A multi-parameter ultrasonic evaluation of mean grain size using optimization

Abstract

An evaluation model based on multiple ultrasonic parameters was developed to control mean absolute error between an actual measured value and a model calculation value. Superalloy GH4169 was used to validate the presented model. A multi-dimensional ultrasonic parameter set was built for each sample by ultrasonic and nonlinear ultrasonic test and parameter calculation. The feature scale of different parameters was restricted to the same range using normalization. The dimensionality of the parameter set was descended by a correlation metric with grain size. A new one-dimensional ultrasonic characteristic parameter was comprised of the select normalized set of ultrasonic parameters by quadratic polynomial, exponential, Gauss kernel and linear mapping functions with undetermined coefficients. The relationship between the new ultrasonic multiple eigenvalues mapping parameter and estimated grain size was expressed using a linear fitting function. An optimization problem aimed at minimizing the mean absolute error between the estimated and quantitative measured grain size was solved using evolutionary algorithms to obtain coefficients for the mapping and fitting functions. These calculations were used to generate four full multi-parameter ultrasonic evaluation models, which were benchmarked against three single parameter evaluation models (i.e. velocity, attenuation coefficient, and backscattering). The performance analysis and verification using leave-one-out cross-validation demonstrate the utility of the MUE model through its high precision, good stabilization, super anti-interference and practicality.