Wavelet density-based adaptive importance sampling method

• The paper presents a new importance sampling method.
• Samples from important regions are generated by adaptive Markov chain.
• Wavelet density estimation can efficiently approximate importance sampling density.
• Four examples demonstrated the accuracy and efficiency of the present method.
• The method is compared with the conventional kernel-based importance sampling.

This paper presents a new importance sampling method for efficient structural reliability assessment. 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 estimation technique. This approach 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. Four examples including a finite element-based reliability analysis are given to demonstrate the proposed method. Comparisons of the new method and the classical kernel-based importance sampling are made.