Location via proxy:   [ UP ]  
[Report a bug]   [Manage cookies]                
Skip to main content
HARKAT  Mohamed-Faouzi  حركات محمد فوزي
  • Faculté des Sciences de l'Ingéniorat
    Département d'Electronique
    BP. 12, ANNABA 23000
    ALGERIE

    http://www.scopus.com/authid/detail.url?authorId=12797877900
    http://www.univ-annaba.dz
  • +213 (0) 6 65 62 78 65
Sensors are essential components of modern control systems. Any faults in sensors will affect the overall performance of a system because their effects can easily propagate to manipulative variables through feedback control loops and also... more
Sensors are essential components of modern control systems. Any faults in sensors will affect the overall performance of a system because their effects can easily propagate to manipulative variables through feedback control loops and also disturb other process variables. The task for sensor validation is to detect and isolate faulty sensors and estimate fault magnitudes afterwards to provide fault-free values. Model-based methods constitute an important approach
to sensor fault detection and isolation (FDI).
A model-based approach consists in generating residuals as the difference between the measurements and the estimates provided by the relationships existing between the various variables of the process. The analysis of these residuals may lead to detect and isolate the faulty sensors. Almost all conventional model-based methods presume the knowledge of an accurate model of the system, e.g. transfer function or system matrices in the state space representation.
Principal component Analysis (PCA) is a data-driven method which is particularly well adapted to reveal linear relationships among the plant variables without formulating them explicitly and has also been employed for system identification. PCA has some other nice features. It can handle high dimensional and correlated process variables, provides a natural solution to the errors-in-variables problem and includes disturbance decoupling (Li & Qin, 2001). Moreover in the FDI field, Gertler & McAvoy (1997) have shown a close link between PCA and parity space method. Principal component analysis (PCA) has then been applied successfully in the monitoring of complex systems (Chiang & Colegrove, 2007; Harkat et al., 2006; Kano & Nakagawa, 2008).

PCA is used to model the normal process behavior from an empirical data set which is representative of a normal process operation. In general, the majority of the training data set is
associated with such normal operating conditions. The remaining data (faulty data, data obtained during shutdown or startup periods or data issued from different operating modes) are referred to as outliers. Often, these outlying observations are not incorrect but they were made under exceptional circumstances. Therefore, they may disturb the correlation structure of the “normal data” and the result will be a model that does not accurately represent the process.
The fact that multiple outliers can contaminate the model derived from a classical PCA has motivated the development of robust methods that are less affected by outliers. Large residuals from that robust fit indicate the presence of outliers. Once a robust model is determined, the next step deals with multiple fault detection and isolation. Indeed, outliers corresponding to either multiple faulty sensors or a priori unknown operating conditions affect many process variables.
This chapter is devoted to the problem of multiple fault detection and isolation. Section 2 presents the classical PCA principle and summarizes the benefits of different indices generally used for fault detection. Section 3, after a definition of outliers, introduces the main robust methods generally used. Next, a new robust method called MMRPCA for MM-estimator Robust Principal Component Analysis is proposed. It extends to all kinds of outliers the robust
subspace estimator of Maronna (2005). Section 4 deals with multiple fault isolation. After a brief state of the art on fault isolation, structured residuals are generated for multiple fault
isolation. These structured residuals are based on the reconstruction principle of process variables (Dunia et al., 1996;Wang et al., 2004a;b). However, instead of considering all the subsets of faulty variables (one up to all sensors), we determine the isolable multiple fault by evaluating the existence condition of these structured residuals. The proposed scheme avoids the combinatorial explosion of faulty scenarios related to the multiple faults to consider. In the
last section 5 this method is applied on a simulated example in order to illustrate the different steps of our method.
ABSTRACT
In this paper a sensor fault detection and isolation procedure based on principal component analysis is proposed to monitor an air quality monitoring network. The PCA model of the network is optimal with respect to a reconstruction error... more
In this paper a sensor fault detection and isolation procedure based on principal component analysis is proposed to monitor an air quality monitoring network. The PCA model of the network is optimal with respect to a reconstruction error criterion. The sensor fault detection is carried out in various residual subspaces using a new detection index. For our application, this index improves the performance compared to classical detection index SPE. The reconstruction approach allows, on one hand, to isolate the faulty sensors and, on the other hand, to estimate the fault amplitudes.
Research Interests:
Research Interests:
Research Interests:
ABSTRACT
ABSTRACT In this paper a new algorithm for adaptive kernel principal component analysis (AKPCA) is proposed for dynamic process monitoring. The proposed AKPCA algorithm combine two existing algorithms, the recursive weighted PCA (RWPCA)... more
ABSTRACT In this paper a new algorithm for adaptive kernel principal component analysis (AKPCA) is proposed for dynamic process monitoring. The proposed AKPCA algorithm combine two existing algorithms, the recursive weighted PCA (RWPCA) and the moving window kernel PCA algorithms. For fault detection and isolation, a set of structured residuals is generated by using a partial AKPCA models. Each partial AKPCA model is performed on subsets of variables. The structured residuals are utilized in composing an isolation scheme, according to a properly designed incidence matrix. The results for applying this algorithm on the nonlinear time varying processes of the Tennessee Eastman shows its feasibility and advantageous performances.
This paper proposes a new method for fault detection using a reduced kernel principal component analysis (RKPCA). The proposed RKPCA method consists on approximating the retained principal components given by the KPCA method by a set of... more
This paper proposes a new method for fault detection using a reduced kernel principal component analysis (RKPCA). The proposed RKPCA method consists on approximating the retained principal components given by the KPCA method by a set of observation vectors which point to the directions of the largest variances with the retained principal components. The proposed method has been tested on a chemical reactor and the results were satisfactory.
This paper proposes a novel index to detect a sensor fault based on principal component analysis (PCA). The main idea behind this index is to evaluate similarity between Principal Components that represent a normal behavior of a system... more
This paper proposes a novel index to detect a sensor fault based on principal component analysis (PCA). The main idea behind this index is to evaluate similarity between Principal Components that represent a normal behavior of a system and a new that represent current function. This index is evaluated on a Chemical Reactor (CSTR) and the results are satisfactory
This paper presents a new adaptive kernel principal component analysis algorithm (AKPCA) for nonlinear time-varying process monitoring. The basic idea is to use a neuronal principal component analysis based on the kernel version of the... more
This paper presents a new adaptive kernel principal component analysis algorithm (AKPCA) for nonlinear time-varying process monitoring. The basic idea is to use a neuronal principal component analysis based on the kernel version of the generalized Hebbian algorithm. The proposed algorithm follows a new methodology to update the KPCA model. At each time instant, when a new data is available, the KPCA model is updated accordingly without having to re-explore all previous data. By using the proposed algorithm, the performance of process monitoring is improved in two aspects; the speed computation and adaptation of the KPCA model, and the storage memory complexity. To identify faults in a dynamic process, the reconstruction based contribution approach is used and adapted in real time. The results for applying this algorithm on the Tennessee Eastman process shows its feasibility and advantageous performances.
Principal component analysis (PCA) is a commonly used approach to process monitoring. However, it has been developed for singleton variables. Whereas, in many real life cases, this leads to a severe loss of information, this can be... more
Principal component analysis (PCA) is a commonly used approach to process monitoring. However, it has been developed for singleton variables. Whereas, in many real life cases, this leads to a severe loss of information, this can be overcome by introducing the interval notion. The present paper deals with the study of fault detection and isolations (FDI) of uncertain process using interval PCA. Interval data are generated according to various models, and the FDI procedure is lead using the reconstruction principle technique, in its new interval form, for three interval PCA methods: Vertices PCA, Centers PCA, and Midpoints/Radius PCA. A comparison is presented where it is reported in which conditions each method performs best for FDI purpose.
This paper proposes a new online principal component analysis (PCA) index-based parameter estimation approach to detect a sensor fault. The proposed index is based on PCA technique and Mahalanobis distance and it is entitled principal... more
This paper proposes a new online principal component analysis (PCA) index-based parameter estimation approach to detect a sensor fault. The proposed index is based on PCA technique and Mahalanobis distance and it is entitled principal component Mahalanobis distance (PCMD).
The principle of the proposed PCMD is to detect a disagreement between the reference PCA model parameter that represent a normal system function and the PCA model parameter that estimated online to represent current system behavior.
Indeed, the PCMD index evaluate the Mahalanobis distance between the principal components (PCs) of the reference PCA model and the new PCs that represent the current function of the system. These PCs are determined online using a Moving Window PCA technique (MWPCA). To evaluate performances of the proposed index, PCMD is applied on a numerical example and a chemical reactor (CSTR), and the results are satisfactory compared to other index such as SPCA and Spca
In this paper a new algorithm for adaptive kernel principal component analysis (AKPCA) is proposed for dynamic process monitoring. The proposed AKPCA algorithm combine two existing algorithms, the recursive weighted PCA (RWPCA) and the... more
In this paper a new algorithm for adaptive kernel principal component analysis (AKPCA) is proposed for dynamic process
monitoring. The proposed AKPCA algorithm combine two existing algorithms, the recursive weighted PCA (RWPCA) and the moving
window kernel PCA algorithms. For fault detection and isolation, a set of structured residuals is generated by using a partial AKPCA
models. Each partial AKPCAmodel is performed on subsets of variables. The structured residuals are utilized in composing an isolation
scheme, according to a properly designed incidence matrix. The results for applying this algorithm on the nonlinear time varying
processes of the Tennessee Eastman shows its feasibility and advantageous performances.
In this paper a new algorithms for adaptive kernel principal component analysis (AKPCA) is proposed for dynamic process monitoring. The proposed AKPCA algorithm combine two existing algorithm, the recursive weighted PCA (RWPCA) and the... more
In this paper a new algorithms for adaptive kernel principal component analysis (AKPCA) is proposed for dynamic process monitoring. The proposed AKPCA algorithm combine two existing algorithm, the recursive weighted PCA (RWPCA) and the moving window kernel PCA algorithms.

For fault detection and isolation, a set of structured residuals is generated by using a partial AKPCA models. Each partial AKPCA model is performed on subsets of variables. The structured residuals are utilized in composing an isolation scheme, according to a properly designed incidence matrix. The results for applying this algorithm on the nonlinear time varying processes of the Tennessee Eastman shows its feasibility and advantageous performances.
In observer-based approach for fault detection and isolation, two schemes are generally considered, namely the dedicated observer scheme (DOS) and the generalized observer scheme (GOS). DOS is a bank of observers sensitive to only one... more
In observer-based approach for fault detection and isolation, two schemes are generally considered, namely the dedicated observer scheme (DOS) and the generalized observer scheme (GOS). DOS is a bank of observers sensitive to only one fault while GOS is composed of observers sensitive to all faults except one. In this paper a new sensor fault diagnosis approach named Reconstruction Observer Scheme (ROS) is proposed, which does not need any bank of observer, only one observer is used. The proposed method based on reconstruction of variables is used to generate a structured residuals for fault isolation. After the fault detection, the reconstruction is carried of all the variables. Reconstruction of a variable consists on the replacement of this variable to the input of the observer by its estimation. This operation eliminates fault effect when a faulty variable is reconstructed. The proposed approach is illustrated by an academic example.
In observer-based approach for fault detection and isolation, two schemes are generally considered, namely the dedicated observer scheme (DOS) and the generalized observer scheme (GOS). DOS is a bank of observers sensitive to only one... more
In observer-based approach for fault detection and isolation, two schemes are generally considered, namely the dedicated observer scheme (DOS) and the generalized observer scheme (GOS). DOS is a bank of observers sensitive to only one fault while GOS is composed of observers sensitive to all faults except one. In this paper a new sensor fault diagnosis approach named Reconstruction Observer Scheme (ROS) is proposed, which does not need any bank of observer, only one observer is used. The proposed method based on reconstruction of variables is used to generate a structured residuals for fault isolation. After the fault detection, the reconstruction is carried of all the variables. Reconstruction of a variable consists on the replacement of this variable to the input of the observer by its estimation. This operation eliminates fault effect when a faulty variable is reconstructed. The proposed approach is illustrated by an academic example.
In this paper a new algorithms for adaptive kernel principal component analysis (AKPCA) is proposed for dynamic process monitoring. The proposed AKPCA algorithm combine two existing algorithm, the recursive weighted PCA (RWPCA) and the... more
In this paper a new algorithms for adaptive kernel principal component analysis (AKPCA) is proposed for dynamic process monitoring. The proposed AKPCA algorithm combine two existing algorithm, the recursive weighted PCA (RWPCA) and the moving window kernel PCA algorithms. For fault detection and isolation, a set of structured residuals is generated by using a partial AKPCA models. Each partial AKPCA model is performed on subsets of variables. The structured residuals are utilized in composing an isolation scheme, according to a properly designed incidence matrix. The results for applying this algorithm on the nonlinear time varying processes of the Tennessee Eastman shows its feasibility and advantageous performances.
In this paper a novel Nonlinear Principal Component Analysis (NLPCA) is proposed. Generally, a NLPCA model is performed by using two sub-models, mapping and demapping. The proposed NLPCA model consists of two cascade three-layer neural... more
In this paper a novel Nonlinear Principal Component Analysis (NLPCA) is proposed. Generally, a NLPCA model is performed by using two sub-models, mapping and demapping. The proposed NLPCA model consists of two cascade three-layer neural networks for mapping and demapping, respectively. The mapping model is identified by using a Radial Basis Function (RBF) neural networks and the demapping is performed by using
an Input Training neural networks (IT-Net). The nonlinear principal components, which represents the desired output of the first network, are obtained by the IT-NET. The proposed approach is illustrated by a simulation example and then applied for fault detection and isolation of the TECP process.
While principal component analysis (PCA) has found wide application in process monitoring, slow and normal process changes often occur in real processes, which lead to false alarms for a fixed-model monitoring approach. In this paper, a... more
While principal component analysis (PCA) has found wide application in process monitoring, slow and normal process changes often occur in real processes, which lead to false alarms for a fixed-model monitoring approach.

In this paper, a new recursive algorithm for adaptive process monitoring based on Adaptive Moving Window is proposed. By using the current model and the updated mean and covariance structures and an Adaptive Moving Window, a new model is derived recursively (AMWPCA). Based on the updated PCA representation the Q-statistic (SPE) (monitoring metric) is calculated and their control limits are updated.
Simulation results are illustrated by application to Tennessee Eastman process.
L'Analyse en Composantes Principales (ACP) est un outil statistique largement utilisé pour l'analyse de données collectées sur des systèmes en cours de fonctionnement afin de surveiller leur comportement. Cependant, d'un point de vue... more
L'Analyse en Composantes Principales (ACP) est un outil statistique largement utilisé pour l'analyse de données collectées sur des systèmes en cours de fonctionnement afin de surveiller leur comportement. Cependant, d'un point de vue statistique, l'un des inconvénients majeurs de l'approche ACP résulte de son utilisation de techniques d'estimation par moindres carrés, techniques qui échouent à prendre en compte les biais de mesures accidentels ce qui est malheureusement assez fréquent sur le plan pratique.
Cette communication présente :
1) la formulation d'une es- timation robuste (vis-à-vis des valeurs aberrantes) de l'état d'un système basée sur l'analyse en composantes principales,
2) une procédure de détection et de localisation de défauts
de mesures. La méthode proposée ne nécessite pas d'étude
préliminaire relative µa la détection et au rejet de valeurs aberrantes ou de grosses erreurs dans les données utilisées pour la conception du modèle ACP. Elle présente l'intérêt d'utiliser directement les données brutes, éventuellement entachées de grosses erreurs, et le modèle ACP est construit à partir de ces données sans être préalable, cette construction étant robuste vis-à-vis de la présence de grosses erreurs.
Le modèle ACP obtenu étant sain, c'est-à-dire non contaminé
par les valeurs aberrantes, son utilisation pour le diagnostic (détection et localisation de défauts de mesure) est alors efficace.
Principal component analysis (PCA) has been applied successfully for data compression.Here, the purpose is to use PCA for detection and isolation of faults affecting measurements by usingboth reconstruction and projection of variables.... more
Principal component analysis (PCA) has been applied successfully for data compression.Here, the purpose is to use PCA for detection and isolation of faults affecting measurements by usingboth reconstruction and projection of variables. Then, this procedure for outliers detection and isolationis successfully applied to an example with multiple faults.
Il a été montré que la combinaison de plusieurs modèles peut donner une meilleure approche pour modéliser des systèmes non linéaires. Nous présentons dans ce papier une nouvelle variante de l'analyse en composantes principales non... more
Il a été montré que la combinaison de plusieurs modèles peut donner une meilleure approche pour modéliser des systèmes non linéaires. Nous présentons dans ce papier une nouvelle variante de l'analyse en composantes principales non linéaires (ACPNL) pour la modélisation et le diagnostic des systèmes non linéaires. Le modèle ACPNL proposé est représenté par des multi-modèles ACP linéaires. Ainsi, une extension du principe de reconstruction, utilisé habituellement dans le cas linéaire, est exploitée à la fois pour la ...
Abstract— Due to its simple construction, low cost, manufacture, and its robustness. The use of induction motors is rapidly and increasingly growing in the industry especially in highly important sectors. This leads us to a serious focus... more
Abstract— Due to its simple construction, low cost, manufacture, and its robustness. The use of induction motors is rapidly and increasingly growing in the industry especially in highly important sectors. This leads us to a serious focus on their operation and their availability. The early ...
Fault detection and process monitoring using principal component analysis (PCA) has been studied intensively and largely applied to industrial processes. This paper proposes an approach to sensor fault detection and isolation via... more
Fault detection and process monitoring using principal component analysis (PCA) has been studied intensively and largely applied to industrial processes. This paper proposes an approach to sensor fault detection and isolation via principal component analysis and its application to sensor failure detection of an air quality monitoring network in Lorraine, France. The method suggested by Dunia et al.(1996) is sensitive to model errors. For this reason, a test on the last principal components is proposed for the detection and the ...
Induction motors have been extensively integrated in most if not all industrial fields, covering a wide range of power, within both grid-connected and variable speed drives. Of particular interest is the squirrel cage induction motor... more
Induction motors have been extensively integrated in most if not
all industrial fields, covering a wide range of power, within both
grid-connected and variable speed drives. Of particular interest
is the squirrel cage induction motor which is popular thanks to
its low cost and the robustness of its rotor whose circuits do
not require any slip-ring systems. However, the squirrel cage
induction motor suffers from relatively frequent faults mainly due
to given rotor failures. In this paper, a dedicated model of the
squirrel cage induction motor, taking into account, as accurately
as possible, the rotor equivalent circuit, is firstly derived. Then
a case study of broken bar faults is treated, considering both
spectral and d-q phasor analysis of the stator phase-currents.
Induction motors (IMs) are currently among the most used in variable speed drives due to their high reliability and their low costs. In spite of these qualities, they are more or less penalized by some drawbacks, such as low efficiency,... more
Induction motors (IMs) are currently among the most used in variable speed drives due to their high reliability and their low costs. In spite of these qualities, they are more or less penalized by some drawbacks, such as low efficiency, low start-up torque and the likelihood of some rotor failures. Within the last drawback, the paper deals with the diagnosis and detection of the IM rotor dynamic eccentricity fault. Firstly, a dedicated IM model is derived taking into account both healthy and faulty operation cases. Then, simulation works are carried out focusing the IM no-load start-up followed by the application of a load torque at steady-state, considering both healthy and faulty operation cases. A special attention is paid to the analysis of the stator current whose harmonic spectrum highlights some specific frequencies around the fundamental one. These represent signatures for the detection and the localization of the IM rotor dynamic eccentricity fault.
Our work is devoted to the problem of multiple sensor fault detection and isolation using principal component analysis. Structured residuals are used for multiple fault isolation. These structured residuals are based on the principle of... more
Our work is devoted to the problem of multiple sensor fault detection and isolation using principal component analysis. Structured residuals are used for multiple fault isolation. These structured residuals are based on the principle of variable reconstruction. However, multiple fault isolation based on reconstruction approach leads to an explosion of the reconstruction combinations. Therefore instead of considering all the subsets of faulty variables, we determine the isolable multiple faults by removing the subsets of variables that have too high minimum fault amplitudes to ensure fault isolation. Unfortunately, in the case of a large number of variables, this scheme yet leads to an explosion of faulty scenarios to consider. An effective approach is to use multi-block reconstruction approach where the process variables are partitioned into several blocks. In the first step of this hierarchical approach, the goal is to isolate faulty blocks and then in the second step, from the faulty blocks, faulty variables have to be isolated. The proposed approach is successfully applied to multiple sensor fault detection and isolation of an air quality monitoring network.
This paper presents a data-driven method based on non-linear principal component analysis to detect and isolate multiple sensor faults. The RBF-NLPCA model is obtained by combining a principal curve algorithm and two three-layer radial... more
This paper presents a data-driven method based on non-linear principal component analysis to detect and isolate multiple sensor faults. The RBF-NLPCA model is obtained by combining a principal curve algorithm and two three-layer radial basis function (RBF) networks. The reconstruction approach for multiple sensors is proposed in the non-linear case and successfully applied for multiple sensor fault detection and isolation of an air quality monitoring network. The proposed approach reduces considerably the number of reconstruction combinations and allows to determine replacement values for the faulty sensors.
The induction motor is one of the most used electric machines in variable speed system in the different field of industry and takes a particular interest for applications requiring high power and variable speed for its robust and... more
The induction motor is one of the most used electric machines in variable speed system in the different field of industry and takes a particular interest for applications requiring high power and  variable speed for its robust and simplicity. The early detection for motor deterioration can increase plant availability and safety in an economical way. Many publications have investigated the detection and diagnosis broken rotor bars in electrical machines supplied directly on line.
However, much fewer research results have been published when the induction motor is fed by pulse width modulation (PWM) voltage source inverter which is the most common drive in the
industry. This paper presents a technique method based on spectral analysis of stator currents to detect broken rotor bars fault in the rotor when it is fed from PWM-VSI. The obtained
results show clearly the possibility of extracting signatures to detect and locate fault.
In this paper a sensor fault detection and isolation procedure based on principal component analysis is proposed to monitor an air quality monitoring network. The PCA model of the network is optimal with respect to a reconstruction error... more
In this paper a sensor fault detection and isolation procedure based on principal component analysis is proposed to monitor an air quality monitoring network. The PCA model of the network is optimal with respect to a reconstruction error criterion. The sensor fault detection is carried out in various residual subspaces using a new detection index. For our application, this index improves the performance compared to classical detection index SPE. The reconstruction approach allows, on one hand, to isolate the faulty sensors and, on the other hand, to estimate the fault amplitudes.
Nous proposons une méthode basée sur l’analyse en composantes principales pour la détection et la localisation de défauts de capteurs d’un réseau de surveillance de la qualité de l’air. Le modèle ACP du réseau de mesures est optimal au... more
Nous proposons une méthode basée sur l’analyse en composantes principales pour la détection et la localisation de défauts de capteurs d’un réseau de surveillance de la qualité de
l’air. Le modèle ACP du réseau de mesures est optimal au sens d’un critère basé sur l’erreur de reconstruction des différentes variables. La détection des défauts de capteurs est réalisée
dans différents sous-espaces résiduels à l’aide d’un nouvel indicateur de détection. Enfin, la reconstruction des variables permet, d’une part, en la combinant avec l’indicateur de détection, de localiser les capteurs défaillants et, d’autre part, d’estimer l’amplitude des défauts
Recently, fault detection and process monitoring using principal component analysis (PCA) were studied intensively and largely applied to industrial process. PCA is the optimal linear transformation with respect to minimizing the mean... more
Recently, fault detection and process monitoring using principal component analysis (PCA) were studied intensively and largely applied to industrial process. PCA is the optimal linear transformation with respect to minimizing the mean squared prediction error. If the data have nonlinear dependencies, an important issue is to develop a technique which can take into account this kind of dependencies. Recognizing the shortcomings of PCA, a nonlinear extension of PCA is developed. This paper proposes an application for sensor failure detection and isolation (FDI) to an air quality monitoring network via nonlinear principal component analysis (NLPCA). The NLPCA model is obtained by using two cascade three layer RBF-Networks. For training these two networks separately,
the outputs of the first network are estimated using principal curve algorithm [7] and the problem is transformed as two nonlinear regression problems.
The aim of this thesis is to study the fault detection and isolation using principal components analysis (PCA). In the first chapter the fundamental principles of linear principal component analysis are presented. PCA is used to model... more
The aim of this thesis is to study the fault detection and isolation using principal components analysis (PCA). In the first chapter the fundamental principles of linear principal component analysis are presented. PCA is used to model normal process behaviour. In the second chapter the problem of fault detection and isolation based on linear PCA is tackled. On the basis of the analysis of the classical detection indices, a new fault detection index based on the last principal components is developed. For fault isolation, the classical methods, using for instance the reconstruction principle or the contribution calculation, are adapted for the proposed fault detection index. The third chapter is focused on the nonlinear PCA. An extension of the PCA for nonlinear systems, combining principal curves algorithm and RBF networks, is proposed. For the determination of the number of principal components to be kept in the NLPCA model, we propose an extension of the unreconstructed variance criteria in the non-linear case. Finally, an application, carried out in collaboration with air quality monitoring network in Lorraine AIRLOR, is presented in the fourth chapter. This application concerns the sensor fault detection and isolation of this network by using the fault detection and isolation procedure developed in the linear case.

Key-Words : Diagnosis – Principal component analysis – Sensor fault detection and isolation – Variable reconstruction – Variable contribution – RBF Neural Networks – Air quality.
The use of principal component analysis (PCA) for process monitoring applications has attracted much attention recently. PCA is the optimal linear transformation with respect to minimizing the mean square prediction error but it only... more
The use of principal component analysis (PCA) for process monitoring applications has attracted much attention recently. PCA is the optimal linear transformation with respect to minimizing the mean square prediction error but it only considers second order statistics. If the data have nonlinear
dependencies, an important issue is to develop a technique
which takes higher order statistics into account and which
can eliminate dependencies not removed by PCA. Recognizing the shortcomings of PCA, a nonlinear extensions of PCA is developed.
The purpose of this paper is to present a non linear generalization of PCA (NLPCA) by combining the principal curves and RBF-Networks. The NLPCA model consists of two RBF networks where the nonlinear transformations of the input
variables (that characterize the nonlinear principal component
analysis) are modelled as a linear sum of radially symmetric
kernel functions by using the first network. The nonlinear principal components, which represents the desired output
of the first network, are obtained by the principal curves
algorithm. The second network tries to perform the inverse
transformation by reproducing the original data. The proposed
approach is illustrated by a simulation example.
Dans ce papier nous étudions deux approches de localisation de défauts, basée sur l'analyse en composantes principales (ACP). Un indice de détection calculé à partir des dernières composantes principales est utilisé pour la détection de... more
Dans ce papier nous étudions deux approches de localisation de défauts, basée sur l'analyse en composantes principales (ACP). Un indice de détection calculé à partir des dernières composantes principales est utilisé pour la détection de défauts. Une fois le défaut détecté, le principe de reconstruction des variables est utilisé pour localiser la variable en défaut. Cependant cette technique de localisation présente certaines limitations (liées au degré de redondance). L'autre alternative de localisation est basée sur le calcul des contributions des variables à l'indice de détection.
Cependant cette méthode est trés sensible aux points de
fonctionnement, car le calcul des contributions dépend directement des amplitudes des variables. On montre dans ce
papier que cet méthode ne peut être utilisée pour la localisation. Un exemple d'illustration sera présenté.
Principal component analysis (PCA) is among the most popular methods for extracting information from data, which has been applied in a wide range of disciplines. In process monitoring with Principal component analysis, PCA is used to... more
Principal component analysis (PCA) is among the most popular methods for extracting information from data, which has been applied in a wide range of disciplines. In process monitoring with Principal component analysis, PCA is used to model normal process behavior and faults are then detected by referencing the measured process behavior against this
model.
It is known that the multivariate projection technique of PCA is linear, therefore it is only applicable for extracting information from linearly correlated process data. However, many industrial processes exhibit
nonlinear behavior. For such nonlinear systems, linear PCA is inappropriate to describe the nonlinearity within the process and it can produce excessive number of false alarms or alternatively, missed detection of process faults, which significantly compromise the reliability of the monitoring systems.
To cope with this problem, extended versions of PCA have been developed such as Nonlinear PCA (NLPCA). Whilst linear PCA identifies the linear correlations between process variables, the objective of
nonlinear PCA is to extract both linear and nonlinear relationships. Hastie and Stuetzle (Hastie and Stuetzle, 1989), proposed a principal curve methodology to provide a nonlinear summary of a m-dimensional
data set. However, this approach is non-parametric and can not be used for continuous mapping of new data. To overcome the parametrization problem, several nonlinear PCA based on neural networks have
been proposed (Kramer, 1991), (Dong and McAvoy, 1996), (Tan and Mavrovouniotis, 1995).
Tan and Mavrovouniotis (Tan and Mavrovouniotis, 1995) formulated an alternative scheme of nonlinear PCA based on an input-training neural network (IT-Net). Under this approach, only the demapping section of the NLPCA model is considered. Compared with the other neural networks, when it is in training, its inputs which represent the desired principal component are not fixed but adjusted simultaneously with the internal network parameters, and it can perform all functions of a five layer neural network.
However, IT-Net has its own limitation. For example, for a new data set or observation, calculation of its corresponding nonlinear principal component require more computation due to the necessity of
an on-line nonlinear optimizer.
To improve this approach, a NLPCA model combinin a principal curve algorithm(Hastie and Stuetzle, 1989) and two cascade three-layer neural networks is proposed to identify mapping and demapping models
(Dong and McAvoy, 1996). Harkat et al. (Harkat et al., 2003) proposes a
similar approach which uses two RBF networks for nonlinear principal component mapping and demapping, respectively. First, the principal curve algorithm is used to estimate the principal components.
Then supervised learning is used to train the two RBF networks. The proposed methodology avoids the use of the principal curve algorithm by replacing the RBF demapping network with an IT-Net, which is able to estimate the principal components during learning.