Limitations of the 1D inverse thermal modelling method for ultrasonic thermometry

Structural health monitoring often involves temperature measurement. However, traditional sensors cannot measure subsurface temperature non-invasively, making them unsuitable for monitoring temperature-driven damage mechanisms such as high-cycle thermal fatigue. This limitation arises, in part, due to effective thermal low-pass filtering caused by material properties. A previous feasibility study demonstrated that subsurface temperature can be inferred non-invasively in mild steel subjected to uniform heating. This was achieved using the ultrasonic-based inverse thermal modelling (ITM) method, which assumes the temperature of a component can be described by a 1D system. This study investigated the behaviour of ITM under non-uniform heating applied to the ‘inaccessible’ surface of a stainless steel sample through experiments and simulations. The experimental results show that ITM over-predicts temperature by as much as 120% when the heated region is small compared with the 10 mm ultrasonic beam size. In simulation, the overestimation was reduced as the size of the heating source increased, effectively making the temperature distribution more uniform across the volume through which the ultrasonic wave travels. Despite the overestimation under non-uniform heating, ITM overcomes the thermal low-pass filtering, allowing the detection of thermal transients compared with a thermocouple mounted on the ‘accessible’ surface of a component. • Experimentally evaluated the inverse thermal modelling (ITM) of ultrasonic thermometry under more realistic thermal conditions (non-uniform heating). • Showed that ITM overestimates temperature under non-uniform heating conditions due to the inability to account for lateral heat diffusion. • Demonstrated that despite over-prediction, ITM enables non-invasive detection of thermal transients on inaccessible surfaces that would be impossible to measure by traditional means. • Extended the ITM algorithm to accept arbitrary polynomial velocity and temperature relationships.