Rapid non-invasive measurement of the time-dependent heat flux and temperature distribution in participating medium under non-Gaussian noise

The particle filter (PF) and extended particle filter (EPF) techniques are proposed to resolve the real-time estimated of the aerothermal heat flux and temperature fields of the thermal protection system (TPS) for the hypersonic vehicle. The TPS is regarded as a typical participating medium. The radiation heat transfer in the participating medium is computed by the Rosseland diffusion model. The finite volume method is utilized to solve the energy equation to obtain measurement temperature. Based on the measurement temperature signal, the Particle filtering technique is applied to reconstruct the surface heat flux and inner temperature field of the TPS. Four typical non-Gaussian noises are added to the simulated temperature signal to investigate the tracking ability and stability of the proposed algorithms. The influence of the measured noise, measured noised covariance, process noise covariance, time step, and number of the particle on the estimated results are discussed in detail. The calculated results indicate that even though the actual time-dependent heat flux measured by NASA is considered, an acceptable estimated result can still be obtained based on the EPF and PF techniques. The normalized root mean square errors of the actual heat flux reconstructed by PF and EPF are 5.45 % and 2.55 %, and the average relative errors of the reconstructed temperature field are 0.1 % and 0.043 %, respectively. All the estimation results illustrate that EPF technique has better tracking ability and robustness compare with the PF method.