A Simple Algorithm Based on a 2D Heat Diffusion Mathematical Model to Extract a Surface Crack Length from a Sonic IR Thermal Image Alone

Sonic infrared (IR) inspection technology is a nondestructive testing method in which a crack manifests itself through frictional heat generation in metallic alloys. In this study, a simple systematic inversion algorithm based on a mathematical model is proposed to extract a crack length from a sonic IR thermal image alone. A two-dimensional heat diffusion model is proposed to estimate the transient temperature distribution around a crack due to an arbitrary heat generation function located along a crack line. Since the physical problem is a linear one, the previously estimated temperature change can be retrieved by summing the temperature distributions from multiple point heat sources located along a crack line. The locations of the positive values of the point heat sources are considered as a trace for the crack location and its length. For a wide range of crack lengths, the proposed inversion algorithm is tested against simulated temperature distributions generated from finite element simulations at different time frames. For zero-noise temperature change, the proposed algorithm retrieved all crack lengths with insignificant error. The noise effect on bias and precision of crack length estimation is demonstrated by updating and adding a random noise ranging between +/- 0.03 K for each pixel in each time frame thermal data per crack length. For peak temperature change ranging between 0.2 and 1.6 K, the proposed algorithm underestimated a crack length with a maximum error of less than 20% at 95% confidence level. Applying the proposed approach over an independently measured sonic IR thermal image underestimated the crack length by 10%.