Statistical Emulation of Large Linear Dynamic Models

Abstract

The article describes a new methodology for the emulation of high-order, dynamic simulation models. This exploits the technique of dominant mode analysis to identify a reduced-order, linear transfer function model that closely reproduces the linearized dynamic behavior of the large model. Based on a set of such reduced-order models, identified over a specified region of the large model’s parameter space, nonparametric regression, tensor product cubic spline smoothing, or Gaussian process emulation are used to construct a computationally efficient, low-order, dynamic emulation (or meta) model that can replace the large model in applications such as sensitivity analysis, forecasting, or control system design. Two modes of emulation are possible, one of which allows for novel ‘stand-alone’ operation that replicates the dynamic behavior of the large simulation model over any time horizon and any sequence of the forcing inputs. Two examples demonstrate the practical utility of the proposed technique and supplementary materials, available online and including Matlab code, provide a background to the methods of transfer function model identification and estimation used in the article.

Keywords:  :

• Dominant mode analysis
• Gaussian process emulation
• Nonparametric regression
• Tensor product cubic spline smoothing
• Transfer function analysis
• Sensitivity analysis