Real-time estimation of time-dependent imposed heat flux in graded index media by KF-RLSE algorithm

Due to the large computational time caused by complex computational process of the existing inversion algorithm, real-time reconstruction of high-magnitude time-dependent heat flux in graded index media is quite challenging. In this study, based on hybrid technology of the Kalman filter and recursive least-square estimator (KF-RLSE), the real time reconstructed high-magnitude time-varying heat flux on graded index media surface, and the measurement information comes from the opposite side of the media. The ideal participating media, which is assumed to be isotropic scattering, constant thermophysical properties, and opaque and diffuse gray boundary, is employed to verify the reliability and validity of the proposed. All the reconstruction results show that the KF-RLSE algorithm can effectively reconstruct the boundary heat flux regardless of the positive or negative gradient of the refractive index. When the refractive index of each position increases or reduces, the transient heat flux on the surface can still be predicted effectively and acceptably. Furthermore, effects of different parameters on the accuracy and stability of the estimated results are also investigated. The reconstructed results show that the time-dependent heat flux can still be effectively reconstructed even when the measurement noise does not match its covariance. Meanwhile, the accuracy of the reconstruction results improves with the decrease of measurement noise covariance when the measurement noise distribution is fixed in a curtain range.