非线性热传导反问题参数辨识

PARAMETERS IDENTIFICATION OF NON-LINEAR INVERSE HEAT CONDUCTION PROBLEM

  • 摘要: 基于一种时域正演精细算法,引入Bregman距离加权函数作为正则项,应用Tikhonov正则化方法,对非线性热传导反问题进行求解。所建正/反演数值模型在便于敏度分析的同时,能够对非线性内热源强度、导温系数和边界条件等多个热学参数进行有效组合识别。该文给出了相关的数值算例,并对信息误差以及不同正则项的计算效率作了探讨,得到满意的计算结果。数值结果表明所提的求解策略在求解非线性热传导反问题时,不仅能够对相关的热学参数进行有效的组合识别,而且具有较高的计算精度、较好的稳定性和一定的抗噪性,采用加权的Bregman距离函数作正则项可以提高计算效率。

     

    Abstract: Tikhonov’s regularization approach has been used to solve non-linear inverse heat conduction problems, using weighted Bregman distances in the construction of regularization terms for the Tikhonov’s function. Combined identifications can be achieved for non-linear inverse heat conduction with source term, thermal diffusivity and boundary conditions etc, facilitating the sensitivity analysis. Satisfactory numerical validation is performed including a preliminary investigation on the effect of noise data and the computational efficiency of different regularization terms. Results show that the proposed method can identify combined thermal parameters and boundary conditions for non-linear inverse heat conduction problems with high computational precision and anti-noisy capability. Moreover, the computational efficiency is improved with the weighted Bregman distances function as regularization terms.

     

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