Probabilistic characterisation of model error using Gaussian mixture model—With application to Charpy impact energy prediction for alloy steel

A novel approach to characterise the model prediction errors using a Gaussian mixture model is proposed. The motivation for this work lies behind many data models that are developed through prediction error minimisation with the assumption of a normal noise distribution. When the noise is non-normal, which may often be the case in complicated data modelling scenarios, the model prediction errors may contain rich information, which can be further exploited for model refinement and improvement. The key contents presented in this paper include: choosing the relevant variables to form the error data, optimising the number of Gaussian components required for the error data modelling, and fitting the Gaussian mixture parameters using an expectation-maximisation algorithm. Application of the proposed method for further model improvement, within the framework of hybrid deterministic/stochastic modelling, is also discussed. Preliminary results on the real industrial Charpy impact energy data for heat-treated steels show its effectiveness for model error characterisation, and the potential for model performance improvement in terms of prediction accuracy as well as providing accurate prediction confidence intervals.