| Structural reliability analysis is one of the essential components in structural design and safety assessment,which may become very difficult when involving stochastic system or dynamical system.The applicability and accuracy of moment methods for structural reliability are directly determined by those of the method for calculating the statistical moments of system response.The point estimate method(PEM)which based on the dimension-reduction method(DRM)is one of the most efficient and widely used approaches for statistical moments.However,there still exist some shortcomings in the current PEM based on DRM,for instance,it is not available for the complex stochastic system composed of complete probability information subsystem and in complete probability information subsystem,and it is difficult to balance the high accuracy and high efficiency,besides,selecting the approximate dimension-reduction model is still a challenge.What is more,in the current moment methods for structural reliability,solving nonlinear equations or complex judgement and selection is always required which make it diffciult to implementation.This dissertation mainly foucus on estimation for statistical moments and moment methods for structural reliability,and an accurate and easy-to-implementation moment methods is developed.The main contents is organized as follows:(1)In most current PEMs,the reference variables is independent standard normal variable which may cause that the accuracy is not guaranteed and unstable unstable,and those PEMs can not be applied to complex stochastic system.To solve thses paoblems,firstly,random variables is are classified into several subvectors according to the known probabilistic information,then each subvector is transformed into corresponding approximate reference subvector in which a new approaches for equivalent correction coefficients based on Mehler’s formula is suggested.Finally,by combing with the adaptive PEM based on brivariate DRM,a generalized PEM for moments of complex stochastic system is proposed,and the implementability and accucacy of the proposed method are verified by several examples.(2)The accuracy of different DRMs depend on the composition of the response function,and it is usually confused to make an approxiamte choice among different DRMs.In the paper,the rigorous and exact dimension reduction method with respect to vector is firstly derived theoretically.Secondly,by introducing the nonnormal-to-normal transformation,original variables are transformed into independent standard normal variables which are classified into several subvectors based on the delineation of cross terms.And then the response moments becomes a function of the moments of multiple component function.Thirdly,by combing with the two different approaches for estimating the moments of component subvector function,an adaptive PEM based on the exact dimension reduction method with respect to vector,which comprises two sub-method,is proposed.Finally,several examples illustrate the accuracy and efficiency of the proposed method.(3)For the difficulty caused by the solution of nonlinear equations or complex judgement and selection which are involved in the current moment methods,and the challenges in the stochastic system reliability analysis or dynamical system reliability analysis,the adaptive dimension-reduction method is introduced firstly,and the statistical moments of response function is estimated.Secondly,based on these moments,the probability density function(PDF)of response function is approximated by a hypothesis NIG distribution,and the reliability analysis becomes a one-dimensional integrals.Thirdly,the proposed method is applied to the reliability at element level,reliability at system level and dynamical reliability in which the last two categories is calculated by combing with the development process of structural nonlinearity or equivalent extreme-value event.Finally,several examples indicated that the proposed method is accurate enough and easy to implement. |
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