Nonlinear System Identification with Selective Recursive Gaussian Process Models

Abstract

The Gaussian process (GP) model has been applied to the identification of a process model. The GP model can be represented by its mean and covariance function. It provides predictive variance to the predictive distribution of the output and estimate of the variance of its predicted output. The GP model based method has shown to be successful but it can encounter a high computation load because of the inversion of matrix. In this work, a method which recursively updates the covariance matrix is proposed. The update scheme is selective by admitting data to the region requiring improvement. This enables the model to be updated without placing a high computation demand. In addition, the process is augmented by a pruning process which removes redundant data from the model to keep the data size compact. A mathematical example as well as an application to an industrial plant is presented to illustrate the applicability of the proposed method as well as to demonstrate its effectiveness in the prediction performance.

Online model regression for nonlinear time-varying manufacturing systems

“…Two types of commonly used online modeling algorithms are compared with the proposed algorithms. One is the the online extreme learning machine (ELM) [28] which is a neural network type algorithm and famous for its high computing speed, and the other is the selective recursive Gaussian process modelling algorithm (SRGPMA) proposed in [7] which is based on the GPR method and similar to our work. The algorithms are simulated in two different scenarios, i.e., U is finite and infinite respectively.…”

“…For example, the online NN or kernel-based learning methods in [48,26,28,19,12,31,32], and the online GPR methods in [27,43,37,42,7,30] provide iterative calculations for sequential data processing so as to reduce the computation load. Specifically in [7], a selective recursive Gaussian process modelling algorithm is proposed, which adaptively selects the data of a given size that are most efficient in reducing the estimation uncertainty so that the computation load is constrained when online streaming data are coming in. In most current works on batch-to-batch control, the conventional model regression methods are only used for obtaining an initial estimate of the system model using historical data during which the model variations are ignored [20,35,29].…”

Multivariate Gaussian process regression for nonlinear modelling with colored noise

“…In real industrial processes, in order to model complex nonlinear systems, various data-driven modelling approaches have gained rapid development and attracted a lot of research interests, such as neural networks, support vector machine, fuzzy models and Gaussian process regression (GPR) models (Dudhagara et al, 2016; Leiterer and Furrer, 2015; Ni and Tan, 2011; Yang et al, 2016; Zhang and Liu, 2013; ). The Gaussian process regression (GPR) model, as a data-driven modelling approach, has been applied in many fields such as system identification, soft sensing, dynamic process modelling and Bayesian learning (Chan et al, 2013; Jin et al, 2015; Likar and Kocijan, 2007; Yuan et al, 2008), owing to its solid theoretical foundation and relatively easy implementation (Choi et al, 2011; He and Liu, 2013; Ni et al, 2012). Compared with other supervised regression models, the GPR model has unique advantages, that is, its hyper-parameters can be adaptively acquired and output prediction is associated with probability distribution (He and Liu, 2013; Ni and Tan, 2011; Rasmussen and Williams, 2005).…”

Gaussian process regression with functional covariates and multivariate response

“…See for example the seminal book [3] and the references therein for details. In chemometrics and related areas, GPR has been applied to a range of problems, such as calibration of spectroscopic analysers [4,5], response surface modelling [6], system identification [7], ensemble learning [5,8], prediction of transmembrane pressure [9], and prediction of percutaneous absorption [10,11], among others.…”