Meta-Modelling of Intensive Computational Models

Engineering process design for applications that use computationally intensive nonlinear dynamical systems can be expensive in time and resources. The presented work reviews the concept of a meta-model as a way to improve the efficiency of this process. The proposed meta-model will have a computational advantage in implementation over the computationally intensive model therefore reducing the time and resources required to design an engineering process. This work proposes to meta-model a computationally intensive nonlinear dynamical system using reduced-order linear parameter varying system modelling approach with local linear models in velocity based linearization form. The parameters of the linear time-varying meta-model are blended using Gaussian Processes regression models. The meta-model structure is transparent and relates directly to the dynamics of the computationally intensive model while the velocity-based local linear models faithfully reproduce the original system dynamics anywhere in the operating space of the system. The non-parametric blending of the meta-model local linear models by Gaussian Processes regression models is ideal to deal with data sparsity and will provide uncertainty information about the meta-model predictions. The proposed meta-model structure has been applied to second-order nonlinear dynamical systems, a small sized nonlinear transmission line model, medium sized fluid dynamics problem and the computationally intensive nonlinear transmission line model of order 5000.