最小二乘法电机故障诊断

Artificial Immune Based Support Vector Machine Algorithm for Fault Diagnosis of Induction Motors İ. AYDIN1, Student Member, IEEE, M. KARAKÖSE2, E. AKIN3, Member IEEE1Computer Technology and Programming Education ProgramKemaliye H. A. AKIN Technical Vocational School of Higher EducationErzincan University, 24600, Kemaliye, Erzincan, Turkey2, 3Computer Engineering DepartmentFırat University, 23119, Elazığ, Turkey{iaydin, mkarakose, eakin}@.trAbstract-The use of induction motors is widespread in industry. Many researchers have studied the condition monitoring and detecting the faults of induction motors at an early stage. Early detection of motor faults results in fast unscheduled maintenance. In this study, a new artificial immune based support vector machine algorithm is proposed for fault diagnosis of induction motors. Support vector machines (SVMs) have become one of the most popular classification methods in soft computing, recently. However, classification accuracy depends on kernel and penalty parameters. Artificial immune system has abilities of learning, memory and self adaptive control. The kernel and penalizes parameters of support vector machine are tuned using artificial immune system. The training data of support vector machine are extracted from three phase motor current. The new feature vector is constructed based on park’s vector approach. The phase space of this feature vector is constructed using nonlinear time series analysis. Broken rotor bar and stator short circuit faults are classified in combined phase space using support vector machines. The experimental data are taken from a three phase induction motor. One, two and three broken rotor bar faults and 10% short circuit of stator faults are detected successfully.Key words: Support vector machines, artificial immune system, time series analysis, fault detection and diagnosis, induction motors, stator and broken rotor bar faults.I. I NTRODUCTIONInduction motors are the most used motors in industry applications. These motors are utilized in petrochemical, domestic and mining industries [1]. Induction motors are also used in military, aerospace and nuclear plants and reliability is important in these applications. These motors are reliably and they present numerous advantage but operation in dusty environments wears away them. This wear causes failures any part of an induction motor. Most motor failures reduce production and interrupt the process [2]. Therefore, many researchers have been studying to reduce maintenance costs and prevent unscheduled downtimes for induction motors. The motor failures are concerned one of three induction motor components: rotor, bearing and stator. The stator and rotor faults are among 14% and 38% of all motor faults, respectively. Although thermal and vibration monitoring have been used for fault diagnosis, motor current has been observed in the most of recent research [3].Parameter estimation and other model based techniques have been used for fault diagnosis and monitoring. These techniques are based on mathematical model of motor and require a deep knowledge about motor components.The fault diagnosis and monitoring of induction motors have been done using artificial intelligence techniques in recent years. These techniques require minimum motor configuration intelligence and any modeling of motor is not required [4]. By using these techniques, motor faults can be detected without an expert. Artificial intelligence techniques usually use current, voltage, speed, vibration signals of an induction motor for fault diagnosis. Fault detection based on motor current relies on amplitudes of frequency components in the current spectrum. Ondel et al. [5] have proposed k-nearest neighbor method for broken rotor bar faults. They have used three phase currents and voltages of an induction motor. One, two and three broken rotor bar faults have been detected under four different load conditions. Artificial neural networks and support vector machines have been compared for bearing fault diagnosis [6]. Bearing faults of an induction motor have been detected using time domain vibration signals. Zhitong et al. [7] have used support vector machines to detect broken rotor bar faults. Motor current signature analysis has been used to extract the features for inputs of support vector machines in their study. A fault diagnosis and monitoring method based on artificial intelligence method has been developed for broken rotor bar and stator faults detection [8]. A new feature vector called as envelope has been achieved using three phase stator current and slip computation. Phase space of this vector is formed using nonlinear time series analysis method. Motor faults have been classified using Bayesian classification algorithm. Aydın et al. [9] have proposed a time series data mining algorithm for broken rotor bar faults. In their study, feature data are extracted from three phase motor currents. One, two and three broken rotor bar faults are diagnosed at four different speeds. In this study, a new fault diagnosis algorithm based on artificial immune and support vector machines is proposed for broken rotor bars and stator faults. Previous fault detection algorithms based on artificial intelligence have monitored minimum two signals for fault detection. Motor current signature analysis is the most used method to detect broken rotor bar faults, but this method requires motor speed for slip1-4244-0891-1/07/$20.00 ©2007 IEEEcomputation and fails for motors with feeding PWM. Our method needs only three phase motor current for fault diagnosis. The kernel and penalize parameter of support vector machines affect performance of this classification method. The optimal values of these parameters have been tuned using artificial immune method.II. PROPOSED ARTIFICIAL IMMUNE BASED SUPPORT VECTOR MACHINE ALGORITHM FOR FAULT DIAGNOSIS OF INDUCTIONMOTORSBroken rotor bars and stator faults have been detected using artificial immune based support vector machine algorithm. One, two and three broken rotor bar faults and stator faults are recognized under four different operation speeds. The proposed method for classification of broken rotor bar faults needs three phase motor currents.A. Data Preprocessing and Obtaining of Feature VectorThe features of broken rotor bar and stator faults are extracted from three phase motor currents. Three phase motor currents are transformed to two park’s vector components. The new feature vector is constructed using these park’s vector components. Park’s vector approach is used to achieve a 2D representation of phase currents of a three phase induction motor. Park’s vector approach is given in (1).cb Ic b a I qd 2121616132−=−−=(1)Under ideal conditions, Park’s vector transformation of balanced three phase currents is shown in (2).2sin(26)sin(26max max πωω−==t I I t I I q d (2)Where I max is the supply phase current maximum value andω is the supply frequency. The Park’s vector is a circularpattern centered on the origin of the coordinates.The proposed fault classification scheme is given in Fig. 1.Park’s vector components are achieved from three phasemotor current and they are termed as I d and I q . The newfeature vector I o is constituted using these park’s vectorcomponents. The feature vector is shown in Fig. 2. After feature vector have been achieved, phase space of feature vector is constructed. The nonlinear time series analysis examines a time series in a phase space [10]. Time delay τ and embedding dimension d are important parameters in constituting a reconstructed phase space or briefly called phase space. For instance, when 2=τ and d=3, the vector ),,(24t t t t x x x X −−=is a point in phase space. Fig. 1. Fault classification scheme.Fig. 2. The new feature vector.Mutual information is used estimating the time delay andfalse nearest neighbor is used determining the embedding dimension. The details of these methods are given in [11]. B. Support Vector Machines (SVMs) SVMs are two classes classification method based on statistical learning theory [12]. For n-dimensional space, input data x i (i=1….k) belongs to class 1 or class 2 and the associated labels be -1 for class 1 and +1 for class 2. If the input data can be separated linearly, the separation hyper plane can be shown in (3). b x w X f T +=)( (3) Where w is n-dimensional weight vector and b is scalar multiplier or bias value. This equation finds a maximum margin to separate positive class from negative class. The decision function is shown in (4). )sgn()(b x w x f T +=(4)If two classes can be separated linearly, the hyper plane that satisfies maximum margin between two classes is found by solving (5). An example for linearly separable data is shown in Fig. 3. ⎪⎭⎪⎬⎫⎪⎩⎪⎨⎧≥+0)(||||212b x w y to Subject w Minimize i i i (5) When the parameters of SVM are well tuned, classificationperformance is increased. SVM training is done by solvingthe optimization problem in (5).⎪⎪⎪⎪⎭⎪⎪⎪⎪⎬⎫⎪⎪⎪⎪⎩⎪⎪⎪⎪⎨⎧=≥=−=∑∑∑===ki for y to subject x x K y y L imize i ki i i k i k j i j i j i j i i ....100),(21)(max 110,αααααα (6)Where K(x i ,x j ) is kernel function, i α are Lagrange multipliers. When the data can not be separated linearly,kernel function mapping changes according to (7).ij j i j i C x x K x x K δ1),(),(+= (7) Where C is penalize parameter and appropriate value of this parameter increase the classification performance. ij δ is Kronecker symbol. In this study, radial based kernel functionis used and this function is given in (8).))2/(exp(),(22σji j i x x x x K −−= (8)Where σis kernel parameter and this parameter affects distributing complexity of data in the feature space.Fig. 3. Hyper plane and support vectors.C. Artificial Immune System and Parameters Optimization of SVMs The immune system is an efficient self-defense method that guards the human body from foreign antigens or pathogens [13]. Artificial immune system is an emerging soft computingmethod inspired by natural immune system. This method is used in pattern recognition, classification, optimization and anomaly detection problems. Clonal selection is an artificial immune algorithm that is used for optimization problems.Clonal selection has not crossover operator, so this method is different from genetic algorithm. Affinity proportionalreproduction and affinity maturation are two distinctiveproperties of clonal selection. Because of these properties,clonal selection converges faster than genetic algorithm anddoesn’t catch local minimum. In this study, optimal parameters of support vector machine are selected using clonal selection. Each antibody is coding as binary string. Its construction is shown in Fig. 4. The proposed clonal selection algorithm is given in Fig. 5. Kernel σ and penalize parameters are selected in the range of [0.1, 2.55] and [1, 255], respectively. Precision of kernel σis 0.1 and penalize parameter is 1. The length of coding is selected as eight bits for each parameter. The mutation rate has been selected as 0.5. Affinity of each antibody iscalculated according to (9).)m e *100100max()antibody (f −= (9)Where e is number of misclassified data and m is length ofdata. It is selected n 1 highest affinity elements of population and generated clones of these individuals proportionally to their affinity with the antigen. If affinity of an individual ishigh, then clones of it are high.Fig. 4. Binary coding of antibodiesFig. 5. Clonal selection.Mutation rate of an individual is inversely proportional of its affinity. In this study inverse of an exponential function is used to establish a relationship between the mutation rate and the normalized affinity. This approach is given in (10). )exp()(**sa a m −= (10)Where a * is normalized affinity and can be determined bya *=a/a max . The control of smoothness is done by parameter sand is selected as 4 in our study.III. EXPERIMENTAL RESULTSWe performed experiments on an actual induction motorfor our analyses. The characteristics of the three phase induction motor used in our experiment are listed in Table I. The motor was tested with a healthy rotor, 10% stator short-circuit fault and with a faulty rotor that had one, two and three broken rotor bars. The diagram of experimental prototype is depicted in Fig. 6. The motor phase currents are saved with 3 kHz sampling frequency for duration 3 seconds. The supply voltages of the each motor condition are 380, 340, 300 and 260 V, respectively. Three phase motor currents, park’s vector component and feature vector are given in Fig. 7 for one broken rotor bar fault supplying with 300 V.TABLE IINDUCTION MOTOR CHARACTERISTIC USED IN THEEXPERIMENTDescription Value Power 0.37 kW Input Voltage 380 V Full Load Current 1.2 A Supply Frequency50 HzNumber of Poles4 Number of Rotor bars 22 Full Load Speed 1390 rpmFig. 6. A diagram of experimental prototype .After the feature vector is achieved, phase space of each condition has been constructed. For phase space, embedding dimension d is selected as two and time delay τ is selected as four by using false nearest neighbor and mutual information methods, respectively. The phase space of healthy motor is shown in Fig. 8. After phase space is constructed for eachmotor data, these phase space are combined as shown in Fig. 9. The artificial immune based SVM method for fault classification algorithm is applied in this phase space. The performance of clonal selection which separates the healthy phase space and one broken rotor bar faults is given in Fig. 10.Fig. 7. Phase currents, Park’s vector component and feature vector.Fig. 8. Healthy motor phase space.Fig. 9. Combined phase space.IterationF i t n e s sFig. 10. Clonal selection performance.SVM is normally a two class classification method. We have used one to other classification method for multiple classifications. The results of classification are given in table 2. The average performance of proposed method is %98.85 and only three phase motor currents are used. The most used methods in literature for stator and rotor faults are based on motor current signature analysis. This method needs motor slip computation to detect these faults. Clonal selection algorithm finds optimal kernel and penalize parameters at e few iteration as shown at Fig. 10.Fig. 11. SVM result with optimal kernel and penalize parameters.TABLE IIRESULTS OF ARTIFICIAL IMMUNE BASED SVM ALGORITHM FORFAULT CLASSIFICATION.Class NSV σ C AccuracyRate (%)CHB1 11 0.27 213 99.00 CHB2 12 0.17 159 99.00 CHB3 15 1.38 140 97.50 CHSF 13 0.38 108 99.00 CB1B2 9 0.38 242 99.00 CB1B3 4 0.63 88 99.00 CB1SF 4 1.01 32 99.00 CB2B3 5 0.45 244 99.00 CB2SF 16 0.19 140 99.00CB3SF 4 0.99 47 99.00 Average Accuracy Rate 98.85Broken Bar FaultsPark vector’s approach has been used for stator faults. But this method uses all of motor current. But our method uses only data relevant to fault and less data uses for fault classification.IV. CONCLUSIONThe stator and rotor faults in an induction motor have been detected using three phase motor currents. The park’s vector components have been extracted from three phase motor currents and new feature vector have been constructed from these components. The healthy and faulty motor conditions are classified in combined phase space using artificial immune based SVM algorithm. The optimal parameters of SVM are obtained using clonal selection algorithm. The motor currents have been taken an actual experimental setup and success results have been obtained.REFERENCES[1]B. Ayhan, M. Y. Chow and M. H. Song, “Multiple Discriminant Analysis and Neural Network-Based Monolith and Partition Fault-Detection Schemes for Broken Rotor Bar in Induction Motors”, IEEE Transactions on Industrial Electronic, Vol. 53, No. 4, pp. 1298-1308, August 2006.[2]M. Haji, H. A. 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