Comparison of Bayesian and other approaches to the estimation of fatigue crack growth rate from 2D textural features

The fatigue crack growth rate can be explained using features of the surface of a structure. Among other methods, linear regression can be used to explain crack growth velocity. Nonlinear transformations of fracture surface texture features may be useful as explanatory variables. Nonetheless, the number of derived explanatory variables increases very quickly, and it is very important to select only few of the best performing ones and prevent overfitting at the same time. To perform selection of the explanatory variables, it is necessary to assess quality of the given sub-model. We use fractographic data to study performance of different information criteria and statistical tests as means of the sub-model quality measurement. Furthermore, to address overfitting, we provide recommendations based on a cross-validation analysis. Among other conclusions, we suggest the Bayesian Information Criterion, which favours sub-models fitting the data considerably well and does not lose the capability to generalize at the same time.