Input Selection for Nonlinear Regression Models

Šindelář, Radek; Babuška, Robert

doi:10.1109/tfuzz.2004.834810

Cited by 88 publications

(27 citation statements)

References 15 publications

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“…The NARX parameters n u and n y are found by the method described in Reference [41]. For both systems, NARX parameters are determined as n u =3 and n y =3, and some GPC parameters appeared in the performance index (2) are chosen as N 1 =1 and m=10 À20 : In our simulations, SVM models of the systems have been obtained by the e-SVR algorithm using N=2000 training points out of the gathered data.…”

Section: Example Systems and The Simulation Resultsmentioning

confidence: 99%

Support vector machines‐based generalized predictive control

İplikçi

2006

Intl J Robust & Nonlinear

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SUMMARYIn this study, we propose a novel control methodology that introduces the use of support vector machines (SVMs) in the generalized predictive control (GPC) scheme. The SVM regression algorithms have extensively been used for modelling nonlinear systems due to their assurance of global solution, which is achieved by transforming the regression problem into a convex optimization problem in dual space, and also their higher generalization potential. These key features of the SVM structures lead us to the idea of employing a SVM model of an unknown plant within the GPC context. In particular, the SVM model can be employed to obtain gradient information and also it can predict future trajectory of the plant output, which are needed in the cost function minimization block. Simulations have confirmed that proposed SVM-based GPC scheme can provide a noticeably high control performance, in other words, an unknown nonlinear plant controlled by SVM-based GPC can accurately track the reference inputs with different shapes. Moreover, the proposed SVM-based GPC scheme maintains its control performance under noisy conditions.

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Section: Example Systems and The Simulation Resultsmentioning

confidence: 99%

Support vector machines‐based generalized predictive control

İplikçi

2006

Intl J Robust & Nonlinear

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“…For the investigated systems, the NARX parameters are determined as n u ¼ 3 and n y ¼ 3 by the method described in Reference [35]. The maximum number of training points used by AOSVR is set to L ¼ 100 and some GPC parameters appeared in the performance index (2) are chosen as N 1 ¼ 1 and m ¼ 10 À20 : Moreover, in order to determine the robustness of the online SVM-based GPC structure with respect to measurement noise, the measured output of the system is contaminated by an additive zero mean Gaussian noise the signal-to-noise ratio (SNR) of which is 40 dB; where SNR is given by…”

Section: Example Systems and The Simulation Resultsmentioning

confidence: 99%

Online trained support vector machines-based generalized predictive control of non-linear systems

İplikçi

2006

Int. J. Adapt. Control Signal Process.

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In this work, an online support vector machines (SVM) training method (Neural Comput. 2003; 15: 2683-2703, referred to as the accurate online support vector regression (AOSVR) algorithm, is embedded in the previously proposed support vector machines-based generalized predictive control (SVM-Based GPC) architecture (Support vector machines based generalized predictive control, under review), thereby obtaining a powerful scheme for controlling non-linear systems adaptively. Starting with an initially empty SVM model of the unknown plant, the proposed online SVM-based GPC method performs the modelling and control tasks simultaneously. At each iteration, if the SVM model is not accurate enough to represent the plant dynamics at the current operating point, it is updated with the training data formed by persistently exciting random input signal applied to the plant, otherwise, if the model is accepted as accurate, a generalized predictive control signal based on the obtained SVM model is applied to the plant. After a short transient time, the model can satisfactorily reflect the behaviour of the plant in the whole phase space or operation region. The incremental algorithm of AOSVR enables the SVM model to learn the new training data pair, while the decremental algorithm allows the SVM model to forget the oldest training point. Thus, the SVM model can adapt the changes in the plant and also in the operating conditions. The simulation results on non-linear systems have revealed that the proposed method provides an excellent control quality. Furthermore, it maintains its performance when a measurement noise is added to the output of the underlying system.

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“…The number of input locations actually used by the model must be reduced to an acceptable level for the sake of model updating speed. Therefore input location selection is a critical aspect of system identification since it directly affects the model accuracy and complexity [21,22]. In a power grid, the measurements in different locations have some underlying relationships, for example, all the bus frequencies change similarly after a generation trip.…”

Section: Methodology Of the Proposed Approachmentioning

confidence: 99%

Measurement‐based correlation approach for power system dynamic response estimation

Bai

Liu

et al. 2015

IET gener. transm. distrib.

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Understanding power system dynamics is essential for online stability assessment and control applications. Global positioning system-synchronised phasor measurement units and frequency disturbance recorders (FDRs) make power system dynamics visible and deliver an accurate picture of the overall operation condition to system operators. However, in the actual field implementations, some measurement data can be inaccessible for various reasons, for example, most notably failure of communication. In this study, a measurement-based approach is proposed to estimate the missing power system dynamics. Specifically, a correlation coefficient index is proposed to describe the correlation relationship between different measurements. Then, the auto-regressive with exogenous input identification model is employed to estimate the missing system dynamic response. The US Eastern Interconnection is utilised in this study as a case study. The robustness of the correlation approach is verified by a wide variety of case studies as well. Finally, the proposed correlation approach is applied to the real FDR data for power system dynamic response estimation. The results indicate that the correlation approach could help select better input locations and thus improve the response estimation accuracy.

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Input Selection for Nonlinear Regression Models

Cited by 88 publications

References 15 publications

Support vector machines‐based generalized predictive control

Support vector machines‐based generalized predictive control

Online trained support vector machines-based generalized predictive control of non-linear systems

Measurement‐based correlation approach for power system dynamic response estimation

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