Research On The Probabilistic Uncertainty Analysis And Optimal Design Method Of Engineering Structures Based On The Method Of Moments

There is inevitably randomness in engineering structures,including material properties,boundary conditions and external loads,which cause randomness in structural response.To ensure the safety of the structure,the probabilistic uncertainty analysis and reliability evaluation of the random response at the component and global level of the engineering structure are particularly critical.At the same time,the traditional deterministic design method usually adopts the safety factor method or the partial coefficient method to consider the influence of randomness,which makes it difficult to balance safety and economy in engineering design,making the design results either relatively conservative or insufficient in safety reserves.Therefore,in order to accurately analyze and design the structure,it is also of great significance to consider the influence of probability uncertainty in the optimization design of engineering structures and to develop corresponding calculation methods.At present,there are still a series of difficult problems in the theory and application of probabilistic uncertainty analysis and probabilistic uncertainty optimization design of engineering structures.To this end,this thesis will carry out systematic research on the above-mentioned problems,and strive to make certain exploratory progress in the analysis and application of structural probabilistic uncertainty and the optimization design of engineering structures considering the probabilistic uncertainty analysis.Specifically,this thesis has carried out and completed the following research work:(1)In view of the dimensional limitation and distribution type limitation of the traditional conjugate unscented transformation(CUT)methods,two types of extended conjugate unscented transformation(ECUT)methods are respectively proposed and applied to the statistical moment estimation of random systems.Based on the traditional CUT methods,through the introduction of variable transformation and high-dimensional decomposition model,the first type of ECUT methods is proposed.Through the exact dimension reduction method based on vectors,the high-dimensional random variable problem is decomposed as multiple sub-vectors.Then,the CUT methods and variable transformation are introduced,and the second type of ECUT methods is proposed.Both of the two proposed methods can solve the problem of dimensionality restriction and distribution type restriction of the traditional conjugate unscented change method.By extending the two types of methods to the statistical moment estimation of random systems,it can be found that the two types of methods proposed have a higher level of accuracy and are quite efficient.Relatively,the second type of ECUT methods has higher accuracy and efficiency than the first type of ECUT methods.(2)Due to the subjective selection of high-order moments,insufficient accuracy of high-order moments,or incomplete information in traditional high-order moment methods,an iterative maximum entropy reliability analysis method based on generalized high-order moments(IMEM-GHM)is proposed.On the basis of the traditional maximum entropy method,the precise estimation of high-order moments is carried out by introducing the GF-deviation and the ECUT methods.Furthermore,combining the maximum entropy integral limit determination method and the convergence criterion,the IMEM-GHM is proposed.At the same time,by deriving the equivalent performance function corresponding to the multi-component common failure problem,the generalized equivalent extrem-value event and equivalent performance function of the bilateral boundary multi-component common failure problem are developed.In addition,by summarizing the equivalent performance functions of components and global reliability problems,the IMEM-GHM is extended to component reliability problems,classical global reliability problems,and global reliability problems of multiple component failures.(3)For the probabilistic optimization design of the bar structure,an optimization design method based on the reliability and robustness of the bar structure is proposed.Firstly,a mathematical model for the probability optimization design of the bar structure based on the probability density function is established.The objective function is defined as the weighted combination of the response mean and standard deviation,and the constrained probability is established by the one-dimensional integral of the response probability density function.Secondly,the statistical moment estimation and probability density function fitting of the objective function and the constraint function are carried out by introducing the ECUT method(GF-deviation)and the IMEM-GHM,respectively.Thirdly,combined with the improved differential evolution algorithm,the probability optimization design of the structure of the bar system is carried out.Finally,the proposed probabilistic optimization design method of the bar structure is extended to the configuration optimization design of the transmission structure.(4)As far as the continuum structure topology optimization design problem is concerned with probabilistic uncertainty,the continuum structure topology optimization methods based on robustness and reliability are proposed,respectively.On the basis of the variable density method,a mathematical model of probabilistic topology optimization of continuum structure based on the method of moments is established.On the one hand,the objective function of the robust topology optimization model is defined by the response mean and standard deviation,and the proposed statistical moment estimation methods are used to calculate the response mean and standard deviation.Besides,the sensitivity of the robust objective function to the design variables is derived,and the gradient-based method of moving asymptotes(MMA)is used to solve the problem.On the other hand,the constraint function of reliability-based topology optimization is established based on the probability density function of the response.The calculation of the reliability probability and the corresponding sensitivity analysis are carried out by the IMEM-GHM.Finally,the MMA is used to solve the reliability-based topology optimization problem.