システム信頼性解析における効率的シミュレーション解法

概要

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An efficient simulation method is developed for time-dependent system reliability analyses, where extremely small probability of system failure is desired. The method is based upon an importance sampling technique, in which the Girsanov theorem is applied to determine an importance sampling measure on a function space. First, expressing the probability of system failure as a functional integral on the function space, we mathematically formulate an importance sampling simulation scheme, where Newton's method to determine the sampling measure is used. Next, a new method to select the optimally sampling measure proposed by the author is briefly surveyed. Finally, two simple numerical examples are shown to examine the computational efficiency of the proposed method, which indicate that the proposed method can give quite accurate estimations for the probability of system failure even if the number of generated samples are small.
日本応用数理学会の論文
2000-09-17