Domain Decomposition Method for Calculating the Failure Probability of Linear Dynamic Systems Subjected to Gaussian Stochastic Loads

Lambros S. Katafygiotis · Sai Hung Cheung

53 citations0/0 files storedJournal of Engineering Mechanics

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Probabilistic and Robust Engineering Design Seismic Performance and Analysis Reliability and Maintenance Optimization

Abstract

In this paper the problem of calculating the probability of failure of linear dynamic systems subjected to random vibrations is considered. This is a very important and challenging problem in structural reliability. The failure domain in this case can be described as a union of linear failure domains whose boundaries are hyperplanes. Each linear limit state function can be completely described by its own design point, which can be analytically determined, allowing for an exact analytical calculation of the corresponding failure probability. The difficulty in calculating the overall failure probability arises from the overlapping of the different linear failure domains, the degree of which is unknown and needs to be determined. A novel robust reliability methodology, referred to as the domain decomposition method (DDM), is proposed to calculate the probability that the response of a linear system exceeds specified target thresholds. It exploits the special structure of the failure domain, given by the union of a large number of linear failure regions, to obtain an extremely efficient and highly accurate estimate of the failure probability. The number of dynamic analyses to be performed in order to determine the failure probability is as low as the number of independent random excitations driving the system. Furthermore, calculating the reliability of the same structure under different performance objectives does not require any additional dynamic analyses. Two numerical examples are given demonstrating the proposed method, both of which show that the method offers dramatic improvement over standard Monte Carlo simulations, while a comparison with the ISEE algorithm shows that the DDM is at least as efficient as the ISEE.

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References

2002Important sampling in high dimensions 2001First excursion probabilities for linear systems by very efficient importance sampling 1997Asymptotic Expansions for Reliability and Moments of Uncertain Systems 2003Equivalent linearization and Monte Carlo simulation in stochastic dynamics 1997On the simulation of stochastic processes by spectral representation 1999Assessment of low probability events of dynamical systems by controlled Monte Carlo simulation

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2020Bounding the first excursion probability of linear structures subjected to imprecise stochastic loading 2020Application of directional importance sampling for estimation of first excursion probabilities of linear structural systems subject to stochastic Gaussian loading 2020An adaptive scheme for reliability-based global design optimization: A Markov chain Monte Carlo approach 2014Estimation of first excursion probabilities for uncertain stochastic linear systems subject to Gaussian load 2021Failure probability estimation of a class of series systems by multidomain Line Sampling 2004A two-stage Subset Simulation-based approach for calculating the reliability of inelastic structural systems subjected to Gaussian random excitations

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