Unsupervised Neural-Network-Based Algorithm for an

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Unsupervised Neural-Network-Based Algorithm for an On-Line Diagnosis of Three-Phase Induction Motor Stator Fault J. F. Martins, Member, IEEE, V. Fernão Pires, Member, IEEE, and A. J. Pires, Member, IEEE

Abstract—In this paper, an automatic algorithm based an unsupervised neural network for an on-line diagnostics of three-phase induction motor stator fault is presented. This algorithm uses the alfa-beta stator currents as input variables. Then, a fully automatic unsupervised method is applied in which a Hebbian-based unsupervised neural network is used to extract the principal components of the stator current data. These main directions are used to decide where the fault occurs and a relationship between the current components is calculated to verify the severity of the fault. One of the characteristics of this method, given its unsupervised nature, is that it does not need a prior identification of the system. The proposed methodology has been experimentally tested on a 1 kW induction motor. The obtained experimental results show the effectiveness of the proposed method. Index Terms—Fault diagnosis, Hebbian learning, induction motors, neural networks, unsupervised learning.

I. INTRODUCTION

P

REVENTIVE maintenance of three-phase induction motors plays a very important role in the industrial life. This requires monitoring their operation for detection of abnormal electrical and mechanical conditions that indicate, or may lead to, a failure of the system. In fact, in the last years monitoring induction motors becomes very important in order to reduce maintenance costs and prevent unscheduled downtimes. Therefore, there has been a substantial amount of research to provide new condition monitoring techniques for ac induction motors. In general, condition monitoring schemes have concentrated on sensing specific failures modes in one of three induction motor components: the stator winding, the rotor winding, or the bearings. Thermal and vibration monitoring have been used for decades [1]. However, vibration transducer is expensive and care should be taken into account for mechanical installation and transmitting the signal. Similar problems exist while working with other sensors, like speed and temperature sensors. Therefore, most of the recent research has been directed toward electrical monitoring of the motor with emphasis on inspecting the stator current of the motor [2]. Manuscript received July 6, 2005; revised December 12, 2005. Abstract published on the Internet November 30, 2006. The authors are with the Laboratório de Sistemas Eléctricos Industriais, Escola Superior Tecnologia de Setúbal, Instituto Politécnico de Setúbal, Setúbal 2914-508, Portugal (e-mail: [email protected]; [email protected]; apires@est. ips.pt). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TIE.2006.888790

Among the most important fault detection based on motor current is the motor current signature analysis (MCSA) [3]–[5]. This method relies on the interpretation of the frequency components in the stator current spectrum. Frequency components have been determined for each specified fault. Another successful fault detection method based on the analysis of the machine line currents is the Park’s vector approach [6], [7]. This diagnostic technique is able to detect several types of faults. The Park’s vector approach is based on the identification of a specified current pattern obtained from the transformation of the three-phase stator currents to an equivalent two-phase system. All the present techniques require the user to have some degree of expertise in order to distinguish a normal operation condition from a potential failure. Therefore, some soft computing tools have been introduced for which references [8]–[19] are a good example. However, many of these tools require a prior identification of the system, and only then they are able to identify some faulty situation. Among several soft computing techniques, artificial neural networks (ANNs) have proven their ability to perform induction motor fault detection. They present some advantages, such as flexibility to learn and do not require an exact mathematical model of the motor. Between the several ANN methods that have been proposed in the literature, one can distinguish between supervised and unsupervised ones. Supervised methods [10], [15] require previous learning before they actually perform fault detection. In [10], the training problem can be overcome with continual on-line training (COT) [16]. Heurist training can also be considered [14]. Unsupervised methods [11]–[13] do not require previous training but they usually involve previously computed fast Fourier transform (FFT). These methods usually decide whether there is a fault by clustering techniques. Turn faults in the stator winding of an induction machine leads to an asymmetry between the three phases, causing undesirable motor behavior. This insulation breakdown in the stator winding corresponds to nearly 40% of the total motor failures. Stator faults can be classified into two distinct categories: laminations or frame faults and stator windings faults (being the later related to the end winding portion or the slot portion) [26]. In this context, this paper proposes an unsupervised neural network on-line diagnosis of three-phase induction motor. The

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Fig. 1. Clarke–Concordia transformation.

Due to its unsupervised nature, the proposed method offers several advantages. First, the absence of previous training, or the incorporation of heuristic knowledge, makes it interesting for industry applications. Second, since there is no need to perform any FFT computation, it makes it simpler to implement. Third, the method is able to indicate the extend of the fault, rather then only detect its presence. II. CLARKE–CONCORDIA APPROACH A three-phase machine with isolated neutral point restricts its phase currents to a plane constructed by two perpendicular static phasors (Fig. 1), since the sum of all phase currents has to be zero at all times according to Kirchoff’s law. Therefore, according to this consideration it is obvious that the current stator equations of any ac machine are reducible to -reference a set of two appropriate variables in the called frame. One straightforward way of transferring variables to -reference frame is a simple vector addition of the the three-phase variables. This vector is obtained applying the or transformation in order to Clarke–Concordia, stator currents are maintain invariant power. Therefore, the given by (1)

Fig. 2. Geometrical interpretation of principal component analysis. (a) Original data. (b) Projected data onto the eigenvector space.

(1) After establishing the correlation matrix of , denoted by on (3), their eigenvectors , and the respective eigenvalues , can be computed III. PRINCIPAL COMPONENTS METHOD A statistical common method for data analysis is the Principal Component Analysis (PCA) [21]. This method was introduced by Pearson in 1901 [20] and widely used in communication theory. Its use is nowadays widespread to a diversity of areas, from engineering to economics. By defining the eigenvectors, this technique is able to obtain the main directions of the data sample on the space-vector [25]. The first step is to obtain a data sample matrix (2). The number of significant samples corresponds to the number of rows of matrix . The induction machine stator currents , form the columns of matrix . The first sample will be and , where denotes the initial time instant and subsequently denotes the sample interval

.. .

.. .

(2)

(3) The eigenvectors and the eigenvalues of the correlation matrix are such that (4) holds true (4) PCA can transform a set of correlated variables to a new set of uncorrelated variables. This new set of uncorrelated variables can be represented as a linear combination of the old ones, in a new space defined by the eigenvectors. The linear combination coefficients are the eigenvectors components. Fig. 2 shows a geometrical interpretation of the principal component space. Fig. 2(a) presents the sample data on its original space, and Fig. 2(b) presents the same data on the eigenvector space, where the correspondent eigenvectors are denoted as and . The principal component is the one where the data has more energy and the second principal direction is the one with the less energy. One should note that can be as

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Fig. 4. Sanger’s neural network.

Fig. 3. Oja’s neural network.

many principal directions as one chooses. Obviously, only the first ones are of interest, because they carry the most of the data energy. IV. UNSUPERVISED HEBBIAN-BASED PRINCIPAL COMPONENT ANALYSIS (PCA) Among others, there are two main advantages for considering neural network PCA computation. First, PCA is traditional associated with linear transformations, which are the simplest and most mathematically tractable function forms for representation. Second, neural network PCA computation does not need to store all the data to be analyzed. This is an important feature when arbitrarily long or infinite sets of data are to be processed. This requires less memory for data storage, since the correlation matrix does not need to be computed. One should note that computation of requires the storage of a large amount of data. Non-neural methods requiring the computation of are of interest only if the data to be processed is not very large. One of the important issues within neural network PCA computation is its unsupervised nature. inputs in the input layer Consider a neural network with and one linear unit in the output layer (no hidden layers are considered) presented in Fig. 3. The output is given by (5), the weights where denotes the inputs and (5) , Oja’s rule (6) finds a unity weight are which maximizes the mean square output [22], where the weights of the ANN presented in Fig. 3. In his paper, Oja showed that a single-layer neuron with a Hebbian-type adaptation rule for its synaptic weights evolves into a filter for the first principal component of the input distribution. In (6), denotes the learning rate (6) For zero-mean data, this is just the first principal component, which is taken along the data direction with the maximum variance. In order to find the other principal components, which correspond to the maximum variance directions in subspaces perpendicular to the previous ones, Sanger’s rule will be used (7). Sanger designed a -output neural network, presented in Fig. 4, that extracts the first principal components [23], being the output given by (8)

Fig. 5. Structure of the proposed algorithm.

(8) As it can be easily seen, the only difference between Oja’s and Sanger’s rules is the introduction by Sanger, of several neurons, in the output layer and the necessary rule adjustment. The obtained weight matrix is the desired principal components vectors. There are several variations on the basic Sanger’a algorithm [24] that accelerate the learning procedure, but the regular Sanger’s rule is sufficient for our purpose. V. UNSUPERVISED NEURAL PCA FAULT DETECTION METHOD The proposed unsupervised ANN-based stator fault detection method is presented in Fig. 5. It is composed by four main simple blocks. The first one performs the Clarke–Concordia transformation (1). The second one is the Hebbian-based unsupervised NN that extracts the prinstator currents. cipal directions (eigenvectors) of the motor currents into The third one performs the projection of the the eigenvector space. This previous procedure is described in currents and the Fig. 2 and is achieved by multiplying the neural network weight matrix (9). One should recall that these matrix elements are the principal components ( and ) of the stator currents (9) By inspecting the projected currents, the last block reports the extend of the fault, just dividing the maximum values of the projected currents according to a severity index defined as (6). This severity index varies between zero and one, being the absence of any fault reported by

(7)

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(10)

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Fig. 6. Simulation results for a healthy motor. (a) Stator currents on the alphabeta state space. (b) Stator currents on the eigenvector space.

To illustrate the fault detection procedure, let us consider a simulated induction motor. Without any stator fault the stator currents components are presented in Fig. 6(a), and the correspondent two principal directions are aligned with the axis. The considered unsupervised neural network, as the one preinputs and outputs, sented in Fig. 4, assumes stator currents and the debeing the dimension of the sired number of PCA to be extracted. Supplying the stator currents, depicted in Fig. 6(a), into the neural network inputs, the network weights evolve towards the first two principal com, ). Using ponents of the stator currents ( the obtained eigenvectors directions, extracted by the neural netstator currents are projected into the new eigenwork, the vector space. These projected currents, shown in Fig. 6(b), still depict a circle, within the eigenvector space, implying the absence of any fault. The proposed algorithm will report a severity index equal to zero, remaining so as long as there is no stator fault. In the presence of a stator fault, in phase b, the corresponding stator currents components are shown in Fig. 7(a). As it can be easily seen, the two principal components are no longer aligned with the axis, denoting the unbalance stator currents caused by a stator fault. In this case, the eigenvectors extracted by the neural network are: , .

Fig. 7. Simulation results for a faulty motor. (a) Stator currents on the alphabeta state space. (b) Stator currents on the eigenvector space.

Projecting the stator currents into the eigenvectors direc. tions, the severity index reports a non-zero value Besides that the obtained principal directions, which are no axis, indicate the phase where the longer aligned with the fault occurred. Considering a fault in phase c, the principal directions are now the ones presented in Fig. 8. The rotation in the principal directions indicate the phase where the fault occurs. In Fig. 8, is also shown the influence of an increasing stator state space. Consequently, as fault over the currents in the long as the fault becomes more severe, the obtained severity index becomes higher. In this illustrative example, Si evolves from 0 (no fault) to 0.12 and 0.26 as long as the fault increases. These values consider 6% of short-circuited stator turns for small fault and 20% for severe fault. From this simulated example, it can be seen that the Hebbian-based ANN (with all the benefits of using unsupervised learning) can be used to detect, and even evaluate, induction motor stator fault. This methodology can also detect other types of stator faults. In the case of two phases winding fault, the correspondent two axis; thereprincipal directions are also not aligned with the fore, the reported severity index (10) is different from zero. VI. EXPERIMENTAL SYSTEM RESULTS To verify the proposed method, experimental results have been obtained from a 1 kW, 220/380 V, 50 Hz induction motor. The machine load is provided by means of an electromagnetic

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Fig. 8. Simulation results for increasing severity stator fault.

Fig. 10. Experimental results for a faulty motor. (a) Stator currents on the alpha-beta state space. (b) Stator currents on the eigenvector space.

state space, and trajectories should create a circle in the the correspondent two principal directions aligned with the axis. However, as it can be seen in Fig. 9(a), the obtained data does not create a perfect circle and the correspondent eigenvec, tors are not exactly aligned with the axis ( ). This is due to a small unbalance present in the supply voltage that forces a small unbalance in the cur, rents. However, the severity index is almost zero reporting a healthy motor. In the presence of a stator fault, the two principal compoaxis, denoting the unnents are no longer aligned with the balance stator currents caused by a stator fault, as can be seen in Fig. 10(a). In this case, the eigenvectors extracted by the neural , . The correnetwork are . sponding severity index assumes a non-zero value VII. CONCLUSION AND REMARKS Fig. 9. Experimental results for a healthy motor. (a) Stator currents on the alpha-beta state space. (b) Stator currents on the eigenvector space.

brake and the stator currents are acquired through a personal computer data acquisition board. The induction motor was initially operated without any fault. stator currents components In this case, the corresponding

In this paper, a fully automatic on-line diagnosis of threephase induction motor stator fault using an unsupervised Hebbian-based neural network-based algorithm was presented. The proposed algorithm, based on the PCA, allows an automatic classification of stator fault (faulty phase and extend of the fault). From the stator current alpha-beta components Hebbian-based unsupervised neural network extracts the principal components (main directions) of the induction motor stator currents. With the obtained eigenvectors, the stator currents are

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projected into the new eigenvector state space and a severity index is easily calculated. The directions of the neural network eigenvectors indicate the phase where the fault occurs and relation between the eigenvector space components is used to discern if the motor is healthy or not, and, if not, the extend of the fault. Experimental results have been presented in order to show the effectiveness of the proposed method. REFERENCES [1] P. J. Tavner and J. Penman, Condition Monitoring of Electrical Machines. New York: Wiley, 1987. [2] B. M. E. Hadremi, “A review of induction motor signature analysis as a medium for fault detection,” IEEE Trans. Ind. Electron., vol. 47, pp. 984–993, Oct. 2000. [3] G. B. Kliman, R. A. Koegl, J. Stein, R. D. Endicott, and M. W. Madden, “Noninvasive detection of broken rotor bars in operating induction motors,” IEEE Trans. Energy Conv., vol. EC-3, no. 4, pp. 873–879, Dec. 1988. [4] S. Nandi and H. A. Toliyat, “Condition monitoring and fault diagnosis of electrical machines—A review,” in Proc. IEEE Ind. Appl. Conf., 1999, vol. 1, pp. 197–204. [5] J. Milimonfared, H. M. Kelk, S. Nandi, A. D. Minassians, and H. A. Toliyat, “A novel approach for broken-rotor-bar detection in cage induction motors,” IEEE Trans. Ind. Appl., vol. 35, no. 5, pp. 1000–1006, Sep.-Oct. 1999. [6] A. J. M. Cardoso, S. M. A. Cruz, J. F. S. Carvalho, and E. S. Saraiva, “Rotor cage fault diagnosis in three-phase induction motors by Park’s vector approach,” in Proc. IEEE Ind. Appl. Conf., 1995, vol. 1, pp. 642–646. [7] A. J. M. Cardoso, S. M. A. Cruz, and D. S. B. Fonseca, “Inter-turn stator winding fault diagnosis in three-phase induction motors, by Park’s vector approach,” IEEE Trans. Energy Conv., vol. 14, pp. 595–598, Sep. 1999. [8] H. Nejjari and M. Benbouzid, “Monitoring and diagnosis of induction motors electrical faults using a current Park’s vector pattern learning approach,” IEEE Trans. Ind. Appl., vol. 36, pp. 730–735, May/Jun. 2000. [9] A. J. M. Cardoso, S. M. A. Cruz, and D. S. B. Fonseca, “Induction motor stator faults diagnosis by a current concordia pattern-based fuzzy decision system,” IEEE Trans. Energy Conv., vol. 18, pp. 469–475, Dec. 2003. [10] R. M. Tallam, T. G. Habetler, and R. G. Harley, “Stator winding turnfault detection for closed-loop induction motor drives,” IEEE Trans. Ind. Appl., vol. 39, pp. 720–724, May/Jun. 2003. [11] R. R. Schoen, B. K. Lin, T. G. Habetler, J. H. Schlag, and S. Farag, “An unsupervised, on-line system for induction motor fault detection using stator current monitoring,” IEEE Trans. Ind. Appl., vol. 31, pp. 1280–1286, Nov./Dec. 1995. [12] S. Wu and T. W. S. Chao, “Induction machine fault detection using SOM-based RBF neural networks,” IEEE Trans. Ind. Appl., vol. 51, pp. 183–194, Feb. 2004. [13] S. Premrudeepreechacharn, T. Utthiyuung, K. Kruepengkul, and P. Puongkaew, “Induction motor fault detection and diagnosis using supervised and unsupervised neural networks,” in Proc. IEEE ICIT, Bangkok, Thailand, 2002, pp. 93–96. [14] P. V. Goode and M. Y. Chow, “Using a neural/fuzzy system to extract heuristic knowledge of incipient faults in induction motors: Part I methodology,” IEEE Trans. Ind. Electron., vol. 42, pp. 131–138, Apr. 1995. [15] S. L. Ho and K. M. Lau, “Detection of faults in induction motors using artificial neural networks,” Proc. IEE Electrical Mach. Drives, pp. 176–181, Sep. 1995. [16] R. M. Tallam, T. G. Habetler, and R. G. Harley, “Continual on-line training of neural networks with applications to electric machine fault diagnostics,” in Proc. IEEE PESC, 2001, vol. 4, pp. 2224–2228. [17] F. Filippetti, G. Franceschini, C. Tassoni, and P. Vas, “Recent developments of induction motor drives fault diagnosis using ai techniques,” in Proc. Annu. Conf. IEEE Ind. Electron. Soc., 1998, vol. 4, pp. 1966–1973.

[18] B. Burton, R. G. Harley, and T. G. Habetler, “High bandwidth direct adaptive neurocontrol of induction motor current and speed using continual on-line random weight change training,” in Proc. Power Electron. Specialists Conf., 1999, vol. 1, pp. 488–494. [19] M.-Y. Chow and S. O. Yee, “Methodology for on-line fault detection in single-phase squirrel-cage induction motors using neural networks,” IEEE Trans. Energy Conv., vol. 6, no. 3, Sep. 1991. [20] K. Pearson, “On lines and planes of closest fit to systems of points in space,” Philosophical Mag., vol. 2, pp. 559–572, 1901. [21] I. T. Jolliffe, Principal Component Analysis. New York: SpringerVerlag, 1986. [22] E. Oja, “A simplified neuron model as a principal component analyzer,” J. Math. Biol., vol. 15, pp. 267–273, 1982. [23] T. D. Sanger, “Optimal unsupervised learning in a single-layer feedforward neural network,” Neural Networks, vol. 12, pp. 459–473, 1989. [24] K. I. Diamantaras and S. Y. Kung, Principal Component Neural Networks: Theory and Applications. New York: Wiley, 1996. [25] V. Cherkassky and F. Mulier, Learning From Data. New York: Wiley, 1998. [26] A. Siddique, G. S. Yadava, and B. Singh, “A review of stator fault monitoring techniques of induction motors,” IEEE Trans. Energy Conv., vol. 20, no. 1, pp. 106–114, Mar. 2005.

J. F. Martins (M’96) was born in Lisbon, Portugal, in 1967. He graduated in electrical engineering at the Instituto Superior Ticnico (IST), Technical University of Lisbon, in 1990. He received the M.Sc. and Ph.D. degrees in electrical engineering from the Instituto Superior Ticnico (IST), Technical University of Lisbon, in 1996 and 2003, respectively. Currently, he is a Professor at the Department of Electrical Engineering, Superior Technical School of Setúbal, Polytechnic Institute of Setúbal, Setúbal, Portugal, and is an invited Auxiliary Professor at the Physics Department, University of Évora, Portugal. He has published more than 15 scientific articles in refereed journals and books and more than 20 articles in refereed conference proceedings. His research areas are in control of electrical drives, advanced learning control techniques for electromechanical systems, grammatical inference learning algorithms, and nonlinear systems.

V. Fernão Pires (M’96) received the B.S. degree in electrical engineering from the Institute Superior of Engineering of Lisbon, Lisbon, Portugal, in 1988, and the M.S. and Ph.D. degrees in electrical and computer engineering from Technical University of Lisbon, in 1995 and 2000, respectively. Since 1991, he has been a Member of Teaching Staff at the Department of Electrical Engineering, Superior Technical School of Setúbal, Polytechnic Institute of Setúbal, Setúbal, Portugal. Presently, he is a Professor teaching Power Electronics and Control of Power Converters. His present research interests are in the areas of modeling and control of converters, electrical drives, and diagnosis of electrical systems.

A. J. Pires (M’05) graduated in electrical engineering at the Instituto Superior Ticnico (IST), Technical University of Lisbon, Lisbon, Portugal, in 1985. He received the M.Sc. and Ph.D. degrees in electrical engineering from the Instituto Superior Ticnico (IST), Technical University of Lisbon, in 1988 and 1994, respectively. Currently, he is a Coordinator Professor in the area of Electrical Engineering at the Polytechnic Institute of Setúbal, Setúbal, Portugal, and is an invited Associate Professor at the Physics Department, University of Évora, Portugal. His research areas are in electrical machines, power electronics, intelligent control systems for electrical drives, and nonlinear systems.

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