# Grain Noise Modeling

In recent years, a number of theoretical models have been developed at Iowa State University to predict the electrical voltage signals seen during ultrasonic inspections of metal components. For example, the Thompson-Gray measurement model can predict the absolute voltage of the echo from a small defect, given information about the host metal (information such as density, sound speeds, surface curvature, etc.), the defect (size, shape, location, etc.), and the inspection system (water path, transducer characteristics, reference echo from a calibration block, etc.). If an additional metal property which characterizes the inherent noisiness of the metal microstructure is known, the independent scatterer model can be used to predict the absolute root-mean-squared (rms) level of the ultrasonic grain noise seen during an inspection. By combining the two models, **signal-to-noise** (S/N) ratios can be calculated.

Accurate model calculations often require intensive computer calculations. However, by making a number of approximations in the formalism, it is possible to obtain rapid first-order estimates of noise levels and S/N ratios. These calculations are for normal-incidence pulse-echo inspections through flat or curved surfaces, and the flaw may be a flat crack or a spherical inclusion. The figure below shows the results of one of the calculations.