基于拟牛顿法的连铸结晶器热传导反问题求解

Continuous Casting Mold Heat Conduction Inverse Problem Based on Quasi-Newton Method

摘要:

在实际的工业过程中,热传导反问题广泛的存在于各个应用领域；由于连铸的生产环境恶劣,给连铸钢坯的测温造成了很大的困难,导致连铸结晶器热传导反问题的求解是很困难的；在研究了热传导反演算法的基础上,基于连铸结晶器的有限的测量点,通过热传导反演算法可以求出结晶器的热流密度,给连铸的优化和控制提供依据；在建立了连铸热传导反问题模型的基础上,提出了基于拟牛顿法的连铸结晶器热传导反问题求解的改进算法,该算法可以有效的利用当前搜索过程中的信息,通过近似目标函数的二阶导数来加快算法的搜索效率,采用了Wolf步长选择规则克服了算法收敛速率慢的缺点,并且该算法无需计算Hessen矩阵,能够有效降低计算的复杂度；实验结果表明该算法能够快速有效的求解该问题；该方法用于连铸结晶器热传导反问题是可行的、有效的。

Abstract:

In the actual industrial process, the inverse problem exists in a wide range of thermal conductivity of various application fields. Due to the harsh environment of continuous casting production to continuous casting billet temperature caused great difficulties, resulting in continuous casting mold inverse heat conduction problem is difficult to solve. On the basis of studies on the thermal conductivity inversion algorithm, based on limited measurement points continuous casting mold by thermal conduction heat flux density inversion algorithm can find the mold, to casting optimization and control to provide evidence. On the basis of the establishment of a continuous casting inverse heat conduction problem model, based on the inverse problem raised conduction heat casting mold quasi-Newton method for solving the improved algorithm can effectively use the information in the current search process, through the approximation of the objective function second derivative to speed up the search efficiency of the algorithm, using a step size selection rules Wolf overcomes the disadvantages of the slow convergence rate and the algorithm without calculating Hessen matrix, can effectively reduce the complexity of calculation. Experimental results show that the algorithm can quickly and effectively solve the problem. The method for solving continuous casting mold inverse heat conduction problem is feasible and effective.