Simulation Validation on Stator Currents Issued from a Coupled Magnetic Circuits Modeling Approach 

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Failures occurrence frequency, origins, and consequences

The distribution of the aforementioned failures within the machine subassemblies is reported in many reliability surveys [2, 20] and are provided in Fig. 1.2. Depending on the type and size of the machine, bearing faults and stator windings faults distributions vary from 80% to 90% from large to small machines. The induction machine may be subjected to various failures that affect mainly three components : the stator, the rotor and/or the bearings (Fig. 1.2(a)). A recent paper dealing with induction machine faults distribution [2] has shown that bearings (69%), stator windings (21%), rotor (7%), and shaft/coupling (3%) are the most failing components (Fig. 1.2(b)).
The faults distribution depends on the industrial application. For instance, wind turbines are generally installed in remote sites, difficult to access, and are potentially vulnerable to very harsh environmental conditions especially for offshore farms [21]. In fact, several failures can occur on such systems which reduce the energy production and increase the overall energy cost [22, 23, 24, 25, 26]. The distribution of wind turbine faults within the systems subassemblies has been presented is several papers [3, 27] dealing with wind turbine parks reliability and availability. In Fig. 1.3, one can notice that the percentage of electrical failures is equal to the one of the mechanical faults. Moreover, it can be concluded that the gearbox, the generator and the drive train stand out as components with the longest downtime.
The failures discussed earlier are due to various causes which are associated with the design, manufacture or employment processes. Faults in the stator and bearings defects are nearly 90% of electrical machines defects. In lower power machines, the stator faults are less frequent, while high speed machines are more concerned by bearing faults and rotor faults. It can be concluded from the previously treated items that bearings and insulation are the weak link in the electromechanical drives [28]. The origins of the electromechanical systems faults are diverse and can be summa-rized as follows:
− Thermal stresses: large number of consecutive starts, mechanical overload, un-balanced power supply, insulation ageing due to natural thermal stresses, poor ventilation;
− Electric origins: deterioration of insulating materials, Voltage stresses due to the use of power inverters, high power variations in inductive circuits, inhomogeneous distribution of voltage in the winding which involves heavy use of insulation and accelerated ageing;
− Mechanical causes: insulating materials or copper wear, eccentricity between the stator and the rotor, tangential and radial forces due to the presence of the magnetic field, vibration, frictional wear for bearings.
− Environmental reasons: contaminated environment (dust, humidity, air acidity, etc.), high ambient temperature.

Condition monitoring of induction machines

Shut-downs of plants due to unexpected breakdowns and failures are extremely costly in terms of time and money. Therefore, reducing operation and maintenance costs (O & M) is becoming a crucial motivation. Several techniques have been pro-posed for condition monitoring and faults detection in order to increase the reliability of such systems and therefore reduce the O&M costs. In order to achieve the condition-based maintenance, condition monitoring and faults detection strategies are required. The condition-based maintenance offers the possibility to schedule the maintenance activities. Moreover, the components may be used until their full life and defects may be detected at an early stage in order to prevent breakdowns and afterwards reduce downtime and maintenance cost. Even though such techniques require additional con-dition monitoring hardware and software, the overall maintenance cost is significantly decreased.
Induction machines are widely used in industrial applications such as traction, wind generation, medical equipment, and aircraft systems. Safety, reliability, efficiency and performance are major concerns that direct the research activities in the field of elec-trical machines. Hence, the emphasis is made on the electrical machines condition monitoring techniques with special reference to induction machines faults detection.

Induction machine condition monitoring and faults detection methods

Condition based maintenance of induction machine in industrial applications is based on performance and parameters monitoring. According to the sensor measure-ment used, most methods for induction machine monitoring could be classified into several categories: vibration monitoring, torque monitoring, temperature monitoring, oil/debris analysis, acoustic emission monitoring, optical fiber monitoring, and cur-rent/power monitoring [29, 30].
Most faults generated in the induction machine or associated components cause ad-ditional vibrations. A bearing faults, for instance, can generate a radial rotor movement and a shaft torque variation in the induction machine, and consequently vibration of the whole electromechanical drive [31, 32]. Vibration monitoring has been intensively studied in academia and widely used in industrial applications. Therefore, commer-cial condition monitoring and fault detection system are mostly performed based on vibration monitoring [33]. However, this technique is sophisticated and costly [34]. Moreover, the vibration sensors are mounted on the surface of the electromechanical drives and can be difficult to access during induction machine operation. These sensors are subject to failures which cause additional maintenance cost and affect the system reliability. For instance, it has been reported that sensor failures contribute to more than 14% of failures in wind turbine systems [23].
It has been demonstrated that most of faults lead to torque oscillations and rotor imbalance[35]. Hence, torque monitoring has been used to detect faults of the induction machine [31]. It has also been applied to detect generator stator windings short-circuit [36] in Wind Turbine Generator (WTG). However, the torque transducers need to be installed in the shaft to measure the electrical machine torque, which increase the cost and the complexity of the monitoring system.
Temperature measurement is generally performed for bearing faults monitoring. The IEEE standard 841 points out that the stabilized bearing temperature rise at the rated load should not exceed 45◦C [37]. Therefore, abrupt temperature increase (for example, the lack of lubrication) means the failure of the bearings. Much like, the temperature of gearbox oil in WTG should be in certain range during wind turbine rated operating conditions. The main drawback of temperature monitoring is that the measured temperature may be affected by multiple factors (environment tempera-ture, stator current heating, and generator rotating speed) [38]. Oil/debris analysis is currently used for condition monitoring in industry [39]. In fact, analyzing the com-position, content, size, and classification of wear particles in lubrication oil of bearings and many other components of induction machine allows to determine their health conditions. However, this method only works for high power rating electrical machines with oil lubricated bearings.
Many other methods exist such as acoustic emission monitoring [40], optical fiber monitoring, flux monitoring [41]. However, these techniques are more complicated in real-world applications and require additional sensors which increase the price/complexity of the monitoring system.
This survey of condition-based maintenance approaches highlights the need for a non-invasive, lower cost, most effective condition monitoring approach. A promising technique relies on current/power monitoring. It is based on current and/or voltage measurements that are already available for control and protection purposes. Hence, no additional sensors and acquisition devices are required. Moreover, current/voltage signals are reliable and easily accessible. It follows that current/power monitoring is of great economic interest and can be adopted by industry. Hence, several research activities have been focused on current based faults detection in electrical machines [42, 43, 44, 45]. Power measurements have also been investigated [46, 47]. However, the challenge in using current and/or voltage signals for condition monitoring is to propose signal processing techniques allowing to extract a fault detection and diagnosis criteria in stationary and non-stationary environment (variable speed drives, WTG, etc.) and intelligent diagnosis scheme able to classify faults and foresee a potential failure.
Among the various techniques presented previously, current analysis has several advantages since it is a non-invasive technique that avoids the use of extra sensors [45, 48, 49, 50]. Hence, most of the recent researches on induction machine faults detection has been directed toward electrical monitoring with emphasis on stator cur-rent supervision. In particular, the current spectrum is analyzed to extract the frequency components introduced by the fault [12, 13]. In order to extract a useful in-formation from current signals, advanced signal processing and statistical analysis are required.

Fault detection techniques

Depending on the modeling approach adopted, the appropriate signal processing for fault detection and diagnosis may be different. Hence, power spectral density estimation techniques and demodulation techniques have been employed for fault feature extrac-tion. The PSD estimation techniques allow to estimate the frequency signature, while the demodulation techniques highlight the modulation presence. Afterwards, several classification techniques have been proposed for decision making. The following sec-tion focuses on the techniques used to process the output electrical currents in order to retrieve reliable diagnosis indices related to the faults. It presents a comprehen-sive bibliography with special reference on condition monitoring of induction machine through stator current processing. The literature on rotating electrical machines con-dition monitoring is abundant. Several books have been published [68, 69] as well as journal papers [12, 13, 29].

Feature extraction

Spectral estimation: It has been shown in section 1.3.3 that fault monitoring could be performed by supervising the current spectrum. In particular, it has been demon-strated that faults introduce additional spectral components in the stator current around the supply frequency [12, 13]. In steady-state conditions, techniques based on conventional PSD estimators have been employed. These techniques can be classi-fied into two categories: the conventional periodogram and its extensions and the high resolution techniques such as MUSIC and ESPRIT [7]. In non-stationary environment, the time-frequency/time-scale techniques have been proposed. It allows to track the fault-related frequency in the time-frequency plane. These representations allow to monitor evolution of the fault and consequently its severity.
Demodulation techniques: The demodulation techniques have also been widely investigated. These techniques include the synchronous demodulator [70], the Concor-dia transform [71], Hilbert transform [44, 72, 73, 74], principal component analysis [45] and other approaches [75]. Once the demodulation has been performed, demodulated signals are further processed in order to measure failure severity.

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Classification approaches

In order to perform an induction machine faults detection based on stator currents monitoring, a further step is required to perform a reliable and efficient diagnosis. The artificial intelligence (AI) techniques have been proposed as useful tools to improve the diagnosis, mainly during the decision process [76, 77, 78, 79]. The AI techniques include several sophisticated approaches such as artificial neural networks [80, 81], support vector machine [82, 83], Fuzzy logic [76, 84]and many others. The genetic algorithm has been used to enhance the fault detection performance using the fuzzy logic [85].
ANN technique: Artificial neural networks (ANNs) are computational models whose design is schematically inspired by the operation of biological neurons of human brain and consists of simple arithmetical units connected in a complex architecture [79, 86]. The artificial neural networks need actual case examples used for learning which is called learning database [87]. The learning database must be sufficiently large de-pending on the structure and complexity of the problem studied. However, a large learning database leads to over-fitting problem and thus degrades the neural networks performance (neural network loses its ability to generalize). Indeed, there is a trade-off between generalization and over-training.
Several research papers have dealt with condition monitoring and faults diagnosis of electrical machines based on ANNs [80, 81]. The ANNs have been applied for several tasks such as pattern recognition, parameter estimation, operating condition clustering, faults classification, and incipient stage fault prediction. SVM technique: Support vector machines (SVM) are a set of supervised learning techniques used to solve problems such as input data clustering, pattern recognition and regression analysis [87]. The SVM is based on developed statistical learning theory. Indeed, the theoretic principal of SVM comprises two steps:
1− Non-linear transform (φ) of input data to high dimensional space.
2− Determination of optimal hyperplane or set of hyperplanes in a high- or infinite-dimensional space allowing to linearly classify the input data in this high-dimensional space.
The SVM are able to work with large number of data and a small number of hyper-parameters. Similarly to ANNs, the SVM requires a learning stage. Various applications in academia have proven that such techniques are well suited to deal with electrical machines diagnosis [82, 83]. In [88], several statistical features have been extracted from vibration signals and used as input for SVM in order to perform a classification allowing to distinguish faulty (rolling elements faults) from healthy case for different faults severity.
Fuzzy logic: Fuzzy logic is a form of probabilistic logic; it is aimed at a formalization of modes of reasoning that is approximate rather than exact. In contrary to traditional binary sets, fuzzy logic variables may have truth value that ranges in degree from 0 to 1. Fuzzy logic is much more general than traditional combinational logic. The greater generality of fuzzy logic is needed to deal with complex problems in the realms of search, question-answering decision and control. Fuzzy logic provides a foundation for the development of new tools for dealing with natural languages and knowledge representation.

Table of contents :

List of Figures
List of Tables
Glossary
Introduction
1 Faults Diagnosis in Induction Machine: State of the Art Review 
1.1 Introduction
1.2 Induction Machine Faults
1.2.1 Typical faults in induction machines
1.2.2 Failures occurrence frequency, origins, and consequences
1.3 Condition monitoring of induction machines
1.3.1 Maintenance strategies
1.3.2 Induction machine condition monitoring and faults detection methods
1.3.3 Faults effect over the stator current
1.3.4 Fault detection techniques
1.3.4.1 Feature extraction
1.3.4.2 Classification approaches
1.4 Stator current processing for induction machine faults features extraction
1.4.1 Stationary techniques
1.4.1.1 Periodogram and its extensions
1.4.1.2 High resolution techniques
1.4.2 Demodulation techniques
1.4.2.1 Synchronous demodulator
1.4.2.2 Hilbert transform
1.4.2.3 Teager energy operator
1.4.2.4 Concordia transform approach
1.4.2.5 Principal component analysis approach
1.4.3 Non-stationary techniques
1.4.3.1 Spectrogram
1.4.3.2 Scalogram
1.4.3.3 Wigner-Ville and other quadratic distributions
1.4.3.4 Hilbert-Huang Transform
1.4.3.5 Time-domain analysis & frequency tracking
1.5 Conclusion
2 Stator Currents Parametric Spectral Estimation for Fault Detection in Induction Machines 
2.1 Introduction
2.2 Stator currents model under fault
2.2.1 Study hypotheses
2.2.2 Induction machine stator current modeling
2.3 Maximum likelihood based approach
2.3.1 Stator current model parameters estimation
2.3.1.1 Exact estimators
2.3.1.2 Approximate estimators
2.3.2 Order estimation
2.4 Multidimensional MUSIC
2.4.1 Parameters estimation
2.4.1.1 Frequency Estimation
2.4.2 Order estimation for MD MUSIC
2.4.3 Efficient implementation of MD MUSIC
2.5 Fault detection scheme
2.5.1 Fault detection criterion
2.5.2 MLE based implementation
2.5.3 MD MUSIC based implementation
2.6 Non-stationary parametric spectral estimation techniques
2.6.1 Mathematical formulation
2.6.2 Non-stationary MLE
2.6.2.1 Estimate of (n)
2.6.2.2 Estimation of L
2.6.3 Non-stationary MD MUSIC
2.6.3.1 Covariance matrix update
2.6.3.2 Non-stationary MD MUSIC for fault frequency tracking
2.7 Simulation results
2.7.1 Numerical optimization
2.7.2 Stationary fault detection approach
2.7.2.1 Fixed model order
2.7.2.2 Time-varying model order
2.7.3 Non-stationary techniques analysis
2.7.3.1 Non-stationary MLE analysis
2.7.3.2 Non-stationary MD MUSIC analysis
2.8 Conclusion
3 Simulation Validation on Stator Currents Issued from a Coupled Magnetic Circuits Modeling Approach 
3.1 Introduction
3.2 Induction machine modeling
3.2.1 Coupled magnetic circuits approach
3.2.2 Inductances calculation
3.2.2.1 Stator coil and rotor mesh winding functions
3.2.2.2 Flux based inductances computation
3.2.2.3 Magnetic energy stored in the airgap based inductances computation
3.2.3 Induction machine faults simulation
3.2.3.1 Broken rotor bars
3.2.3.2 Static, dynamic and mixed eccentricity faults
3.3 Numerical simulation of the induction machine
3.3.1 Healthy induction machine
3.3.2 Broken rotor bars simulation
3.3.2.1 Simulation results
3.3.2.2 Broken rotor bars detection with the proposed techniques
3.3.3 Simulation of the eccentricity faults
3.3.3.1 Simulation results
3.3.3.2 Eccentricity fault detection using the proposed approaches
3.4 Conclusion
4 Validation and Experimental Analysis 
4.1 Introduction
4.2 Test facility description
4.2.1 Test rig
4.2.2 Measured quantities
4.3 Bearing faults detection
4.3.1 Stationary spectral estimation
4.3.1.1 Periodogram and Welch periodogram
4.3.1.2 MUSIC, ESPRIT and Prony methods
4.3.1.3 Summary on PSD estimation
4.3.2 Demodulation techniques
4.3.2.1 Synchronous demodulator
4.3.2.2 Concordia Transform
4.3.2.3 Principal Component Analysis
4.3.2.4 Hilbert transform
4.3.2.5 Teager energy operator
4.3.2.6 Summary on demodulation techniques
4.3.3 Time-frequency/time-scale techniques
4.3.3.1 Representation readability and easiness of interpretation
4.3.3.2 Computational Complexity
4.3.3.3 Summary of the time-frequency/time-scale representations
4.3.4 MLE-based approach
4.3.4.1 Fault detection results for stationary environment .
4.3.4.2 Non-stationary MLE for fault detection
4.3.5 Multidimensional MUSIC based method
4.3.5.1 Experimental results analysis in stationary operating conditions
4.3.5.2 Non-stationary MD MUSIC-based bearing faults detection
4.4 Online condition monitoring
4.4.1 Machinery Fault Simulator Description
4.4.2 Further Investigations in Future Works
4.5 Conclusion
5 Conclusions and Recommendations for Future Research 
6 Contribution à la détection et au diagnostic des défauts dans les machines asynchrones
6.1 Introduction
6.2 État de l’art des techniques existantes pour la détection des défauts de la machine asynchrone
6.2.1 L’impact des défauts sur le courant statorique
6.2.2 Techniques non-paramétriques
6.2.3 Techniques paramétriques
6.2.4 Techniques de démodulation
6.2.4.1 Le démodulateur synchrone
6.2.4.2 La transformée de Hilbert
6.2.4.3 L’opérateur d’énergie de Teager
6.2.4.4 La transformée de Concordia
6.2.4.5 L’analyse en composantes principales
6.2.5 Techniques temps-fréquence/temps-échelle
6.2.5.1 Spectrogramme
6.2.5.2 Scalogramme
6.2.5.3 Distributions temps-fréquence quadratiques
6.2.5.4 La transformée de Hilbert-Huang et ses extensions
6.2.6 Limitations et perspectives
6.3 Estimation paramétrique dédiée à la détection des défauts dans un contexte stationnaire
6.3.1 Modèle analytique du courant statorique de la machine asynchrone
6.3.2 Estimation paramétrique de la DSP
6.3.2.1 Les estimateurs de v et
6.3.2.2 L’estimateur de l’ordre du modèle L
6.3.3 Lien avec la transformée de Fourier discrète
6.3.4 MUSIC multi-dimensionnel pour l’estimation de la DSP
6.3.4.1 Les hypothèses de l’étude
6.3.4.2 Estimation de la DSP
6.3.4.3 ’estimation de l’ordre du modèle pour le MUSIC multidimensionnel
6.3.4.4 Estimation de l’amplitude des composantes fréquentielles
6.3.5 Critère de décision automatique
6.3.5.1 Le critère proposé
6.3.5.2 Synthèse de l’algorithme
6.4 Estimation paramétrique adaptée à un fonctionnement dans un contexte non-stationnaire
6.4.1 Maximum de vraisemblance non-stationnaire
6.4.1.1 Estimateur MV de (n)
6.4.1.2 Estimateur de l’ordre du modèle L
6.4.1.3 Algorithme de l’estimateur MV non-stationnaire
6.4.2 MD MUSIC non-stationnaire
6.4.2.1 Mise à jour de la matrice de covariance
6.4.2.2 MD MUSIC non-stationnaire pour le suivi des fréquences
6.5 Validation en simulation sur des signaux issus d’un modèle basé sur les circuits électrique magnétiquement couplés
6.5.1 Élément sur la modélisation d’une machine asynchrone en défaut
6.5.2 Détection des défauts d’excentricité
6.5.3 Détection des défauts de rupture de barres rotoriques
6.6 Validation expérimentale
6.6.1 Banc expérimental
6.6.2 Détection des défauts de roulements par la méthode du EMV
6.6.3 Détection des défauts de roulements par la méthode MD MUSIC
6.7 Conclusions et perspectives
Appendix A Stator currents samples
Appendix B Link with discrete Fourier transform
Appendix C Synchronous demodulator demonstration
References

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