Research On Sensitivity Analysis And Optimization Design Method For Time-dependent Reliability Problems

Uncertainty widely exists in all kinds of engineering problems.Therefore,these uncertainties should be fully taken into account in reliability analysis,which helps to improve the quality and safety of the structure.Traditional structural reliability does not change with time,which is also called time-invariant reliability.However,in the long-term use process,with the cumulative service time of the structure,the deterioration of material properties and other factors,structural reliability usually shows time-varying characteristics.So it is also known as time-dependent reliability.The design optimization method based on time-dependent reliability analysis can consider the influence of time-dependent factors on structural performance in the optimization process,making the structure more secure and reliable.However,since the time-dependent reliability analysis is complicated,there are often problems in solving the time-dependent reliability based design optimization.Sensitivity analysis for reliability issues mainly studies the degree of influence of uncertain parameters on structural reliability.If the sensitivity of time-dependent reliability to parameters can be obtained,it can not only provide guidance for engineering,but also make time-dependent reliability based design optimization problems simplified and improve their computational efficiency.At present,in the field of time-dependent reliability,there are relatively few studies on sensitivity analysis.For this purpose,the following two research contents are made:(1)A time-dependent reliability sensitivity analysis method based on process discretization(i TRPD)is proposed.First,the design period is discretized,and the time-invariant reliability and the correlation coefficients between discrete elements are calculated.Then,the time-dependent reliability is transformed into the time-invariant reliability system problem.The chain differential rule and derivative technique for the multivariate standard normal probability distribution are applied to obtain the first derivative of time-dependent reliability probability for parameters,i.e.local sensitivity.Compared with the traditional central difference method,this method does not need to perform time-dependent reliability analysis twice,only one time-dependent reliability analysis is needed to obtain local sensitivity,and the solution efficiency is improved.In addition,this method is more stable and accurate than the central difference method in some problems.(2)A simplified method for solving the time-dependent reliability design optimization problem is proposed.Firstly,Sobol method is used to analyze the global sensitivity of the time-dependent reliability of the structure,and the total order coefficients of the time-dependent reliability probability with different constraints are obtained.The total order coefficients are weighted according to the target time-dependent reliability of different constraints.Then,the weighted total order coefficients of each variable and parameter are obtained.The coefficients can reflect the degree of influence of variables and parameters on the overall reliability constraints.Sort the weighted total order coefficients according to the order from large to small.Finally,the parameters with small influence on reliability constraints are transformed into deterministic variables.This method not only ensures the accuracy of solution,but also simplifies the time-dependent reliability optimization design problem and improves the computational efficiency.