Research On Structural Reliability Analysis Methods Based On Wavelet Analysis And Metamodels

Structural reliability analysis has great significance for ensuring the safety,serviceability and durability of engineering structures.Although the existing methods of structural reliability analysis has gain significant progress,some difficulties still exist when these methods are applied to practical complex engineering structural problems.Considering the difficulty that adequate accuracy and efficiency cannot be obtained simultaneously confronted by the existing structural reliability analysis methods,this dissertation employs the mathematic tools such as wavelet density estimator,wavelet frame neural network and Markov Chain simulation to perform thoroughly research on structural reliability methods,and proposes highly efficient and applicable structural reliability analysis methods,which offer new ways for the reliability analysis of practical complex engineering structures.The main research contents are as follows:(1)In order to overcome the shortcoming of the design point-based importance sampling methods,such as the difficulty of obtaining the design point and inefficiency,when applied to problems with multiple design points,noisy or highly nonlinear limit state functions,the adaptive Markov Chain simulation is used to simulate samples from the failure region.Then linear wavelet density estimator and nonlinear wavelet thresholding density estimator is employed to construct the importance density,respectively.As a result,the linear wavelet density-based and the nonlinear wavelet thresholding density-based adaptive importance sampling method for structural reliability analysis are proposed,respectively.Numerical examples show that the proposed methods can adaptively search the important regions.Compared with the existing importance sampling methods,the proposed method effectively reduces the number of structure analysis and greatly improves the efficiency.Besides,the proposed method expands the application of the importance sampling methods in the structural reliability analysis.(2)Considering the widely existed problems of the existing neural networks,such as over-learning,poor generalization ability and local optimum,the single-scaling multidimensional wavelet frame is used as the activation functions in the hidden layer,and the adaptive wavelet frame neural network is constructed efficiently by the time-frequency localization and the matching pursuit algorithm to approximate the complex failure borders.Then the wavelet frame neural network-based structural reliability analysis method is proposed.Numerical examples show that the proposed method can effectively improve the generalization ability of the network and overcome the difficulty of determining the structure and parameters of the neural network.Compared with the existing neural network-based reliability analysis methods,the proposed method improves the efficiency.What's more,the proposed single-scaling multidimensional wavelet frame neural network significantly expands the application of the wavelet neural network in high-dimensional problems.(3)In order to overcome the commonly existed shortcoming that it's hard to quantify the error of existing metamodel methods for structural reliability analysis,a correction term is introduced to quantify the error of the metamodels.By expressing the failure probability as a product of the metamodel failure probability and the correction term,an unbiased estimator of the failure probability is constructed.Then an iterative algorithm for adaptively refining the metamodel and the correction term is proposed.At last,an unbiased metamodel method for structural reliability analysis is proposed.Numerical examples show that the proposed correction term can effectively quantify and eliminate the error of the metamodel methods,tackling the disadvantage that it's difficult to quantify the approximation error of the traditional metamodel method.The proposed method is of great importance for applying the metamodel methods to solve practical engineering problems.(4)Since that it's hard to obtain samples from multiple failure regions,which makes that the ergodicity of the Markov Chains used to estimate the correction term cannot be guaranteed,application of the unbiased metmodel method for structures with multiple failure modes is restricted.Therefore,the Pseudo-Markov Chain simulation and the adaptive clustering algorithm is employed to identify the failure regions and simulate the failure samples,respectively,based on which the unbiased metamodel method for reliability analysis of structures with multiple failure modes is proposed.Numerical examples show that both of the Pseudo-Markov Chain simulation and the adaptive clustering algorithm can effectively identify multiple failure regions and provide new method for obtaining the information of failure regions.The proposed method can effectively improve the accuracy and efficiency of the reliability analysis of structures with multiple failure modes,which offers effective means for the commonly existed problems with multiple failure modes in practical engineering.