Failure Probability Estimate Of Highly Reliable Structures And Its Applications

The essence of reliability evaluation of high reliability structure is to estimate the small failure probability of the structure,i.e.accurately describe the tail distribution of the extreme response of the structure.An important index to evaluate the utility of the reliability analysis method is whether the method can obtain a more accurate calculation result with less calculation.At present,there are many numerical simulation methods,such as Monte Carlo method,important sampling method and subset simulation method and so on,which have been widely applied and developed in the corresponding fields.However,some unsolved problems still exist in practical engineering applications,Such as the expensive computation cost of Monte Carlo method,poor strategy of subset simulation method to increase sample points,and the dependency of important sampling method on efficient sampling domains.It is generally believed that the accelerated simulation methods such as the He-Gong method(which based on SGLD model)and the asymptotic sampling method have higher efficiency and wider applicability.However,the relative superiority of the two methods has not been further studied.Therefore,it is very important to carry out the comparative study on the effectiveness of the asymptotic sampling method and He-Gong method.The main research contents of this paper include:1)Analyzing the distribution characteristics of SGLD model in He-Gong method,and the moment method and extrapolation method for calculating 4 parameters in SGLD model;2)Illustrating the theoretical basis of asymptotic sampling method and its numerical simulation analysis process,and learned the basic principles of two methods to improve the computational efficiency;3)Comparing and analyzing the utility of the two numerical simulations in detail by the reliability analysis of a static structure and a single-degree-of-freedom hysteretic oscillator model under earthquake-type ground excitation;4)Appling He-Gong method to analyze the reliability of a simplified jack-up units under stochastic waves.Based on the research above,this paper deeply comprehended the numerical method of simulating random earthquake acceleration and stochastic ocean wave,and summarized the equations of motion of structures under different stochastic loads and their solutions,discussed the applicability and superiority of the two methods in different fields,and gave some suggestions on the comparison results and method selection.This paper also expanded the scope of the He-Gong method application.The research in this paper shows that both the asymptotic sampling method and He-Gong method can efficiently estimate the small failure probability of the structure.In addition,He-Gong method can approximate the tail distribution of the limit state function based on a random simulation process,while the asymptotic sampling method does not have this feature.Therefore,it is suggested that the He-Gong method should be prioritized when there is a need to change the safety margin,whereas in other cases both methods can be used.