基于一种时域正演精细算法,引入Bregman距离函数作为Tikhonov函数的正则项,建立了求解多宗量一维瞬态非线性热传导反问题的数学模型,可对非线性内热源强度、导温系数和边界条件等多个热学参数进行组合识别。对信息测量误差作了初步探讨,数值验证给出令人满意的结果。
A general numerical model to identify multi-variables of the unidimensional non-linear inverse problem of heat conduction in transient state is presented by a precise algorithm for direct heat conduction, based on Bregman distances in the construction of regularization terms in Tikhonov's function. Combination of identifications can be carried out for non-linear source term, thermal diffusivity and boundary conditions etc. Satisfactory numerical results including a preliminary investigation of effect of noise data and initial value on the results are given as well.