Optimal design of double-layer barrel vaults using genetic and pattern search algorithms and optimized neural network as surrogate model

Abstract

This paper presents a combined method based on optimized neural networks and optimization algorithms to solve structural optimization problems. The main idea is to utilize an optimized artificial neural network (OANN) as a surrogate model to reduce the number of computations for structural analysis. First, the OANN is trained appropriately. Subsequently, the main optimization problem is solved using the OANN and a population-based algorithm. The algorithms considered in this step are the arithmetic optimization algorithm (AOA) and genetic algorithm (GA). Finally, the abovementioned problem is solved using the optimal point obtained from the previous step and the pattern search (PS) algorithm. To evaluate the performance of the proposed method, two numerical examples are considered. In the first example, the performance of two algorithms, OANN + AOA + PS and OANN + GA + PS, is investigated. Using the GA reduces the elapsed time by approximately 50% compared with using the AOA. Results show that both the OANN + GA + PS and OANN + AOA + PS algorithms perform well in solving structural optimization problems and achieve the same optimal design. However, the OANN + GA + PS algorithm requires significantly fewer function evaluations to achieve the same accuracy as the OANN + AOA + PS algorithm.

Graphical abstract

Keywords

optimization / surrogate models / artificial neural network / SAP2000 / genetic algorithm

References

[1] HaftkaR TGürdal Z. Elements of Structural Optimization. 3rd ed. Berlin: Springer Science & Business Media, 1992

[2] Shobeiri V, Ahmadi-Nedushan B. Bi-directional evolutionary structural optimization for strut-and-tie modelling of three-dimensional structural concrete. Engineering Optimization, 2017, 49(12): 2055–2078

[3] Fathnejat H, Ahmadi-Nedushan B. An efficient two-stage approach for structural damage detection using meta-heuristic algorithms and group method of data handling surrogate model. Frontiers of Structural and Civil Engineering, 2020, 14(4): 907–929

[4] Bekdaş G, Yücel M, Nigdeli S M. Estimation of optimum design of structural systems via machine learning. Frontiers of Structural and Civil Engineering, 2021, 15(6): 1441–1452

[5] Nguyen-Thoi T, Tran-Viet A, Nguyen-Minh N, Vo-Duy T, Ho-Huu V. A combination of damage locating vector method (DLV) and differential evolution algorithm (DE) for structural damage assessment. Frontiers of Structural and Civil Engineering, 2018, 12(1): 92–108

[6] Es-HaghiMSShishegaran ARabczukT. Evaluation of a novel Asymmetric Genetic Algorithm to optimize the structural design of 3D regular and irregular steel frames. Frontiers of Structural and Civil Engineering, 2020, 14(5):1110–1130

[7] Ghasemi H, Park H S, Rabczuk T. A multi-material level set-based topology optimization of flexoelectric composites. Computer Methods in Applied Mechanics and Engineering, 2018, 332: 47–62

[8] Ahmadi-NedushanBVaraeeH. Optimal design of reinforced concrete retaining walls using a swarm intelligence technique. In: The First International Conference on Soft Computing Technology in Civil, Structural and Environmental Engineering. Funchal: Civil-Comp Press, 2009

[9] ShakibaMAhmadi-Nedushan B. Engineering optimization using opposition based differential evolution. In: The First International Conference on Soft Computing Technology in Civil, Structural and Environmental Engineering. Funchal: Civil-Comp Press, 2009

[10] Ahmadi-Nedushan B, Varaee H. Minimum cost design of concrete slabs using particle swarm optimization with time varying acceleration coefficients. World Applied Sciences Journal, 2011, 13(12): 2484–2494

[11] Ahmadi-Nedushan B, Fathnejat H. A modified teaching–learning optimization algorithm for structural damage detection using a novel damage index based on modal flexibility and strain energy under environmental variations. Engineering with Computers, 2022, 38: 847–874

[12] Abualigah L, Diabat A, Mirjalili S, Abd Elaziz M, Gandomi A H. The arithmetic optimization algorithm. Computer Methods in Applied Mechanics and Engineering, 2021, 376: 113609

[13] GoldbergD E. Genetic Algorithms in Search and Optimization. Optimization. 13th ed. Boston: Addison-Wesley Professional, 1989

[14] Booker A J, Dennis J E, Frank P D, Serafini D B, Torczon V, Trosset M W. A rigorous framework for optimization of expensive functions by surrogates. Structural Optimization, 1999, 17(1): 1–13

[15] Latif M A, Saka M P. Optimum design of tied-arch bridges under code requirements using enhanced artificial bee colony algorithm. Advances in Engineering Software, 2019, 135: 102685

[16] NguyenT HVu A T. Using neural networks as surrogate models in differential evolution optimization of truss structures. In: International Conference on Computational Collective Intelligence. Da Nang: Springer, 2020

[17] Vellido A, Lisboa P J G, Vaughan J. Neural networks in business: A survey of applications (1992−1998). Expert Systems with Applications, 1999, 17(1): 51–70

[18] Papadrakakis M, Lagaros N D, Tsompanakis Y. Optimization of large-scale 3-D trusses using evolution strategies and neural networks. International Journal of Space Structures, 1999, 14(3): 211–223

[19] Kaveh A, Gholipour Y, Rahami H. Optimal design of transmission towers using genetic algorithm and neural networks. International Journal of Space Structures, 2008, 23(1): 1–19

[20] Krempser E, Bernardino H S, Barbosa H J C, Lemonge A C C. Differential evolution assisted by surrogate models for structural optimization problems. Civil-Comp Proc., 2012, 100

[21] Penadés-Plà V, García-Segura T, Yepes V. Accelerated optimization method for low-embodied energy concrete box-girder bridge design. Engineering Structures, 2019, 179: 556–565

[22] Wang J H, Jiang J H, Yu R Q. Robust back propagation algorithm as a chemometric tool to prevent the overfitting to outliers. Chemometrics and Intelligent Laboratory Systems, 1996, 34(1): 109–115

[23] Panchal G, Ganatra A, Shah P, Panchal D. Determination of over-learning and over-fitting problem in back propagation neural network. International Journal of Soft Computing, 2011, 2(2): 40–51

[24] Dietterich T. Overfitting and undercomputing in machine learning. ACM Computing Surveys, 1995, 27(3): 326–327

[25] LawrenceSGiles C LTsoiA C. Lessons in neural network training: overfitting may be harder than expected. In: Proceedings of the 14th National Conference on Artificial Intelligence. Menlo Park: AAAI, 1997

[26] SarleW S. Stopped Training and Other Remedies for Overfitting. In: Proceedings of the 27th Symposium on the Interface of Computing Science and Statistics. Pittsburgh: Interface Foundation of North America, 1995

[27] MathWorks. MATLAB Documantation. Natick: MathWorks, 2019

[28] BartonR RMeckesheimer M. Handbooks in Operations Research and Management Science 13. 2006

[29] Simpson T W, Peplinski J D, Koch P N, Allen J K. Metamodels for computer-based engineering design: Survey and recommendations. Engineering with Computers, 2001, 17(2): 129–150

[30] Jin R, Chen W, Simpson T W. Comparative studies of metamodelling techniques under multiple modelling criteria. Structural and Multidisciplinary Optimization, 2001, 23(1): 1–13

[31] Li Y F, Ng S H, Xie M, Goh T N. A systematic comparison of metamodeling techniques for simulation optimization in Decision Support Systems. Applied Soft Computing, 2010, 10(4): 1257–1273

[32] Kim B S, Bin Lee Y, Choi D H. Comparison study on the accuracy of metamodeling technique for non-convex functions. Journal of Mechanical Science and Technology, 2009, 23(4): 1175–1181

[33] MoustaphaMBourinet J MGuillaumeBSudretB. Comparative study of Kriging and support vector regression for structural engineering applications. ASCE-ASME Journal of Risk and Uncertainty in Engineering Systems. Part A: Civil Engineering, 2018, 4(2): 0000950

[34] Jiang C, Cai X, Qiu H, Gao L, Li P. A two-stage support vector regression assisted sequential sampling approach for global metamodeling. Structural and Multidisciplinary Optimization, 2018, 58(4): 1657–1672

[35] Ahmadi NedushanBChouinardL E. Statistical analysis in real time of monitoring data for Idukki Arch Dam. In: Annual Conference of the Canadian Society for Civil Engineering. Moncton: Canadian Society for Civil Engineering, 2003

[36] GhanemRSpanos P D. Stochastic Finite Elements: A Spectral Approach. New York: Springer, 2003

[37] Deng L Y. The design and analysis of computer experiments. Technometrics, 2004, 46(4): 488–489

[38] Smola A J, Schölkopf B. A tutorial on support vector regression. Statistics and Computing, 2004, 14(3): 199–222

[39] Ahmadi NedushanBChouinardL E. Use of artificial neural networks for real time analysis of dam monitoring data. In: Annual Conference of the Canadian Society for Civil Engineering. Moncton: Canadian Society for Civil Engineering, 2003

[40] Deng J, Gu D, Li X, Yue Z Q. Structural reliability analysis for implicit performance functions using artificial neural network. Structural Safety, 2005, 27(1): 25–48

[41] Mukhopadhyay A, Iqbal A. Prediction of mechanical properties of hot rolled, low-carbon steel strips using artificial neural network. Materials and Manufacturing Processes, 2005, 20(5): 793–812

[42] Mukhopadhyay A, Iqbal A. Comparison of ANN and MARS in prediction of property of steel strips. Applied Soft Computing Technologies, 2006, 34: 329–341

[43] Shahani A R, Setayeshi S, Nodamaie S A, Asadi M A, Rezaie S. Prediction of influence parameters on the hot rolling process using finite element method and neural network. Journal of Materials Processing Technology, 2009, 209(4): 1920–1935

[44] CSI. SAP2000 Integrated Software for Structural Analysis. Berkeley, CA: Computers & Structures Inc., 2011

[45] Javanmardi R, Ahmadi-Nedushan B. Cost optimization of steel-concrete composite I- girder bridges with skew angle and longitudinal slope, using the Sm toolbox and the parallel pattern search algorithm. International Journal of Optimization in Civil Engineering, 2021, 11(3): 357–382

[46] ShahBahramiJ S. Parallel Processing and Programming by GPU (In Persian). Tehran: Nas, 2016

[47] Mirjalili S. Genetic algorithm. Nature Computational Science, 2015, 28: 21–42

[48] ShapiroJ.. Genetic algorithms in machine learning. In Advanced Course on Artificial Intelligence, pp. 146-168. Springer, Berlin, Heidelberg, 1999

[49] Holland J H. Genetic algorithms. Scientific American, 1992, 267(1): 66–72

[50] GreenW A. Vibrations of space structures. In: Hodnett, F. In: Hodnett, F. Verlag: European Consortium for Mathematics in Industry, 1991

[51] Shimoda M, Liu Y, Wakasa M. Free-form optimization method for frame structures aiming at controlling time-dependent responses. Structural and Multidisciplinary Optimization, 2021, 63(1): 479–497

[52] MakowskiZ S. Book review: analysis, design and construction of steel space frames. International Journal of Space Structures, 2002, 17(2–3): 243–243

[53] Kaveh A, Moradveisi M. Size and geometry optimization of double-layer grids using CBO and ECBO algorithms. Iranian Journal of Science and Technology. Transaction of Civil Engineering, 2017, 41(2): 101–112

[54] MakowskiZ S. Analysis, Design and Construction of Braced Barrel Vaults. Boca Raton: CRC Press, 2016

[55] Kaveh A, Eskandari A, Eskandary A. Analysis of double-layer barrel vaults using different neural networks; a comparative study. International Journal of Optimization in Civil Engineering, 2021, 11(1): 113–141

[56] NowakA SCollins K R. Reliability of Structures. 2nd ed. Boca Raton: CRC Press, 2012

[57] CSI. Open Application Programming Interface (OAPI). Berkeley: Computers and Structures Inc., California, 2011

[58] HuZDuX. A random field approach to reliability analysis with random and interval variables. ASCE-ASME Journal of Risk and Uncertainty in Engineering Systems, Part B: Mechanical Engineering, 2015, 1(4): 041005

[59] JiangCLi W XHanXLiuL XLeP H. Structural reliability analysis based on random distributions with interval parameters. Computers & Structures, 2011, 89(23−24): 2292−2302

[60] Wang L, Wang X, Wang R, Chen X. Reliability-based design optimization under mixture of random, interval and convex uncertainties. Archive of Applied Mechanics, 2016, 86(7): 1341–1367

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