Research On Efficient Numerical Methods For Structural Reliability Analysis

As is known,there are many unavoidable uncertainties inherent in the engineering structure systems,so the use of deterministic analysis methods may often lead to severe consequences.Structural reliability analysis provides theoretical basis and computational approaches for the propagation and quanti cation of uncertainty in structural engineering systems,where the moments method(MM)is widely used as an non-intrusive method.Assessing the statistical moments of the performance function(PF)and reconstructing the unknown probability distribution of the PF based on moments are two key problems in the MM.However,it is still challenging to apply the traditional MM to problems with strong nonlinearity and high dimension.In order to further develop the MM,the following studies are carried out in this thesis.(1)A new fourth-moment method(FMM)is proposed for structural reliability analysis.In this method,in order to achieve the tradeoff between the accuracy and efficiency,an improved bivariate dimension-reduction method(BDRM)based on the high-order unscented transformation(HUT)is rstly developed to evaluate the rst-four central moments of the PF.Then,a exible four-parameter probability distribution,namely shifted generalized lognormal distribution(SGLD),is adopted to reconstruct the probability distribution of the PF in the entire distribution region,especially for the distribution tail.Finally,ve numerical examples are investigated to validate the efficiency of the proposed method by comparison with several state-of-the-art methods.(2)An efficient algorithm for reconstructing the probability distribution by tting therst-four moments is proposed.In the traditional FMM,the unknown distribution of the PF is generally expressed by subjectively assuming a speci c probability distribution model with four parameters,so in some cases,there will be large errors.In this thesis,a new distribution system with three four-parameter probability distribution models as candidates is proposed to simultaneously represent the underlying distribution,where the involved parameters of the candidates can be obtained by the method of moments.Then,we propose a two-step selection algorithm to pick out the most appropriate model to recover the distribution of concern.The feasibility of the proposed method is veri ed by approximating several theoretical distributions,the probability distribution of a real data set,and also by applying to three reliability analysis numerical examples based on the MM.(3)A new fth-moment method is proposed for efficient structural reliability analysis.Because of the difficulty in calculating the high-order statistical moments,the traditional MM mainly focuses on the rst-four statistical moments of the PF and higher-order moments are ignored,which will lead to the de ciency of some probability information closely related to the tail of the PF.In addition,most of the four-parameter probability distribution models used in the traditional FMM are unimodal,so it is impossible to represent the bimodal distributions that may encounter in practice.Based on this,a mixed-degree cubature formula(MDCF)is proposed to assess the rst-ve central moments of the PF,and then a mixture of two normal distributions(MTND)with ve free parameters is developed to reconstruct the unknown distribution of the PF.Thus,the unimodal and bimodal distributions of the PF can be reconstructed in a uni ed way.Finally,six numerical examples are used to verify the accuracy and efficiency of the proposed method.(4)An efficient method based on fractional moments is proposed for seismic reliability analysis of nonlinear structures under non-stationary stochastic ground motions.Firstly,a mixture of inverse Gaussian distribution and lognormal distributions(MIGLD)is developed to represent the extreme value distribution(EVD)of the stochastic structural response,where the involved ve free parameters are determined by using ve low-order fractional moments of the EVD.The Latinized partially strati ed sampling(LPSS)is then employed to calculate the fractional moments of the EVD of nonlinear structures with considerations of the uncertainties both from external seismic excitations and structural parameters.Thus,the unknown probability distribution of the EVD can be reconstructed by the proposed MIGLD with efficiency and accuracy,and the failure probability can be obtained directly from the recovered EVD.Finally,two numerical examples are used to illustrate the efficiency of the proposed method for seismic reliability analysis.In the last chapter of the thesis,some main conclusions and points need to be further investigated are given.