反求铝合金淬火边界条件的序列LM梯度算法  

Sequential LM gradient algorithm for inverse solving quenching boundary conditions of aluminum alloy

作　　者：王志鑫 秦国华[1] 林锋[1] 郭瑞超 WANG Zhixin;QIN Guohua;LIN Feng;GUO Ruichao(School of Aeronautical Manufacturing Engineering,Nanchang Hangkong University,Nanchang 330063,China;College of Aeronautical Engineering,Shandong University of Aeronautics,Binzhou 256600,China)

机构地区：[1]南昌航空大学航空制造工程学院,南昌330063 [2]山东航空学院航空工程学院,滨州256600

出　　处：《中国有色金属学报》2024年第8期2602-2614,共13页The Chinese Journal of Nonferrous Metals

基　　金：江西省自然科学基金重点项目(20232ACB204019);江西省主要学科学术和技术带头人资助计划(20172BCB22013);山东省高等学校“青创团队计划”资助项目(2023KJ275);江西省研究生创新专项资金资助项目(YC2023-S693)。

摘　　要：准确获取边界条件在淬火仿真中至关重要。为此,根据瞬态热传导模型,利用正则化方法建立反求热通量的目标函数,结合序列函数指定法与LM梯度法,通过最小化目标函数推导出序列LM梯度算法,实现末端淬火实验中热通量的迭代计算。其次,通过训练观测点的平均绝对误差的“3-7-3”神经网络预测模型,建立了序列LM梯度算法关键参数的遗传算法优化方法。最后,以换热系数为边界条件建立淬火仿真模型。结果表明:在相同淬火时间内,一维序列LM梯度算法、一点法和两点法,在观测点的仿真温度平均相对误差分别为5.6%、5.9%、12.6%,17.1%、15.4%、15.3%和17.7%、16.0%、15.6%。因此,与一点法、两点法相比,序列LM梯度算法具有更高的精度。It is very important for the quenching simulation to obtain accurate boundary conditions.Therefore,according to the transient heat conduction model,the objective function was established to inverse the heat flux by the regularization method.In combination with the sequential function specification method,the LM gradient method is depended on to derive the sequential LM gradient algorithm according to the minimization of the objective function so that it is workable to calculate the heat flux in end quenching experiment.Secondly,when a“3-7-3”neural network prediction model is trained for the average absolute percentage error of measurement points,a genetic algorithm optimization method was proposed for key parameters of the sequential LM gradient algorithm.Finally,the quenching simulation model was established with the heat transfer coefficient as the boundary condition.The results show that the average relative errors of simulated temperature between onedimensional sequential LM gradient algorithm,one-point method and two-point method at measurement points are 5.6%,5.9%,12.6%,17.1%,15.4%,15.3%and 17.7%,16.0%,15.6%,respectively in the same quenching time.Thus,compared with one-point method and two-point method,the sequential LM gradient algorithm has higher accuracy.

关 键 词：热传导反问题 序列函数指定法 Levenberg-Marquardt法 边界条件 参数优化 

分 类 号：TG156[金属学及工艺—热处理] TP391.9[金属学及工艺—金属学]