EFFICIENT ESTIMATION OF DYNAMIC RELIABILITY BASED ON SIMPLE ADDITIVE RULES OF PROBABILITY

Importance sampling technique based on elementary failure regions and domain decomposition method are efficient for dealing with problems with high-dimensional small failure probability. According to importance sampling technique, the identification of elementary failure regions is firstly proposed in this paper, which is corresponding to the failure of a particular output response at a particular instant. Then, according to domain decomposition method, mutual exclusive sets are proposed. According to the relation between elementary failure regions and mutual exclusive sets, and the simple additive rules of probability, the failure probability can be obtained. The key problems are the determination of unit impulse response function and the number of samples falling in the mutual exclusive sets. A single degree-of-freedom system and a two-degree-of-freedom system subjected to Gaussian white noise are analyzed numerically. Results show that the proposed method has higher efficiency than Monte Carlo method to estimate small failure probability, and similar efficiency to importance sampling based on elementary failure regions and domain decomposition method.