From Dominant Mode Analysis to Dynamical Meta-Modelling

The simplest Transfer Function (TF) model is a linear regression in which the dependent output variable is computed as an additive sum of several "input" variables. The statistical identification and estimation of such models is straightforward and can be accomplished by ordinary multiple regression analysis. However, transfer functions are normally used for the modelling of linear, constant parameter, discrete or continuous-time dynamic systems. Such models, which are simply an alternative form of the equivalent ordinary difference and differential equations, can be obtained from measured input-output data using statistical methods of identification and estimation for TF models, such as those available in the CAPTAIN Toolbox for MatlabTM. Furthermore, TF models can be generalized in two major ways to include Time Variable Parameter (TVP) and State Dependent Parameter (SDP) transfer function relationships. The TVP model represents non-stationary systems, where the parameters can vary over time in an unknown, stochastic manner; while the parameters in the SDP model are dependent on other time variable states and so can represent a wide class of nonlinear, stochastic systems. Once again, identification and estimation of such models can be accomplished with the help of algorithms in the CAPTAIN Toolbox. The present paper will show how this generalized class of TF model can also be utilized to improve the computational and statistical efficiency of sensitivity analysis and facilitate the ‘emulation’ of large system models. It will first outline the nature of SDP models for stochastic static and dynamic systems and introduce methods for the non-parametric identification and parametric estimation of such models. It will then show how such an approach can be used to efficiently process the Monte Carlo Simulation (MCS) results obtained from sensitivity analysis. The paper will also show how generalized TF modelling can be used in Dominant Mode Analysis (DMA), a useful form of model reduction, and it will demonstrate how this can provide a basis for the synthesis of computationally efficient emulation versions of large simulation models. These various methodological procedures will be illustrated by two main examples. The first example will show how SDP estimation is able to identify and estimate an SDP model for a simulated Lorenz Strange Attractor system based on noisy measurements of its three state variables. The second example will show how the generalized TF modelling can be used to obtain an emulation version of a large macro-economic simulation model.

YOUNG Peter C.;  RATTO Marco; 

2007-12-20

University of Budapest

JRC37292

http://samo2007.chem.elte.hu/abstract/Young.doc,    https://publications.jrc.ec.europa.eu/repository/handle/JRC37292,