DOI QR코드

DOI QR Code

Modelling the deflection of reinforced concrete beams using the improved artificial neural network by imperialist competitive optimization

  • Li, Ning (School of Resource and Environment Engineering, Wuhan University of Technology) ;
  • Asteris, Panagiotis G. (Computational Mechanics Laboratory, School of Pedagogical and Technological Education) ;
  • Tran, Trung-Tin (Department of Information Technology, FPT University) ;
  • Pradhan, Biswajeet (Centre for Advanced Modelling and Geospatial Information Systems (CAMGIS), School of Civil and Environmental Engineering, Faculty of Engineering & IT, University of Technology Sydney) ;
  • Nguyen, Hoang (Hanoi University of Mining and Geology)
  • Received : 2020.10.23
  • Accepted : 2022.03.17
  • Published : 2022.03.25

Abstract

This study proposed a robust artificial intelligence (AI) model based on the social behaviour of the imperialist competitive algorithm (ICA) and artificial neural network (ANN) for modelling the deflection of reinforced concrete beams, abbreviated as ICA-ANN model. Accordingly, the ICA was used to adjust and optimize the parameters of an ANN model (i.e., weights and biases) aiming to improve the accuracy of the ANN model in modelling the deflection reinforced concrete beams. A total of 120 experimental datasets of reinforced concrete beams were employed for this aim. Therein, applied load, tensile reinforcement strength and the reinforcement percentage were used to simulate the deflection of reinforced concrete beams. Besides, five other AI models, such as ANN, SVM (support vector machine), GLMNET (lasso and elastic-net regularized generalized linear models), CART (classification and regression tree) and KNN (k-nearest neighbours), were also used for the comprehensive assessment of the proposed model (i.e., ICA-ANN). The comparison of the derived results with the experimental findings demonstrates that among the developed models the ICA-ANN model is that can approximate the reinforced concrete beams deflection in a more reliable and robust manner.

Keywords

Acknowledgement

This research was supported by the Supported by the National Key R&D Program of China (Grant No. 2019YFC0605304).

References

  1. Abd-Elazim, S. and Ali, E. (2016), "Imperialist competitive algorithm for optimal STATCOM design in a multimachine power system", Int. J. Electric. Power Energy Syst., 76, 136-146. https://doi.org/10.1016/j.ijepes.2015.09.004.
  2. Abdeljaber, O., Avci, O., Kiranyaz, S., Gabbouj, M. and Inman, D. J. (2017), "Real-time vibration-based structural damage detection using one-dimensional convolutional neural networks", J. Sound Vib., 388, 154-170. https://doi.org/10.1016/j.jsv.2016.10.043.
  3. Abdelkarim, O.I., Ahmed, E.A., Mohamed, H.M. and Benmokrane, B. (2019), "Flexural strength and serviceability evaluation of concrete beams reinforced with deformed GFRP bars", Eng. Struct., 186, 282-296. https://doi.org/10.1016/j.engstruct.2019.02.024.
  4. Ahmed, S.U. (2007), Study on Deflections of Reinforced Concrete Flat Plates under Service Load.
  5. Ai, L., Soltangharaei, V., Bayat, M., Van Tooren, M. and Ziehl, P. (2021), "Detection of impact on aircraft composite structure using machine learning techniques", Measure. Sci. Technol., 32(8), 084013. https://doi.org/10.1088/1361-6501/abe790
  6. Al-Kamyani, Z., Guadagnini, M. and Pilakoutas, K. (2019), "Impact of shrinkage on crack width and deflections of reinforced concrete beams with and without steel fibres", Eng. Struct., 181, 387-396. https://doi.org/10.1016/j.engstruct.2018.12.031.
  7. Alkayem, N.F., Cao, M., Zhang, Y., Bayat, M. and Su, Z. (2018), "Structural damage detection using finite element model updating with evolutionary algorithms: a survey", Neural Comput. Appl., 30(2), 389-411. https://doi.org/10.1007/s00521-017-3284-1
  8. Asteris, P. and Cotsovos, D. (2012), "Numerical investigation of the effect of infill walls on the structural response of RC frames", Open Constr Build Technol J, 6(1), 164-181. https://doi.org/10.1007/s00521-017-3284-1.
  9. Asteris, P., Kolovos, K., Douvika, M. and Roinos, K. (2016), "Prediction of self-compacting concrete strength using artificial neural networks", Europ. J. Environ. Civil Eng., 20(sup1), s102-s122. https://doi.org/10.1080/19648189.2016.1246693.
  10. Asteris, P.G. and Kolovos, K.G. (2019), "Self-compacting concrete strength prediction using surrogate models", Neural Comput. Appl., 31(1), 409-424. https://doi.org/10.1007/s00521-017-3007-7.
  11. Asteris, P.G. and Nikoo, M. (2019), "Artificial bee colony-based neural network for the prediction of the fundamental period of infilled frame structures", 31(9), 4837-4847. Neural Comput. Appl., 1-11. https://doi.org/10.1007/s00521-018-03965-1.
  12. Asteris, P.G. and Plevris, V. (2017), "Anisotropic masonry failure criterion using artificial neural networks", Neural Comput. Appl., 28(8), 2207-2229. https://doi.org/10.1007/s00521-016-2181-3
  13. Asteris, P.G., Argyropoulos, I., Cavaleri, L., Rodrigues, H., Varum, H., Thomas, J. and Lourenco, P.B. (2008), "Masonry compressive strength prediction using artificial neural networks", In International Conference on Transdisciplinary Multispectral Modeling and Cooperation for the Preservation of Cultural Heritage, Springer
  14. Asteris, P.G., Lemonis, M.E., Le, T.T. and Tsavdaridis, K.D. (2021a), "Evaluation of the ultimate eccentric load of rectangular CFSTs using advanced neural network modeling", Eng. Struct., 248, 113297. https://doi.org/10.1016/j.engstruct.2021.113297.
  15. Asteris, P.G., Lourenco, P.B., Hajihassani, M., Adami, C.E.N., Lemonis, M.E., Skentou, A.D., Marques, R., Nguyen, H., Rodrigues, H. and Varum, H. (2021b), "Soft computing-based models for the prediction of masonry compressive strength", Eng. Struct., 248, 113276. https://doi.org/10.1016/j.engstruct.2021.113276.
  16. Asteris, P.G., Nozhati, S., Nikoo, M., Cavaleri, L. and Nikoo, M. (2019), "Krill herd algorithm-based neural network in structural seismic reliability evaluation", Mech. Advan. Mater. Struct., 26(13), 1146-1153. https://doi.org/10.1080/15376494.2018.1430874.
  17. Asteris, P.G., Tsaris, A.K., Cavaleri, L., Repapis, C.C., Papalou, A., Di Trapani, F. and Karypidis, D.F. (2016), "Prediction of the fundamental period of infilled RC frame structures using artificial neural networks", Comput. Intell. Neurosci., 2016, 20. https://doi.org/10.1155/2016/5104907.
  18. Atashpaz-Gargari, E. and Lucas, C. (2007), "Imperialist competitive algorithm: an algorithm for optimization inspired by imperialistic competition", In 2007 IEEE Congress on Evolutionary Computation.
  19. Attouch, H. and Cabot, A. (2019), "Convergence of a Relaxed Inertial Forward-Backward Algorithm for Structured Monotone Inclusions", Appl. Mathem. Optimization. 80(3), 547-598. https://doi.org/10.1007/s00245-019-09584-z.
  20. Avci, O., Abdeljaber, O., Kiranyaz, S., Hussein, M., Gabbouj, M. and Inman, D.J. (2021), "A review of vibration-based damage detection in civil structures: From traditional methods to machine learning and Deep Learning applications", Mech. Syst. Signal Processing, 147, 107077. https://doi.org/10.1016/j.ymssp.2020.107077.
  21. Bayat, M., Pakar, I. and Bayat, M. (2013), "On the large amplitude free vibrations of axially loaded Euler-Bernoulli beams", Steel Compos. Struct., 14(1), 73-83. https://doi.org/10.12989/scs.2013.14.1.073.
  22. Bayat, M., Pakar, I. and Emadi, A. (2013), "Vibration of electrostatically actuated microbeam by means of homotopy perturbation method", Struct. Eng. Mech., 48(6), 823-831. https://doi.org/10.12989/sem.2013.48.6.823.
  23. Betti, M., Facchini, L. and Biagini, P. (2015), "Damage detection on a three-storey steel frame using artificial neural networks and genetic algorithms", Meccanica, 50(3), 875-886. https://doi.org/10.1007/s11012-014-0085-9.
  24. Bischoff, P.H. (2005). "Reevaluation of deflection prediction for concrete beams reinforced with steel and fiber reinforced polymer bars", J. Struct. Eng., 131(5), 752-767. https://doi.org/10.1061/(ASCE)0733-9445(2005)131:5(752).
  25. Bui, X.N., Muazu, M.A. and Nguyen, H. (2019), "Optimizing Levenberg-Marquardt backpropagation technique in predicting factor of safety of slopes after two-dimensional OptumG2 analysis", Eng. Comput., https://doi.org/10.1007/s00366-019-00741-0.
  26. Bui, X.N., Nguyen, H., Le, H.A., Bui, H.B. and Do, N.H. (2019), "Prediction of blast-induced air over-pressure in open-pit mine: Assessment of different artificial intelligence techniques", Nat. Resource. Res., https://doi.org/10.1007/s11053-019-09461-0.
  27. Cai, J., Burgess, I. and Plank, R. (2003), "A generalised steel/reinforced concrete beam-column element model for fire conditions", Eng. Struct., 25(6), 817-833. https://doi.org/10.1016/S0141-0296(03)00019-1.
  28. Cao, Q., Zhou, J., Wu, Z. and Ma, Z.J. (2019), "Flexural behavior of prestressed CFRP reinforced concrete beams by two different tensioning methods", Eng. Struct., 189, 411-422. https://doi.org/10.1016/j.engstruct.2019.03.051.
  29. Cascardi, A., Micelli, F. and Aiello, M.A. (2017), "An Artificial Neural Networks model for the prediction of the compressive strength of FRP-confined concrete circular columns", Eng. Struct., 140, 199-208. https://doi.org/10.1016/j.engstruct.2017.02.047.
  30. Cha, Y.J. and Buyukozturk, O. (2015), "Structural damage detection using modal strain energy and hybrid multiobjective optimization", Comput. Aided Civil Infrastruct. Eng., 30(5), 347-358. https://doi.org/10.1111/mice.12122.
  31. Chatterjee, S., Sarkar, S., Hore, S., Dey, N., Ashour, A.S. and Balas, V.E. (2017), "Particle swarm optimization trained neural network for structural failure prediction of multistoried RC buildings", Neural Comput. Appl. 28(8), 2005-2016. https://doi.org/10.1007/s00521-016-2190-2.
  32. Chopra, P., Sharma, R.K. and Kumar, M. (2016), "Prediction of compressive strength of concrete using artificial neural network and genetic programming", Adv. Mater. Sci. Eng., 2016. https://doi.org/10.1155/2016/7648467.
  33. Chou, J.S., Ngo, N.T. and Pham, A.D. (2015), "Shear strength prediction in reinforced concrete deep beams using nature-inspired metaheuristic support vector regression", J. Comput. Civil Eng., 30(1), 04015002. https://doi.org/10.1061/(ASCE)CP.1943-5487.0000466.
  34. Darain, K.M., Shamshirband, S., Jumaat, M.Z. and Obaydullah, M. (2015), "Adaptive neuro fuzzy prediction of deflection and cracking behavior of NSM strengthened RC beams", Construct. Build. Mater., 98, 276-285. https://doi.org/10.1016/j.conbuildmat.2015.08.096.
  35. De Granrut, M., Simon, A. and Dias, D. (2019), "Artificial neural networks for the interpretation of piezometric levels at the rock-concrete interface of arch dams", Eng. Struct., 178, 616-634. https://doi.org/10.1016/j.engstruct.2018.10.033.
  36. Eckstein, S. and Kupper, M. (2019), "Computation of optimal transport and related hedging problems via penalization and neural networks", Appl. Mathem. Opimization. https://doi.org/10.1007/s00245-019-09558-1.
  37. Facchini, L., Betti, M. and Biagini, P. (2014), "Neural network based modal identification of structural systems through output-only measurement", Comput. Struct., 138, 183-194. https://doi.org/10.1016/j.compstruc.2014.01.013.
  38. Fathalla, E., Tanaka, Y. and Maekawa, K. (2018), "Remaining fatigue life assessment of in-service road bridge decks based upon artificial neural networks", Eng. Structures, 171, 602-616. https://doi.org/10.1016/j.engstruct.2018.05.122.
  39. Flood, I., Muszynski, L. and Nandy, S. (2001), "Rapid analysis of externally reinforced concrete beams using neural networks". Comput. Struct., 79(17), 1553-1559. https://doi.org/10.1016/S0045-7949(01)00033-5.
  40. Frankish, K. and Ramsey, W.M. (2014), The Cambridge Handbook of Artificial Intelligence: Cambridge University Press.
  41. Friedman, J., Hastie, T. and Tibshirani, R. (2010), "Regularization paths for generalized linear models via coordinate descent", J. Statistic. Software, 33(1), 1-22.
  42. Gao, W., Karbasi, M., Hasanipanah, M., Zhang, X. and Guo, J. (2018), "Developing GPR model for forecasting the rock fragmentation in surface mines", Eng. Comput., 34(2), 339-345. https://doi.org/10.1007/s00366-017-0544-8.
  43. Gao, W., Raftari, M., Rashid, A.S.A., Mu'azu, M.A. and Jusoh, W. A.W. (2019), "A predictive model based on an optimized ANN combined with ICA for predicting the stability of slopes", Eng. Comput., 1-20. https://doi.org/10.1007/s00366-019-00702-7.
  44. Gerist, S. and Maheri, M.R. (2016), "Multi-stage approach for structural damage detection problem using basis pursuit and particle swarm optimization", J. Sound Vib., 384, 210-226. https://doi.org/10.1016/j.jsv.2016.08.024.
  45. Gerist, S. and Maheri, M.R. (2019), "Structural damage detection using imperialist competitive algorithm and damage function", Appl. Soft Comput., 77, 1-23. https://doi.org/10.1016/j.asoc.2018.12.032.
  46. Ghali, A., Favre, R. and Elbadry, M. (2018), Concrete Structures: Stresses and Deformations: Analysis and Design for Serviceability, CRC Press.
  47. Hajihassani, M., Armaghani, D.J., Marto, A. and Mohamad, E.T. (2015), "Ground vibration prediction in quarry blasting through an artificial neural network optimized by imperialist competitive algorithm", Bull. Eng. Geology Environ., 74(3), 873-886. https://doi.org/10.1007/s10064-014-0657-x.
  48. Hammer, P.L. and Rudeanu, S. (2012), Boolean Methods in Operations Research and Related Areas, Springer Science & Business Media.
  49. Hegazy, T., Tully, S. and Marzouk, H. (1998), "A neural network approach for predicting the structural behavior of concrete slabs", Canadian J. Civil Eng., 25(4), 668-677. https://doi.org/10.1139/l98-009.
  50. Hosseini, S. and Al Khaled, A. (2014), "A survey on the imperialist competitive algorithm metaheuristic: implementation in engineering domain and directions for future research", Appl. Soft Comput., 24, 1078-1094. https://doi.org/10.1016/j.asoc.2014.08.024.
  51. Issa, M.S., Metwally, I.M. and Elzeiny, S.M. (2011), "Influence of fibers on flexural behavior and ductility of concrete beams reinforced with GFRP rebars", Eng. Struct., 33(5), 1754-1763. https://doi.org/10.1016/j.engstruct.2011.02.014.
  52. Kaczmarek, M. and Szymanska, A. (2016), "Application of artificial neural networks to predict the deflections of reinforced concrete beams", Studia Geotechnica Mechanica, 38(2), 37-46. https://doi.org/10.1515/sgem-2016-0017
  53. Kaklauskas, G. (2004), "Flexural layered deformational model of reinforced concrete members", Magazine Concrete Res., 56(10), 575-584. https://doi.org/10.1680/macr.2004.56.10.575
  54. Kardani, N., Bardhan, A., Samui, P., Nazem, M., Asteris, P.G. and Zhou, A. (2022), "Predicting the thermal conductivity of soils using integrated approach of ANN and PSO with adaptive and time-varying acceleration coefficients", Int. J. Thermal Sci., 173, 107427. https://doi.org/10.1016/j.ijthermalsci.2021.107427.
  55. Kaveh, A. and Talatahari, S. (2010), "Imperialist competitive algorithm for engineering design problems".
  56. Kennedy, C. and Ward, R. (2019), "Greedy Variance Estimation for the LASSO", Appl. Mathem. Optimization. 82(3), 1161-1182. https://doi.org/10.1007/s00245-019-09561-6
  57. Khademi, F. and Behfarnia, K. (2016), "Evaluation of concrete compressive strength using artificial neural network and multiple linear regression models", Iran Univ. Sci. Technol., 6(3), 423-432.
  58. Khademi, F., Akbari, M., Jamal, S.M., and Nikoo, M. (2017), "Multiple linear regression, artificial neural network, and fuzzy logic prediction of 28 days compressive strength of concrete", Front. Struct. Civil Eng., 11(1), 90-99. https://doi.org/10.1007/s11709-016-0363-9.
  59. Kim, S.H., Jung, C.Y. and Ahn, J.H. (2011), "Ultimate strength of composite structure with different degrees of shear connection", Steel Compos. Struct., 11(5), 375-390. https://doi.org/10.12989/scs.2011.11.5.375.
  60. Lapko, A. and Urbanski, M. (2015), "Experimental and theoretical analysis of deflections of concrete beams reinforced with basalt rebar". Archives Civil Mech. Eng., 15(1), 223-230. https://doi.org/10.1016/j.acme.2014.03.008.
  61. Lemonis, M., Hatzigeorgiou, G. and Asteris, P. (2022), "Seismic behaviour of irregular steel frames with beam and joint energy dissipation", Soil Dyn. Earthq. Eng., 152, 107052. https://doi.org/10.1016/j.soildyn.2021.107052.
  62. Mansouri, I., Shariati, M., Safa, M., Ibrahim, Z., Tahir, M. and Petkovic, D. (2019), "Analysis of influential factors for predicting the shear strength of a V-shaped angle shear connector in composite beams using an adaptive neuro-fuzzy technique", J. Intell. Manufact., 30(3), 1247-1257. https://doi.org/10.1007/s10845-017-1306-6
  63. Melchers, R.E., Li, C.Q. and Lawanwisut, W. (2008), "Probabilistic modeling of structural deterioration of reinforced concrete beams under saline environment corrosion", Struct. Safety, 30(5), 447-460. https://doi.org/10.1016/j.strusafe.2007.02.002.
  64. Mikaeil, R., Haghshenas, S.S., Haghshenas, S.S. and Ataei, M. (2018), "Performance prediction of circular saw machine using imperialist competitive algorithm and fuzzy clustering technique", Neural Comput. Appl., 29(6), 283-292. https://doi.org/10.1007/s00521-016-2557-4.
  65. Mishra, M., Agarwal, A. and Maity, D. (2019), "Neural-network-based approach to predict the deflection of plain, steel-reinforced, and bamboo-reinforced concrete beams from experimental data", SN Applied Sci., 1(6), 584. https://doi.org/10.1007/s42452-019-0622-1.
  66. Moayedi, H., Moatamediyan, A., Nguyen, H., Bui, X.N., Bui, D.T. and Rashid, A.S.A. (2019a), "Prediction of ultimate bearing capacity through various novel evolutionary and neural network models", Eng. Comput., 36(2), 671-687. https://doi.org/10.1007/s00366-019-00723-2.
  67. Moayedi, H., Raftari, M., Sharifi, A., Jusoh, W.A.W. and Rashid, A.S.A. (2019b), "Optimization of ANFIS with GA and PSO estimating α ratio in driven piles", Eng. Comput., 36(1), 227-238. https://doi.org/10.1007/s00366-018-00694-w.
  68. Mohamedbhai, G.T. (1971), A Study of the Deflections of Reinforced Concrete Flexural Members, The University of Manchester (United Kingdom).
  69. Mohammadhassani, M., Nezamabadi-Pour, H., Jumaat, M., Jameel, M., Hakim, S. and Zargar, M. (2013a), "Application of the ANFIS model in deflection prediction of concrete deep beam", Struct. Eng. Mech., 45(3), 323-336. https://doi.org/10.12989/sem.2013.45.3.323.
  70. Mohammadhassani, M., Nezamabadi-pour, H., Jumaat, M.Z., Jameel, M. and Arumugam, A. (2013b), "Application of artificial neural networks (ANNs) and linear regressions (LR) to predict the deflection of concrete deep beams", Comput. Concrete, 11(3), 237-252. https://doi.org/10.12989/cac.2013.11.3.237.
  71. Mohammadhassani, M., Saleh, A., Suhatril, M. and Safa, M. (2015), "Fuzzy modelling approach for shear strength prediction of RC deep beams", Smart Struct. Syst., 16(3), 497-519. https://doi.org/10.12989/sss.2015.16.3.497.
  72. Mokhtari, G., Ghanizadeh, A.J. and Ebrahimi, E. (2012), "Application of imperialist competitive algorithm to solve constrained economic dispatch", Int. J. Electric. Eng. Informatic., 4(4), 553. https://doi.org/10.15676/ijeei.2012.4.4.2
  73. Naderpour, H., Poursaeidi, O. and Ahmadi, M. (2018), "Shear resistance prediction of concrete beams reinforced by FRP bars using artificial neural networks", Measurement, 126, 299-308. https://doi.org/10.1016/j.measurement.2018.05.051.
  74. Naderpour, H., Rafiean, A.H. and Fakharian, P. (2018), "Compressive strength prediction of environmentally friendly concrete using artificial neural networks", J. Build. Eng., 16, 213-219. https://doi.org/10.1016/j.jobe.2018.01.007.
  75. Neumayer, S., Nimmer, M., Setzer, S. and Steidl, G. (2019), "On the Robust PCA and Weiszfeld's Algorithm", Appl. Mathem. Optimization. 82(3), 1017-1048. https://doi.org/10.1007/s00245-019-09566-1.
  76. Nguyen, H. (2019), "Support vector regression approach with different kernel functions for predicting blast-induced ground vibration: a case study in an open-pit coal mine of Vietnam", SN Appl. Sci., 1(4), 1-10. https://doi.org/10.1007/s42452-019-0295-9.
  77. Nguyen, H., Bui, X.N., Bui, H.B. and Cuong, D.T. (2019a), "Developing an XGBoost model to predict blast-induced peak particle velocity in an open-pit mine: a case study", Acta Geophysica, 67(2), 477-490. https://doi.org/10.1007/s11600-019-00268-4.
  78. Nguyen, H., Bui, X.N., Bui, H.B., and Mai, N.L. (2018a), "A comparative study of artificial neural networks in predicting blast-induced air-blast overpressure at Deo Nai open-pit coal mine, Vietnam", Neural Comput. Appl., 1-17. https://doi.org/10.1007/s00521-018-3717-5.
  79. Nguyen, H., Bui, X.N., Tran, Q.H., and Mai, N.L. (2019b), "A new soft computing model for estimating and controlling blast-produced ground vibration based on hierarchical K-means clustering and cubist algorithms", Appl. Soft Comput., 77, 376-386. https://doi.org/10.1016/j.asoc.2019.01.042.
  80. Nguyen, H., Bui, X.N., Tran, Q.H., Le, T.Q., Do, N.H. and Hoa, L. T.T. (2018b), "Evaluating and predicting blast-induced ground vibration in open-cast mine using ANN: A case study in Vietnam", SN Appl. Sci., 1(1), 125. https://doi.org/10.1007/s42452-018-0136-2.
  81. Nguyen, H., Drebenstedt, C., Bui, X.N., and Bui, D.T. (2019c), "Prediction of blast-induced ground vibration in an open-pit mine by a novel hybrid model based on clustering and artificial neural network", Nat. Resouce Res., https://doi.org/10.1007/s11053-019-09470-z.
  82. Nguyen, H., Moayedi, H., Foong, L.K., Al Najjar, H.A.H., Jusoh, W.A.W., Rashid, A.S.A. and Jamali, J. (2019d), "Optimizing ANN models with PSO for predicting short building seismic response", Eng. Comput., https://doi.org/10.1007/s00366-019-00733-0.
  83. Nguyen, H., Moayedi, H., Jusoh, W.A.W. and Sharifi, A. (2019e), "Proposing a novel predictive technique using M5Rules-PSO model estimating cooling load in energy-efficient building system", Eng. Comput.,https://doi.org/10.1007/s00366-019-00735-y.
  84. Nie, J., Fan, J. and Cai, C. (2008), "Experimental study of partially shear-connected composite beams with profiled sheeting", Eng. Struct., 30(1), 1-12. https://doi.org/10.1016/j.engstruct.2007.02.016.
  85. Nikoo, M., Torabian Moghadam, F. and Sadowski, L. (2015), "Prediction of concrete compressive strength by evolutionary artificial neural networks", Advan. Mater. Sci. Eng., 2015. https://doi.org/10.1155/2015/849126.
  86. Ogutu, J.O., Schulz-Streeck, T. and Piepho, H.P. (2012), "Genomic selection using regularized linear regression models: ridge regression, lasso, elastic net and their extensions", In BMC proceedings, BioMed Central.
  87. Pakar, I. and Bayat, M. (2012), "741. Analytical study on the nonlinear vibration of Euler-Bernoulli beams", Methods, 10, 17.
  88. Pakar, I. and Bayat, M. (2013), "An analytical study of nonlinear vibrations of buckled Euler Bernoulli beams", Methods, 18, 25.
  89. Parsajoo, M., Armaghani, D.J. and Asteris, P.G. (2021), "A precise neuro-fuzzy model enhanced by artificial bee colony techniques for assessment of rock brittleness index", Neural Comput. Appl.. https://doi.org/10.1007/s00521-021-06600-8.
  90. Rad, M.Y., Haghshenas, S.S. and Haghshenas, S. (2014), Mechanostratigraphy of cretaceous rocks by fuzzy logic in East Arak, Iran. In The 4th International Workshop on Computer Science and Engineering-Summer, WCSE, 2014
  91. Ritter, S., Barrett, D.G., Santoro, A. and Botvinick, M.M. (2017), "Cognitive psychology for deep neural networks: A shape bias case study", In Proceedings of the 34th International Conference on Machine Learning-Volume 70.
  92. Russell, S.J. and Norvig, P. (2016), Artificial Intelligence: A Modern Approach. Pearson Education Limited.
  93. Safa, M., Shariati, M., Ibrahim, Z., Toghroli, A., Baharom, S.B., Nor, N.M. and Petkovic, D. (2016), "Potential of adaptive neuro fuzzy inference system for evaluating the factors affecting steel-concrete composite beam's shear strength", Steel Compos Struct, 21(3), 679-688. https://doi.org/10.12989/scs.2016.21.3.679.
  94. Sakr, M.A. and Sakla, S.S. (2008), "Long-term deflection of cracked composite beams with nonlinear partial shear interaction: I-Finite element modeling", J. Construct. Steel Research, 64(12), 1446-1455. https://doi.org/10.1016/j.jcsr.2008.01.003.
  95. Sakr, M.A. and Sakla, S.S. (2009). "Long-term deflection of cracked composite beams with nonlinear partial shear interaction-a study using neural networks", Eng. Struct., 31(12), 2988-2997. https://doi.org/10.1016/j.engstruct.2009.07.027.
  96. Shabani, H., Vahidi, B. and Ebrahimpour, M. (2013), "A robust PID controller based on imperialist competitive algorithm for load-frequency control of power systems", ISA Transactions, 52(1), 88-95. https://doi.org/10.1016/j.isatra.2012.09.008.
  97. Shin, S., Seo, D. and Han, B. (2009), "Performance of concrete beams reinforced with GFRP bars", J. Asian Architect. Build. Eng., 8(1), 197-204. https://doi.org/10.3130/jaabe.8.197.
  98. Tadesse, Z., Patel, K., Chaudhary, S. and Nagpal, A. (2012), "Neural networks for prediction of deflection in composite bridges", J. Construct. Steel Res., 68(1), 138-149. https://doi.org/10.1016/j.jcsr.2011.08.003.
  99. Venkateshwaran, A. and Tan, K.H. (2018), "Load-carrying capacity of steel fiber reinforced concrete beams at large deflections", Struct. Concrete, 19(3), 670-683. https://doi.org/10.1002/suco.201700129.
  100. Vila, J.P. and Gauchi, J.P. (2019), "Predictive control of discrete time stochastic nonlinear state space dynamical systems: A particle nonparametric approach", Appl. Mathem. Optimization, 80(1), 165-194. https://doi.org/10.1007/s00245-017-9462-9.
  101. Visintin, P., Sturm, A.B. and Oehlers, D.J. (2018), "Long-and short-term serviceability behavior of reinforced concrete beams: Mechanics models for deflections and crack widths", Struct. Concrete, 19(2), 489-507. https://doi.org/10.1002/suco.201700022.
  102. Walczak, S. (2019), "Artificial neural networks", In Advanced Methodologies and Technologies in Artificial Intelligence, Computer Simulation, and Human-Computer Interaction.
  103. Xing, Y., Han, Q., Xu, J., Guo, Q. and Wang, Y. (2016), "Experimental and numerical study on static behavior of elastic concrete-steel composite beams", J. Construct. Steel Res., 123, 79-92. https://doi.org/10.1016/j.jcsr.2016.04.023.
  104. Xu, J., Zhao, X., Yu, Y., Xie, T., Yang, G. and Xue, J. (2019), "Parametric sensitivity analysis and modelling of mechanical properties of normal-and high-strength recycled aggregate concrete using grey theory, multiple nonlinear regression and artificial neural networks", Construct. Build. Mater., 211, 479-491. https://doi.org/10.1016/j.conbuildmat.2019.03.234.
  105. Xu, S., Wang, Y., and Huang, A. (2014), "Application of imperialist competitive algorithm on solving the traveling salesman problem", Algorithms, 7(2), 229-242. https://doi.org/10.3390/a7020229.
  106. Yaseen, Z.M., Deo, R.C., Hilal, A., Abd, A.M., Bueno, L.C., Salcedo-Sanz, S. and Nehdi, M.L. (2018), "Predicting compressive strength of lightweight foamed concrete using extreme learning machine model", Advan. Eng. Software, 115, 112-125. https://doi.org/10.1016/j.advengsoft.2017.09.004.
  107. Yuan, H., Deng, H., Yang, Y., Weijian, Y. and Zhenggeng, Z. (2016), "Element-based effective width for deflection calculation of steel-concrete composite beams", J. Construct. Steel Res., 121, 163-172. https://doi.org/10.1016/j.jcsr.2016.02.010.
  108. Zhang, R., Castel, A. and Francois, R. (2009), "Serviceability limit state criteria based on steel-concrete bond loss for corroded reinforced concrete in chloride environment", Mater. Struct. 42(10), 1407. https://doi.org/10.1617/s11527-008-9460-0.
  109. Zhang, X., Nguyen, H., Bui, X.N., Tran, Q.H., Nguyen, D.A., Bui, D.T. and Moayedi, H. (2019), "Novel soft computing model for predicting blast-induced ground vibration in open-pit mines based on particle swarm optimization and XGBoost", Nat. Resources Res., 29(2), 711-721. https://doi.org/10.1007/s11053-019-09492-7.