Improved Moment Methods For Structural Static And Dynamic Reliability Analysis

Uncertainties,such as the uncertainty of structural properties and loads,are ubiquitous in engineering structures,resulting in the uncertainty of output structural response.To ensure structural safety,it is essential to implement the structural reliability analysis with uncertainty.Among the existing structural reliability analysis approaches,the method of moments is extensively used in engineering because of its advantages of simplicity and solvability.In the structural reliability analysis based on the method of moments,how to calculate the statistical moments of the limit state function and how to reconstruct the unknown probability distribution of the limit state function based on moments are still full of challenges.Specifically,since the engineering structures inevitably exhibit highly nonlinear characteristics and their responses are always represented by implicit functions of basic random parameters,analytical solutions of statistical moments are unavailable because of complex multidimensional integrals.Additionally,the existing moment-based probability distribution reconstruction models may encounter problems of tail estimation error and restriction of application range due to the limitation of free model parameters.Therefore,this thesis aims to develop structural static and dynamic reliability analysis methods that enable to achieve both efficiency and accuracy.The main research work is as follows:（1）An improved central moment-based adaptive bivariate dimension-reduction method is developed to deal with the problem for the expensive calculation time and unsatisfactory accuracy existed in numerical integrals.This method first identifies the cross terms of two-dimensional integrals,and groups the random variables in terms of the cross terms.A combination method based on the two-dimensional cubature formula and Gaussian Hermite integral is used to calculate the moments of multiple component sub-vector functions.A shifted generalized lognormal distribution model based on the first four central moments is used to reconstruct the unknown probability distribution of the limit state function.The proposed method is applied to both explicit and implicit limit state functions for structural reliability analysis.Results verify that the proposed method can balance accuracy and efficiency in statistical moment evaluation and structural reliability analysis;（2）A method for estimating small failure probability based on the mixed-degree cubature formula is proposed.The mixed-degree cubature formula employs a sphericalradial transformation based on Gaussian weight integration combining with the 5thorder spherical rule and the 7th-order radial rule,and calculates statistical moments with the 5-7 degree of algebraic accuracy.A power transformation is implemented over the limit state function to reduce the skewness of the distribution and normalize the distribution.The mixed-degree cubature formula is utilized to estimate the statistical moment of the transformed limit state function.The integer moment-based maximum entropy method is employed to reconstruct the probability density function of the transformed limit state function.The feasibility of this method is investigated by explicit and implicit limit state functions.Results illustrate that this method is able to balance the accuracy and efficiency of small failure probability estimation;（3）An adaptive Hermite distribution model based on probability weighted moments is proposed to deal with the seismic reliability analysis of complex nonlinear structures under fully non-stationary random ground motions.Compared with central moments,the probability weighted moments are insensitive to sample sampling outliers,and can be applied to characterize a wide range of distribution functions.The Hermite polynomial normal transformation model is applied to estimate the extreme value distribution,where the degree of polynomial is adaptively selected through a two-step criterion.An efficient high-dimensional sampling technique is introduced to generate samples of extreme value for estimating probability weight moments.The failure probability and reliability index can be obtained through the integral calculation of the extreme value distribution.The efficacy and feasibility of this approach is testified by the seismic reliability analysis of two complex nonlinear structures;（4）In order to further verify the practical engineering feasibility of the proposed method,the seismic reliability of the ultra-large cooling tower structure under seismic ground motion is investigated.Take a large cooling tower with a height of about 250 m as an example.The maximum top node displacement of the structure is considered.The extreme value distribution method is implemented to estimate the structural random seismic response.The results demonstrate that the proposed method enables to study the dynamic reliability of large-scale engineering structures.