.8 1038 89.931 382 D mm Input 480 660.5 880 56.108 330 B kg Input 370 523.4 733 71.221 363 - Input 1.95 7.75 19.2 3.844 17.2 kg Input 0.74 21.84 4.669 21.1 - Input 0.6 0.86 0.0935 0.4 MPa Output 10.2 48.22 86.8 17.555 69.8 Variable W/B V-funnel test SP L-box Compressive strength 1St.D: standard deviation Electronic copy available at: https://ssrn.com/abstract=3970696 Herein, the proposed ANN model is trained using 70 percent of the 115 experiments, while 30 percent of the data are utilized to evaluate the model Thus, there are 81 samples for the training data set and 34 samples used to determine the projected performance of the ANN network All data are scaled within the range of [0,1] to reduce the numerical errors while conducting simulations, as recommended in Witten et al [56], using Equation (1):  scaled = 2(  -  ) - -  (1) where  and  are respectively the and max values of variables, and  is the corresponding variable's value to be scaled 2.3 Quality assessment criteria In this study, six statistical indicators were employed to assess the accuracy of the proposed model, which are the correlation coefficient (R), root mean square error (RMSE), index of agreement (IA), mean absolute error (MAE), slope, and mean absolute percentage error (MAPE) To measure the correlation between the actual and predicted values in regression problems, the R criterion, which is generally in the range [-1; 1], is extensively employed in the literature [57] The average degree of inaccuracy between actual and predicted outputs is measured by the root mean square error (RMSE), mean absolute error (MAE), and mean absolute percentage error (MAPE) [58] In terms of quantitative accuracy, the smaller the values of RMSE, MAE, and MAPE are, as well as the closer the absolute value of the Electronic copy available at: https://ssrn.com/abstract=3970696 correlation coefficient is to one, the more accurate the machine learning model is These values are represented by: N   Q j ,AV  Q j , PV  N j 1 (2) N  Q j , AV  Q j , PV N j 1 (3) RMSE  MAE  MAPE  N Q j , AV  Q j , PV  100% N j 1 Q j , AV (4)   Q j , AV  QAV  Q j , PV  QPV  N R j 1   Q j , AV  QAV    Q j , PV  QPV  N N j 1 (5) j 1 𝑁 ∑ (𝑄 𝐼𝐴 = ‒ 𝐴𝑉 ‒ 𝑄𝑃𝑉) 𝑗=1 (6) 𝑁 ∑ (| 𝑄 𝐴𝑉 ‒ | + |𝑄𝑃𝑉 ‒ | )2 𝑗=1 where: N is the number of databases; QAV and QAV are the actual values and the average real values; QPV and QPV are predicted values and average predicted values are calculated according to the forecasting model 2.4 Partial Dependence Plot 10 Electronic copy available at: https://ssrn.com/abstract=3970696 quantify the sensitivity of a model based on input variables In particular, an unique ninedimensional input space was created by including the probability density distributions of each variable Herein, input data was monitored at the following percentiles: 0, 10, 20, 30, 40, 50, 60, 70, 80, 90, and 100 One input parameter was chosen prior to running the model eleven times (i.e., from to 100% values) During running time, the other parameters were maintained at median values (i.e., 50%) Principally, the approach delivered the changes in the deviation of the output variable while changing the input parameters In the current study, deviation of the output, or the sensitivity rate  mn , for the nth input parameter is calculated as follows:  mn  Qmn  Qref (9) Qref where Qref is the reference output, and Qmn is the one utilizing nth input at the corresponding mth percentile In addition, the following formula was used to obtain the global percentage of sensitivity of each input: 11  n    mn (10) m 1 Table lists the output variable of the ANN-GWO model proposed for each percentile According to the PDP, the sensitivity of the input variables is shown in Fig It can be seen that the input parameters W/B (water to powder ratio), and C (coarse aggregate) were impacted on the predicted results significantly Next is the influence of the input parameter 26 Electronic copy available at: https://ssrn.com/abstract=3970696 P (Fly ash percentage) The remaining parameters were insignificantly impacted on ANNGWO outputs compared to W/B, C, P Table The sensitivity level  mn of inputs at different percentiles in defining the  50n of nth input is Variable Q0 Q10 Q20 Q30 Q40 Q60 Q70 Q80 Q90 Q100 W/B 58 45 37 24 17 -4 -11 -18 -20 -29 C -60 -40 -29 -20 -10 15 19 22 45 P 39 21 17 -5 -9 -16 -20 -25 F -9 -8 -5 -4 -2 23 D -23 -8 -4 -3 -1 16 B -8.5 -8 -4 -3 -1 18 V-funnel -8 -6 -5 -3 -2 17 SP -7 -5 -4 -3 -1 17 L-box 0.5 0.3 0.2 0.1 -0.01 -0.06 -0.07 -0.08 -0.1 27 Electronic copy available at: https://ssrn.com/abstract=3970696 Based on the sensitivity analysis, the percentage of W/B, C, and FA play a vital role in the input variable In other words, excluding one of these parameters from the input variables can change the accuracy of the proposed model Fig 10 depicts the overall percentage of sensitivity determined by adding all degrees of sensitivity for each input variable and calculating the result [64] Indeed, it is noticed that the ratio W/B and C are the two most important factors (accounting for 20% and 29%) affecting the compressive strength of SCC, followed by the input parameter P (accounting for 16.5%), the third most important input group includes five parameters, namely F, D, B, V-funnel and SP (whose sensitivity index ranges from 4% to 5.5%) Finally, the parameter that has the most negligible influence on the compressive strength of the SCC is L-box (only about 1%) 60 B P W/B 40 F C SP D L-box V-funnel 60 70 PDP 20 -20 -40 -60 10 20 30 40 50 80 90 100 Lowest (0%) to Highest (100%) Fig Evaluation of PDP for each input variable 28 Electronic copy available at: https://ssrn.com/abstract=3970696 Sensitivity index (%) 30 25 20 15 10 W/B C P F D B V-funnel SP L-box Input Fig 10 Sensitivity index ranking Conclusion and outlook In this research, an ANN model is used to estimate the compressive strength of selfcompacting concrete utilizing the GWO algorithm to find the optimum values of neurons' weights and biases Several input factors were taken into consideration, including the mix component, namely binder, fly ash, water to powder ratio, fine aggregate, coarse aggregate, superplasticizer, and the fresh properties of SCC, including slump flow, V-funnel test, and L-box test This model was constructed using an experimental database including 115 observations In addition, six statistical criteria were used to evaluate the relationship between forecast values generated by the ANN-GWO model and actual experimental values The findings indicate that ANN-GWO is a promising approach for predicting the compressive strength of self-compacted concrete, with R, IA, Slope, RMSE, MAE, and MAPE values of 0.951, 0.974, 0.904, 5.132, 4.112, and 9.293 for the training data set, 29 Electronic copy available at: https://ssrn.com/abstract=3970696 respectively Similarly, for the testing data set, the six criteria had values of 0.94, 0.969, 0.96, 5.515, 4.427, and 10.2, respectively Additionally, a sensitivity analysis based on PDP is conducted to determine the importance of all input factors The findings suggested that the critical factors are the water to powder ratio, the coarse aggregate content, and the fly ash content Within this study, it is shown that the ANN-GWO model can be employed as a robust and trustworthy solution for highly nonlinear issues, including the prediction of SCC's compressive strength with great accuracy Declaration of competing interest The authors declare no known competing financial interests or personal relationships that may appear to influence the work reported in this paper References [1] A.M Neville, M Adam, Properties of Concrete, England, 2011 [2] K Kovler, N Roussel, Properties of fresh and hardened concrete, Cement and Concrete Research 41 (2011) 775–792 https://doi.org/10.1016/j.cemconres.2011.03.009 [3] V Wiktor, H.M Jonkers, Quantification of crack-healing in novel bacteria-based selfhealing concrete, Cement and Concrete Composites 33 (2011) 763–770 https://doi.org/10.1016/j.cemconcomp.2011.03.012 30 Electronic copy available at: https://ssrn.com/abstract=3970696 [4] A Kan, R Demirboğa, A novel material for lightweight concrete production, Cement and Concrete Composites 31 (2009) 489–495 https://doi.org/10.1016/j.cemconcomp.2009.05.002 [5] Y.F Houst, P Bowen, F Perche, A Kauppi, P Borget, L Galmiche, J.-F Le Meins, F Lafuma, R.J Flatt, I Schober, P.F.G Banfill, D.S Swift, B.O Myrvold, B.G Petersen, K Reknes, Design and function of novel superplasticizers for more durable high performance concrete (superplast project), Cement and Concrete Research 38 (2008) 1197–1209 https://doi.org/10.1016/j.cemconres.2008.04.007 [6] H Okamura, Self-Compacting High-Performance Concrete, CI 19 (1997) 50–54 [7] K OZAWA, High-Performance Concrete based on the Durability Design of Concrete Structures, Proc of the Second East Asia-Pacific Conference on Structural Engineering and Construction, 1989 (1989) https://ci.nii.ac.jp/naid/10027017729/ (accessed April 11, 2020) [8] P.L Domone, A review of the hardened mechanical properties of self-compacting concrete, Cement and Concrete Composites 29 (2007) 1–12 https://doi.org/10.1016/j.cemconcomp.2006.07.010 [9] C Shi, Z Wu, K Lv, L Wu, A review on mixture design methods for selfcompacting concrete, Construction and Building Materials 84 (2015) 387–398 https://doi.org/10.1016/j.conbuildmat.2015.03.079 [10] H Okamura, M Ouchi, Self-Compacting Concrete, Journal of Advanced Concrete Technology (2003) 5–15 https://doi.org/10.3151/jact.1.5 31 Electronic copy available at: https://ssrn.com/abstract=3970696 [11] P.L Domone, Self-compacting concrete: An analysis of 11 years of case studies, Cement and Concrete Composites 28 (2006) 197–208 https://doi.org/10.1016/j.cemconcomp.2005.10.003 [12] H.J.H Brouwers, H.J Radix, Self-Compacting Concrete: Theoretical and experimental study, Cement and Concrete Research 35 (2005) 2116–2136 https://doi.org/10.1016/j.cemconres.2005.06.002 [13] C Shi, W Yanzhong, Mixture Proportioning and Properties of Self-Consolidating Lightweight Concrete Containing Glass Powder, ACI Materials Journal 102 (2005) 355 [14] V.G Haach, G Vasconcelos, P.B Lourenỗo, Influence of aggregates grading and water/cement ratio in workability and hardened properties of mortars, Construction and Building Materials 25 (2011) 2980–2987 https://doi.org/10.1016/j.conbuildmat.2010.11.011 [15] M Molero, I Segura, M.A.G Izquierdo, J.V Fuente, J.J Anaya, Sand/cement ratio evaluation on mortar using neural networks and ultrasonic transmission inspection, Ultrasonics 49 (2009) 231–237 https://doi.org/10.1016/j.ultras.2008.08.006 [16] H Okamura, K Ozawa, M Ouchi, Self-compacting concrete, Structural Concrete (2000) 3–17 https://doi.org/10.1680/stco.2000.1.1.3 [17] B Esmaeilkhanian, K.H Khayat, A Yahia, D Feys, Effects of mix design parameters and rheological properties on dynamic stability of self-consolidating concrete, Cement 32 Electronic copy available at: https://ssrn.com/abstract=3970696 and Concrete Composites 54 (2014) 21–28 https://doi.org/10.1016/j.cemconcomp.2014.03.001 [18] E Yaar, Y Erdoan, A Klỗ, Effect of limestone aggregate type and water–cement ratio on concrete strength, Materials Letters 58 (2004) 772–777 https://doi.org/10.1016/j.matlet.2003.06.004 [19] M Uysal, H Tanyildizi, Estimation of compressive strength of self compacting concrete containing polypropylene fiber and mineral additives exposed to high temperature using artificial neural network, Construction and Building Materials 27 (2012) 404–414 https://doi.org/10.1016/j.conbuildmat.2011.07.028 [20] D Sathyan, K.B Anand, A.J Prakash, B Premjith, Modeling the Fresh and Hardened Stage Properties of Self-Compacting Concrete using Random Kitchen Sink Algorithm, Int J Concr Struct Mater 12 (2018) 24 https://doi.org/10.1186/s40069018-0246-7 [21] M Sonebi, Applications of Statistical Models in Proportioning Medium-Strength SelfConsolidating Concrete, MJ 101 (2004) 339–346 https://doi.org/10.14359/13418 [22] M Sonebi, Medium strength self-compacting concrete containing fly ash: Modelling using factorial experimental plans, Cement and Concrete Research 34 (2004) 1199– 1208 https://doi.org/10.1016/j.cemconres.2003.12.022 [23] D.V Dao, H.-B Ly, S.H Trinh, T.-T Le, B.T Pham, Artificial Intelligence Approaches for Prediction of Compressive Strength of Geopolymer Concrete, Materials (Basel) 12 (2019) https://doi.org/10.3390/ma12060983 33 Electronic copy available at: https://ssrn.com/abstract=3970696 [24] H.-B Ly, B.T Pham, D.V Dao, V.M Le, L.M Le, T.-T Le, Improvement of ANFIS Model for Prediction of Compressive Strength of Manufactured Sand Concrete, Applied Sciences (2019) 3841 https://doi.org/10.3390/app9183841 [25] T.-H Le, H.-L Nguyen, B.T Pham, M.H Nguyen, C.-T Pham, N.-L Nguyen, T.-T Le, H.-B Ly, Artificial Intelligence-Based Model for the Prediction of Dynamic Modulus of Stone Mastic Asphalt, Applied Sciences 10 (2020) 5242 https://doi.org/10.3390/app10155242 [26] M Sebastiá, I Fernández Olmo, A Irabien, Neural network prediction of unconfined compressive strength of coal fly ash–cement mixtures, Cement and Concrete Research 33 (2003) 1137–1146 https://doi.org/10.1016/S0008-8846(03)00019-X [27] S.-C Lee, Prediction of concrete strength using artificial neural networks, Engineering Structures 25 (2003) 849–857 https://doi.org/10.1016/S0141-0296(03)00004-X [28] H.-B Ly, M.H Nguyen, B.T Pham, Metaheuristic optimization of Levenberg– Marquardt-based artificial neural network using particle swarm optimization for prediction of foamed concrete compressive strength, Neural Comput & Applic (2021) https://doi.org/10.1007/s00521-021-06321-y [29] I.-C Yeh, Modeling of strength of high-performance concrete using artificial neural networks, Cement and Concrete Research 28 (1998) 1797–1808 https://doi.org/10.1016/S0008-8846(98)00165-3 [30] O Belalia Douma, B Boukhatem, M Ghrici, A Tagnit-Hamou, Prediction of properties of self-compacting concrete containing fly ash using artificial neural 34 Electronic copy available at: https://ssrn.com/abstract=3970696 network, Neural Comput & Applic 28 (2017) 707–718 https://doi.org/10.1007/s00521-016-2368-7 [31] R Siddique, P Aggarwal, Y Aggarwal, Prediction of compressive strength of selfcompacting concrete containing bottom ash using artificial neural networks, Advances in Engineering Software 42 (2011) 780–786 https://doi.org/10.1016/j.advengsoft.2011.05.016 [32] I.-C Yeh, Modeling of strength of high-performance concrete using artificial neural networks, Cement and Concrete Research 28 (1998) 1797–1808 https://doi.org/10.1016/S0008-8846(98)00165-3 [33] İ.B Topỗu, M Sardemir, Prediction of rubberized concrete properties using artificial neural network and fuzzy logic, Construction and Building Materials 22 (2008) 532– 540 https://doi.org/10.1016/j.conbuildmat.2006.11.007 [34] G Trtnik, F Kavčič, G Turk, Prediction of concrete strength using ultrasonic pulse velocity and artificial neural networks, Ultrasonics 49 (2009) 53–60 https://doi.org/10.1016/j.ultras.2008.05.001 [35] W.P.S Dias, S.P Pooliyadda, Neural networks for predicting properties of concretes with admixtures, Construction and Building Materials 15 (2001) 371–379 https://doi.org/10.1016/S0950-0618(01)00006-X [36] B Pradhan, S Lee, Landslide susceptibility assessment and factor effect analysis: backpropagation artificial neural networks and their comparison with frequency ratio 35 Electronic copy available at: https://ssrn.com/abstract=3970696 and bivariate logistic regression modelling, Environmental Modelling & Software 25 (2010) 747–759 https://doi.org/10.1016/j.envsoft.2009.10.016 [37] Neural Network Model for Preformed-Foam Cellular Concrete, MJ 98 (2001) https://doi.org/10.14359/10730 [38] M Delnavaz, B Ayati, H Ganjidoust, Prediction of moving bed biofilm reactor (MBBR) performance for the treatment of aniline using artificial neural networks (ANN), Journal of Hazardous Materials 179 (2010) 769–775 https://doi.org/10.1016/j.jhazmat.2010.03.069 [39] B.G Aiyer, D Kim, N Karingattikkal, P Samui, P.R Rao, Prediction of compressive strength of self-compacting concrete using least square support vector machine and relevance vector machine, KSCE J Civ Eng 18 (2014) 1753–1758 https://doi.org/10.1007/s12205-014-0524-0 [40] S Mirjalili, S.M Mirjalili, A Lewis, Grey Wolf Optimizer, Advances in Engineering Software 69 (2014) 46–61 https://doi.org/10.1016/j.advengsoft.2013.12.007 [41] B Li, H Yan, J Zhang, N Zhou, Compaction property prediction of mixed gangue backfill materials using hybrid intelligence models: A new approach, Construction and Building Materials 247 (2020) 118633 https://doi.org/10.1016/j.conbuildmat.2020.118633 [42] A Behnood, E.M Golafshani, Predicting the compressive strength of silica fume concrete using hybrid artificial neural network with multi-objective grey wolves, 36 Electronic copy available at: https://ssrn.com/abstract=3970696 Journal of Cleaner Production 202 (2018) 54–64 https://doi.org/10.1016/j.jclepro.2018.08.065 [43] E.M Golafshani, A Behnood, M Arashpour, Predicting the compressive strength of normal and High-Performance Concretes using ANN and ANFIS hybridized with Grey Wolf Optimizer, Construction and Building Materials 232 (2020) 117266 https://doi.org/10.1016/j.conbuildmat.2019.117266 [44] R Gettu, J Izquierdo, G Pcc, A Josa, Development of high-strength self compacting concrete with fly ash: A four-step experimental methodology, Proc 27 Conf on Our World in Concrete & Structuresth (2002) 217–224 [45] R Patel, Development of statistical models to simulate and optimize selfconsolidating concrete mixes incorporating high volumes of fly ash., (2004) [46] M Uysal, K Yilmaz, Effect of mineral admixtures on properties of self-compacting concrete, Cement and Concrete Composites 33 (2011) 771–776 [47] B Mahalingam, K Nagamani, Effect of processed fly ash on fresh and hardened properties of self compacting concrete, Int J Earth Sci Eng (2011) 930–940 [48] A.F Bingöl, İ Tohumcu, Effects of different curing regimes on the compressive strength properties of self compacting concrete incorporating fly ash and silica fume, Materials & Design 51 (2013) 12–18 37 Electronic copy available at: https://ssrn.com/abstract=3970696 [49] R Siddique, P Aggarwal, Y Aggarwal, Influence of water/powder ratio on strength properties of self-compacting concrete containing coal fly ash and bottom ash, Construction and Building Materials 29 (2012) 73–81 [50] M.C Nepomuceno, L.A Pereira-de-Oliveira, S.M.R Lopes, Methodology for the mix design of self-compacting concrete using different mineral additions in binary blends of powders, Construction and Building Materials 64 (2014) 82–94 [51] R Siddique, P Aggarwal, Y Aggarwal, Prediction of compressive strength of selfcompacting concrete containing bottom ash using artificial neural networks, Advances in Engineering Software 42 (2011) 780–786 [52] E Güneyisi, M Gesoğlu, E Özbay, Strength and drying shrinkage properties of selfcompacting concretes incorporating multi-system blended mineral admixtures, Construction and Building Materials 24 (2010) 1878–1887 [53] P Krishnapal, R.K Yadav, C Rajeev, Strength characteristics of self compacting concrete containing fly ash, Res J Eng Sci ISSN 2278 (2013) 9472 [54] S Dhiyaneshwaran, P Ramanathan, I Baskar, R Venkatasubramani, Study on durability characteristics of self-compacting concrete with fly ash, Jordan Journal of Civil Engineering (2013) 342–352 [55] M Şahmaran, İ.Ö Yaman, M Tokyay, Transport and mechanical properties of self consolidating concrete with high volume fly ash, Cement and Concrete Composites 31 (2009) 99–106 38 Electronic copy available at: https://ssrn.com/abstract=3970696 [56] I.H Witten, E Frank, Data mining: practical machine learning tools and techniques with Java implementations, Acm Sigmod Record 31 (2002) 76–77 [57] S Menard, Coefficients of Determination for Multiple Logistic Regression Analysis, The American Statistician 54 (2000) 17–24 https://doi.org/10.1080/00031305.2000.10474502 [58] C Willmott, K Matsuura, Advantages of the Mean Absolute Error (MAE) over the Root Mean Square Error (RMSE) in Assessing Average Model Performance, Climate Research 30 (2005) 79 https://doi.org/10.3354/cr030079 [59] J.H Friedman, Greedy Function Approximation: A Gradient Boosting Machine, Annals of Statistics 29 (2001) 1189–1232 [60] G Cybenko, Approximation by superpositions of a sigmoidal function, Mathematics of Control, Signals and Systems (1989) 303–314 https://doi.org/10.1007/BF02551274 [61] Bounds, Lloyd, Mathew, Waddell, A multilayer perceptron network for the diagnosis of low back pain, in: IEEE 1988 International Conference on Neural Networks, 1988: pp 481–489 vol.2 https://doi.org/10.1109/ICNN.1988.23963 [62] E.T Mohamad, R.S Faradonbeh, D.J Armaghani, M Monjezi, M.Z.A Majid, An optimized ANN model based on genetic algorithm for predicting ripping production, Neural Computing and Applications 28 (2017) https://doi.org/10.1007/s00521-016-2359-8 39 Electronic copy available at: https://ssrn.com/abstract=3970696 393–406 [63] F Stern, M Muste, M Beninati, W.E Eichinger, Summary Of Exerimental Uncertainty Assessmet Methodology, (1999) [64] H.-B Ly, L Le, D Huan, T Nguyen, T Phạm, T.-T Le, V Le, L Nguyen-Ngoc, B Pham, Hybrid Artificial Intelligence Approaches for Predicting Critical Buckling Load of Structural Members under Compression Considering the Influence of Initial Geometric Imperfections, Applied Sciences (2019) https://doi.org/10.3390/app9112258 40 Electronic copy available at: https://ssrn.com/abstract=3970696 2258 ... technique show the best performance of the ANN-GWO model obtained when the number of neurons is 21, and the population size is 240 Then, all the performance evaluation criteria of the model are satisfied... increase in performance The case where the number of neurons increases while increasing the number of population sizes allows the model' s performance to increase The results of the mesh search... need for predicting the properties of SCC in both the fresh and hardened stages The traditional applications of analytical models to represent the influence of each of these parameters on the