A nonlinear wavelet density-based importance sampling for reliability analysis Wang, Wei; Dai, Hongzhe
Importance sampling is a commonly used variance reduction technique for estimating reliability of a structural system. The performance of importance sampling is critically dependent on the choice of the sampling density. For the commonly used adaptive importance sampling method, the construction of the sampling density relies on the kernel-based density estimation. However, the choice of the initial bandwidth of the local windows may heavily affect the accuracy of the kernel method, particularly when the number of samples is not very large. To overcome this difficulty, this study develops a new adaptive importance sampling method based on nonlinear wavelet thresholding density estimator. The method utilizes the adaptive Markov chain simulation to generate samples that can adaptively populate the important region. The importance sampling density is then constructed using nonparametric wavelet density to implement the importance sampling. The methods takes advantage of the attractive properties of the Daubechies’ wavelet family (e.g., localization, various degrees of smoothness, and fast implementation) to provide good density estimations. Compared with the kernel density estimator, the nonlinear wavelet thresholding density estimator has a high degree of flexibility in terms of convergence rate and smoothness. Moreover, the choice of the initial parameters slightly affects the accuracy of the method. Two examples are given to demonstrate the proposed method.
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