Abstract In this paper, a sequential conjugate gradient method is presented to reconstruct the undetermined surface heat flux for nonlinear inverse heat conduction problem (IHCP). This modified method combines the merits of sequential function specification method (SFSM) and conjugate gradient method (CGM). The proposed method can effectively eliminate the leading error which is inevitably generated in SFSM due to the existence of temporary assumption of the unknown parameters and reduce the computing time of nonlinear IHCP. The square wave and sine wave heat flux are used to evaluate the proposed method and the influence of the number of future time steps and measurement errors on the predicted results is studied. The numerical experiments verify the effectiveness and timeliness of the proposed nonlinear IHCP algorism in reconstructing the heat flux. The comparisons with the typical SFSM and CGM are conducted to demonstrate the superiority of the proposed method. The results show that proposed method is more accurate compared with that of the SFSM under the condition of large measurement errors and the computing time is much faster than that of CGM.

中文翻译：

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非线性逆热传导问题热通量估计的序贯共轭梯度法

摘要 在本文中，提出了一种序列共轭梯度方法来重建非线性逆热传导问题（IHCP）的未定表面热通量。这种改进的方法结合了顺序函数指定方法（SFSM）和共轭梯度方法（CGM）的优点。该方法能有效消除SFSM中由于未知参数临时假设的存在而不可避免地产生的超前误差，减少非线性IHCP的计算时间。方波和正弦波热通量用于评估所提出的方法，并研究了未来时间步长和测量误差对预测结果的影响。数值实验验证了所提出的非线性 IHCP 算法在重建热通量方面的有效性和及时性。与典型的 SFSM 和 CGM 进行了比较，以证明所提出方法的优越性。结果表明，在测量误差较大的情况下，该方法与SFSM方法相比精度更高，计算时间也比CGM方法快很多。