Research On Uncertain Computational Inverse Methods Based On Polygonal Convex Set Model

Due to the fluctuation of structure properties,the limitation of problem cognition and the randomness of measurement data,uncertainties are widely found in the engineering inverse problems,such as structural load identification,traffic accident reconstruction and material characteristic parameter identification.According to the sources of uncertainties,the uncertain inverse problem can be classified as measured response uncertain inverse problem,model uncertain inverse problem and multi-source uncertain inverse problem.The sources and forms of uncertainty in engineering inverse problems are various.Under the coupling effect of complex structures,structural performance may have the risk of failure.Therefore,the research on the uncertain inverse problem is of great significance to solve the practical problems in engineering.In recent years,the uncertain computational inverse method has been developed,but there are still some problems to be solved in the inverse problem with uncertainty,such as the measurement of correlated uncertain parameters,the transformation of the uncertain inverse problem and the mixed coexistence of multi-source uncertainties.Therefore,based on the polygonal convex set model and Taylor expansion method,dimension reduction decomposition method and manifold learning method,this paper focuses on the computational inverse methods of model uncertain inverse problem and multi-source uncertain inverse problem.The main research work of this paper is as follows:(1)In view of the correlation between the uncertain model parameters,an inverse method based on polygonal convex set model and Taylor series expansion is developed.It is difficult to obtain sufficient samples information of model parameters due to insufficient cognition of the problem and high experimental cost.Therefore,this paper uses the polygonal convex set model to measure the uncertainty of response parameters.In order to realize the inverse propagation process of the inverse model uncertainty to the identified parameters,the first-order Taylor series expansion of the inverse parameters is taken as the approximate inverse system equation at the midpoint of the uncertain model parameter,and the polygonal convex set model of the model parameters is taken as the constraint condition,and the simplex method is used to solve the interval of the inverse parameters.The solution of Taylor series expansion involves the process of deterministic inverse calculation.Usually,the optimization algorithm is used to solve the inverse problem.For the inverse problems with high uncertainty or high nonlinearity,the polygonal convex set model is divided into multiple sub polygonal convex sets.In each sub polygonal convex set model,the above inverse strategy is used to solve the inverse parameters,so as to improve the accuracy of the calculation results.(2)In order to solve the inverse problems that both the response and the model contain cognitive uncertainty,an inverse method based on dimension reduction decomposition is proposed.The interval model is used to measure the uncertainty of measurement response,the polygonal convex set model is used to measure the uncertainty of model parameters,and the interval model is used to measure the inverse parameters.The inverse problem with response uncertainty and model uncertainty is decoupled by dimension reduction decomposition method.The inverse parameters are expanded at the mean value of uncertain model parameters,and the edge configuration points are evenly arranged on the expansion axis.In this paper,the uncertain inverse method based on high-dimensional surrogate model and affine algorithm is used to solve the interval of inverse parameter at the edge configuration points,and then the intervals at all joint configuration points are predicted by interpolation.The intervals of the inverse parameters are obtained by counting the solution results of the inverse parameters at all the configuration points in the polygonal convex set field.(3)Aiming at the mixed coexistence of random uncertainty of response and cognitive uncertainty of model,an inverse method of based on manifold learning is proposed.The polygonal convex set model and probability model are used to measure the uncertainty of model parameters and measurement response respectively,and the probability box model is used to measure the uncertainty of inverse parameters.By establishing a manifold mapping model between model parameters and the cumulative distribution curve(CDF)of inverse parameters,the proposed method realizes the decoupling of uncertainties in responses and model,and the complex multi-source uncertainty inverse problem is transformed into the forward propagation problem of model uncertainty.The optimal Latin hypercube sampling is carried out in the model parameter space,and the uncertain inverse method based on the advanced first-order second moment is adopted to solve the CDF curve of the inverse parameters under the determined sample points.The manifold learning method is used to transform the high-dimensional CDF curve into the feature parameters in the low dimensional manifold space.The manifold mapping model is established by the radial basis model and the feature basis vector between the model parameters and the feature parameters.Through the manifold mapping model,the probability box model of the inverse parameters can be obtained by the uncertainty propagation of the polygonal convex set for the model parameters.