Bayesian meta-modelling of engineering design simulations: a sequential approach with adaptation to irregularities in the response behaviour

Among current meta-modelling approaches, Bayesian-based interpolative methods have received significant attention in the literature. These methods are particularly known for their capability to adapt to the response function behaviour in order to generate good meta-models with fewer experiments. Current Bayesian adaptation techniques, however, are mainly based on the assumption that some variables are more important (or sensitive) than others. These less sensitive variables are weighted less or ignored to reduce the dimension of the design space. This assumption limits the scope and applicability of these models since in many practical cases none of the variables can be completely ignored or weighted less than others. This paper proposes a pragmatic approach that identifies regions of the design space where more experiments are needed based on the response function behaviour. The proposed approach adaptively utilizes the information obtained from previous experiments, builds interim meta-models, and identifies ‘irregular’ regions in which more experiments are needed. The behaviour of the interim meta-model is then quantified as a spatial function and incorporated into the next stage of the design to sequentially improve the accuracy of the obtained meta-model. The performance of the new approach is demonstrated using a numerical and an engineering example