Using input estimation to estimate heat source in nonlinear heat conduction problem

The nonlinear heat conduction problem will become more complicated when the thermal conductivity is a quadratic temperature function and the volumetric heat capacity is a linear temperature function. In this paper, the input estimation algorithm, including the extended Kalman filter and the weighted recursive least-squares estimator, is proposed to estimate the unknown time-varying heat source in this nonlinear heat conduction problem. The simulation results show that the proposed algorithm can estimate the unknown time-varying heat source online with more accuracy. If the nonlinear heat conduction problem is regarded as the linear heat conduction problem, the differences of the temperature distribution and the unknown time-varying heat source estimated by the Kalman filter with the weighted recursive least-squares estimator are also illustrated in this work.