Research On Structural Reliability And Global Sensitivity Analysis

A large quantity of uncertainties are often encountered in engineering structures in the filed such as aerospace.These uncertainties will also cause the uncertainty in the output response of structure,and even affect the safety and robustness of the structure significantly.Uncertainty analysis can effectively estimate the uncertainty of the structural output response and the relative contribution of the input uncertainty to the uncertainty of the output response,which will help researchers understand the structural risk level and provide important reference for structural performance evaluation and risk control.In this paper,the reliability analysis and sensitivity analysis in structural uncertainty analysis are studied,and several efficient methods for estimating the structural failure probability are obtained.At the same time,the influence of the input uncertainty and the uncertainty of their distribution parameters on the structural failure probability is studied,and the effective measurement criterion and efficient sampling method are obtained.In addition,the more general multivariate global sensitivity analysis is studied in detail,and meaningful sensitivity indices are obtained.The contents are detailed as follows:(1)For the estimation of failure probability,we first consider that the estimation of failure probability itself is an integral problem.Therefore,an efficient method to solve the failure probability is proposed by using the idea of complex integral in numerical integration.Firstly,the input variable space is divided into several subspaces,and then the corresponding expectation is estimated in each subspace through the unscented transformation.Then the failure probability of the structure is estimated more efficiently and accurately.The computational cost of this method increases linearly with the growth of the dimension of input variables.Secondly,we consider that the fourth-order moment method is an effective method to estimate the failure probability,its key is to estimate the first four moments of the performance function,and the higher order unscented transformation can effectively estimate the first four moments of the response function.Therefore,an effective method to estimate the structural failure probability is obtained by combining the fourth-order moment method and the higher order unscented transformation.Finally,we consider that the Monte Carlo simulation is a widely used method,but its computational efficiency is low.For given subintervals and total sample size,an optimal conditional importance sampling method is proposed to improve the efficiency of Monte Carlo simulation method by combining importance sampling and condition sampling.(2)For the problem of reliability sensitivity analysis,firstly,the meaning of the reliability sensitivity index based on the failure probability is further explored,and another meaningful explanation of this index is derived from the perspective of output classification.Secondly,based on the idea of output classification,a new reliability sensitivity index is proposed to measure the influence of the interaction between two different input variables on the structural failure probability,so that the influence of the input variable on the structural failure probability can be measured more comprehensively.Finally,considering that uncertainties may be encountered in the distribution parameters of input variables,which will also affect the structural failure probability,the elementary effect sensitivity analysis method with a more efficient redial-based sampling strategy is used to measure the influence of the distribution parameters of input variables on the structural failure probability.The proposed radial-based sampling strategy can detect the important input variables more effectively and stably.(3)For the global sensitivity analysis of multiple outputs,we first studied the multivariate global sensitivity analysis from the perspective of variance.For the existing global sensitivity index based on covariance decomposition,an efficient estimation method based on unscented transformation is proposed.Since the existing global sensitivity analysis method based on covariance decomposition only considers the variance of multi-output variables but ignores the covariance of multi-output variables,a new sensitivity analysis method based on covariance decomposition is proposed,which can consider both the variance and covariance of multi-output variables.At last,considering that the principal component analysis can separate the variance and covariance of multi-output variables,a new sensitivity index based on principal component analysis is proposed.The proposed sensitivity index can effectively measure the effect of input variables on the covariance of multi-output variables.(4)We further studied the multivariate global sensitivity analysis from the perspective of probability distribution.Firstly,based on energy distance,a new multivariate global sensitivity analysis method is proposed,it not only can measure the effect of input variables on the probability distribution of multi-output variables but also can br easily calculated.Secondly,since many of the existing sensitivity indices are defined based on the correlation measure or can be regarded as a correlation measure,and the distance correlation can effectively measure the correlation between random vectors,a multivariate global sensitivity analysis method based on distance correlation is proposed.At last,a more general multivariate global sensitivity analysis method based on distance component analysis is also proposed.The covariance decomposition based multivariate global sensitivity analysis method and the traditional variance based sensitivity analysis method both can be regarded as special cases of the proposed sensitivity analysis method.