An inverse problem in nondestructive evaluation of spotwelds.

摘要

This work concerns the modeling and analysis of an inverse problem arising in a thermal imaging method for nondestructive evaluation of spotwelds. The method uses ultrasonic transducers to vibrate joined metal sheets while surface temperature of one of the sheets is measured. It is shown that there is anomalous heating in the vicinity of the welds. The inverse problem is to assess the quality of the weld from the measured temperature.; A full mathematical model for the generation of surface temperature distributions from a vibration-induced internal heat source in a sheet of metal is stated. A simplification from three space dimensions to two, coupled with a nondimensionalization and leading-order approximation, provides a more manageable model. To solve the inverse problem, a time step formulation is introduced to match the statement of the model to the format of the data. Numerical reconstructions are performed from simulated data, and sources correctly identified even with significant simulated noise. The analysis of the problem, together with the results of these computations provide confidence that the heat source can be accurately reconstructed from the measured data.