Estimation of small failure probabilities in high dimensions by subset simulation

Abstract

A new simulation approach, called`subset simulation', is proposed to compute small failure probabilities encountered in reliability analysis of engineering systems. The basic idea is to express the failure probability as a product of larger conditional failure probabilities by introducing intermediate failure events. With a proper choice of the conditional events, the conditional failure probabilities can be made suf®ciently large so that they can be estimated by means of simulation with a small number of samples. The original problem of calculating a small failure probability, which is computationally demanding, is reduced to calculating a sequence of conditional probabilities, which can be readily and ef®ciently estimated by means of simulation. The conditional probabilities cannot be estimated ef®ciently by a standard Monte Carlo procedure, however, and so a Markov chain Monte Carlo simulation (MCS) technique based on the Metropolis algorithm is presented for their estimation. The proposed method is robust to the number of uncertain parameters and ef®cient in computing small probabilities. The ef®ciency of the method is demonstrated by calculating the ®rst-excursion probabilities for a linear oscillator subjected to white noise excitation and for a ®ve-story nonlinear hysteretic shear building under uncertain seismic excitation. q

Seismic Safety Assessment by an Enhanced Monte Carlo Method

“…Different methods exist to estimate small failure probabilities by Monte Carlo simulation at reasonable computational costs, e.g. Asymptotic Sampling [3] or Subset Simulation [4].…”

Probabilistic Analysis of a Rock Salt Cavern with Application to Energy Storage Systems

“…The probability of a rare event is equal to the probability of a not-so-rare event multiplied by the probability of the not-so-rare event happens (Au & Beck, 2001). …”

“…The required number of samples (N ) to achieve a given accuracy is inversely proportional to the failure probability (Au & Beck, 2001). The accuracy of the failure probability estimated by Monte Carlo simulation can be assessed by the following equation proposed by Ang & Tang (2007)Ĉ 6) whereĈOV F is the coefficient of variation of the estimated P F .…”

Review and application of Artificial Neural Networks models in reliability analysis of steel structures

“…The simulation techniques have their origin in Monte Carlo simulation (MCS) method, which generates a large sample set of limit state evaluations and approximates the true value of the probability of failure by = , where is the number of samples lying in the failure region and S the total number of samples. In order to further improve the computational efficiency of MCS, many variance reduction techniques have been proposed [9], including importance sampling ( [10], [11]), directional simulation [12] or subset simulation ( [13], [14]). Despite these improvements, the MCS method is still timeconsuming and further development is crucial.…”