- Email: [email protected]
SVM practical industrial application for mechanical faults diagnostic
Expert Systems with Applications 38 (2011) 6980–6984
Contents lists available at ScienceDirect
Expert Systems with Applications journal homepage: www.elsevier.com/locate/eswa
SVM practical industrial application for mechanical faults diagnostic Lane Maria Rabelo Baccarini ⇑, Valceres Vieira Rocha e Silva, Benjamim Rodrigues de Menezes, Walmir Matos Caminhas Department of Electrical Engineering, Federal University of São João del Rei, Praça Frei Orlando, 170 – Centro – 36307-352, Minas Gerais, Brazil Department of Electronics Engineering, Federal University of Minas Gerais, Brazil Department of Electrical Engineering, Federal University of Minas Gerais, Av. Antônio Carlos 6627-31270-010, Brazil
a r t i c l e
i n f o
a b s t r a c t
Keywords: Fault diagnosis Vibration analysis SVM Practical application
A large percentage of the total induction motor failures are due to mechanical faults. It is well known that, machine’s vibration is the best indicator of its overall mechanical condition, and an earliest indicator of arising defects. Support vector machines (SVM) is also well known as intelligent classifier with strong generalization ability. In this paper, both, machine‘s vibrations and SVM are used together for a new intelligent mechanical fault diagnostic method. Using only one vibration sensor and only four SVM’s it was achieved improved results over the available approaches for this purpose in the literature. Therefore, this method becomes more attractive for on line monitoring without maintenance specialist intervention. Vibration signals turns out to occur in different directions (axial, horizontal or vertical) depending on the type of the fault. Thus, to diagnose mechanical faults it is necessary to read signals at various positions or use more them one accelerometer. From this work we also determined the best position for signals acquisition, which is very important information for the maintenance task. Ó 2010 Elsevier Ltd. All rights reserved.
1. Introduction
faults in the frequency domain. Every kind of mechanical failure causes a specific alteration of the frequency spectrum compared to the right one. Many techniques have been implemented for working conditions monitoring and fault diagnosis of induction motors aiming to provide high-degree of reliability and motor life. The application of intelligent system for induction motor fault diagnosis has been widely used in recent years. Widodo and Yang (2007) presented a survey of machine condition and fault diagnostic using support vector machine (SVM). This paper surveys articles form 1996 to 2006. The authors concluded that ‘‘. . . applications of SVM in machine condition and fault diagnosis still need more encouragement and attention due the lack of existed paper. The efforts to find a new novel idea must be encouraged to give more contributions in robust machine condition monitoring and diagnosis’’. Different methods for induction motor fault diagnosis on the basis of current signals were proposed in Niu et al. (2008), Rodrigues, Negrea, and Arkkio (2008) and Radhika, Sabareesh, Jagadanand, and Sugumaran (2009). Tran, Yang, Oh, and Tan (2009) suggested a new mechanism for fault diagnosis of induction motors on the basis of start-up transient current, which combined the advantages of wavelet analysis and decision-level fusion technique to improve diagnosis accuracy. The applications of intelligent system for motor rolling elements bearings are proposed in Lei, He, and Zi (2008, 2009). It is known that the voltage unbalance has a potential source of effects on motor efficiency, rotor losses, and temperature rises.
Induction motors are fundamental components in many industrial processes since they are robust, mechanically simple and adaptable to wide variety of operation conditions although simple to control. Induction motors are frequently exposed to different loading and environmental conditions (Baccarini, Menezes, & Caminhas, 2010). These conditions together with the natural aging of the motor may lead to many failures (Bonett & Soukup, 1992). Once it is not economical to keep redundant backup machines, online monitoring for induction machines is important for safe operation and production quality (Wu & Chow, 2004). Hence, monitoring the motor condition is essential to detect any fault in early stage to avoid severe motor damages (Emara, Ammar, Bahgat, & Dorrah, 2003). The most common types of induction rotating machine faults have always been related to the rotor or machine shaft, such as mechanical unbalance, misalignment, and bearing fault (Chow & Hai, 2004). Vibration is the best indicator of overall mechanical condition and the earliest indicator of arising defects. Vibration analysis is based on the principle that faults can be detected by particular frequencies associated also with particular types of ⇑ Corresponding author at: Department of Electrical Engineering, Federal University of São João del Rei, Praça Frei Orlando, 170 - Centro - 36307-352, Minas Gerais, Brazil. E-mail address: [email protected] (L.M.R. Baccarini). 0957-4174/$ - see front matter Ó 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.eswa.2010.12.017
L.M.R. Baccarini et al. / Expert Systems with Applications 38 (2011) 6980–6984
Çakir, Çalis, and Küçüksille (2009) described an approach for detection of the supply unbalance condition in induction motors by using data mining process. Also the works presented in Widodo and Yang (2008) and Widodo et al. (2007) studied the application of independent component analysis (ICA) and SVM to detect and diagnose induction motor faults. The ICA is used for feature extraction and data reduction from original features. The total 78 features (13 parameters and six signals) are calculated from 10 feature parameters of time domain and three parameters from frequency domain (rms, frequency center and root variance frequency) using three vibration acceleration signals and three-phase current signals. The authors concluded that the number of SVMs decreased due the feature reduction. The maximum number of SVM’s used was 110 and the minimum was 45. Considering that machine’s vibration is the best indicator of its overall mechanical condition and also that SVM is a classifier with strong generalization ability, this paper presents an intelligent mechanical fault diagnostic system using support vector machines and only one accelerometer sensor. The SVM’s training used only the first rotation frequencies components of the vibration signals. Only four SVM’s were applied for this purpose either. It made the method rather simple and therefore very attractive for online monitoring without maintenance specialist intervention. Vibration signals turns out to be in different directions (axial, horizontal or vertical) depending on the type of the fault. To diagnose mechanical faults it is necessary to acquire signals at various positions or use more them one accelerometer, since analysis based only on one accelerometer position can mislead the results. From this work, we also determined the best position for signals acquisition, which is very important for the maintenance task. This is a valuable information to reduce the number of sensors and to reduce the maintenance costs. For the purposes of this work the vibration signals are collected by an accelerometer connected to a data acquisition systems. Those signals are transformed by fast Fourier transform (FFT) into signals in the frequency domain, which can be analyzed and processed easier than those in the time domain. Then, some features are extracted from the frequency-domain signals to become inputs of classifiers. This paper is organized as follows: Section 2 gives a brief description of the various mechanical faults associated to featured frequencies in the vibration spectrum. SVM method basic concepts are given in Section 3. The test bed used to obtain the vibrations signals is described in Section 4. In Section 5, it is showed how is implemented the fault diagnostic algorithm and the results are analyzed. Section 6 presents the concluding remarks.
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combinations. Most of the mechanical problems can be detected by the first harmonics of the motor rotation. Following, sources of vibration due to mechanical problems are enhanced. 2.1. Unbalance The motor unbalance occurs due the motor’s mass unbalance around the rotation axis caused by asymmetries, material and construction imperfections. It is practically impossible to manufacture a motor that is perfectly balanced. The degree of unbalance that affects the motor dictates whether it is a problem or not. The unbalance creates a periodic vibration signal with the same amplitude in each shaft rotation. The vibration amplitude depends of the magnitude of the unbalance. 2.2. Misalignments They are sources of machine components deterioration that occur when two machines are coupled. There are two types of misalignments: angular and parallel, and sometimes a combination of both. Angular misalignment happens when the central position of both machines mismatches. High axial vibrations are representative of angular misalignments that come together with high multiple levels of rotation. Parallel misalignment happens when both axes should work in parallel position. The dominant vibration is radial from double rotational speed. It can be vertical or horizontal. The misalignment direction is given by the direction of the higher level vibration. 2.3. Mechanical looseness Machines are constructed in such a way that the fundamental structure can not move freely. Whether screws lose or the concrete base deteriorates it can result movement in between the surfaces, generating harmonic peaks in vibration, oscillating at the same frequency of the rotation. Mechanical looseness can lead to residual misalignment, relatively small, that can cause high level of vibrations. The frequency spectrum can indicate misalignment, distorted shaft and/or unbalance, depending on how the rotor and structure are affected by the back slash. In the early stages, mechanical looseness causes vibrations at one rotational frequency and also at its double one. Further deterioration of the motor condition results in fractional harmonics increasing in amplitude. These harmonics are most visible in signals taken when the machine in only lightly loaded. 3. SVM
2. Modelling vibration fenomenum 3.1. Formalization The machine‘s vibration is a result of the electrical and mechanical forces and the motors‘ structure. Vibration analysis is a multidisciplinary problem. It requires the bringing together of some disciplines knowledge: Analysis of errors: information about the dynamic signals of interest, modulation and conditioning, decomposition by frequency components. Fault identification: tools for vibration signals analysis to allow for faults diagnostic. Vibration measurement system: signal conditioning, choices of the most important parameters, knowledge of available instrumentation with hardware and software for signal analysis. Therefore, to diagnose a machine vibration it is necessary to learn the changing patterns of the signals and the possible dynamic
SVM is a technique used to train the classifiers based on the structural risk minimizations concept. This technique was developed by Vapnik (1999) and has been widely applied since 90’s in various pattern recognition and classification problems. SVMs can be used to classify data in two classes: positive (+ ve) and negative ( ve). Assuming a set of points of these two classes, the SVM description is as follows: a SVM establishes the hyperplane that allocates the majority of points of the same class in the same side, whilst maximizes the distance between the two classes to this hyperplane. The distance between one class and a hyperplane is the smallest distance between the hyperplane and the other points of the same class and is called the optimal separating hyperplane. The hyperplane created by SVM contains a subset of points of the two classes called support vectors. Fig. 1 presents an example of optimal separating hyperplane of two datasets.
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Actually the necessary changes to implement the non linear SVM’s in a higher dimension space is minimal by only substituting x by /(x) in the previous equations, where / is a non linear mapping of the input space on the feature space. 3.2. Multiple classes
Fig. 1. Optimal hyperplane.
Assuming a training set {xi, yi}, where x 2 Rn and y 2 { 1, 1}, i = 1, . . . , N xi is an input vector and yi is the required classification. The aim is to estimate a function f, using the training set that classifies the pairs {xi, yi} which have not been correctly used yet. The optimal hyperplane is defined by:
wx þ b ¼ 0;
ð1Þ n
where w 2 R is a vector of weights and the scalar b is the bias. A vector xi of the same class of yi, y 2 { 1, 1}, must satisfy the equation:
yi ðwxi þ bÞ 1 P 0;
ð2Þ
where w is normal to the hyperplane. The Euclidian distance between this hyperplane and the points over the separating margin, i.e., yi(wxi + b) = 1 is determined by Eq. (3)
yi ðwxi þ bÞ 1 ¼ : kwk kwk
ð3Þ
Thus, to minimize kwk is equivalent to maximize the separating hyperplane. Using Lagrange multipliers theory the following equation can be established:
Jðw; b; aÞ ¼
N X 1 a½yi ðwxi þ bÞ 1; ðwwÞ 2 i¼1
ð4Þ
where ai are the Lagrange multipliers. The optimization problem solution is obtained through minimization of J(w, b, a) subject to a. When patterns are not linearly separated, machines that generate input data in a higher dimension space are used to decrease the computational efforts of the support machines. By choosing a nonlinear mapping a priori, the SVM constructs an optimal separating hyperplane in this higher dimensional space called feature space. The problem can be solved by introducing variables to enlarge the margin by relaxing the linear SVM constraints allowing some misclassification errors in the margin, but penalizing these errors through the penalty parameter C in Eq. (6). These changes allow that the Eq. (2) can be violated, or:
yi ðwxi þ bÞ þ ni P 1;
The SVM’s were first developed for binary classifications. In case of more than two classes, two techniques exist to reduce the problem of multiple classes to a set of binary problems: one-against-one class separation and one-against-all class decomposition. One-against-one technique classifies the classes in pairs and use a binary SVM to differentiate each pair of classes. Support vector machines are then created. The final classification is obtained by all SVM’s results. One-against-all technique is based on the creation of k SVM’s binary classification to separate one class from the others. Then, the results of all SVM’s are grouped by classifying in k desirable classes. Thus, the technique consists in k SVM’s creation, where k is the amount of classes. When generating each one of these machines, one class is taken as positive and the others negative. Predicting a x pattern class, only the k SVM’s maximum value output is chosen (Hsu & Lin, 2002). This technique is more antique and more used due to its processing simplicity and speed. Hence, oneagainst-all technique will be used in this work. 4. Experimental results 4.1. Bed test description Fig. 2 illustrates the bed test that undergoes the experiments. It consists of a 5 HP, 220/380 V, 60 Hz, four poles, 1730 rpm, squirrelcage induction motor. The mechanical load was provided by a separate DC generator which feeds the variable resistor. In order to allow tests to be performed at different load levels, the DC excitation current and load resistor were both controlled. The mechanical structure where the motors are settled offers the possibility to move the two machines, in a way the system can be either aligned or different degrees of misalignment can be tested. The accelerometer A0720GP, SN6714, 0.1000 mV accuracy was used for vibration spectra acquisition. Hamming window of 3200 lines and the average of 10 samples was selected for a frequency width from 0 to 400 Hz and the amplitude measured in speed
ð5Þ
where ni are non-negative variables associated to each training vector. If 0 6 ni 6 1, xi will be on the right side of the margin, what means that the pattern is classified correctly. If ni > 1, xi will be in the wrong side of the margin. The cost function for this problem in this case is given by Eq. (6)
/ðw; nÞ ¼
N X 1 ðwwÞ þ C nj ; 2 j¼1
ð6Þ
where C is the training parameter that determines the balance between the model complexity and the training error, and is known by regulating constant.
Fig. 2. Bed tests: [1] Ultraspec analyzer; [2] computer; [3] accelerometer; [4] induction motor; [5] DC machine; [6] resistor bank; [7] coupling mechanism [8]; DC control panel.
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(mm/s). The signals were taken from the accelerometer at vertical, horizontal and axial positions respectively at both sides of fan cooling and motor coupling. The equipment Ultraspec 8000 was used to acquire the accelerometer data. Once the existing test bed became critically reliable to analyze the results, another experimental setup was designed and built to guarantee data repeatability and accuracy. Therefore, correct shaft alignment in the setup was guaranteed by using a laser alignment tool from the Ultraspec 8000 specific firmware. The baseline measurements for this experiment were recorded for the test case of minimum vibration magnitude. Three types of mechanical faults: radial and angular shaft misalignment, mechanical looseness and rotor unbalances were performed. Each of these types was induced mechanically to different degrees of intensity (or fault level) and with different load conditions. Radial misalignments were created by installing additional shims of specific thickness under the motor‘s base to lift it up slightly from the coupled load shaft. Angular misalignments were created by rotating the machine at specific angles away from the original position of the coupled load shaft. Load unbalances were created by adding a steel bolt and 21 g nut of mass placed at different radial distances from the rotor shaft on a balanced metal disk. Mechanical looseness was caused by a structural looseness of induction motor base. For each test, the sensor was placed in different parts of the motor like:
P1- Vertical position over the cooling fan (VCF). P2 - Axial position in the front of the cooling fan (ACF). P3 - Horizontal position by the cooling fan (HCF). P4- Vertical position over the motor coupling (VMC). P5 - Axial position in the front side of the motor coupling (AMC). P6 - Horizontal position by the motor coupling (HMC).
4.2. Vibration signals selecting Data obtained from vibration spectrum analysis contain not only information about faults through the deterministic frequencies, but also some other that can be neglected, like noise. Brito (2002) designed a system to select the input data from the rotation frequencies, using a filter to reject vibrations at different frequencies of: fr, 2fr, 3fr and 4fr. The accelerometer standard distribution analysis placed in a vertical and horizontal position at the fan side is presented previously to fault classification studies through SVM. Figs. 3 and 4 show the vibration amplitude values in R3 space for the frequencies frx2frx3fr when the accelerometer is fixed at horizontal (P3-HCF) and axial (P2-ACF) positions at the cooling fan. It can
Fig. 3. Pattern distribuition for the horizontal position by the cooling fan (HCF).
Fig. 4. Pattern distribution for the axial position in the front of the cooling fan (ACF).
be noticed that the sampled data are grouped and overlaid and thus, can not be linearly split. 5. Mechanical faults diagnosis Table 1 presents the selected patterns to train and test the net for each fault and sensor position, totalizing 978 training patterns and 312 validation patterns. The input patterns are the vibrations magnitudes for the rotation frequencies fr and their multiples: 2fr, 3fr and 4fr. Fig. 5 shows the proposed system for fault diagnostic. Acceleration signals are translated into the frequency domain. After filtered Table 1 Data used to train and validate the network for each kind of fault. P1 VCF
P2 ACF
P3HCF
P4 VMC
P5 AMC
P6 HMC
Training Patterns No faults 36 Misalignment 33 Unbalance 61 Losseness 32
38 33 60 32
37 33 60 32
38 33 60 33
38 33 60 32
38 33 60 33
Testing Patterns No faults Misalignment Unbalance Loseness
13 10 20 10
12 10 20 10
11 10 20 10
12 10 20 10
12 10 20 10
12 10 20 10
Fig. 5. The proposed system for fault diagnostic.
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Table 2 C and r parameters values of the four SVM’s according to the sensor’s positions. P1-VCF
SVM SVM SVM SVM
1 2 3 4
P2-ACF
P3-HCF
P5-AMC
P6-HMC
C
r
C
r
C
r
C
r
C
r
C
r
100 100 100 100
0.01 0.01 1 0.001
100 100 1000 100
1 1 1 1
100 100 100 100
1 1 1 1
100 100 1000 100
0.01 0.1 0.1 0.01
100 1 100 100
1 1 1 0.1
100 100 100 100
1 1 0.1 0.1
Table 3 Diagnostic system final results.
Final Diagnosis (%)
P4-VMC
References
P1 VCF
P2 ACF
P3 HCF
P4 VMC
P5 AMC
P6 HMC
96
90
92
92
92
94
the magnitudes of the frequencies (fr, 2fr, 3fr and 4fr) are used as input patterns of the nets. The support vector machines are trained to classify: SVM1 - No Faults; SVM2 - Unbalance; SVM3 - Misalignment and SVM4 Mechanical Looseness. The one-against all classifier will give the final diagnose, grouping the four support vector machine (SVM1, SVM2, SVM3 and SVM4). The output will be one of the following messages: no fault, misalignment, unbalance or mechanical looseness. The method can be applied for the acceleration sensor fixed at any of the six positions. Kernel RBF was used for all the SVM’s parameters varying according to the kind of faults and accelerometer position (Table 2). Table 3 shows the final results of the nets outputs for each acceleration sensor position for the data used to test the diagnosed system. It was found that the best signals acquisition and sensor’s position for analysis is vertical, with a 96% of hits. 6. Conclusions Applying artificial intelligence to faults detection helps to detect faults without maintenance specialists’ intervention. An important vector machines feature is the good generalization capability. Thus, the main objective of this work was to establish a diagnostic method for three phase induction motors mechanical faults (unbalance, misalignment and mechanical looseness) using support vector machines; monoaxial accelerometer signals are used as patterns when dealing with mechanical faults. A flexible test bed was created and vibration signals were taken at six different positions for each test. The signals were filtered and only the multiple rotation frequencies were chosen. The proposed approach came up with very good results. From this work we also realized that the best position for signals acquisition and analysis is vertical over the cooling fan, which is considered a very important information for the maintenance workers. Acknowledgements The authors gratefully acknowledge financial support from CAPES (Procad UFMG/UDESC/UFPE/UFSJ), Fapemig and CNPQ for purchasing the required instruments and equipments.
Baccarini, L. M. R., Menezes, B. R., & Caminhas, W. M. (2010). Fault induction dynamic model, suitable for computer simulation: Simulation results and experimental validation. Mechanical Systems and Signal Processing, 24(1), 300–311. ISSN 0888-3270, doi:10.1016/j.ymssp.2009.06.014. Bonett, A. H., & Soukup, G. C. (1992). Cause and analysis of stator and rotor failures in three-phase squirrel cage induction motors. IEEE Transactions on Industry Applications, 28(4), 921–927. Brito, J. N. (2002). Desenvolvimento de um sistema inteligente hibrido para diagnostico de falhas em motores de indução trifásicos, Ph.d. thesis, Faculdade de Engenharia Mecanica - Unicamp. Çakir, A., Çalis, H., & Küçüksille, E. U. (2009). Data mining approach for supply unbalance detection in induction motor. Expert Systems and Applications, 36(9), 11808–11813. ISSN 0957-4174, doi:10.1016/j.eswa.2009.04.006. Chow, T. W. S., & Hai, S. (2004). Induction machine fault diagnostic analysis with wavelet technique. IEEE Transactions on Industrial Electronics, 51(3), 558–565. ISSN 0278-0046, doi:10.1109/TIE.2004.825325. Emara, H. M., Ammar, M. E., Bahgat, A. & Dorrah, H. T. (2003). Stator fault estimation in induction motors using particle swarm optimization, In: Electric Machines and Drives Conference, (pp. 1469–1475). Hsu, C. W., & Lin, C. J. (2002). A comparison of methods for multi-class support vector machines. IEEE Transactions on Neural Networks, 13, 415–425. ISSN 10459227 doi:10.1109/72.991427. Lei, Y., He, Z., & Zi, Y. (2008). A new approach to intelligent fault diagnosis of rotating machinery. Expert Systems and Applications, 35(4), 1593–1600. ISSN 0957-4174, doi:10.1016/j.eswa.2007.08.072. Lei, Y., He, Z., & Zi, Y. (2009). Application of an intelligent classification method to mechanical fault diagnosis. Expert Systems and Applications, 36(6), 9941–9948. ISSN 0957-4174, doi:10.1016/j.eswa.2009.01.065. Niu, G., Widodo, A., Son, J. D., Yank, B. S., Hwang, D. H., & Kang, D. S. (2008). Decision-level fusion based on wavelet decomposition for induction motor fault diagnosis using transient current signal. Expert Systems with Applications, 35(3), 918–928. ISSN 0957-4174, doi:10.1016/j.eswa.2007.08.024. Radhika, S., Sabareesh, G. R., Jagadanand, G., & Sugumaran, V. (2009). Precise wavelet for current signature in 3/ IM. Expert Systems with Applications, 37(1), 450–455. ISSN 0957-4174, doi:10.1016/j.eswa.2009.05.046. Rodrigues, P. V. J., Negrea, M., & Arkkio, A. (2008). A simplified scheme for induction motor condition monitoring. Mechanical Systems and Signal Processing, 22(5), 1216–1236. ISSN 0888-3270, doi:10.1016/j.ymssp.2007.11.018. Tran, V. T., Yang, B. S., Oh, M. S., & Tan, A. C. C. (2009). Fault diagnosis of induction motor based on decision trees and adaptive neuro-fuzzy inference. Expert Systems with Applications, 36(2), 1840–1849. ISSN 0957-4174, doi:10.1016/ j.eswa.2007.12.010. Vapnik, V. (1999). An overview of statistical learning theory. IEEE Transactions on Neural Networks, 10(5), 988–999. ISSN 1045-9227, doi:10.1109/72.788640. Widodo, A., & Yang, B. S. (2007). Support vector machine in machine condition monitoring and fault diagnosis. Mechanical Systems and Signal Processing, 21(6), 2560–2574. ISSN 0888-3270, doi:10.1016/j.ymssp.2006.12.007. Widodo, A., & Yang, B. S. (2008). Wavelet support vector machine for induction machine fault diagnosis based on transient current signal. Expert Systems with Applications, 35(1–2), 307–316. ISSN 0957-4174, doi:10.1016/ j.eswa.2007.06.018. Widodo, A., Yang, B. S., & Han, T. (2007). Combination of independent component analysis and support vector machines for intelligent faults diagnosis of induction motors. Expert Systems with Applications, 32(2), 299–312. ISSN 0957-4174, doi:10.1016/j.eswa.2005.11.031. Wu, S., & Chow, T. W. S. (2004). Induction machine fault detection using SOM-based RBF neural networks, Industrial Electronics. IEEE Transactions on, 51(1), 183–194. ISSN 0278-0046, doi:10.1109/TIE.2003.821897.
Contents lists available at ScienceDirect
Expert Systems with Applications journal homepage: www.elsevier.com/locate/eswa
SVM practical industrial application for mechanical faults diagnostic Lane Maria Rabelo Baccarini ⇑, Valceres Vieira Rocha e Silva, Benjamim Rodrigues de Menezes, Walmir Matos Caminhas Department of Electrical Engineering, Federal University of São João del Rei, Praça Frei Orlando, 170 – Centro – 36307-352, Minas Gerais, Brazil Department of Electronics Engineering, Federal University of Minas Gerais, Brazil Department of Electrical Engineering, Federal University of Minas Gerais, Av. Antônio Carlos 6627-31270-010, Brazil
a r t i c l e
i n f o
a b s t r a c t
Keywords: Fault diagnosis Vibration analysis SVM Practical application
A large percentage of the total induction motor failures are due to mechanical faults. It is well known that, machine’s vibration is the best indicator of its overall mechanical condition, and an earliest indicator of arising defects. Support vector machines (SVM) is also well known as intelligent classifier with strong generalization ability. In this paper, both, machine‘s vibrations and SVM are used together for a new intelligent mechanical fault diagnostic method. Using only one vibration sensor and only four SVM’s it was achieved improved results over the available approaches for this purpose in the literature. Therefore, this method becomes more attractive for on line monitoring without maintenance specialist intervention. Vibration signals turns out to occur in different directions (axial, horizontal or vertical) depending on the type of the fault. Thus, to diagnose mechanical faults it is necessary to read signals at various positions or use more them one accelerometer. From this work we also determined the best position for signals acquisition, which is very important information for the maintenance task. Ó 2010 Elsevier Ltd. All rights reserved.
1. Introduction
faults in the frequency domain. Every kind of mechanical failure causes a specific alteration of the frequency spectrum compared to the right one. Many techniques have been implemented for working conditions monitoring and fault diagnosis of induction motors aiming to provide high-degree of reliability and motor life. The application of intelligent system for induction motor fault diagnosis has been widely used in recent years. Widodo and Yang (2007) presented a survey of machine condition and fault diagnostic using support vector machine (SVM). This paper surveys articles form 1996 to 2006. The authors concluded that ‘‘. . . applications of SVM in machine condition and fault diagnosis still need more encouragement and attention due the lack of existed paper. The efforts to find a new novel idea must be encouraged to give more contributions in robust machine condition monitoring and diagnosis’’. Different methods for induction motor fault diagnosis on the basis of current signals were proposed in Niu et al. (2008), Rodrigues, Negrea, and Arkkio (2008) and Radhika, Sabareesh, Jagadanand, and Sugumaran (2009). Tran, Yang, Oh, and Tan (2009) suggested a new mechanism for fault diagnosis of induction motors on the basis of start-up transient current, which combined the advantages of wavelet analysis and decision-level fusion technique to improve diagnosis accuracy. The applications of intelligent system for motor rolling elements bearings are proposed in Lei, He, and Zi (2008, 2009). It is known that the voltage unbalance has a potential source of effects on motor efficiency, rotor losses, and temperature rises.
Induction motors are fundamental components in many industrial processes since they are robust, mechanically simple and adaptable to wide variety of operation conditions although simple to control. Induction motors are frequently exposed to different loading and environmental conditions (Baccarini, Menezes, & Caminhas, 2010). These conditions together with the natural aging of the motor may lead to many failures (Bonett & Soukup, 1992). Once it is not economical to keep redundant backup machines, online monitoring for induction machines is important for safe operation and production quality (Wu & Chow, 2004). Hence, monitoring the motor condition is essential to detect any fault in early stage to avoid severe motor damages (Emara, Ammar, Bahgat, & Dorrah, 2003). The most common types of induction rotating machine faults have always been related to the rotor or machine shaft, such as mechanical unbalance, misalignment, and bearing fault (Chow & Hai, 2004). Vibration is the best indicator of overall mechanical condition and the earliest indicator of arising defects. Vibration analysis is based on the principle that faults can be detected by particular frequencies associated also with particular types of ⇑ Corresponding author at: Department of Electrical Engineering, Federal University of São João del Rei, Praça Frei Orlando, 170 - Centro - 36307-352, Minas Gerais, Brazil. E-mail address: [email protected] (L.M.R. Baccarini). 0957-4174/$ - see front matter Ó 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.eswa.2010.12.017
L.M.R. Baccarini et al. / Expert Systems with Applications 38 (2011) 6980–6984
Çakir, Çalis, and Küçüksille (2009) described an approach for detection of the supply unbalance condition in induction motors by using data mining process. Also the works presented in Widodo and Yang (2008) and Widodo et al. (2007) studied the application of independent component analysis (ICA) and SVM to detect and diagnose induction motor faults. The ICA is used for feature extraction and data reduction from original features. The total 78 features (13 parameters and six signals) are calculated from 10 feature parameters of time domain and three parameters from frequency domain (rms, frequency center and root variance frequency) using three vibration acceleration signals and three-phase current signals. The authors concluded that the number of SVMs decreased due the feature reduction. The maximum number of SVM’s used was 110 and the minimum was 45. Considering that machine’s vibration is the best indicator of its overall mechanical condition and also that SVM is a classifier with strong generalization ability, this paper presents an intelligent mechanical fault diagnostic system using support vector machines and only one accelerometer sensor. The SVM’s training used only the first rotation frequencies components of the vibration signals. Only four SVM’s were applied for this purpose either. It made the method rather simple and therefore very attractive for online monitoring without maintenance specialist intervention. Vibration signals turns out to be in different directions (axial, horizontal or vertical) depending on the type of the fault. To diagnose mechanical faults it is necessary to acquire signals at various positions or use more them one accelerometer, since analysis based only on one accelerometer position can mislead the results. From this work, we also determined the best position for signals acquisition, which is very important for the maintenance task. This is a valuable information to reduce the number of sensors and to reduce the maintenance costs. For the purposes of this work the vibration signals are collected by an accelerometer connected to a data acquisition systems. Those signals are transformed by fast Fourier transform (FFT) into signals in the frequency domain, which can be analyzed and processed easier than those in the time domain. Then, some features are extracted from the frequency-domain signals to become inputs of classifiers. This paper is organized as follows: Section 2 gives a brief description of the various mechanical faults associated to featured frequencies in the vibration spectrum. SVM method basic concepts are given in Section 3. The test bed used to obtain the vibrations signals is described in Section 4. In Section 5, it is showed how is implemented the fault diagnostic algorithm and the results are analyzed. Section 6 presents the concluding remarks.
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combinations. Most of the mechanical problems can be detected by the first harmonics of the motor rotation. Following, sources of vibration due to mechanical problems are enhanced. 2.1. Unbalance The motor unbalance occurs due the motor’s mass unbalance around the rotation axis caused by asymmetries, material and construction imperfections. It is practically impossible to manufacture a motor that is perfectly balanced. The degree of unbalance that affects the motor dictates whether it is a problem or not. The unbalance creates a periodic vibration signal with the same amplitude in each shaft rotation. The vibration amplitude depends of the magnitude of the unbalance. 2.2. Misalignments They are sources of machine components deterioration that occur when two machines are coupled. There are two types of misalignments: angular and parallel, and sometimes a combination of both. Angular misalignment happens when the central position of both machines mismatches. High axial vibrations are representative of angular misalignments that come together with high multiple levels of rotation. Parallel misalignment happens when both axes should work in parallel position. The dominant vibration is radial from double rotational speed. It can be vertical or horizontal. The misalignment direction is given by the direction of the higher level vibration. 2.3. Mechanical looseness Machines are constructed in such a way that the fundamental structure can not move freely. Whether screws lose or the concrete base deteriorates it can result movement in between the surfaces, generating harmonic peaks in vibration, oscillating at the same frequency of the rotation. Mechanical looseness can lead to residual misalignment, relatively small, that can cause high level of vibrations. The frequency spectrum can indicate misalignment, distorted shaft and/or unbalance, depending on how the rotor and structure are affected by the back slash. In the early stages, mechanical looseness causes vibrations at one rotational frequency and also at its double one. Further deterioration of the motor condition results in fractional harmonics increasing in amplitude. These harmonics are most visible in signals taken when the machine in only lightly loaded. 3. SVM
2. Modelling vibration fenomenum 3.1. Formalization The machine‘s vibration is a result of the electrical and mechanical forces and the motors‘ structure. Vibration analysis is a multidisciplinary problem. It requires the bringing together of some disciplines knowledge: Analysis of errors: information about the dynamic signals of interest, modulation and conditioning, decomposition by frequency components. Fault identification: tools for vibration signals analysis to allow for faults diagnostic. Vibration measurement system: signal conditioning, choices of the most important parameters, knowledge of available instrumentation with hardware and software for signal analysis. Therefore, to diagnose a machine vibration it is necessary to learn the changing patterns of the signals and the possible dynamic
SVM is a technique used to train the classifiers based on the structural risk minimizations concept. This technique was developed by Vapnik (1999) and has been widely applied since 90’s in various pattern recognition and classification problems. SVMs can be used to classify data in two classes: positive (+ ve) and negative ( ve). Assuming a set of points of these two classes, the SVM description is as follows: a SVM establishes the hyperplane that allocates the majority of points of the same class in the same side, whilst maximizes the distance between the two classes to this hyperplane. The distance between one class and a hyperplane is the smallest distance between the hyperplane and the other points of the same class and is called the optimal separating hyperplane. The hyperplane created by SVM contains a subset of points of the two classes called support vectors. Fig. 1 presents an example of optimal separating hyperplane of two datasets.
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Actually the necessary changes to implement the non linear SVM’s in a higher dimension space is minimal by only substituting x by /(x) in the previous equations, where / is a non linear mapping of the input space on the feature space. 3.2. Multiple classes
Fig. 1. Optimal hyperplane.
Assuming a training set {xi, yi}, where x 2 Rn and y 2 { 1, 1}, i = 1, . . . , N xi is an input vector and yi is the required classification. The aim is to estimate a function f, using the training set that classifies the pairs {xi, yi} which have not been correctly used yet. The optimal hyperplane is defined by:
wx þ b ¼ 0;
ð1Þ n
where w 2 R is a vector of weights and the scalar b is the bias. A vector xi of the same class of yi, y 2 { 1, 1}, must satisfy the equation:
yi ðwxi þ bÞ 1 P 0;
ð2Þ
where w is normal to the hyperplane. The Euclidian distance between this hyperplane and the points over the separating margin, i.e., yi(wxi + b) = 1 is determined by Eq. (3)
yi ðwxi þ bÞ 1 ¼ : kwk kwk
ð3Þ
Thus, to minimize kwk is equivalent to maximize the separating hyperplane. Using Lagrange multipliers theory the following equation can be established:
Jðw; b; aÞ ¼
N X 1 a½yi ðwxi þ bÞ 1; ðwwÞ 2 i¼1
ð4Þ
where ai are the Lagrange multipliers. The optimization problem solution is obtained through minimization of J(w, b, a) subject to a. When patterns are not linearly separated, machines that generate input data in a higher dimension space are used to decrease the computational efforts of the support machines. By choosing a nonlinear mapping a priori, the SVM constructs an optimal separating hyperplane in this higher dimensional space called feature space. The problem can be solved by introducing variables to enlarge the margin by relaxing the linear SVM constraints allowing some misclassification errors in the margin, but penalizing these errors through the penalty parameter C in Eq. (6). These changes allow that the Eq. (2) can be violated, or:
yi ðwxi þ bÞ þ ni P 1;
The SVM’s were first developed for binary classifications. In case of more than two classes, two techniques exist to reduce the problem of multiple classes to a set of binary problems: one-against-one class separation and one-against-all class decomposition. One-against-one technique classifies the classes in pairs and use a binary SVM to differentiate each pair of classes. Support vector machines are then created. The final classification is obtained by all SVM’s results. One-against-all technique is based on the creation of k SVM’s binary classification to separate one class from the others. Then, the results of all SVM’s are grouped by classifying in k desirable classes. Thus, the technique consists in k SVM’s creation, where k is the amount of classes. When generating each one of these machines, one class is taken as positive and the others negative. Predicting a x pattern class, only the k SVM’s maximum value output is chosen (Hsu & Lin, 2002). This technique is more antique and more used due to its processing simplicity and speed. Hence, oneagainst-all technique will be used in this work. 4. Experimental results 4.1. Bed test description Fig. 2 illustrates the bed test that undergoes the experiments. It consists of a 5 HP, 220/380 V, 60 Hz, four poles, 1730 rpm, squirrelcage induction motor. The mechanical load was provided by a separate DC generator which feeds the variable resistor. In order to allow tests to be performed at different load levels, the DC excitation current and load resistor were both controlled. The mechanical structure where the motors are settled offers the possibility to move the two machines, in a way the system can be either aligned or different degrees of misalignment can be tested. The accelerometer A0720GP, SN6714, 0.1000 mV accuracy was used for vibration spectra acquisition. Hamming window of 3200 lines and the average of 10 samples was selected for a frequency width from 0 to 400 Hz and the amplitude measured in speed
ð5Þ
where ni are non-negative variables associated to each training vector. If 0 6 ni 6 1, xi will be on the right side of the margin, what means that the pattern is classified correctly. If ni > 1, xi will be in the wrong side of the margin. The cost function for this problem in this case is given by Eq. (6)
/ðw; nÞ ¼
N X 1 ðwwÞ þ C nj ; 2 j¼1
ð6Þ
where C is the training parameter that determines the balance between the model complexity and the training error, and is known by regulating constant.
Fig. 2. Bed tests: [1] Ultraspec analyzer; [2] computer; [3] accelerometer; [4] induction motor; [5] DC machine; [6] resistor bank; [7] coupling mechanism [8]; DC control panel.
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(mm/s). The signals were taken from the accelerometer at vertical, horizontal and axial positions respectively at both sides of fan cooling and motor coupling. The equipment Ultraspec 8000 was used to acquire the accelerometer data. Once the existing test bed became critically reliable to analyze the results, another experimental setup was designed and built to guarantee data repeatability and accuracy. Therefore, correct shaft alignment in the setup was guaranteed by using a laser alignment tool from the Ultraspec 8000 specific firmware. The baseline measurements for this experiment were recorded for the test case of minimum vibration magnitude. Three types of mechanical faults: radial and angular shaft misalignment, mechanical looseness and rotor unbalances were performed. Each of these types was induced mechanically to different degrees of intensity (or fault level) and with different load conditions. Radial misalignments were created by installing additional shims of specific thickness under the motor‘s base to lift it up slightly from the coupled load shaft. Angular misalignments were created by rotating the machine at specific angles away from the original position of the coupled load shaft. Load unbalances were created by adding a steel bolt and 21 g nut of mass placed at different radial distances from the rotor shaft on a balanced metal disk. Mechanical looseness was caused by a structural looseness of induction motor base. For each test, the sensor was placed in different parts of the motor like:
P1- Vertical position over the cooling fan (VCF). P2 - Axial position in the front of the cooling fan (ACF). P3 - Horizontal position by the cooling fan (HCF). P4- Vertical position over the motor coupling (VMC). P5 - Axial position in the front side of the motor coupling (AMC). P6 - Horizontal position by the motor coupling (HMC).
4.2. Vibration signals selecting Data obtained from vibration spectrum analysis contain not only information about faults through the deterministic frequencies, but also some other that can be neglected, like noise. Brito (2002) designed a system to select the input data from the rotation frequencies, using a filter to reject vibrations at different frequencies of: fr, 2fr, 3fr and 4fr. The accelerometer standard distribution analysis placed in a vertical and horizontal position at the fan side is presented previously to fault classification studies through SVM. Figs. 3 and 4 show the vibration amplitude values in R3 space for the frequencies frx2frx3fr when the accelerometer is fixed at horizontal (P3-HCF) and axial (P2-ACF) positions at the cooling fan. It can
Fig. 3. Pattern distribuition for the horizontal position by the cooling fan (HCF).
Fig. 4. Pattern distribution for the axial position in the front of the cooling fan (ACF).
be noticed that the sampled data are grouped and overlaid and thus, can not be linearly split. 5. Mechanical faults diagnosis Table 1 presents the selected patterns to train and test the net for each fault and sensor position, totalizing 978 training patterns and 312 validation patterns. The input patterns are the vibrations magnitudes for the rotation frequencies fr and their multiples: 2fr, 3fr and 4fr. Fig. 5 shows the proposed system for fault diagnostic. Acceleration signals are translated into the frequency domain. After filtered Table 1 Data used to train and validate the network for each kind of fault. P1 VCF
P2 ACF
P3HCF
P4 VMC
P5 AMC
P6 HMC
Training Patterns No faults 36 Misalignment 33 Unbalance 61 Losseness 32
38 33 60 32
37 33 60 32
38 33 60 33
38 33 60 32
38 33 60 33
Testing Patterns No faults Misalignment Unbalance Loseness
13 10 20 10
12 10 20 10
11 10 20 10
12 10 20 10
12 10 20 10
12 10 20 10
Fig. 5. The proposed system for fault diagnostic.
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Table 2 C and r parameters values of the four SVM’s according to the sensor’s positions. P1-VCF
SVM SVM SVM SVM
1 2 3 4
P2-ACF
P3-HCF
P5-AMC
P6-HMC
C
r
C
r
C
r
C
r
C
r
C
r
100 100 100 100
0.01 0.01 1 0.001
100 100 1000 100
1 1 1 1
100 100 100 100
1 1 1 1
100 100 1000 100
0.01 0.1 0.1 0.01
100 1 100 100
1 1 1 0.1
100 100 100 100
1 1 0.1 0.1
Table 3 Diagnostic system final results.
Final Diagnosis (%)
P4-VMC
References
P1 VCF
P2 ACF
P3 HCF
P4 VMC
P5 AMC
P6 HMC
96
90
92
92
92
94
the magnitudes of the frequencies (fr, 2fr, 3fr and 4fr) are used as input patterns of the nets. The support vector machines are trained to classify: SVM1 - No Faults; SVM2 - Unbalance; SVM3 - Misalignment and SVM4 Mechanical Looseness. The one-against all classifier will give the final diagnose, grouping the four support vector machine (SVM1, SVM2, SVM3 and SVM4). The output will be one of the following messages: no fault, misalignment, unbalance or mechanical looseness. The method can be applied for the acceleration sensor fixed at any of the six positions. Kernel RBF was used for all the SVM’s parameters varying according to the kind of faults and accelerometer position (Table 2). Table 3 shows the final results of the nets outputs for each acceleration sensor position for the data used to test the diagnosed system. It was found that the best signals acquisition and sensor’s position for analysis is vertical, with a 96% of hits. 6. Conclusions Applying artificial intelligence to faults detection helps to detect faults without maintenance specialists’ intervention. An important vector machines feature is the good generalization capability. Thus, the main objective of this work was to establish a diagnostic method for three phase induction motors mechanical faults (unbalance, misalignment and mechanical looseness) using support vector machines; monoaxial accelerometer signals are used as patterns when dealing with mechanical faults. A flexible test bed was created and vibration signals were taken at six different positions for each test. The signals were filtered and only the multiple rotation frequencies were chosen. The proposed approach came up with very good results. From this work we also realized that the best position for signals acquisition and analysis is vertical over the cooling fan, which is considered a very important information for the maintenance workers. Acknowledgements The authors gratefully acknowledge financial support from CAPES (Procad UFMG/UDESC/UFPE/UFSJ), Fapemig and CNPQ for purchasing the required instruments and equipments.
Baccarini, L. M. R., Menezes, B. R., & Caminhas, W. M. (2010). Fault induction dynamic model, suitable for computer simulation: Simulation results and experimental validation. Mechanical Systems and Signal Processing, 24(1), 300–311. ISSN 0888-3270, doi:10.1016/j.ymssp.2009.06.014. Bonett, A. H., & Soukup, G. C. (1992). Cause and analysis of stator and rotor failures in three-phase squirrel cage induction motors. IEEE Transactions on Industry Applications, 28(4), 921–927. Brito, J. N. (2002). Desenvolvimento de um sistema inteligente hibrido para diagnostico de falhas em motores de indução trifásicos, Ph.d. thesis, Faculdade de Engenharia Mecanica - Unicamp. Çakir, A., Çalis, H., & Küçüksille, E. U. (2009). Data mining approach for supply unbalance detection in induction motor. Expert Systems and Applications, 36(9), 11808–11813. ISSN 0957-4174, doi:10.1016/j.eswa.2009.04.006. Chow, T. W. S., & Hai, S. (2004). Induction machine fault diagnostic analysis with wavelet technique. IEEE Transactions on Industrial Electronics, 51(3), 558–565. ISSN 0278-0046, doi:10.1109/TIE.2004.825325. Emara, H. M., Ammar, M. E., Bahgat, A. & Dorrah, H. T. (2003). Stator fault estimation in induction motors using particle swarm optimization, In: Electric Machines and Drives Conference, (pp. 1469–1475). Hsu, C. W., & Lin, C. J. (2002). A comparison of methods for multi-class support vector machines. IEEE Transactions on Neural Networks, 13, 415–425. ISSN 10459227 doi:10.1109/72.991427. Lei, Y., He, Z., & Zi, Y. (2008). A new approach to intelligent fault diagnosis of rotating machinery. Expert Systems and Applications, 35(4), 1593–1600. ISSN 0957-4174, doi:10.1016/j.eswa.2007.08.072. Lei, Y., He, Z., & Zi, Y. (2009). Application of an intelligent classification method to mechanical fault diagnosis. Expert Systems and Applications, 36(6), 9941–9948. ISSN 0957-4174, doi:10.1016/j.eswa.2009.01.065. Niu, G., Widodo, A., Son, J. D., Yank, B. S., Hwang, D. H., & Kang, D. S. (2008). Decision-level fusion based on wavelet decomposition for induction motor fault diagnosis using transient current signal. Expert Systems with Applications, 35(3), 918–928. ISSN 0957-4174, doi:10.1016/j.eswa.2007.08.024. Radhika, S., Sabareesh, G. R., Jagadanand, G., & Sugumaran, V. (2009). Precise wavelet for current signature in 3/ IM. Expert Systems with Applications, 37(1), 450–455. ISSN 0957-4174, doi:10.1016/j.eswa.2009.05.046. Rodrigues, P. V. J., Negrea, M., & Arkkio, A. (2008). A simplified scheme for induction motor condition monitoring. Mechanical Systems and Signal Processing, 22(5), 1216–1236. ISSN 0888-3270, doi:10.1016/j.ymssp.2007.11.018. Tran, V. T., Yang, B. S., Oh, M. S., & Tan, A. C. C. (2009). Fault diagnosis of induction motor based on decision trees and adaptive neuro-fuzzy inference. Expert Systems with Applications, 36(2), 1840–1849. ISSN 0957-4174, doi:10.1016/ j.eswa.2007.12.010. Vapnik, V. (1999). An overview of statistical learning theory. IEEE Transactions on Neural Networks, 10(5), 988–999. ISSN 1045-9227, doi:10.1109/72.788640. Widodo, A., & Yang, B. S. (2007). Support vector machine in machine condition monitoring and fault diagnosis. Mechanical Systems and Signal Processing, 21(6), 2560–2574. ISSN 0888-3270, doi:10.1016/j.ymssp.2006.12.007. Widodo, A., & Yang, B. S. (2008). Wavelet support vector machine for induction machine fault diagnosis based on transient current signal. Expert Systems with Applications, 35(1–2), 307–316. ISSN 0957-4174, doi:10.1016/ j.eswa.2007.06.018. Widodo, A., Yang, B. S., & Han, T. (2007). Combination of independent component analysis and support vector machines for intelligent faults diagnosis of induction motors. Expert Systems with Applications, 32(2), 299–312. ISSN 0957-4174, doi:10.1016/j.eswa.2005.11.031. Wu, S., & Chow, T. W. S. (2004). Induction machine fault detection using SOM-based RBF neural networks, Industrial Electronics. IEEE Transactions on, 51(1), 183–194. ISSN 0278-0046, doi:10.1109/TIE.2003.821897.