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首页> 外文期刊>Engineering analysis with boundary elements >The inverse methods based on S-FEMs with an adaptive SVD regularization technique for solving Cauchy inverse heat transfer problems
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The inverse methods based on S-FEMs with an adaptive SVD regularization technique for solving Cauchy inverse heat transfer problems

机译：基于S-FEM和自适应SVD正则化技术的逆方法，解决柯西逆热传递问题

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摘要

This paper presents three inverse models based on S-FEMs with adaptive singular value decomposition (SVD) regularization technique for solving inverse heat transfer problems of Cauchy type with noisy input data "measured" on the domain boundary. The smoothed finite element methods (S-FEMs) are used as forward solvers, including edge-based S-FEM (ES-FEM), node-based S-FEM (NS-FEM) and cell-based S-FEM (CS-FEM that is the same as the standard FEM using T3 elements). First, the full-size S-FEM system equation is created based on the S-FEM theory. A set of local nodal temperature equations is then extracted from the full-size equations through a matrix partitioning operation, considering the nodes related to the heat flux on the Cauchy boundary. The Fourier heat convection theory is used to establish a relationship between the local nodal temperatures and the known heat fluxes on the Cauchy boundary. This procedure effectively converts a Cauchy type inverse problem to a forward-like problem with a set of ill-posed equations for inverse analyses. In order to mitigate the ill-posedness and to achieve a reliable and accurate inverse solution, we propose an adaptive SVD technique to regularize the solution, through minimizing the error between the approximate heat fluxes of the inverse model and the given ("measured") flux values on the Neumann boundaries. The proposed adaptive procedure effectively determines the number of small singular values to be deleted, and hence the noises in the input data cannot be magnified. The present techniques are tested using a number of Cauchy type heat transfer problems, and it is concluded that our inverse procedure is much more effective compared to the widely used Tikhonov regularization technique, and it is a systematic procedure for accurate, reliable and stable inverse solutions with noisy input data.
机译：本文提出了三种基于S-FEM的逆模型，该模型具有自适应奇异值分解（SVD）正则化技术，用于解决在域边界上“测量”有噪声输入数据的柯西式逆传热问题。平滑有限元方法（S-FEM）用作正向求解器，包括基于边缘的S-FEM（ES-FEM），基于节点的S-FEM（NS-FEM）和基于单元的S-FEM（CS- FEM与使用T3元素的标准FEM相同）。首先，基于S-FEM理论建立全尺寸S-FEM系统方程。然后，通过矩阵划分操作，考虑与柯西边界上的热通量有关的节点，从全尺寸方程中提取出一组局部节点温度方程。傅里叶热对流理论用于建立局部节点温度与柯西边界上已知热通量之间的关系。此过程通过将一组不适定方程用于反分析，有效地将Cauchy型反问题转换为正向问题。为了减轻不适定性并获得可靠且准确的逆解，我们提出了一种自适应SVD技术，通过最小化逆模型的近似热通量与给定（“测得”）之间的误差来对解进行正则化Neumann边界上的通量值。所提出的自适应过程有效地确定了要删除的小奇异值的数量，因此无法放大输入数据中的噪声。通过使用许多柯西型传热问题对本技术进行了测试，得出的结论是，与广泛使用的Tikhonov正则化技术相比，我们的逆过程更为有效，并且它是用于精确，可靠和稳定的逆解决方案的系统过程输入数据嘈杂。

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