Application of varying parameters modelling with Gaussian processes (original) (raw)

Comprising Prior Knowledge in Dynamic Gaussian Process Models

Identification of nonlinear dynamic systems from experimental data can be difficult when, as often happens, more data are available around equilibrium points and only sparse data are available far from those points. The probabilistic Gaussian Process model has already proved to model such systems efficiently. The purpose of this paper is to show how one can relatively easily combine measured data and linear local models in this model. It is shown how uncertainty can be propagated through such models when predicting ahead in time in an iterative manner with Markov Chain Monte Carlo approach. The approach is illustrated with a simple numerical example.

Implementation of Gaussian process models for nonlinear system identification

'Proceedings 5th MATHMOD, Vienna, February 2006', Editors I. Troch, F. Breitenecker, 2006

Abstract This thesis is concerned with investigating the use of Gaussian Process (GP) models for the identification of nonlinear dynamic systems. The Gaussian Process model is a nonparametric approach to system identification where the model of the underlying system is to be identified through the application of Bayesian analysis to empirical data. The GP modelling approach has been proposed as an alternative to more conventional methods of system identification due to a number of attractive features.

Gaussian process models for systems identification

Different models can be used for nonlinear dy-namic systems identification and the Gaussian process model is a relatively new option with several interesting features: model predictions contain the measure of confidence, the model has a small number of training parameters and facilitated structure determination, and different possibilities of including prior knowledge exist. In this paper the framework for the identification of a dynamic system model based on the Gaussian processes is presented and a short survey with a comprehensive bibliography of published works on application of Gaussian processes for modelling of dynamic systems is given.

GAUSSIAN PROCESS MODELLING CASE STUDY WITH MULTIPLE OUTPUTS

The Gaussian-process (GP) model is an example of a probabilistic, non-parametric model with uncertainty predictions. It can be used for the modelling of complex nonlinear systems and also for dynamic systems identification. The output of the GP model is a normal distribution, expressed in terms of the mean and variance. At present it is applied mostly for the modelling of dy-namic systems with one output. A possible channel structure for multiple-input multiple-output model and a case study for the modelling of a system with more than one output, namely a gas-liquid separator, is given in this paper.

Modelling and Control of Dynamic Systems Using Gaussian Process Models

2016

This monograph opens up new horizons for engineers and researchers in academia and in industry dealing with or interested in new developments in the field of system identification and control. It emphasizes guidelines for working solutions and practical advice for their implementation rather than the theoretical background of Gaussian process (GP) models. The book demonstrates the potential of this recent development in probabilistic machine-learning methods and gives the reader an intuitive understanding of the topic. The current state of the art is treated along with possible future directions for research. Highlights: - Explains how theoretical work in Gaussian process models can be applied in the control of real industrial systems - Provides the engineer with practical guidance is not unduly encumbered by complicated theory - Shows the academic researcher the potential for real-world application of a recent branch of control theory More information about the book on the Springer web page (http://www.springer.com/us/book/9783319210209).

Dynamic systems identification with Gaussian processes

2005

This paper describes the identification of nonlinear dynamic systems with a Gaussian process (GP) prior model. This model is an example of the use of a probabilistic non-parametric modelling approach. GPs are flexible models capable of modelling complex nonlinear systems.

Incorporating knowledge about model structure in the identification of Gaussian-process models

2013

Dynamic system identification with Gaussian-process prior model is a probabilistic, nonparametric modelling method for identification. Gaussian-process models provide, besides the prediction, also the information about prediction uncertainty based on the availability or uncertainty of the data used for the modelling. An advantage of this kind of model is a small number of training parameters, a facilitated structure determination and the possibility to include various sorts of prior knowledge into the model. One of possibilities is to include blockstructure knowledge like Hammerstein model structure. The identification procedure of Gaussian-process model with Hammerstein model structure will be presented and illustrated with an example. Key–Words: System identification, Gaussian process models, dynamic systems, Hammerstein model.

An example of Gaussian process model identification

The paper describes the identification of nonlinear dynamic systems with a Gaussian process prior model. This approach is an example of a probabilistic, non-parametric modelling. Gaussian process model can be considered as the special case of radial basis function network and as such an alternative to neural networks or fuzzy black box models. An attractive feature of Gaussian process model is that the variance, associated with the model response, is readily obtained. Variance can be seen as uncertainty of the model and can be used to obtain more accurate multi-step ahead prediction. The method is demonstrated on laboratory pilot plant identification.

A Bayesian data modelling framework for chemical processes using adaptive sequential design with Gaussian process regression

Applied Stochastic Models in Business and Industry, 2022

Accurate simulators are relied upon in the process industry for plant design and operation. Typical simulators, based on mechanistic models, require considerable resources: skilled engineers, computational time, and proprietary data. This article explores the complexities of developing a statistical modelling framework for chemical processes, focusing on inherent non-linearity in phenomena and the difficulty of obtaining data. A Bayesian approach to modelling is forwarded in this article, utilising Bayesian sequential design to maximise information gain for each experiment. Gaussian process regression is used to provide a highly flexible model class to capture non-linearities in the process data. A non-linear process simulator, modelled in Aspen Plus is used as a surrogate for a real chemical process, to test the capabilities of the framework.

The concept for Gaussian process model based system identification toolbox

Proceedings of the 2007 international conference on Computer systems and technologies - CompSysTech '07, 2007

The Gaussian process model is an example of a flexible, probabilistic, nonparametric model with uncertainty predictions. It can be used for the modelling of complex nonlinear systems and recently it has also been used for dynamic systems identification. A need for the supporting software, in particular for dynamic system identification, has been recognised. Consequently, a Matlab toolbox concept for Gaussian Process based System Identification was generated. The use of the supporting software is illustrated with a nonlinear dynamic system identification example.