A Quasi-ARMAX approach to modelling of non-linear systems

Hu, Jinglu; Kumamaru, Kousuke; Hirasawa, Kotaro

doi:10.1080/00207170110089770

Cited by 49 publications

(43 citation statements)

References 16 publications

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“…For instance, neural network (e.g. Tokar & Johnson,1999) and neuro-fuzzy models have attracted a great deal of attention in recent years but they are the epitome of black box modelling, revealing very little of their internal structure that has any physical meaning (see the discussion in Young (2001c) on the paper by Hu et al(2001) where a neuro-fuzzy model with 102 parameters can be replaced by a nonlinear TF model with only 15 parameters if the internal structure of the model is identified and taken into consideration). For this reason, many hydrologists tend to mistrust such a black box model as a basis for something as important as flood forecasting.…”

Section: Rainfall-flow Modellingmentioning

confidence: 99%

Advances in real–time flood forecasting

Young

2002

Philosophical Transactions of the Royal Society of London. Seri

204

167

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A shorter version of this report has been published (Young, 2002a)The report discusses the modelling of rainfall-flow (rainfall-runoff) and flow routing processes in river systems within the context of real-time flood forecasting. It is argued that deterministic, reductionist (or 'bottom-up') models are inappropriate for real-time forecasting because of the inherent uncertainty that characterizes river catchment dynamics and the problems of model over-parametrization. The advantages of alternative, efficiently parameterized Data-Based Mechanistic (DBM) models, identified and estimated using statistical methods, are discussed. It is shown that such models are in an ideal form for incorporation in a real-time, adaptive data assimilation and forecasting system based on recursive state space estimation (an adaptive version of the stochastic Kalman Filter algorithm). An illustrative example, based on the analysis of a limited set of hourly rainfall-flow data from the River Hodder in NW England, demonstrates the utility of this methodology and illustrates the advantages of incorporating real-time state and parameter adaption.

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Section: Rainfall-flow Modellingmentioning

confidence: 99%

Advances in real–time flood forecasting

Young

2002

Philosophical Transactions of the Royal Society of London. Seri

204

167

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“…Moreover, since Q-ARX-WN model is linear-in-parameter when the nonlinear part is determined and fixed, nonlinear systems could be controlled online and with only linear parameters adjusted each iteration, even sudden changes are happened on the system. For a minimum prediction error adaptive controller, consider a criterion function [10] as…”

Section: Q-arx-wn For Nonlinear Adaptive Controlmentioning

confidence: 99%

“…However, similar with NNs, most of WNs are used as black-box methods, which emphasize on the input-output representation ability and neglect some properties of the highly successful linear black-box modeling, such as the linear structure and simplicity [8]. Especially, the linear structure makes the model to be user-friendly and favorable to applications of nonlinear system control [9][10][11].…”

Section: Introductionmentioning

confidence: 99%

Quasi-ARX wavelet network for SVR based nonlinear system identification

Wang

2011

NOLTA

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Abstract:In this paper, quasi-ARX wavelet network (Q-ARX-WN) is proposed for nonlinear system identification. There are mainly two contributions are clarified. Firstly, compared with conventional wavelet networks (WNs), it is equipped with a linear structure, where WN is incorporated to interpret parameters of the linear ARX structure, thus Q-ARX-WN prediction model could be constructed and it is easy-to-use in nonlinear control. Secondly, guidelines for network construction are well considered due to the introduction of WNs, and Q-ARX-WN could be represented in a linear-in-parameter way. Therefore, linear support vector regression (SVR) based identification scheme may be introduced for the robust performance. Moreover, in adaptive control procedure, only linear parameters are needed to be adjusted when sudden changes have happened on the nonlinear system, thus the controller can track reference signal quickly. The effectiveness and robustness of the proposed nonlinear system identification method are validated by applying it to identify a real data system and a mathematical example, and an example of nonlinear system control is given to show usefulness of the proposed model.

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“…To obtain the nonlinear models favorable to applications, a quasi-linear autoregressive with exogenous inputs (quasi-ARX) modeling scheme has been proposed with two parts included: a macro-part and a core-part [14]. As shown in Figure 1, the macro-part is a user-friendly interface favorable to specific applications, and the core-part is used to represent the complicated coefficients of the macro-part.…”

Section: Introductionmentioning

confidence: 99%

“…A structured nonlinear parameter optimization method (SNPOM) has been presented in [9] to optimize both the nonlinear and the linear parameters simultaneously for a RBF-type state-dependent parameter model, and improvement has been further given in [19,22]. On the other hand, by using heuristic prior knowledge, the authors in [14,23] estimate the nonlinear parameters of a quasi-ARX NFN model, and the least square algorithm is used to estimate the linear parameters. Similarly, a prior knowledge has been used for nonlinear parameters in a quasi-ARX wavelet network (WN) model, where identification can be explained in an integrated approach [24,25].…”

Section: Introductionmentioning

confidence: 99%

Nonlinear System Identification Using Quasi-ARX RBFN Models with a Parameter-Classified Scheme

Wang

Liang

et al. 2017

Complexity

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Quasi-linear autoregressive with exogenous inputs (Quasi-ARX) models have received considerable attention for their usefulness in nonlinear system identification and control. In this paper, identification methods of quasi-ARX type models are reviewed and categorized in three main groups, and a two-step learning approach is proposed as an extension of the parameter-classified methods to identify the quasi-ARX radial basis function network (RBFN) model. Firstly, a clustering method is utilized to provide statistical properties of the dataset for determining the parameters nonlinear to the model, which are interpreted meaningfully in the sense of interpolation parameters of a local linear model. Secondly, support vector regression is used to estimate the parameters linear to the model; meanwhile, an explicit kernel mapping is given in terms of the nonlinear parameter identification procedure, in which the model is transformed from the nonlinear-in-nature to the linear-in-parameter. Numerical and real cases are carried out finally to demonstrate the effectiveness and generalization ability of the proposed method.

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A Quasi-ARMAX approach to modelling of non-linear systems

Cited by 49 publications

References 16 publications

Advances in real–time flood forecasting

Advances in real–time flood forecasting

Quasi-ARX wavelet network for SVR based nonlinear system identification

Nonlinear System Identification Using Quasi-ARX RBFN Models with a Parameter-Classified Scheme

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