Accelerated subset simulation with neural networks for reliability analysis. (English) Zbl 1253.74073

Summary: Subset Simulation (SS) is a powerful tool, simple to implement and capable of solving a broad range of reliability analysis problems. In many cases however, SS leads to reliability predictions that exhibit a large variability due to the fact that the robustness of the SS prediction depends on the selection of an adequate width of the proposal distribution when applying the modified Metropolis algorithm. In this work a Neural Network-based SS (SS-NN) methodology is proposed in which NN are effectively trained over smaller sub-domains of the total random variable space which are generated progressively at each SS level by the modified Metropolis algorithm. NN are then used as robust meta-models in order to increase the efficiency of SS by increasing significantly the samples per SS level with a minimum additional computational effort. In the numerical examples considered, it is demonstrated that the training of a sufficiently accurate NN meta-model in the context of SS simulation leads to more robust estimations of the probability of failure both in terms of mean and variance of the estimator.


74P05 Compliance or weight optimization in solid mechanics
90B25 Reliability, availability, maintenance, inspection in operations research
Full Text: DOI


[1] Bucher, C.G., Adaptive sampling – an iterative fast Monte Carlo procedure, Struct. saf., 5, 119-126, (1998)
[2] Schuëller, G.I.; Pradlwarter, H.J., Benchmark study on reliability estimation in higher dimensions of structural systems – an overview, Struct. saf., 29, 167-182, (2007)
[3] Au, S.K.; Beck, J.L., A new adaptive importance sampling scheme, Struct. saf., 21, 135-158, (1999)
[4] Au, S.K.; Beck, J.L., Estimation of small failure probabilities in high dimensions by subset simulation, Probab. eng. mech., 16, 4, 263-277, (2001)
[5] Papadrakakis, M.; Papadopoulos, V.; Lagaros, N.D., Structural reliability analysis of elastic-plastic structures using neural networks and Monte Carlo simulation, Comp. meth. appl. mech. eng., 136, 145-163, (1996) · Zbl 0893.73079
[6] Hurtado, J.E.; Alvarez, D.A., Neural – network-based reliability analysis: A comparative study, Comput. methods appl. mech. engrg., 191, 1-2, 113-132, (2002) · Zbl 1016.74044
[7] Lagaros, N.D.; Garavelas, A.Th.; Papadrakakis, M., Innovative seismic design optimization with reliability constraints, Comput. methods appl. mech. engrg., 198, 1, 28-41, (2008) · Zbl 1194.74249
[8] Mesbahi, E.; Pu, Y., Application of ANN-based response surface method to prediction of ultimate strength of stiffened panels, Journal of structural engineering, 134, 10, 1649-1656, (2008)
[9] Cheng, J.; Li, Q.S., Reliability analysis of structures using artificial neural network based genetic algorithms, Comput. methods appl. mech. engrg., 197, 45-48, 3742-3750, (2008) · Zbl 1194.74515
[10] Bucher, C.; Most, T., A comparison of approximate response functions in structural reliability analysis, Probab. engrg. mech., 23, 2-3, 154-163, (2008)
[11] Hurtado, J.E., Filtered importance sampling with support vector margin: A powerful method for structural reliability analysis, Struct. saf., 29, 1, 2-15, (2007)
[12] Metropolis, N.; Rosenbluth, A.W.; Rosenbluth, M.N.; Teller, A.H., Equations of state calculations by fast computing machines, J chem phys, 21, 6, 1087-1092, (1953)
[13] Lagaros, N.D.; Papadrakakis, M., Improving the condition of the Jacobian in neural network training, Adv. in engng soft., 35, 1, 9-25, (2004)
[14] Papadrakakis, M.; Lagaros, N.D.; Tsompanakis, Y., Structural optimization using evolution strategies and neural networks, Comput. methods appl. mech. engrg., 156, 309-333, (1998) · Zbl 0964.74045
[15] MacKay, D.J.C., A practical Bayesian framework for backprop networks, Neural comput., 4, 448-472, (1992)
[16] Schiffmann, W.; Joost, M.; Werner, R., Optimization of the back-propagation algorithm for training multi-layer perceptrons, (1993), University of Koblenz, Institute of Physics Technical Report
[17] M. Riedmiller, H. Braun, A direct adaptive method for faster back-propagation learning: the RPROP algorithm, in: Proceedings of the IEEE International Conference on Neural Networks (ICNN), San Francisco, 1993, pp. 586-591.
[18] Riedmiller, M., Advanced supervised learning in multi-layer perceptrons – from back-propagation to adaptive learning algorithms, Int. journal of computer standards and interfaces, 16, 265-278, (1994)
[19] EN 1998-1(2003): Eurocode 8: Design of Structures for Earthquake Resistance. Part 1: General rules, seismic actions and rules for buildings. Commission of the European Communities, European Committee for Standardization, October 2003.
[20] PrEN 1992-1-1(2002): Eurocode 2: Design of Concrete Structures - Part 1: General Rules and Rules for Buildings. Commission of the European Communities, European Committee for Standardization, December 2002.
[21] I. Papaioannou, M. Fragiadakis, M. Papadrakakis, Inelastic analysis of framed structures using the fibre approach, in: Proceedings of the 5th International Congress on Computational Mechanics (GRACM 05), Limassol, Cyprus, June 29-July 1.
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.