An efficient adaptive importance samping method for structural reliability analysis

This study develops an efficient adaptive importance sampling method based on adaptive Markov chain Monte Carlo and fast Gauss transform technique for reliability analysis. In the proposed method, the samples on the failure domain are generated by the adaptive Metropolis algorithm, then the importance sampling density is constructed by means of adaptive kernel density estimation method, and the fast Gauss transform are finally adopted to accelerate the computation of the kernel function in the importance sampling procedure. The adaptive Metropolis algorithm can obtain more different samples on failure domain with the same computational effort when compared with the original Metropolis method. In another word, it can effectively decrease the number of structural analyses and thereby can improve the efficiency of the proposed method. The fast Gauss transform can considerably decrease the computational complexity of the kernel density estimation method and avoid mounts of CPU time needed in the importance sampling procedure. Numerical examples illustrate that the proposed method can provide accurate and computationally efficient solutions of the problem.