zbMATH — the first resource for mathematics

Neural-network-based realibility analysis: A comparative study. (English) Zbl 1016.74044
Summary: We summarize a study on the applicability of different kinds of neural networks for the probabilistic analysis of structures, when the sources of randomness can be modeled as random variables. The networks are employed as numerical devices for substituting the finite element code needed by Monte Carlo simulation. The comparison comprehends two network types (multi-layer perceptrons and radial basis function classifiers), cost functions (sum of square errors and cross-entropy), optimization algorithms (back-propagation, Gauss-Newton, Newton-Raphson), sampling methods for generating the training population (using uniform and actual distributions of the variables) and purposes of neural network use (as functional approximators and data classifiers). The comparative study is performed over four examples, corresponding to different types of limit state function and structural behaviors. The analysis indicates some recommended ways of employing neural networks in this field.

74K99 Thin bodies, structures
92B20 Neural networks for/in biological studies, artificial life and related topics
62N05 Reliability and life testing
Full Text: DOI
[1] Ang, G.L; Ang, A.H.S; Tang, W.H, Optical importance sampling density estimator, J. eng. mech., 118, 1146-1163, (1991)
[2] Ayyub, B; McCuen, R.H, Simulation-based reliability methods, (), 53-69
[3] T.T. Binh, U. Korn, Scalar optimization with linear and nonlinear constraints using evolution strategies, in: B. Reusch (Ed.), Computational Intelligence Theory and Applications, Lecture Notes in Computer Science, vol. 1226, Springer, Berlin, 1997
[4] Box, G.E.P; Draper, N.R, Empirical model building and response surfaces, (1987), Wiley New York · Zbl 0482.62065
[5] Bucher, C.G, Adaptive sampling: an iterative fast Monte-Carlo procedure, Struct. safety, 5, 119-126, (1988)
[6] Chapman, O.J; Crossland, A.D, Neural networks in probabilistic structural mechanics, (), 317-330
[7] Cichocki, A; Unbehauen, R, Neural networks for optimization and signal processing, (1993), Wiley Chichester · Zbl 0824.68101
[8] Ditlevsen, O; Madsen, H.O, Structural reliability methods, (1999), Wiley Chichester
[9] Enevoldsen, I; Faber, M.H; Sorensen, J.D, Adaptive response surface techniques in reliability estimation, (), 1257-1264
[10] Faravelli, L, Response-surface approach for reliability analysis, J. eng. mech., 115, 2763-2781, (1989)
[11] Hartman, E.J; Keeler, J.D; Kowalski, J.M, Layered neural networks with Gaussian hidden units as universal approximations, Neural comput., 2, 210-215, (1990)
[12] Hornik, K.M; Stinchcommbe, M; White, H, Multilayer feedforward networks are universal approximators, Neural networks, 2, 359-366, (1989) · Zbl 1383.92015
[13] J.E. Hurtado, D.A. Alvarez, Reliability assessment of structural systems using neural networks, in: Proc. ECCOMAS-2000, ECCOMAS, Barcelona, 2000
[14] Hurtado, J.E; Barbat, A.H, Monte Carlo techniques in computational stochastic mechanics, Arch. comput. meth. eng., 4, 3-30, (1998)
[15] Ishibuchi, H; Tanaka, H, Fuzzy regression analysis using neural networks, Fuzzy set syst., 50, 257-265, (1987)
[16] Kim, S.H; Na, S.W, Response surface method using vector projected points, Struct. safety, 19, 3-19, (1997)
[17] Melchers, R.E, Structural reliability: analysis and prediction, (1999), Wiley Chichester
[18] Papadrakakis, M; Papadopoulos, V; Lagaros, N.D, Structural reliability analysis of elastic – plastic structures using neural networks and Monte Carlo simulation, Comput. methods appl. mech. engrg., 136, 145-163, (1996) · Zbl 0893.73079
[19] Resnikoff, H.L; Wells, R.O, Wavelet analysis, (1998), Springer New York
[20] Ripley, B.D, Pattern recognition and neural networks, (1996), Cambridge University Press Cambridge · Zbl 0853.62046
[21] Rubinstein, R.Y, Monte Carlo optimization, simulation and sensitivity of queueing network, (1992), Krieger Malabar
[22] Saraiva, J.M.F; Ebecken, N.F.F, Application of neural networks in structural reliability analysis, Rev. int. met. num. calc. dis. ing., 14, 167-180, (1998), (in Portuguese)
[23] Schuëller, G.I; Stix, R, A critical appraisal of methods to determine failure probabilities, Struct. safety, 4, 293-309, (1987)
[24] Theodoridis, S; Koutroumbas, K, Pattern recognition, (1999), Academic Press London
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.