Mathematical modeling for quantitativ] ultrasonics

A fundamental approach to quantitative ultrasonics must be based on mathematical modeling of ultrasonic wave phenomena. Measurement models must be developed to predict from first principles a measurement system’s response to specific anomalies in a given material or structure. Once a mathematical model has been verified by comparison with a sufficiently wide range of experimental data, reliable synthetic data can be generated with little effort. The modeling approach aids in the design of efficient testing configurations and in the interpretation of experimental results and field data. Measurement models can be used to optimize the operation of NDE systems. Synthetic data can play an important role in the training of a neural network or to establish a knowledge base for an expert system. Quantitative modeling of the interaction of ultrasound with internal, surface breaking and near-surface cracks is discussed in some detail. As an example a measurement model is described for the line-focus acoustic microscope.