Study On The Analytical Methods Of Structural System Reliability

It is a great advance to design and evaluate engineering structures based on the reliability theory. But, this application is only limited to the component level in the past several decades. It is common knowledge that most of the structures are structural systems which are composed of many components. So, recently, more and more attention is paid to the calculation of system reliability. How to find the failure modes and how to calculate the failure probability are two key points in the structural system reliability analysis. The search work in this paper was made around the above two key points, and the main results are as follows:A new numerical algorithm is proposed in this paper, which is applicable to those reliability problems when the performance function has no explicit expression. In this method, if the design point is close to the limit state surface, the current reliability index and design point can be found by solving nonlinear equations, otherwise by solving approximate linear functions. In this way, the design point becomes more and more close to the limit state surface. Because the response surface function does not need to be constructed in this method, the calculation becomes very simple. By this method, the calculation amount is decreased by 30-40 percent compared to the traditional method. The calculation efficiency is increased quite a lot. So, this new method is applicable for the reliability analysis of large and complicated engineering structures.A new method for calculating system failure probability is advanced in this paper, in which the conditional failure mode is approximated to a linear equivalent failure mode. Based on the analytical expression of the linear equivalent failure mode and principle of conditional probability, this new method is derived, by which the multinomal integration is simplified to a simple algebra calculation. This method is suitable not only for the parallel systems but also for the series systems. By this method, the calculation accuracy is increased and the calculation amount is decreased, and the non-convergence problem does not exist.An improved differential equivalent recursion algorithm is given in this article. Firstly, the analytical expression of the equivalent failure mode is derived; Secondly, the reasons of error occurred in the process of finding system failure probability by using the equivalent failure mode are analyzed; Finally, a corresponding revised formula is proposed. This algorithm has high accuracy and less calculation amount. So, it lays a very good foundation for the differential equivalent recursion algorithm to be used in finding system failure modes and in calculating system failure probability.Based on the probability evaluation system, a new algorithm named generalized bounding method for finding main failure modes is proposed. (1) In order to let the components with large failure probabilities involved in the main failure modes, the joint failure probabilities ofstage failure paths should be satisfied with the condition of stage bound; (2) In order to delete the failure paths with less influences to failure probability of whole system, the failure probability of stage failure paths should be satisfied with the condition of whole bound; (3) In order to delete the failure paths with the same performance functions, the increment of loads should be positive value when components are failure. This method has high accuracy and significant efficiency, and the main failure modes of system usually could not be missed.