Conventional Monte-Carlo integration for high reliability systems is extremely inefficient. It is possible to use a rather simple technique, known in the literature as importance sampling, to dramatically improve sampling efficiency (or the in the integral for a given amount of sampling). This technique, unlike some other variance reduction techniques, can be applied in a systematic manner to problems with one or more limit state functions, including unions and intersections of limit states. These applications as well as the theory, are outlined in this report. (Author/TRRL)
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