Optimized inspection design for the thermographic characterization of sub-pixel sized through cracks

• Laser pulse thermography is used to characterize through cracks in thin metal panels.
• Nascent-stage cracks fall under the spatial resolution of the thermal imaging system.
• Mathematical framework guides the design of an optimal inspection design.
• Markov chain Monte Carlo is used to characterize cracks from thermographic data.

Non-destructive evaluation of structural components is critical for reducing costs from unnecessary replacements and maintenance. We study the utility of a non-contact modality for the inspection of thin metal plates for the presence of through cracks. Sensitivity to early stages of deterioration allows for simpler and less expensive repair than if a flaw propagates and becomes more damaging. Hence, we focus on the characterization of very small cracks with a thermal imaging technique. Through cracks interact with the flow of heat within a component, so that the characterization of cracks from a thermal image amounts to solving an inverse problem to discover unknown parameters that describe the crack.We consider cracks with length of less than a millimeter, falling under the pixel resolution of the recording thermal camera. Although these flaws are not directly visible from imaging data, the well-understood theory of heat conduction can be used in inference of crack properties. Herein we present a method to design an inspection modality that yields optimal data for such inference. Numerical experiments are performed to compare our optimized inspection setup to previous thermographic inspection scenarios found in the literature. Our design is found to produce the same quality of inference as these previous experiments which require much more expensive equipment (e.g. more powerful lasers and more sensitive IR cameras).