When gun barrels are multiple fired, monitoring the non-smooth heat flux of the gun with the additional input data makes it possible to identify the corrosion of the gun. Based on this background, we study the identification of the non-smooth heat flux in a 1-dimensional heat transfer system. Aiming to overcome the non-smoothness of the unknown heat flux and to simplify the choice of regularization parameter, we transform the inverse problem to a constraint optimization problem and prove the existence and convergence properties of the regularization solution. Then an algorithm based on minimizing the data-match term and penalty term alternatively is proposed. Finally, a numerical experiment supports our regularization scheme quantitatively, especially for input data with high noise level.

当枪管被多次发射时，通过附加的输入数据监视枪的非平稳热通量，可以识别枪的腐蚀。基于此背景，我们研究了一维热传递系统中非光滑热通量的识别。为了克服未知热通量的非光滑性，简化正则化参数的选择，我们将反问题转化为约束优化问题，证明了正则化解的存在性和收敛性。然后提出了一种基于最小化数据匹配项和惩罚项的算法。最后，数值实验定量地支持了我们的正则化方案，尤其是对于具有高噪声水平的输入数据。