Abstract
Structural reliability is defined as the safety probability of the structure under the influence of uncertain factors over a given period of time. The direct integration method from the definition of reliability is closer to the true value. However, the complex integration domain and the calculation of multiple integrals bring difficulties for reliability calculation. This study proposes a multiple correlation neural networks (MCNN) method to solve these problems. In the first step, a set of artificial neural networks (ANNs) are built to approximate the safety domain of structural reliability. Then, the trained ANNs are connected with improved dual neural networks to form the MCNN method. Using the correlation of ANNs in MCNN, the solution of multiple definite integrals with the implicit integral domain is obtained. The proposed method has significant accuracy and efficiency compared with other existing methods and increases the computational stability of ANN-based reliability calculation methods. The performances of the newly proposed method in calculation accuracy and efficiency are analyzed for several structural reliability problems.
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References
Aljarah I, Faris H, Mirjalili S (2018) Optimizing connection weights in neural networks using the whale optimization algorithm. Soft Comput 22(1):1–15. https://doi.org/10.1007/s00500-016-2442-1
Allahviranloo T (2005) Romberg integration for fuzzy functions. Appl Math Comput 168(2):866–876. https://doi.org/10.1016/j.amc.2004.09.036
Asteris PG, Nozhati S, Nikoo M, Cavaleri L, Nikoo M (2019) Krill herd algorithm-based neural network in structural seismic reliability evaluation. Mech Adv Mater Struct 26(13):1146–1153. https://doi.org/10.1080/15376494.2018.1430874
Au SK, Beck JL (2001) Estimation of small failure probabilities in high dimensions by subset simulation. Probab Eng Mech 16(4):263–277. https://doi.org/10.1016/S0266-8920(01)00019-4
Bucher C, Most T (2008) A comparison of approximate response functions in structural reliability analysis. Probab Eng Mech 23(2–3):154–163. https://doi.org/10.1016/j.probengmech.2007.12.022
Cardoso JB, Almeida JRD, Dias JM, Coelho PG (2008) Structural reliability analysis using monte carlo simulation and neural networks. Adv Eng Softw 39(6):505–513. https://doi.org/10.1016/j.advengsoft.2007.03.015
Cheng J, Li QS (2008) Reliability analysis of structures using artificial neural network based genetic algorithms. Comput Methods Appl Mech Eng 197(45–48):3742–3750. https://doi.org/10.1016/j.cma.2008.02.026
Chojaczyk AA, Teixeira AP, Neves LC, Cardoso JB, Soares CG (2015) Review and application of artificial neural networks models in reliability analysis of steel structures. Struct Saf 52(3):78–89. https://doi.org/10.1016/j.strusafe.2014.09.002
Dai H, Zhang H, Wang W (2015) A multiwavelet neural network-based response surface method for structural reliability analysis. Comput Aided Civ Infrastruct Eng 30(2):151–162. https://doi.org/10.1111/mice.12086
Dey A, Miyani G, Sil A (2020) Application of artificial neural network (ANN) for estimating reliable service life of reinforced concrete (RC) structure bookkeeping factors responsible for deterioration mechanism. Soft Comput 24:2109–2123. https://doi.org/10.1007/s00500-019-04042-y
Du J, Li H (2019) Direct integration method based on dual neural networks to solve the structural reliability of fuzzy failure criteria. Proc Inst Mech Eng Part C J Mech Eng Sci 233(19–20):7183–7196. https://doi.org/10.1177/0954406219868498
Genz AC, Malik AA (1980) Remarks on algorithm 006: an adaptive algorithm for numerical integration over an N-dimensional rectangular region. J Comput Appl Math 6(4):295–302. https://doi.org/10.1016/0771-050X(80)90039-X
Goh AT, Kulhawy FH (2003) Neural network approach to model the limit state surface for reliability analysis. Can Geotech J 40(6):1235–1244. https://doi.org/10.1139/t03-056
Gomes HM, Awruch AM (2004) Comparison of response surface and neural network with other methods for structural reliability analysis. Struct Saf 26(1):49–67. https://doi.org/10.1016/S0167-4730(03)00022-5
Hagan MT, Menhaj MB (1994) Training feedforward networks with the Marquardt algorithm. IEEE Trans Neural Netw 5(6):989–993. https://doi.org/10.1109/72.329697
Jin N, Liu D (2008) Wavelet basis function neural networks for sequential learning. IEEE Trans Neural Netw 19(3):523–528. https://doi.org/10.1109/TNN.2007.911749
Kaymaz I, McMahon CA (2005) A response surface method based on weighted regression for structural reliability analysis. Probab Eng Mech 20(1):11–17. https://doi.org/10.1016/j.probengmech.2004.05.005
Kim SH, Na SW (1997) Response surface method using vector projected sampling points. Struct Saf 19(1):3–19. https://doi.org/10.1016/S0167-4730(96)00037-9
Li J, Wang H, Kim NH (2012) Doubly weighted moving least squares and its application to structural reliability analysis. Struct Multidiplinary Optim 46(1):69–82. https://doi.org/10.1007/s00158-011-0748-2
Li H, He Y, Nie X (2018) Structural reliability calculation method based on the dual neural network and direct integration method. Neural Comput Appl 29(7):425–433. https://doi.org/10.1007/s00521-016-2554-7
Li H, Li Y, Li S (2019) Dual neural network method for solving multiple definite integrals. Neural Comput 31(1):208–232. https://doi.org/10.1162/neco_a_01145
Li SJ, Huang XZ, Wang DH (2022) Stochastic configuration networks for multi-dimensional integral evaluation. Inf Sci 601:323–339. https://doi.org/10.1016/j.ins.2022.04.005
Liao SH, Hsieh JG, Chang JY, Lin CT (2015) Training neural networks via simplified hybrid algorithm mixing nelder—mead and particle swarm optimization methods. Soft Comput 19(3):679–689. https://doi.org/10.1007/s00500-014-1292-y
Liu P, Kiureghian AD (1991) Optimization algorithms for structural reliability. Struct Saf 9(3):161–177. https://doi.org/10.1016/0167-4730(91)90041-7
Liu D, Peng Y (2012) Reliability analysis by mean-value second-order expansion. J Mech Des 134(6):061005. https://doi.org/10.1115/1.4006528
Lloyd S, Irani RA, Ahmadi M (2020) Using neural networks for fast numerical integration and optimization. IEEE Access 8:84519–84531. https://doi.org/10.1109/ACCESS.2020.2991966
Nezhad HB, Miri M, Ghasemi MR (2019) New neural network-based response surface method for reliability analysis of structures. Neural Comput Appl 31(3):777–791. https://doi.org/10.1007/s00521-017-3109-2
Nie J, Ellingwood BR (2000) Directional methods for structural reliability analysis. Struct Saf 22(3):233–249. https://doi.org/10.1016/s0167-4730(00)00014-x
Niederreiter H, Spanier J (2000) Monte Carlo and quasi-Monte Carlo methods. Springer, Heidelberg
Papadopoulos V, Giovanis DG, Lagaros ND, Papadrakakis M (2012) Accelerated subset simulation with neural networks for reliability analysis. Comput Methods Appl Mech Eng 223:70–80. https://doi.org/10.1016/j.cma.2012.02.013
Papadrakakis M, Lagaros ND (2002) Reliability-based structural optimization using neural networks and Monte Carlo simulation. Comput Methods Appl Mech Eng 191(32):3491–3507. https://doi.org/10.1016/S0045-7825(02)00287-6
Papadrakakis M, Papadopoulos V, Lagaros ND (1996) Structural reliability analyis of elastic-plastic structures using neural networks and Monte Carlo simulation. Comput Methods Appl Mech Eng 136(1–2):145–163. https://doi.org/10.1016/0045-7825(96)01011-0
Place J, Stach J (1999) Efficient numerical integration using Gaussian quadrature. SIMULATION 73(4):232–237. https://doi.org/10.1177/003754979907300405
Rajashekhar MR, Ellingwood BR (1993) A new look at the response surface approach for reliability analysis. Struct Saf 12(3):205–220. https://doi.org/10.1016/0167-4730(93)90003-J
Ren Y, Bai G (2011) New neural network response surface methods for reliability analysis. Chin J Aeronaut 24(1):25–31. https://doi.org/10.1016/S1000-9361(11)60004-6
Roussouly N, Petitjean F, Salaun M (2013) A new adaptive response surface method for reliability analysis. Probab Eng Mech 32:103–115. https://doi.org/10.1016/j.probengmech.2012.10.001
Rubinstein RY, Kroese DP (2007) Simulation and the Monte-Carlo method. Wiley, New York
Shayanfar MA, Barkhordari MA, Barkhori M, Barkhori M (2018) An adaptive directional importance sampling method for structural reliability analysis. Struct Saf 70:14–20. https://doi.org/10.1016/j.strusafe.2017.07.006
Simos TE (2009) Closed Newton-cotes trigonometrically-fitted formulae of high order for long-time integration of orbital problems. Appl Math Lett 22(10):1616–1621. https://doi.org/10.1016/j.aml.2009.04.008
Su H, Lan F, He Y, Chen J (2019) A modified downhill simplex algorithm interpolation response surface method for structural reliability analysis. Eng Comput 37(4):1423–1450. https://doi.org/10.1108/EC-03-2019-0085
Tvedt L (1990) Distribution of quadratic forms in normal space—application to structural reliability. J Eng Mech 116(6):1183–1197. https://doi.org/10.1061/(ASCE)0733-9399(1990)116:6(1183)
Wang DH, Li M (2017) Stochastic configuration networks: fundamentals and algorithms. IEEE Trans Cybern 47(10):3466–3479. https://doi.org/10.1109/TCYB.2017.2734043
Yan F, Lin Z (2016) New strategy for anchorage reliability assessment of GFRP bars to concrete using hybrid artificial neural network with genetic algorithm. Compos B Eng 92:420–433. https://doi.org/10.1016/j.compositesb.2016.02.008
Yoon S, Lee YJ, Jung HJ (2020) Accelerated monte carlo analysis of flow-based system reliability through artificial neural network-based surrogate models. Smart Struct Syst 26(2):175–184. https://doi.org/10.12989/sss.2020.26.2.175
Zeng ZZ, Wang YN, Wen H (2006) Numerical integration based on a neural network algorithm. Comput Sci Eng 8(4):42–48. https://doi.org/10.1109/MCSE.2006.73
Zhang W, Cui W (1997) Direct integration method for structural reliability calculation. J Shanghai Jiao Tong Univ 31(2):114–116
Zhang J, Du X (2010) A second-order reliability method with first-order efficiency. J Mech Des 132(10):101006. https://doi.org/10.1115/1.4002459
Zhang T, He D (2018) An improved high-order statistical moment method for structural reliability analysis with insufficient data. Proc Inst Mech Eng Part C J Mech Eng Sci 232(6):1050–1056. https://doi.org/10.1177/0954406217694662
Zhang Z, Jiang C, Wang GG, Han X (2015) First and second order approximate reliability analysis methods using evidence theory. Reliab Eng Syst Saf 137:40–49. https://doi.org/10.1016/j.ress.2014.12.011
Acknowledgments
The work was supported by National Natural Science Foundation of China (51975110), Liaoning Revitalization Talents program (XLYC1907171), and Fundamental Research Funds for the Central Universities (N2003005).
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Li, S., Huang, X., Wang, X. et al. A new reliability analysis approach with multiple correlation neural networks method. Soft Comput 27, 7449–7458 (2023). https://doi.org/10.1007/s00500-022-07685-6
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DOI: https://doi.org/10.1007/s00500-022-07685-6