| Recent years have seen increasing interest in numerical simulation technology,a popular field of research where two categories of problems are receiving universal attention from researchers.One includes problems of establishing a complete numerical model and calculating output responses using the given input parameters(in short,the forward problem).Another refers to the inverse calculation of the incomplete parameters of a model,using the given output response parameters(in short,the inverse problem).On the other hand,there is usually much uncertainty in such factors as geometric dimensions,material properties,loads,boundary conditions,and constitutive models,which accumulates in the system,ultimately affecting the engineering analysis result to a large extent,and leading to forward problems of structural uncertainty(also known as uncertainty propagation problems)and uncertainty inverse problems,on the basis of numerical simulation technology.Currently,various methods of uncertainty measurement,propagation and inverse calculation have been developed in an attempt to address forward/ inverse problems of uncertainty.Most of them,however,are only able to tackle a single type of uncertainty problems,but unable to deal with the actual situation of engineering where frequent occurrences of multiple uncertain factors is common,especially when an engineering problem includes both random variables and interval variables.In response to such hybrid uncertainty problems,some researchers propose integrating the probability model and the interval model into an integrated model called P-box.However,researches on P-box remain inadequate in terms of its theoretical foundation,the completeness of the process,its adaptability to engineering applications,the robustness of computations,etc.This paper presents some fairly systematic studying we have done on the aspects of propagation methods,inversion strategies,application methods,etc.,with some breakthroughs made.The specifics are as below:(1)For propagation problems with separated hybrid uncertainty,we proposed a two-level expansion strategy to deal with the interval and probability variables.For the outer interval variables,we adopted the optimal Latin hypercube sampling method to obtain a small number of samples,and constructed an interpolation function based on the finite samples to establish the functional relationship between the interval variables and the response.For the propagation of inner probability variables,we chose the propagation method of statistic moment,which greatly increased the efficiency of propagation,and in response to the multiple integral problem involved in statistic moment calculation,we employed a univariate dimension-reduction integration method to transform the original system into a univariate subsystem for analysis,thus iteratively generating the statistical moments of the original system by calculating the moments of the one-dimensional subsystem.Finally,the system response was obtained from the intervals of statistic moments.Compared with current methods,this one used relatively little sample point information while guaranteeing the same level of calculation accuracy to obtain a comparatively accurate system response.It incorporated both the advantages of analysis based on optimization and that on statistic moments,solving the problem of sampling efficiency in high-dimensional problems through the highly accurate approximation strategy.(2)For inverse problems with separated hybrid uncertainty,on the basis of the forward problem,we proposed a structurally hybrid uncertainty inversion method based on joint optimization algorithm.The system samples were acquired through Latin hypercube sampling,and a high-precision polynomial proxy model was established to reduce the computing time during system calls.Through genetic algorithm and improved homotopy algorithm,the optimization efficiency in the deterministic inversion process of the inner layer was improved.The method was used in the identification of material characteristic parameters with high elastic modulus,and by combining it with experiments,the practicality of the method was proved.Besides,in order to ensure that the parameters to be inversed possesed a certain sensitivity to the measurement,a sensitivity analysis method based on variance and Bhattacharyya distance was proposed.(3)For the hybrid-uncertainty propagation problem with parameterized P-box in the input parameters or system parameters,an uncertainty propagation method based on manifold analysis and optimal polynomial response surface was proposed.First,three quantization methods of P-box were given from three perspectives of vertical discretization,horizontal discretization,and internal discretization for the response P-box,and it was found that horizontal discretization was more conducive to the propagation of parameterized P-box.Then,when the response P-box was regarded as the boundary of a two-dimensional manifold,the propagation problem was transformed into a boundary acquisition problem in manifold analysis.At the same time,for the problem of function fitting with less input and more output,manifold analysis method was used to sample the discrete points of the output,and the high-dimensional vector composed of the original sampling points was,based on PCA,replaced with a linear combination of a few lowdimensional vectors.The problem was,therefore,transformed into a function fitting problem between interval variables and eigenvector coefficients.Finally,the optimal polynomial method based on the error reduction ratio was used to establish the functional relationship,so as to quickly obtain the response P-box.(4)For the hybrid-uncertainty inverse problem where the distribution parameters contain interval uncertainty,we proposed a hybrid-uncertainty inverse method based on the secondorder derivative λ-PDF.On the basis of the traditional λ-PDF,the fitting range was expanded through polynomial derivation,a measurement method conforming to the general formal parameterized P-box given.At the same time,by further improving the manifold learning method,a hybrid uncertainty inversion method based on improved manifold analysis and second-order derivative λ-PDF was developed.This method was to establish the manifold analysis space based on the forward problem by sampling the inverse space,discretizing and POD decomposing the system response CDF corresponding to the sampling point,obtain the functional relationship from the inverse parameter space to the manifold space,and use the second-order derivative λ-PDF to fit the CDF of the inverse parameters.(5)For more general hybrid uncertainty propagation problems,the discretization method in the form of evidence was first used to discretize the non-parametric P-box considering that the uncertainty of the input parameters was measured by the non-parametric P-box,to obtain the multiple intervals after decomposition.Then,the P-box propagation method of multi-interval collaborative optimization was proposed to carry out uncertainty propagation,and finally obtain the system response in the form of evidence.In order to verify the practical application effect of this method,it was applied to the uncertainty analysis of the active phased array radar of large-scale complex electromechanical coupling equipment. |
