An importance sampling procedure for estimating failure probabilities of non-linear dynamic systems

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Journal of Vibration and Shock ›› 2013, Vol. 32 ›› Issue (4) : 163-166.

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An importance sampling procedure for estimating failure probabilities of non-linear dynamic systems

Ren Limei，Xu Wei ，Li Zhanguo

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Abstract

The failure probability is one of the most important reliability measures in structural reliability assessment of dynamical systems. This paper suggests a procedure for estimating failure probabilities of non-linear systems based on importance sampling technique. Firstly ,by used of Rice formula，the paper obtains the equivalent linear version of the non-linear systems. The paper uses design point of the equivalent linear systems to construct control function. Secondly, an importance sampling technique is used in order to estimate excursion probabilities for the non-linear system. Finally, the paper takes Duffing oscillator for example. The simulation results show the method of the paper to be correct and effective. The number of samples and the computational time are reduced significantly compared with direct Monte Carlo simulations.

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First excursion probability / Importance sampling / Mean up-crossing rate

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Ren Limei;Xu Wei;Li Zhanguo. An importance sampling procedure for estimating failure probabilities of non-linear dynamic systems[J]. Journal of Vibration and Shock, 2013, 32(4): 163-166