To deal with the ill-posed nature of the inverse heat conduction problem (IHCP), the regularization parameter alpha can be incorporated into a minimization problem, which is known as Tikhonov regularization method, a popular technique to obtain stable sequential solutions. Because alpha is a penalty term, its excessive use may cause large bias errors. Ridge regression was developed as an estimator of the optimal alpha to minimize the magnitude of a gain coefficient matrix appropriately. However, the sensitivity coefficient matrix included in the gain coefficient matrix depends on the time integrator; thus, certain parameters of the time integrators should be carefully considered with alpha to handle instability. Based on this motivation, we propose an effective iterative hybrid parameter selection algorithm to obtain stable inverse solutions.

翻译：为了处理反热导问题(IHCP)的错误性质,可将正统参数阿尔法纳入一个最小化问题,即称为Tikhonov正规化方法,这是一种获得稳定的连续解决方案的流行技术。由于阿尔法是一个惩罚术语,因此其过度使用可能造成很大的偏差错误。山脊回归是作为最佳α系数矩阵的估测器开发的,以适当尽量减少增益系数矩阵的大小。然而,收益系数矩阵中包含的敏感系数矩阵取决于时间集成器;因此,时间集成器的某些参数应该与阿尔法一起仔细考虑,以便处理不稳定问题。基于这一动机,我们建议一种有效的迭代混合参数选择算法,以获得稳定的反向解决方案。