Simulation of foamed concrete compressive strength prediction using adaptive neuro-fuzzy inference system optimized by nature-inspired algorithms

Ahmad SHARAFATI , H. NADERPOUR , Sinan Q. SALIH , E. ONYARI , Zaher Mundher YASEEN

Front. Struct. Civ. Eng. ›› 2021, Vol. 15 ›› Issue (1) : 61 -79.

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Front. Struct. Civ. Eng. ›› 2021, Vol. 15 ›› Issue (1) : 61 -79. DOI: 10.1007/s11709-020-0684-6
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TRANSDISCIPLINARY INSIGHT

Simulation of foamed concrete compressive strength prediction using adaptive neuro-fuzzy inference system optimized by nature-inspired algorithms

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Abstract

Concrete compressive strength prediction is an essential process for material design and sustainability. This study investigates several novel hybrid adaptive neuro-fuzzy inference system (ANFIS) evolutionary models, i.e., ANFIS–particle swarm optimization (PSO), ANFIS–ant colony, ANFIS–differential evolution (DE), and ANFIS–genetic algorithm to predict the foamed concrete compressive strength. Several concrete properties, including cement content (C), oven dry density (O), water-to-binder ratio (W), and foamed volume (F) are used as input variables. A relevant data set is obtained from open-access published experimental investigations and used to build predictive models. The performance of the proposed predictive models is evaluated based on the mean performance (MP), which is the mean value of several statistical error indices. To optimize each predictive model and its input variables, univariate (C, O, W, and F), bivariate (C–O, C–W, C–F, O–W, O–F, and W–F), trivariate (C–O–W, C–W–F, O–W–F), and four-variate (C–O–W–F) combinations of input variables are constructed for each model. The results indicate that the best predictions obtained using the univariate, bivariate, trivariate, and four-variate models are ANFIS–DE– (O) (MP= 0.96), ANFIS–PSO– (C–O) (MP= 0.88), ANFIS–DE– (O–W–F) (MP= 0.94), and ANFIS–PSO– (C–O–W–F) (MP= 0.89), respectively. ANFIS–PSO– (C–O) yielded the best accurate prediction of compressive strength with an MP value of 0.96.

Keywords

foamed concrete / adaptive neuro fuzzy inference system / nature-inspired algorithms / prediction of compressive strength

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Ahmad SHARAFATI, H. NADERPOUR, Sinan Q. SALIH, E. ONYARI, Zaher Mundher YASEEN. Simulation of foamed concrete compressive strength prediction using adaptive neuro-fuzzy inference system optimized by nature-inspired algorithms. Front. Struct. Civ. Eng., 2021, 15(1): 61-79 DOI:10.1007/s11709-020-0684-6

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References

[1]

Khan K A, Ahmad I, Alam M. Effect of Ethylene Vinyl Acetate (EVA) on the setting time of cement at different temperatures as well as on the mechanical strength of concrete. Arabian Journal for Science and Engineering, 2019, 44: 4075–4084

[2]

Zhang C, Liu H, Li S, Liu C, Qin L, Chang J, Cheng R.Experimental study on the expansion of a new cement-based borehole sealing material using different additives and varied water-cement ratios. Arabian Journal for Science and Engineering, 2019, 44: 1–9

[3]

DeRousseau M A, Kasprzyk J R, Srubar W V. Computational design optimization of concrete mixtures: A review. Cement and Concrete Research, 2018, 109: 42–53

[4]

Guo Y, Xie J, Zhao J, Zuo K. Utilization of unprocessed steel slag as fine aggregate in normal- and high-strength concrete. Construction & Building Materials, 2019, 204: 41–49

[5]

Kearsley E P. Just Foamed Concrete—An overview. Specialist Techniques and Materials for Concrete Construction. London: Thomas Telford Publishing, 1999.

[6]

Nehdi M, Djebbar Y, Khan A. Neural network model for preformed-foam cellular concrete. ACI Materials Journal, 2001, 98(5): 402409

[7]

Yaseen Z M, Deo R C, Hilal A, Abd A M, Bueno L C, Salcedo-Sanz S, Nehdi M L. Predicting compressive strength of lightweight foamed concrete using extreme learning machine model. Advances in Engineering Software, 2018, 115: 112–125

[8]

Kovler K, Roussel N. Properties of fresh and hardened concrete. Cement and Concrete Research, 2011, 41(7): 775–792

[9]

Ayub T, Shafiq N, Fadhil Nuruddin M. Stress-strain response of high strength concrete and application of the existing models. Research Journal of Applied Sciences, Engineering and Technology, 2014, 8(10): 1174–1190

[10]

Al-Mufadi F, Sherif H A. Effect of multiwalled carbon nanotubes on sensing crack initiation and ultimate strength of cement nanocomposites. Arabian Journal for Science and Engineering, 2019, 44: 1403–1413

[11]

Liu L, Xin J, Feng Y, Zhang B, Song K I. Effect of the cement-tailing ratio on the hydration products and microstructure characteristics of cemented paste backfill. Arabian Journal for Science and Engineering, 2019, 44(7): 6547–6556

[12]

Hilal A A, Thom N H, Dawson A R. On void structure and strength of foamed concrete made without/with additives. Construction & Building Materials, 2015, 85: 157–164

[13]

Kearsley E P, Wainwright P J. The effect of porosity on the strength of foamed concrete. Cement and Concrete Research, 2002, 32(2): 233–239

[14]

Bing C, Zhen W, Ning L. Experimental research on properties of high-strength foamed concrete. Journal of Materials in Civil Engineering, 2012, 24(1): 113–118

[15]

Lim J C, Ozbakkaloglu T. Stress-strain model for normal- and light-weight concretes under uniaxial and triaxial compression. Construction & Building Materials, 2014, 71: 492–509

[16]

Liu J, Tang K, Qiu Q, Pan D, Lei Z, Xing F. Experimental investigation on pore structure characterization of concrete exposed to water and chlorides. Materials (Basel), 2014, 7(9): 6646–6659

[17]

Thakrele MH. Experimental study on foam concrete. International Journal of Civil, Structural, Environmental and Infrastructure Engineering Research and Development 2014, 4(1): 145–157

[18]

Ma C, Chen B. Properties of foamed concrete containing water repellents. Construction & Building Materials, 2016, 123: 106–114

[19]

Falliano D, De Domenico D, Ricciardi G, Gugliandolo E. Experimental investigation on the compressive strength of foamed concrete: Effect of curing conditions, cement type, foaming agent and dry density. Construction & Building Materials, 2018, 165 : 735–749

[20]

Abd A M, Abd S M. Modelling the strength of lightweight foamed concrete using support vector machine (SVM). Case Studies in Construction Materials, 2017, 6: 8–15

[21]

Young B A, Hall A, Pilon L, Gupta P, Sant G. Can the compressive strength of concrete be estimated from knowledge of the mixture proportions? New insights from statistical analysis and machine learning methods. Cement and Concrete Research, 2019, 115: 379–388

[22]

Nambiar E K K, Ramamurthy K. Models relating mixture composition to the density and strength of foam concrete using response surface methodology. Cement and Concrete Composites, 2006, 28(9): 752–760

[23]

Nambiar E K K, Ramamurthy K. Models for strength prediction of foam concrete. Materials and Structures/Materiaux et Constructions, 2008, 41(2): 247–254

[24]

Mydin M A O. Modeling of transient heat transfer in foamed concrete slab. Journal of Engineering Science and Technology 2013, 8(3): 326–343

[25]

Wang W Y, Li J, Liu W, Liu Z K. Integrated computational materials engineering for advanced materials: A brief review. Computational Materials Science, 2019, 158: 42–48

[26]

Adeli H. Neural networks in civil engineering: 1989–2000. Computer-Aided Civil and Infrastructure Engineering, 2001, 16: 126–142

[27]

Van Dao D, Ly H B, Trinh S H, Le T T, Pham B T. Artificial Intelligence Approaches for Prediction of Compressive Strength of Geopolymer Concrete. Materials (Basel), 2019, 12: 983

[28]

Lu Z H, Zhao Y G. Empirical stress-strain model for unconfined high-strength concrete under uniaxial compression. Journal of Materials in Civil Engineering, 2010, 22(11): 1181–1186

[29]

Bhargava K, Ghosh A K, Mori Y, Ramanujam S. Corrosion-induced bond strength degradation in reinforced concrete-Analytical and empirical models. Nuclear Engineering and Design, 2007, 237(11): 1140–1157

[30]

Yaseen Z M, Keshtegar B, Hwang H J, Nehdi M L. Predicting reinforcing bar development length using polynomial chaos expansions. Engineering Structures, 2019, 195: 524–535

[31]

Onyari E K, Ikotun B D. Prediction of compressive and flexural strengths of a modified zeolite additive mortar using artificial neural network. Construction & Building Materials, 2018, 187: 1232–1241

[32]

Hamdia K M, Arafa M, Alqedra M. Structural damage assessment criteria for reinforced concrete buildings by using a Fuzzy Analytic Hierarchy process. Underground Space, 2018, 3: 243–249

[33]

Anitescu C, Atroshchenko E, Alajlan N, Rabczuk T. Artificial neural network methods for the solution of second order boundary value problems. Computers, Materials and Continua 2019, 59(1): 345–359

[34]

Hamdia K M, Ghasemi H, Zhuang X, Alajlan N, Rabczuk T. Computational machine learning representation for the flexoelectricity effect in truncated pyramid structures. Computers, Materials and Continua, 2019, 59(1): 79–87

[35]

Jang J S R. ANFIS: Adaptive-network-based fuzzy inference system. IEEE Transactions on Systems, Man, and Cybernetics, 1993, 23: 665–685

[36]

Yaseen Z M, Ramal M M, Diop L, Jaafar O, Demir V, Kisi O. Hybrid adaptive neuro-fuzzy models for water quality index estimation. Water Resources Management, 2018, 32: 2227–2245

[37]

Yaseen Z M, Ghareb M I, Ebtehaj I, Bonakdari H, Ravinesh D, Siddique R, Heddam S, Yusif A A, Deo R. Rainfall pattern forecasting using novel hybrid intelligent model based ANFIS-FFA. Water Resources Management, 2017, 32(1): 105–122

[38]

Moosavi V, Vafakhah M, Shirmohammadi B, Ranjbar M. Optimization of wavelet-ANFIS and wavelet-ANN hybrid models by taguchi method for groundwater level forecasting. Arabian Journal for Science and Engineering, 2012, 39(3): 1785–1796

[39]

Kose U, Arslan A. Forecasting chaotic time series via anfis supported by vortex optimization algorithm: applications on electroencephalogram time series. Arabian Journal for Science and Engineering, 2017, 42(8): 3103–3114

[40]

Khademi F, Jamal S M, Deshpande N, Londhe S. Predicting strength of recycled aggregate concrete using Artificial Neural Network, Adaptive Neuro-Fuzzy Inference System and Multiple Linear Regression. International Journal of Sustainable Built Environment, 2016, 5(2): 355–369

[41]

Sadrmomtazi A, Sobhani J, Mirgozar M A. Modeling compressive strength of EPS lightweight concrete using regression, neural network and ANFIS. Construction & Building Materials, 2013, 42: 205–216

[42]

Saridemir M. Predicting the compressive strength of mortars containing metakaolin by artificial neural networks and fuzzy logic. Advances in Engineering Software, 2009, 40(9): 920–927

[43]

Sobhani J, Najimi M, Pourkhorshidi A R, Parhizkar T. Prediction of the compressive strength of no-slump concrete: A comparative study of regression, neural network and ANFIS models. Construction & Building Materials, 2010, 24: 709–718

[44]

Madandoust R, Bungey J H, Ghavidel R. Prediction of the concrete compressive strength by means of core testing using GMDH-type neural network and ANFIS models. Computational Materials Science, 2012, 51(1): 261–272

[45]

Ahmadi-Nedushan B. Prediction of elastic modulus of normal and high strength concrete using ANFIS and optimal nonlinear regression models. Construction & Building Materials, 2012, 36: 665–673

[46]

Amani J, Moeini R. Prediction of shear strength of reinforced concrete beams using adaptive neuro-fuzzy inference system and artificial neural network. Scientia Iranica, 2012, 19: 242–248

[47]

Taylan O, Darrab I A. Determining optimal quality distribution of latex weight using adaptive neuro-fuzzy modeling and control systems. Computers & Industrial Engineering, 2011, 61(3): 686–696

[48]

Karaboga D, Kaya E. Training ANFIS by using an adaptive and hybrid artificial bee colony algorithm (aABC) for the identification of nonlinear static systems. Arabian Journal for Science and Engineering, 2019, 44: 3531–3547

[49]

Al-Musawi A A, Alwanas A A H, Salih S Q, Ali Z H, Tran M T, Yaseen Z M. Shear strength of SFRCB without stirrups simulation: Implementation of hybrid artificial intelligence model. Engineering with Computers, 2018, 36(1): 1–11

[50]

Jayaram M A, Nataraja M C, Ravi Kumar C N. Design of high performance concrete mixes through particle swarm optimization. Journal of Intelligent Systems, 2010, 19(3): 249–264

[51]

Flint M, Grünewald S, Coenders J. Ant colony optimization for ultra high performance concrete structures. Designing and Building with UHPFRC, 2013, 4(9): 12164–12177

[52]

Quaranta G, Fiore A, Marano G C. Optimum design of prestressed concrete beams using constrained differential evolution algorithm. Structural and Multidisciplinary Optimization, 2014, 49(3): 441–453

[53]

Christiansen A D, Hernández F S. A simple genetic algorithm for the design of reinforced concrete beams. Engineering with Computers, 1997, 13(4): 185–196

[54]

Yaseen Z M, Tran M T, Kim S, Bakhshpoori T, Deo R C. Shear strength prediction of steel fiber reinforced concrete beam using hybrid intelligence models: A new approach. Engineering Structures, 2018, 177: 244–255

[55]

Ashrafian A, Shokri F, Amiri M J T, Yaseen Z M, Rezaie-Balf M. Compressive strength of Foamed Cellular Lightweight Concrete simulation: New development of hybrid artificial intelligence model. Construction & Building Materials, 2020, 230: 117048

[56]

Bui Q T, Van Pham M, Nguyen Q H, Nguyen L X, Pham H M. Whale Optimization Algorithm and Adaptive Neuro-Fuzzy Inference System: A hybrid method for feature selection and land pattern classification. International Journal of Remote Sensing, 2019, 40: 1–16

[57]

Jaafari A, Zenner E K, Panahi M, Shahabi H. Hybrid artificial intelligence models based on a neuro-fuzzy system and metaheuristic optimization algorithms for spatial prediction of wildfire probability. Agricultural and Forest Meteorology, 2019, 266: 198–207

[58]

Elbaz K, Shen S L, Zhou A, Yuan D J, Xu Y S. Optimization of EPB shield performance with adaptive neuro-fuzzy inference system and genetic algorithm. Applied Sciences (Basel, Switzerland), 2019, 9(4): 780–797

[59]

Sari P A, Suhatril M, Osman N, Mu’azu M A, Katebi J, Abavisani A, Ghaffari N, Chahnasir E S, Wakil K, Khorami M, Petkovic D. Developing a hybrid adoptive neuro-fuzzy inference system in predicting safety of factors of slopes subjected to surface eco-protection techniques. Engineering with Computers, 2019, 36(4): 1347 1354

[60]

Kearsley E P, Wainwright P J. The effect of high fly ash content on the compressive strength of foamed concrete. Cement and Concrete Research, 2001, 31(1): 105–112

[61]

Tikalsky P J, Pospisil J, MacDonald W. A method for assessment of the freeze-thaw resistance of preformed foam cellular concrete. Cement and Concrete Research, 2004, 34(5): 889–893

[62]

Jones M R, McCarthy A. Preliminary views on the potential of foamed concrete as a structural material. Magazine of Concrete Research, 2005, 57(1): 21–31

[63]

Pan Z, Hiromi F, Wee T. Preparation of high performance foamed concrete from cement, sand and mineral admixtures. Journal Wuhan University of Technology, Materials. Science Editor, 2007, 22(2): 295–298

[64]

Sun H Y, Gong A M, Peng Y L, Wang X. The study of foamed concrete with polypropylene fiber and high volume fly ash. Applied Mechanics and Materials, 2011, 9093: 1039–1043

[65]

Abellan-Nebot J V, Subrión F R. A review of machining monitoring systems based on artificial intelligence process models. International Journal of Advanced Manufacturing Technology, 2009, 47(1–4): 237–257

[66]

Yaseen Z, Ebtehaj I, Kim S, Sanikhani H, Asadi H, Ghareb M, Bonakdari H, Mohtar W H M W, Al-Ansari N, Shahid S. Novel hybrid data-intelligence model for forecasting monthly rainfall with uncertainty analysis. Water (Basel), 2019, 11: 502

[67]

Naderpour H, Kheyroddin A, Amiri G G. Prediction of FRP-confined compressive strength of concrete using artificial neural networks. Composite Structures, 2010, 92(12): 2817–2829

[68]

Naderpour H, Alavi S A. A proposed model to estimate shear contribution of FRP in strengthened RC beams in terms of Adaptive Neuro-Fuzzy Inference System. Composite Structures, 2017, 170: 215–227

[69]

Demir F. A new way of prediction elastic modulus of normal and high strength concrete-fuzzy logic. Cement and Concrete Research, 2005, 35(8): 1531–1538

[70]

Fullér R. Neural Fuzzy Systems. Turku: Abo Akademi University, 1995

[71]

Eberhart R, Kennedy J. A new optimizer using particle swarm theory. In: MHS’95 Proceedings of the Sixth International Symposium on Micro Machine and Human Science. Nagoya: IEEE, 1995: 39–43

[72]

Shi Y, Eberhart R C. Empirical study of particle swarm optimization. Evolutionary computation, 1999. CEC 99. In: Proceedings of the 1999 Congress. 1999, 1945–1950

[73]

Dorigo M, Socha K. Ant Colony Optimization. Handbook of Approximation Algorithms and Metaheuristics. 2007

[74]

Dorigo M, Di Caro G. Ant colony optimization: A new meta-heuristic. In: Proceedings of the 1999 Congress on Evolutionary Computation, CEC 1999. Washington, D.C.: IEEE, 1999

[75]

Merkle D, Middendorf M, Schmeck H. Ant colony optimization for resource-constrained project scheduling. IEEE Transactions on Evolutionary Computation, 2002, 6(4): 333–346

[76]

Storn R, Price K. Differential evolution—A simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization, 1997, 11: 341–359

[77]

Price K, Storn R M, Lampinen J A. Differential evolution: A practical approach to global optimization (natural computing Series). Journal of Heredity, 2005, 41(1): 124–130

[78]

García-Martínez C, Rodriguez F J, Lozano M. Genetic Algorithms. Handbook of Heuristics. 2018

[79]

Golberg D E. Genetic algorithms in search, optimization, and machine learning. Choice Reviews Online, 2013, 27(2): 301–315

[80]

Harik G R, Lobo F G, Goldberg D E. The compact genetic algorithm. IEEE Transactions on Evolutionary Computation, 1999, 3(4): 287–297

[81]

Shoorehdeli M A, Teshnehlab M, Sedigh A K. Novel hybrid learning algorithms for tuning ANFIS parameters using adaptive weighted PSO. In: 2007 IEEE International Fuzzy Systems Conference. London: IEEE, 2007, 1–6

[82]

Yang H, Hasanipanah M, Tahir M M, Bui D T. Intelligent prediction of blasting-induced ground vibration using ANFIS optimized by GA and PSO. Natural Resources Research, 2019, 29: 1–12

[83]

Marzi H, Haj Darwish A, Helfawi H. Training ANFIS using the enhanced Bees Algorithm and least squares estimation. Intelligent Automation & Soft Computing, 2017, 23: 227–234

[84]

Alwanas A A H, Al-Musawi A A, Salih S Q, Tao H, Ali M, Yaseen Z M. Load-carrying capacity and mode failure simulation of beam-column joint connection: Application of self-tuning machine learning model. Engineering Structures, 2019, 194: 220–229

[85]

Keshtegar B, Bagheri M, Yaseen Z M. Shear strength of steel fiber-unconfined reinforced concrete beam simulation: Application of novel intelligent model. Composite Structures, 2019, 212: 230–242

[86]

Yaseen Z M, Awadh S M, Sharafati A, Shahid S. Complementary data-intelligence model for river flow simulation. Journal of Hydrology (Amsterdam), 2018, 567: 180–190

[87]

Yaseen Z M, Ehteram M, Sharafati A, Shahid S, Al-Ansari N, El-Shafie A. The integration of nature-inspired algorithms with Least Square Support Vector regression models: Application to modeling river dissolved oxygen concentration. Water (Switzerland), 2018, 10(9): 1124–1131

[88]

Al-Sudani Z A, Salih S Q, Yaseen Z M. Development of multivariate adaptive regression spline integrated with differential evolution model for streamflow simulation. Journal of Hydrology (Amsterdam), 2019, 573: 1–12

[89]

Sharafati A, Tafarojnoruz A, Shourian M, Yaseen Z M. Simulation of the depth scouring downstream sluice gate: The validation of newly developed data-intelligent models. Journal of Hydro-environment Research, 2019, 29: 20–30

[90]

Sharafati A, Khosravi K, Khosravinia P, Ahmed K, Salman S A, Yaseen Z M, Shahid S. The potential of novel data mining models for global solar radiation prediction. International Journal of Environmental Science and Technology, 2019, 16(11): 7147– 7164

[91]

Sharafati A, Yasa R, Azamathulla H M. Assessment of stochastic approaches in prediction of wave-induced pipeline scour depth. Journal of Pipeline Systems Engineering and Practice, 2018, 9: 4018024

[92]

Fazel Zarandi M H, Türksen I B, Sobhani J, Ramezanianpour A A. Fuzzy polynomial neural networks for approximation of the compressive strength of concrete. Applied Soft Computing, 2008, 8(1): 488–498

[93]

Chou J S, Chiu C K, Farfoura M, Al-Taharwa I. Optimizing the prediction accuracy of concrete compressive strength based on a comparison of data-mining techniques. Journal of Computing in Civil Engineering, 2011, 25: 242–253

[94]

Nikoo M, Torabian Moghadam F, Sadowski Ł. Prediction of concrete compressive strength by evolutionary artificial neural networks. Advances in Materials Science and Engineering, 2015, 2015: 1–8

[95]

Vu-Bac N, Zhuang X, Rabczuk T. Uncertainty quantification for mechanical properties of polyethylene based on fully atomistic model. Materials (Basel), 2019, 12(21): 3613–3628

[96]

Vu-Bac N, Rafiee R, Zhuang X, Lahmer T, Rabczuk T. Uncertainty quantification for multiscale modeling of polymer nanocomposites with correlated parameters. Composites. Part B, Engineering, 2015, 68: 446–464

[97]

Kozłowski M, Kadela M. Mechanical characterization of lightweight foamed concrete. Advances in Materials Science and Engineering, 2018, 2018: 1–8

[98]

Vu-Bac N, Lahmer T, Zhuang X, Nguyen-Thoi T, Rabczuk T. A software framework for probabilistic sensitivity analysis for computationally expensive models. Advances in Engineering Software, 2016, 100: 19–31

[99]

Vu-Bac N, Lahmer T, Keitel H, Zhao J, Zhuang X, Rabczuk T. Stochastic predictions of bulk properties of amorphous polyethylene based on molecular dynamics simulations. Mechanics of Materials, 2014, 68: 70–84

[100]

Vu-Bac N, Duong T X, Lahmer T, Zhuang X, Sauer R A, Park H S, Rabczuk T. A NURBS-based inverse analysis for reconstruction of nonlinear deformations of thin shell structures. Computer Methods in Applied Mechanics and Engineering, 2018, 27(14): 713–715

[101]

Vu-Bac N, Duong T X, Lahmer T, Areias P, Sauer R A, Park H S, Rabczuk T. A NURBS-based inverse analysis of thermal expansion induced morphing of thin shells. Computer Methods in Applied Mechanics and Engineering, 2019, 350: 480–510

[102]

Salih S Q, Alsewari A A. A new algorithm for normal and large-scale optimization problems: Nomadic People Optimizer. Neural Computing & Applications, 2019, 32: 1–28

[103]

Ghorbani M A, Deo R C, Yaseen Z M, Kashani M H. Pan evaporation prediction using a hybrid multilayer perceptron-firefly algorithm (MLP-FFA) model: Case study in North Iran. Theotetical and Applied Climatology, 2017, 133: 1119–1131

[104]

Hamdia K M, Ghasemi H, Bazi Y, AlHichri H, Alajlan N, Rabczuk T. A novel deep learning based method for the computational material design of flexoelectric nanostructures with topology optimization. Finite Elements in Analysis and Design, 2019, 165: 21–30

[105]

Guo H, Zhuang X, Rabczuk T. A deep collocation method for the bending analysis of Kirchhoff plate. Computers, Materials and Continua, 2019, 59(2): 433–456

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