Research On Hybrid Uncertain Propagation And Reliability Analysis Algorithms Considering Time-Variant Effects

A large number of uncertain factors exist in engineering structures,which seriously affect the safety and service life of structures.How to conduct reasonable whole-life safety assessment based on time-variant reliability theory is an important issue in the engineering field.However,the traditional time-variant reliability method needs to calculate the outcrossing rate for all discrete moments,which leads to low calculation efficiency and the complicate calculation process.In addition,the probabilistic and non-probabilistic uncertain parameters always exist in engineering structures simultaneously,so the crucial difficulty is how to accurately characterize uncertainty and measure reliability.To address the above two problems,a semi-analytical extreme method for time-variant reliability analysis is proposed,and the probabilistic and non-probabilistic hybrid exponential model is established.The research work is summarized as follows:(1)A semi-analytical extreme method is proposed.Firstly,the stochastic process is discretized by expansion optimal linear estimation,which converts the time-variant functions to multiple instantaneous functions of discrete time nodes.Then,the approximate performance function is constructed for each time node based on first-order Taylor expansion,and the instantaneous reliability analysis is performed directly by the first-order reliability method to search the most probable point.Finally,the time-variant failure probability is calculated by the extreme method based on sampling strategy.In addition,to avoid the high computational cost of reliability analysis caused by a large number of equivalent random variables,the analytical expression of random sensitivity is derived.The results show that the semi-analytical extreme method has higher accuracy and efficiency than the traditional outcrossing rate method and extreme method.(2)A hybrid reliability analysis method is proposed based on direct probability integration and exponential convex model.Firstly,a hybrid reliability analysis model is constructed based on probability theory and non-probabilistic exponential model.The model is composed of nested double optimization layers.The outer layer is probabilistic analysis,and the inner layer is exponential non-probabilistic reliability analysis.Secondly,a hybrid exponential probability integral method is proposed by combining direct probability integral method and exponential nominal iterative method,which achieves efficient calculation of hybrid uncertainty propagation and reliability analysis.Examples show that hybrid exponential probability integral method not only can deal with static and dynamic structure simultaneously,but also can obtain the hybrid probability density function,hybrid cumulative density function,and hybrid failure probability of their response.It provides a new path to solve the safety assessment problem of static and dynamic structures with hybrid aleatory and epistemic uncertainties.