A new inverse analysis method based on a relaxation factor optimization technique for solving transient nonlinear inverse heat conduction problems
A new inverse analysis method based on a relaxation factor optimization technique for solving transient nonlinear inverse heat conduction problems
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DOI：
10.1016/j.ijheatmasstransfer.2015.07.009
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发表时间：
2015-11
影响因子：
5.2
通讯作者：
M. Cui;W. Duan;Xiaowei Gao
中科院分区：
文献类型：
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作者：
M. Cui;W. Duan;Xiaowei Gao
松弛因子是基于梯度的反演和优化方法以及使用迭代技术求解非线性方程的关键参数。在基于梯度的反演方法中，松弛因子直接影响反演效率和收敛稳定性。一般来说，弛豫因子越大，反转过程越快。然而，如果松弛因子太大，可能会出现发散。因此，每次迭代时都应该有一个最优的松弛因子值，保证较高的反演效率和良好的收敛稳定性。在目前的工作中，提出了一种优化技术，利用该技术，松弛因子在每次迭代时自适应更新，而不是在整个迭代过程中保持恒定。在此基础上，提出了一种新的反分析方法来求解多维瞬态非线性逆热传导问题。涉及一维和二维瞬态非线性逆热传导问题，并重新考虑了先前工作中出现的不稳定问题。结果表明，与之前的最小二乘法相比，本文提出的新的反演分析方法具有同样高的精度、同样好的鲁棒性和更高的反演效率。最重要的是，通过在每次迭代时创新地优化和自适应更新松弛因子，新方法更加稳定。
The relaxation factor is a key parameter in gradient-based inversion and optimization methods, as well as in solving nonlinear equations using iterative techniques. In gradient-based inversion methods, the relaxation factor directly affects the inversion efficiency and the convergence stability. In general, the bigger the relaxation factor is, the faster the inversion process is. However, divergences may occur if the relaxation factor is too big. Therefore, there should be an optimal value of the relaxation factor at each iteration, guaranteeing a high inversion efficiency and a good convergence stability. In the present work, an optimization technique is proposed, using which the relaxation factor is adaptively updated at each iteration, rather than a constant during the whole iteration process. Based on this, a new inverse analysis method is developed for solving multi-dimensional transient nonlinear inverse heat conduction problems. One- and two-dimensional transient nonlinear inverse heat conduction problems are involved, and the instability issues occurred in the previous works are reconsidered. The results show that the new inverse analysis method in the present work has the same high accuracy, the same good robustness, and a higher inversion efficiency, compared with the previous least-squares method. Most importantly, the new method is more stable by innovatively optimizing and adaptively updating the relaxation factor at each iteration.