一个基于无迹卡尔曼滤波的传热反问题求解方法

A heat transfer inverse problem solving method based on unscented Kalman filter

准确估计材料的物性参数、初始条件、边界条件等对于热能工程领域具有重要意义。导热反问题(Inverse HeatConduction Problems,IHCP)提供了一种获取上述参数的有效途径,IHCP的成功应用在一定程度上取决于反演算法的效率。文章提出一种同时考虑被反演对象演化信息和测量信息的反演模型,原始IHCP问题被转化为一个状态-空间问题,无迹卡尔曼滤波(Unscented Kalman Filter,UKF)方法被发展用于求解该反演模型。数值模拟结果表明,该算法能够改善反演精度,而且,该算法的执行并不要求计算目标函数的梯度信息、雅克比矩阵和黑森矩阵,有效地降低了计算的复杂性与代价,从而为求解IHCP问题提供了一个有效途径。

Accurately estimating the thermal physical properties, boundary conditions, or the initial conditions of materials is highly de- sirable for real applications. The inverse heat conduction problems （IHCP） analysis method provides a promising approach for obtain- ing such parameters, in which the efficiency of the inversion algorithms plays an important role in successful applications of the IHCP method. In this paper, a generalized inversion model that simultaneously utilizes the evolution information of the inversion object and the measurement information is proposed, and the original IHCP is reformulated into a state-space problem. The unscented Kalman fil- ter （UKF） method is developed for solving the proposed inversion model. Numerical simulation results indicate that the proposed algo- rithm can improve the accuracy of an inversion solution. Furthermore, the implementation of the proposed method does not require the gradient vector, the Jacobian matrix or the Hessian matrix, which effectively reduces the computational complexity and cost. As a re- suit, a promising method is introduced for solving the IHCP.