A Physical-Constrained Decomposition Method of Infrared Thermography: Pseudo Restored Heat Flux Approach Based on Ensemble Bayesian Variance Tensor Fraction

In this study, we propose a new post processing algorithm, using a stable low-rank decomposed pseudo restored heat flux based on the ensemble variational Bayes tensor factorization (EVBTF-RPHF) algorithm for performing periodic square wave thermographic nondestructive testing (thermographic NDT). Previous studies have shown that both RPHF and EVBTF can separately improve the detectability of thermography by enhancing some defect features. However, both methods are limited by their particularly constraints: RPHF are heavily degraded by noises and missing data due to the assumptions under which the physical models are derived while efficiency of EVBT reduces when the lateral heat diffusion weights out. By embedding RPHF into the stable low-rank decomposition EVBTF, the proposed algorithm allows to improve the detectability of defects in thermographic NDT using a periodic heat flux with low-rank spatial distribution. The study verifies the capacity of the proposed method by theoretical analysis. Then, experiments were conducted on a carbon fiber composite panel with foreign inserts buried up to 5 mm deep. The sampled data are processed by the proposed method. The results are compared with existing methods such as phase-locked RPHF and EVBTF. The experimental results demonstrated that defects with normalized diameter-to-depth ratios as small as 0.9, barely detected with other available techniques, can reliably be detected by EVBTF-RPHF. The signal to noise ratio and the contrast are used as figure of merit to quantitatively compare the capacity of the proposed method with existing methods. However, the computation efficiency of the proposed algorithms needs further improvement.