Application of unscented Rauch-Tung-Striebel smoother to nonlinear inverse heat conduction problems

Abstract

Based on the concept of future measurement information, an unscented Rauch-Tung-Striebel smoother is developed to solve nonlinear inverse heat conduction problems. Numerical experiments are used to discuss the effect of the standard deviation of heat flux error, sampling time, sensor locations, the number of future time steps and the form of heat flux function on inversion results of the Rauch-Tung-Striebel smoother. The comparison with the unscented Kalman filter is conducted, and it shows that the Rauch-Tung-Striebel smoother greatly improves the time delay problem of the unscented Kalman filter, and reduces the sensitivity to measurement error. The inversion results of Kalman filter, extended Kalman filter, unscented Kalman filter and their corresponding smoothers for different nonlinear degrees are also compared, and it shows that for linear inverse problems, the Rauch-Tung-Striebel smoother is the optimal technology, for weak nonlinear inverse problems, the extended Rauch-Tung-Striebel smoother is a more appropriate choice, for the strong nonlinear inverse problems, the unscented Rauch-Tung-Striebel smoother is recommended.