This paper presents a new adaptive importance sampling method that finds a near-optimal sampling density by minimizing Kullback-Leibler cross entropy, i.e. a measure of the difference between the absolute best sampling density and the importance sampling density. In particular, the proposed method employs a nonparametric multimodal probability density model called Gaussian mixture as the importance sampling density in order to fit the complex shape of the best sampling density through very few rounds of pre-sampling. The final importance sampling using the near-optimal density requires far less samples than crude Monte Carlo simulation or cross-entropy-based importance sampling employing a unimodal density function requires for achieving the desired level of convergence. The proposed method is applicable to various component and system reliability problems that have complex limit-state surfaces including those with multiple important regions. The parameters of the converged Gaussian mixture can be used to identify important regions and quantify their relative importance.
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