Characterisation of model error for Charpy impact energy of heat treated steels using probabilistic reasoning and a Gaussian mixture model

Data-driven modelling has gained much momentum recently, with modelling algorithms being evolved into more complex structures capable of dealing with highly non-linear multi-dimensional systems. However, it is widely accepted that data-driven models are typically obtained under the principle of error minimisation, with the assumption of normal error distribution. The latter assumption is often not valid in more complex modelling environments, leading to sub-optimal model predictions. In this paper, a new modelling strategy aimed at exploiting the rich information contained in the model error data using a Gaussian mixture model (GMM) is proposed. The GMM error model can provide a probability characterisation of the error distribution, which can then be used complementally with the original data model. This combination often produces improvements in prediction performances, as will be illustrated in the case study relating to the hybrid modelling of the Charpy impact energy of heat-treated steels