A support vector density‐based importance sampling for reliability assessment

An importance sampling method based on the adaptive Markov chain simulation and support vector density estimation is developed in this paper for efficient structural reliability assessment. The methodology involves the generation of samples that can adaptively populate the important region by the adaptive Metropolis algorithm, and the construction of importance sampling density by support vector density. The use of the adaptive Metropolis algorithm may effectively improve the convergence and stability of the classical Markov chain simulation. The support vector density can approximate the sampling density with fewer samples in comparison to the conventional kernel density estimation. The proposed importance sampling method can effectively reduce the number of structural analysis required for achieving a given accuracy. Examples involving both numerical and practical structural problems are given to illustrate the application and efficiency of the proposed methodology.