An algorithm for bounded-error identification of nonlinear systems based on DC functions

Bravo, José Manuel; Álamo, T.; Redondo, Manuel Jiménez; Camacho, Eduardo F.

doi:10.1016/j.automatica.2007.05.026

Cited by 17 publications

(6 citation statements)

References 18 publications

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“…Examples of these sets used in literature are boxes [50], parallelotopes [51] and ellipsoids [52]. In this paper, the use of zonotopes is proposed [38,39,53]. Using these sets yields interval predictions without having to use iterative methods to solve the optimization problem.…”

Section: Modified Fault-detection Algorithmmentioning

confidence: 99%

“…This in turn leads to the possibility of obtaining interval predictions of the behaviour of the system, which include information on the reliability of the prediction itself. This implies that a parametric model of the system is also assumed [38,39], with a finite number of parameters to identify. A comparison with two fault-detection methods has also been included.…”

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confidence: 99%

“…The majority of the bounded-error identification methods present in literature are based on parametric approaches. This implies that a parametric model of the system is also assumed [38,39], with a finite number of parameters to identify. These parameters must be consistent with the input-output measurements obtained from the system, the error bound in the measurements, and with the parametric model considered.…”

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Data‐driven bounded‐error fault detection

Fábrega

Bravo²,

Herrera

et al. 2013

Adaptive Control & Signal

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In this paper, a new data-driven fault-detection method is proposed. This method is based on a new nonparametric system identification approach, which constitutes the principal contribution to this work. The fault-detection method is a parametric model-free approach that can be applied to nonlinear systems that work at various operating points. Not only can the fault-detection process be applied to the steady state of each operating point, but it can also be applied to the transient state resulting from a change in the operating point. In order to detect faults, the proposed method uses an interval predictor based on bounded-error techniques. The utilization of techniques based on bounded error enables system uncertainties to be included in an explicit way. This in turn leads to the possibility of obtaining interval predictions of the behaviour of the system, which include information on the reliability of the prediction itself. In order to show the effectiveness of the fault-detection method, two examples are presented: in the form of a simulated process (counter-flow shell-and-tube heat-exchanger system) and an example of a real application (two-tanks system). A comparison with two fault-detection methods has also been included.This model can be obtained in several different ways, such as using the physical knowledge of the system or by conventional identification methods. Model-based methods (MBMs) can be grouped into a few approaches: signal-processing methods [14], observer-based methods [15,16], parityrelation methods [17,18], parameter-estimation methods [19,20] and Kalman filter-based methods [21,22].The fault-detection method proposed in this work is parametric model free, so this previous knowledge about the system is not necessary. On the other hand, data-driven fault-detection methods use large volumes of data collected from industrial processes. These methods use an inference system based on statistical techniques [23] or by machine learning [9] applied to the historical data available. The most commonly used statistical techniques are principal component analysis (PCA) [12,24], partial least squares (PLS) [12], Fisher's discriminant analysis [25] and independent component analysis [26]. In general, these methods assume a linear relation in the studied variables of the system. To apply these statistical techniques to nonlinear systems, the corresponding nonlinear versions of the statistical techniques should be used: PCA [27,28] and PLS [5,29]. These nonlinear methods are usually related to a nonlinear optimization problem, and an iterative search algorithm is needed to be applied. These iterative search algorithms can suffer from convergence problems and can be overly sensitive to small data fluctuations [12]. The fault-detection method proposed in this work can be used for nonlinear systems; however, an iterative search algorithm is not needed.The most widely used artificial intelligence techniques include neural networks [30], expert systems [31], support vector machines [32], case-based reasoning...

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Section: Modified Fault-detection Algorithmmentioning

confidence: 99%

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confidence: 99%

mentioning

confidence: 99%

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Data‐driven bounded‐error fault detection

Fábrega

Bravo²,

Herrera

et al. 2013

Adaptive Control & Signal

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“…This nonlinear case has also been studied in literature. Signomial programming [12], branch and bound algorithms [13], Hammerstein models [14] and DC functions [15], [16] have been used to obtain the AF SSs.…”

Section: Introductionmentioning

confidence: 99%

Interval predictor based on a Reversed Huber's error function

Bravo

Álamo

Gegúndez

et al. 2015

2015 European Control Conference (ECC)

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In dynamical systems context, a predictor is a method that provides an estimation of the future system output using past information of the system. An interval predictor provides an outer estimation of the future output. The center of this interval can be used as central or nominal prediction. A method to formulate interval predictors is to assume an unknown but bounded error in the system measurements. The aim of this work is to study the benefits of using a Reversed Huber's function as error function in this kind of predictors. A Reversed Huber's function is a convex function, piecewise linear near zero but quadratic for large values. The paper provides a nonparametric formulation of the interval predictor and shows by a real world example that the proposed predictor can improve the performance of the central prediction.

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“…、直接采用优化的方法 [4,5] 、区间分析的方法 [6,7] 以及支持向量机(Support Vector Machine 简记SVM)的方法 [8] [11][12][13][14][15] 。本文将SLLE与最近均值分类器 [16] (Nearest Mean …”

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Set membership identification using SLLE and NMC

Chai

Sun

Qiao

2010

2010 8th World Congress on Intelligent Control and Automation

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A set membership identification method by pattern classification is proposed for nonlinear-in-parameter regression models with unknown but bounded(UBB) noises. Suppose that the points in the parameter space can be divided into two classes according to whether they are in the feasible solution set or not, the problem of set membership identification is to construct a pattern classifier to decide which class a point belongs to. The method has three steps. Firstly, the training data are selected uniformly in the parameter space and are decided by equation error whether they are in the feasible solution set. Secondly, supervised locally linear embedding(SLLE) is used to map the training data into low-dimensional space. Thirdly, nearest mean classifier(NMC) is trained on the mapped training data. This method not only can describe the feasible solution set approximately in the high-dimensional parameter space, but also can characterize it in the low-dimensional feature space. Simulation results show the effectiveness of the proposed method.

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An algorithm for bounded-error identification of nonlinear systems based on DC functions

Cited by 17 publications

References 18 publications

Data‐driven bounded‐error fault detection

Data‐driven bounded‐error fault detection

Interval predictor based on a Reversed Huber's error function

Set membership identification using SLLE and NMC

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