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A new inverse analysis method based on a relaxation factor optimization technique for solving transient nonlinear inverse heat conduction problems

机译:一种基于松弛因子优化技术的逆分析方法,用于求解瞬态非线性逆导热问题

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摘要

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.
机译: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式的关键参数。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。通常,弛豫因子越大,反演过程越快。但是,如果弛豫因子太大,则可能会发散。因此,每次迭代都应有一个最佳的松弛因子值,以确保高的反演效率和良好的收敛稳定性。在当前的工作中,提出了一种优化技术,使用该技术在每次迭代中自适应地更新松弛因子,而不是在整个迭代过程中恒定不变。在此基础上,提出了一种新的逆分析方法,用于求解多维瞬态非线性逆导热问题。涉及一维和二维瞬态非线性逆导热问题,并重新考虑先前工作中发生的不稳定性问题。结果表明,与以前的最小二乘方法相比,本文新的反分析方法具有相同的高精度,相同的鲁棒性和较高的反演效率。最重要的是,通过在每次迭代中创新性优化和自适应更新松弛因子,新方法将更加稳定。

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