换热反问题输入数据的正则预处理及其对解的影响
REGULARIZATION PROCESSING OF INPUT DATA IN INVERSE HEAT TRANSFER PROBLEM AND ITS INFLUENCE ON THE SOLUTION
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摘要: 基于Tikhonov的正则平滑思想,对换热反问题中的输入数据进行平滑处理。通过对模拟实测数据的处理与求解表明,平滑后可以显著地提高反问题求解的精度与稳定性。这种正则平滑法比通常用的基于最小二乘原理的滑动平均法更为优越。Abstract: The major difficulty of the inverse problem lies in the fact that its solution does not depend continuously on the data and therefore is ill-posed.Based on Tikhonov's regularization method,a numerical procedure is provided for processing the input data in the inverse heat transfer problem,so that a uniform approximation is obtained both for the data function and its derivative.The effectiveness of the methods illustrated through simulated experiments using inexact data.The results demonstrate that the accuracy and stability of the inverse problem solution are significantly improved.The influence of the time step and the regularization parameter is also investigated.In addition,it is also shown that such a regularizing smooth procedure is obviously superior to the ordinary least square approximate method.
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Key words:
- Heat transfer /
- Regularization /
- Precision /
- Stability
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