Quantitative characterization of deep defects in granular systems via inverse transient heat transfer analysis of active thermography

Abstract

Accurate quantification of subsurface structural defect and thermal anomalies in granular systems (GS) is essential for optimizing heat transfer in energy storage, thermal management, and construction materials. Conventional modalities such as X-ray CT, ultrasound, and GPR are often ineffective in highly scattering granular media, while active thermography (AT), though practical and non-destructive, has previously offered only qualitative or shallow defect insights. Here, we address the inverse transient heat transfer problem in GS by presenting a robust quantitative framework for simultaneous measurement of sizes and depths of defects at the millimeter scale. Our approach introduces a novel, spatially-informed figure of merit (FOM) to objectively benchmark contemporary thermogram denoising and transformation algorithms—including for defect contrast enhancement under high noise. The workflow integrates this optimized processing with segmentation-based feature extraction and systematically compared and optimized a suite of regression and machine learning approaches for mapping extracted features to defect geometry. Analytical model validation and finite element simulations, augmented with realistic synthetic noise, enable rigorous uncertainty analysis and robust performance assessment. The proposed method achieves mean relative errors of 3.6% for depth and 15.5% for radius, substantially outperforming conventional two-step direct thermogram regression (22.3% and 43.1% errors, respectively), and reliably quantifies defects with depth-to-diameter ratios up to 1.5 for both spherical and non-spherical geometries. This generalizable framework advances quantitative inverse analysis of transient heat transfer in granular systems, providing an effective tool for thermal quality control and optimization across energy, manufacturing, and infrastructure applications.