Research On Inverse Transient Heat Conduction Problems Based On Gradient-based Algorithms And Radial Integral Boundary Element Method

In order to accurately analyze the complex thermodynamic problems of thermal protection materials such as spatial heterogeneity,temperature-dependent nonlinear thermophysical properties and possible physical damage and deformation in the aerospace field,this paper adopts the radial integral Boundary Element Method(RIBEM)combined with the gradient-based optimization algorithms to identify the spatial heterogeneity and temperature-dependent nonlinear thermophysical properties,and then analyze the unknown structural deformation,and the main contents are as follows:In the positive transient heat conduction problems,the radial integral boundary element method is used to accurately evalute the transient temperature field of non-homogeneous and temperature-dependent nonlinear materials.In order to facilitate the implementation of the complex variable derivative method,the numerical simulation process is extended from the real domain to the complex domain,and then the accuracy of the complex domain boundary element method is further fully tested.Compared with other numerical methods,such as the finite element method,the finite difference method and the finite volume method,etc.,the boundary element method plays a huge advantage by virtue of its only discrete calculation domain boundary.Especially in the inverse problem of variable geometry,the boundary element method effectively avoids the problem of mesh deformity that is easily generated during the generation and reorganization of internal elements of the structure.After successfully introducing the complex variable derivation method,the sensitivity matrix in the gradient-based optimization algorithms can be solved accurately and efficiently,which greatly improves the calculation accuracy and calculation efficiency of the entire inverse heat conduction problems.In addition,for the linear convergence characteristics of the traditional conjugate gradient method,the combination with the steepest descent method effectively modifies the shortcomes such as the slow convergence speed and even the inability to converge to the optimal solution in the convergence process,thereby significantly improving the iterative process of the optimization algorithm.In the specific cases of inverse transient heat conduction problems,based on the method proposed in this paper,we have completed the identification of non-homogeneous,temperature-dependent nonlinear complex thermophysical parameter and the unknown geometric shapes.In addition,taking the practical engineering application into consideration,this paper further analyzes the impact of different measurement errors and different initial value selections on the final identification results,in order to fully verify the robustness and practicality of this method.In particular,taking the characteristics of the huge calculation amount of the boundary element method when solving large-scale,nonlinear heat conduction problems into consideration,this paper additionally conducts model feature analysis for the radial integral Boundary Element Method,and establishes a physical reduced-order model that is suitable for the nonlinear boundary element method.After that,it greatly decreases the degree of freedom of the concerned problem,and thus greatly improves the computational efficiency of the radial integral Boundary Element Method when solving nonlinear transient heat conduction problems.The research work in this paper provides some theoretical guidance for the determination of thermophysical parameters of composite materials and identification of structural deformation in the aerospace field,and provides some new ideas for the improvement of algorithm accuracy and calculation efficiency.