A wavelet thresholding density-based adaptive importance samping method

This study develops an efficient adaptive importance sampling method based on nonlinear wavelet thresholding for reliability analysis. In the proposed method, the pre-sampling samples, which fall in the failure region, are used to estimate the density via the nonlinear wavelet thresholding estimator, and the density obtained is applied as the near-optimal sampling density to implement the importance sampling. 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. Therefore, the proposed method can achieve comparable accuracy with fewer pre-sampling samples and improve the computational efficiency of the traditional method. Numerical examples show that the proposed method is applicable for wide-range reliability problems with multi-design points or noisy limit state functions.