Evaluation of BP Neural Network Algorithms for Predicting Elastic Buckling Loads on Cold-Formed Steel Components

DAI Yiling; WANG Shaokuai; YIN Lingfeng

doi:10.21656/1000-0887.450050

Volume 46 Issue 2

Feb. 2025

Turn off MathJax

Article Contents

Article Navigation > Applied Mathematics and Mechanics > 2025 > 46(2): 129-141

DAI Yiling, WANG Shaokuai, YIN Lingfeng. Evaluation of BP Neural Network Algorithms for Predicting Elastic Buckling Loads on Cold-Formed Steel Components[J]. Applied Mathematics and Mechanics, 2025, 46(2): 129-141. doi: 10.21656/1000-0887.450050

Citation:

PDF( 4488 KB)

Evaluation of BP Neural Network Algorithms for Predicting Elastic Buckling Loads on Cold-Formed Steel Components

doi: 10.21656/1000-0887.450050

School of Civil Engineering, Southeast University, Nanjing 211189, P.R.China

Received Date: 2024-02-22
Rev Recd Date: 2024-04-23
Publish Date: 2025-02-01

Abstract

Abstract

The elastic buckling critical load is a crucial indicator for accurately assessing the load-bearing capacity of cold-formed steel components. The artificial neural networks were used to predict the buckling loads on cold-formed flanged steel columns, with geometric parameters and finite strip method results as the dataset. Six optimization algorithms based on the optimization theory were applied to train the networks, with their performances compared. Optimal hyperparameters were determined through random grid search. Three statistical parameters were used to evaluate the networks' post-training performances. The Levenberg-Marquardt (L-M) algorithm demonstrates higher accuracy in nonlinear least squares problems, significantly reducing prediction errors after multiple trainings, and outperforming other algorithms.
- BP neural network,
- optimization theory,
- elastic buckling critical load,
- cold-formed steel,
- nonlinear least squares

FullText(HTML)

References(39)

References

[1]	VON KÁRMÁN T, SECHLER E E, DONNELL L H. The strength of thin plates in compression[J]. Journal of Fluids Engineering, 1932, 54(2): 53-56.
[2]	杨梦欢. 冷弯薄壁卷边槽钢受压柱畸变屈曲性能的研究[D]. 武汉: 武汉理工大学, 2013. YANG Menghuan. Distortional buckling behavior of cold-formed thin-wall steel lipped channel columns under compression[D]. Wuhan: Wuhan University of Technology, 2013. (in Chinese)
[3]	高段. 冷弯薄壁卷边槽钢受弯构件畸变屈曲性能研究[D]. 武汉: 武汉理工大学, 2013. GAO Duan. Study on distortional buckling of cold-formed thin-walled lipped channel steel in bending[D]. Wuhan: Wuhan University of Technology, 2013. (in Chinese)
[4]	陈骥. 冷弯薄壁型钢构件的直接强度设计法[J]. 建筑钢结构进展, 2003, 5(4): 5-13. CHEN Ji. Direct strength method for the design of cold-formed lipped channel members[J]. Progress in Steel Building Structures, 2003, 5(4): 5-13. (in Chinese)
[5]	CHEUNG Y, THAM L. Finite Strip Method[M]. CRC Press, 1997.
[6]	LI Z, SCHAFER B W. Buckling analysis of cold-formed steel members with general boundary conditions using CUFSM conventional and constrained finite strip methods[C]// 20 th International Specialty Conference on Cold-Formed Steel Structures. St Louis, Missouri, 2010.
[7]	ÁDÁNY S, SCHAFER B W. Buckling mode decomposition of single-branched open cross-section members via finite strip method: derivation[J]. Thin-Walled Structures, 2006, 44(5): 563-584. doi: 10.1016/j.tws.2006.03.013
[8]	UNGUREANU V, DUBINA D. Recent research advances on ECBL approach, part Ⅰ: plastic-elastic interactive buckling of cold-formed steel sections[J]. Thin-Walled Structures, 2004, 42(2): 177-194. doi: 10.1016/S0263-8231(03)00056-9
[9]	DAVIES J M. Recent research advances in cold-formed steel structures[J]. Journal of Constructional Steel Research, 2000, 55(1/2/3): 267-288.
[10]	WANG T, ZHA Z, PAN C. Prediction for elastic local buckling stress and ultimate strength of H-section beam[J]. Heliyon, 2023, 9(4): e14700. doi: 10.1016/j.heliyon.2023.e14700
[11]	ZARRINGOL M, THAI H T, THAI S, et al. Application of ANN to the design of CFST columns[J]. Structures, 2020, 28: 2203-2220. doi: 10.1016/j.istruc.2020.10.048
[12]	WU T Y, EL-TAWIL S, MCCORMICK J. Effect of cyclic flange local buckling on the capacity of steel members[J]. Engineering Structures, 2019, 200: 109705. doi: 10.1016/j.engstruct.2019.109705
[13]	PITTON S F, RICCI S, BISAGNI C. Buckling optimization of variable stiffness cylindrical shells through artificial intelligence techniques[J]. Composite Structures, 2019, 230: 111513. doi: 10.1016/j.compstruct.2019.111513
[14]	TOHIDI S, SHARIFI Y. Neural networks for inelastic distortional buckling capacity assessment of steel Ⅰ-beams[J]. Thin-Walled Structures, 2015, 94: 359-371. doi: 10.1016/j.tws.2015.04.023
[15]	张广江, 杨德泽, 楚锡华. 基于人工神经网络的颗粒材料本构关系及边值问题研究[J]. 应用数学和力学, 2024, 45(2): 155-166. doi: 10.21656/1000-0887.440248 ZHANG Guangjiang, YANG Deze, CHU Xihua. Study on constitutive relations and boundary value problems of granular materials based on artificial neural networks[J]. Applied Mathematics and Mechanics, 2024, 45(2): 155-166. (in Chinese) doi: 10.21656/1000-0887.440248
[16]	KAVEH A, BAKHSHPOORI T, HAMZE-ZIABARI S M. GMDH-based prediction of shear strength of FRP-RC beams with and without stirrups[J]. Computers and Concrete, 2018, 22(2): 197-207.
[17]	KAVEH A, ELMIEH R, SERVATI H. Prediction of moment-rotation characteristic for semi-rigid connections using BP neural networks[C]//Computational Engineering Using Metaphors From Nature, 2001: 15-24.
[18]	IRANMANESH A, KAVEH A. Structural optimization by gradient-based neural networks[J]. International Journal for Numerical Methods in Engineering, 1999, 46(2): 297-311. doi: 10.1002/(SICI)1097-0207(19990920)46:2<297::AID-NME679>3.0.CO;2-C
[19]	KAVEH A, IRANMANESH A. Comparative study of back propagation and improved counter propagation neural nets in structural analysis and optimization[J]. International Journal of Space Structures, 1998, 13(4): 177-185. doi: 10.1177/026635119801300401
[20]	MOJTABAEI S M, BECQUE J, HAJIRASOULIHA I, et al. Predicting the buckling behaviour of thin-walled structural elements using machine learning methods[J]. Thin-Walled Structures, 2023, 184: 110518. doi: 10.1016/j.tws.2022.110518
[21]	WASZCZYSZYN Z, BARTCZAK M. Neural prediction of buckling loads of cylindrical shells with geometrical imperfections[J]. International Journal of Non-Linear Mechanics, 2002, 37(4/5): 763-775.
[22]	MARKOPOULOS A P, MANOLAKOS D E, VAXEVANIDIS N M. Prediction of the collapse modes of PVC cylindrical shells under compressive axial loads using artificial neural networks[C]//The International Federation for Information Processing. Boston, MA, 2007: 251-258.
[23]	PALA M. A new formulation for distortional buckling stress in cold-formed steel members[J]. Journal of Constructional Steel Research, 2006, 62(7): 716-722.
[24]	PALA M, CAGLAR N. A parametric study for distortional buckling stress on cold-formed steel using a neural network[J]. Journal of Constructional Steel Research, 2007, 63(5): 686-691.
[25]	GUZELBEY I H, CEVIK A, ERKLIG A. Prediction of web crippling strength of cold-formed steel sheetings using neural networks[J]. Journal of Constructional Steel Research, 2006, 62(10): 962-973.
[26]	DEGTYAREV V V. Neural networks for predicting shear strength of CFS channels with slotted webs[J]. Journal of Constructional Steel Research, 2021, 177: 106443.
[27]	DEGTYAREV V V, NASER M Z. Boosting machines for predicting shear strength of CFS channels with staggered web perforations[J]. Structures, 2021, 34: 3391-3403.
[28]	ÁDÁNY S, SCHAFER B W. A full modal decomposition of thin-walled, single-branched open cross-section membersvia the constrained finite strip method[J]. Journal of Constructional Steel Research, 2008, 64(1): 12-29.
[29]	NOORZAEI J, HAKIM S, JAAFAR M, et al. An optimal architecture of artificialneural network for predicting compressive strength of concrete[J]. Indian Concrete Journal, 2007, 81(8): 17-24.
[30]	FARZINPOUR A, DEHCHESHMEH E M, BROUJERDIAN V, et al. Efficient boosting-based algorithms for shear strength prediction of squat RC walls[J]. Case Studies in Construction Materials, 2023, 18: e01928.
[31]	BAI C, NGUYEN H, ASTERIS P G, et al. A refreshing view of soft computing models for predicting the deflection of reinforced concrete beams[J]. Applied Soft Computing, 2020, 97: 106831. http://www.zhangqiaokeyan.com/journal-foreign-detail/0704028534301.html
[32]	HAKIM S J S, PAKNAHAD M, KAMARUDIN A F, et al. Buckling prediction in steel columns: unveiling insights with artificial neural networks[J]. International Journal of Engineering Trends and Technology, 2023, 71(9): 322-330.
[33]	AHMAD A, COTSOVOS D M, LAGAROS N D. Assessing the reliability of RC code predictions through the use of artificial neural networks[C]//School of Energy, Geoscience, Infrastructure and SocietyInstitute for Infrastructure & Environment. 2016.
[34]	HAGAN M T, DEMUTH H B, BEALE M. Neural Network Design[M]. PWS Publishing Co, 1997.
[35]	The MathWorks[M]. Natick, MA: MATLAB, 2012.
[36]	DENNIS JR J E, SCHNABEL R B. Numerical Methods for Unconstrained Optimization and Nonlinear Equations[M]. SIAM, 1996.
[37]	MARQUARDT D W. An algorithm for least-squares estimation of nonlinear parameters[J]. Journal of the Society for Industrial and Applied Mathematics, 1963, 11(2): 431-441.
[38]	M∅LLER M F. A scaled conjugate gradient algorithm for fast supervised learning[J]. Neural Networks, 1993, 6(4): 525-533.
[39]	WORKS M. Statistics and Machine Learning Toolbox User's Guide[M]. Matwork Inc, 2017.