Particle filter algorithms for on-line prediction of transient heat flux of participating medium

The particle filter (PF) and corresponding improved algorithm (unscented particle filter (UPF)) are introduced to solve the on-line prediction of transient heat flux (q(t)) on the boundary of participating medium for the first time. The temperature-dependent thermophysical properties of the medium result in a highly nonlinear heat transfer system. The graded index medium (caused by the temperature-varying refractive index) is also taken into account, in which the radiation transfer is more complex than that in the uniform refractive index medium. The finite volume method is employed to address the transient coupled radiative and conductive heat transfer in medium. The impacts of particle number, process error covariance, measurement error covariance, sampling time interval, forms of heat flux and measurement errors on prediction results are researched in detail. The UPF algorithm, in which unscented Kalman filter technique is applied to pick an appropriate proposal density function to ameliorate the degradation phenomenon in original PF algorithm, outperforms the PF algorithm in terms of stability and accuracy of estimation results. All the prediction results demonstrate that UPF method is effective and reliable to solve the real-time reconstruction of q(t) even with measurement errors.