Structural Reliability And Reliability Sensitivity Analysis, Digital Simulation Method

Based on the previous works in reliability, a series of reliability analysis methods and probabilistic sensitivity analysis (PSA) methods are developed and improved, the major novelties are listed as follows:1. Based on the linear regression (LR) PSA method, an improved PSA method is presented by use of weighted linear regression (WLR). In the presented method, the hyperplane is approximated by the WLR though introducing rational weighted coefficients. Thus the reliability sensitivity results by WLR are robuster than that by the LR. In addition, two strategies of selecting the samples are proposed, by which the hyperplane can be approximated more efficiently and quickly.2. By use of the efficiency and adaptability of Markov chain simulating sample in the interested region, a PSA method is presented on the basis of the Markov chainsimulation and WLR, and a PSA integral method based on the Markov chain simulation is presented as well. Comparing with the Monte Carlo simulation based LR method, the presented PSA method based on Markov chain simulation and WLR possesses higher efficiency and precision. Comparing with Monte Carlo simulation based PSA integral method, the presented PSA integral method based on Markov chain simulation has higher efficiency, especially in case of small failure probability.3. A conditional probability simulation method with high efficiency is presented to evaluate structural failure probability. In the presented method, a failure region whose failure probability can be obtained analytically is introduced firstly, and the structure failure probability is transformed as the product of the failure probability in the introduced failure region and a characteristic factor. The characteristic factor is the ratio of the conditional probability of the introduced failure region and that of the structural failure region, which can be evaluated by Markov chain simulation. The presented method has high efficiency and strong applicability to the implicit limit state function.