Estimation of moving heat source for an instantaneous three-dimensional heat transfer system based on step-renewed Kalman filter

Abstract Inverse estimation of moving heat source is a common issue in many fields. A real-time method based on Kalman filter is proposed and further developed to identify the moving heat source in a three-dimensional heat transfer system. Firstly, a step-renewed state space model considering the source position is established according to principle of source contribution. Using this model, a technique coupling fuzzy adaptive Kalman filter with weight recursive least squares algorithm is implemented to realize the simultaneous estimation of moving heat source and temperature field. Different spatiotemporal changes of heat source and measurement noises are assumed to validate the feasibility and test its performances of this technique. Results illustrates that this method can be used to inversely estimate moving heat source with different changes rates and directions. When the moving velocity varies as 0.25, 0.50, 1.00 mm/s and the time period is employed as 100, 200, 400, 800 s, the estimated heat source can accurately agree with exact one while the reconstructed temperature field is of low deviation. The mean relative errors of estimated heat source are no more than 3.25% and mean relative errors of temperature are smaller than 1.37% while standard deviation of measurement noises increases from 0.01 to 5.00, which demonstrates that this method is of high robustness and can be used under a deteriorated condition.