A sequential importance sampling method for efficiently estimating posterior augmented mean of structural performance

The augmented mean (AM) is the expected structural performance with respect to random input vector and its distribution parameter vector. In practical engineering, the prior AM may deviate from actual value due to limited prior information, thus it is necessary to calibrate the prior AM, so that the posterior AM can match the gradually collected observations during structure service. The posterior AM can be more objective to assess the statistical structure performance by incorporating the new observations into the prior information in engineering applications. For the method lack of efficiently calibrating AM to obtain posterior AM, this paper proposes a sequential importance sampling (IS) method with three contributions. The first is constructing an optimal IS density (oISd) to minimize the variance of posterior AM estimation. To solve the sampling difficulty caused by the irregularity and implicit nature of the oISd, an easy sampling quasi-oISd (q-oISd) is proposed on the Kriging model of performance, and a strategy of adaptively training the Kriging model is also proposed to make q-oISd approach oISd accurately. The second is to propose an accept-reject method for sampling q-oISd and prove its correctness. The third is to derive the estimation format of the posterior AM and establish an adaptive strategy for updating the Kriging model to make the estimation approach the true value. Due to the maximum variance reduction of the posterior AM estimation resulted from the proposed oISd, and the number decrease of the performance evaluation resulted from adaptively updating Kriging model sequentially, the efficiency of the proposed IS method is higher than that of some existing methods, which is verified by the presented examples.