Fault diagnosis of induction motors using signal processing based methods and optimal feature selection

공학박사 학위논문 최적 특징 선택과 신호처리기법을 이용한 유도전동기 고장 진단 Fault Diagnosis of Induction Motors using Signal Processing based Methods and Optimal Feature Selection 울산대학교 대학원 전기전자정보시스템공학부 웬옥투 최적 특징 선택과 신호처리기법을 이용한 유도전동기 고장 진단 Fault Diagnosis of Induction Motors using Signal Processing based Methods and Optimal Feature Selection 지도교수 이홍희 이 논문을공학박사학위 논문으로 제출함 2008 년 12 월 울산대학교 대학원 전기전자정보시스템공학부 웬옥투 Fault Diagnosis of Induction Motors using Signal Processing based Methods and Optimal Feature Selection Ngoc-Tu Nguyen A thesis submitted to the School of Electrical Engineering in fulfillment of the thesis requirements for the degree of Doctor of Philosophy in the Graduate School, University of Ulsan December 2008 Abstract Fault detection and diagnosis in rotating machines have been used widely in commercial systems over the past few decades Numerous works on machine conditions have been implemented with the aid of the MCSA (Motor Current Signature Analysis) method, the vibration-based methods, etc The purpose of these methods is to detect and diagnose faults in an early stage and therefore allow contingency plans to be put into place before the problems worsen The dynamic and vibratory behaviours of the machine, such as vibration, sound, and temperature… are affected if the running condition is changed The behaviours can be useful indicators to detect problems within the machine as they vary abnormally from a standard when a fault occurs Of the many signals which can be measured, the vibration signal has been the most useful to monitor the machine condition as in many cases the time domain vibration signals are sufficient to diagnose and can be easily measured with accelerometers The signal processing methods for induction motor fault detection have recently received great attention because they not need a typical mathematical model Many signal processing diagnostic procedures have been studied in this work to identify faults of the machines The decision tree, support vector machine (SVM), artificial neural network (ANN), adaptive neurofuzzy inference system (ANFIS), and k-nearest neighbour (K-NN) have been applied to diagnose the condition of machines with rather high accuracy These methods have used vibration data as an indicator for monitoring the fault conditions In this work, the vibration data are measured in three dimensions to collect as much information as possible Then an optimal feature selection is proposed in this work for improving the classification performance of the diagnostics system The classification results have proved the efficiency of the proposed optimal feature selection and the suitability of vibration data as an indicator for induction motor fault diagnosis i Acknowledgements University of Ulsan, Ulsan, Korea School of Electrical Engineering Ngoc-Tu Nguyen This work has been carried out in Industrial Network and Power Electronics Laboratory, School of Electrical Engineering, University of Ulsan The work has been done during 20052008 under the support of the Research Fund of University of Ulsan and the Network-based Automation Research Center (NARC) I would like to thank my supervisor of this work, Professor Hong-Hee Lee, for his helping and interest in my research work that give me the opportunity to carry out this thesis I would also thank all people in my laboratory, especially Jeong-Min Kwon, for helping me greatly during the research Additionally, I wish to thank Huyndai Heavy Industries (HHI) for supporting the faulty motors I would like to thank the examiners of this thesis, Professor Young-Soo Suh, Professor Jin Hur, Professor Myeong-Jae Yi, and Professor Heung-Geun Kim for their valuable comments and corrections ii Table of Contents Abstract i Acknowledgements ii Table of Contents iii List of Figures v List of Tables vii Abbreviations viii Introduction 1.1 Background and motivation 1.2 Previous works 1.3 Objective and contribution 1.4 The structure of the thesis Understanding the Basis of Induction Motor Faults 2.1 Bearing Damage 9 2.2 Electrical Induced Faults 12 2.3 Others 16 Methods for Fault Diagnosis of Induction Motor 3.1 FFT-based method 23 23 3.1.1 Case study – Looseness case 23 3.1.2 Case study – Stator winding fault 24 3.1.3 Case study – Rub fault 24 3.1.4 Case study – Unbalance Rotor 25 3.2 Model-based methods 25 3.3 Signal processing-based methods 26 3.3.1 ANFIS 26 3.3.2 K-Nearest Neighbor 27 3.3.3 Decision Tree 29 3.3.4 Random Forest 32 3.3.5 Support Vector Machine 33 Vibration Measurements 36 Experimental Results 41 5.1 Genetic Algorithm 41 5.2 Feature Selection 41 iii 5.2.1 Genetic algorithm based feature selection 42 5.2.2 Principal Component Analysis 44 5.3 Some Experimental Results 47 5.3.1 K-Nearest Neighbor 47 5.3.2 Decision Tree 51 5.3.2.1 Decision Tree using PCA based feature extraction 51 5.3.2 Decision Tree using GA based feature selection 54 5.3.3 Random Forest 58 5.3.4 Support Vector Machine 62 5.3.5 ANFIS 65 5.4 Summary 71 Conclusions 74 References 75 Publications 79 iv List of Figures Fig Typical causes for machine failures Fig Bearing structural defects Fig Ball bearing geometry Fig Bearing time-domain vibration signals and FFT spectrum, (a) normal, and (b) defective bearing Fig Frequency domain and time domain vibration signals of a rotor unbalance case in three directions Fig Frequency domain and time domain vibration signals of a stator unbalance case in three directions Fig Frequency domain and time domain vibration signals of a rub case in three directions Fig Frequency domain and time domain vibration signals of a distortion case in three directions Fig Frequency domain and time domain vibration signals of a misalignment case in three directions Fig 10 Vibration spectrums (a) in radial direction (b) in axial direction Fig 11 Vibration spectrums of case study Fig 12 Vibration spectrums (a) in radial direction (b) in axial direction Fig 13 Vibration spectrums in radial direction Fig 14 General model based fault detection scheme Fig 15 An adaptive network-based fuzzy inference system Fig 16 An example of a k-NN classification The test pattern x can be classified either as positive or negative class Fig 17 Typical structure of a decision tree Fig 18 Hyperplanes for the SVM trained with two-class samples Fig 19 Experimental setup Fig 20 Accelerometer (a) is used in this work and induced faults (b) rotor unbalance, (c) bearing damage and (d) sensor measuring position Fig 21 Time signal waveforms in dimensions (Horizontal-Axial-Vertical): (a) Bearing damage (b) Bearing looseness (c) Rotor unbalance (d) Stator fault (e) Normal condition Fig 22 GA process Fig 23 Weighted values of 18 features given by the genetic algorithm Fig 24 (a) Normal bearing (horizontal, axial, and vertical); (b) Defective bearing time signals v Fig.25 Extracted features, (-, blue) normal and ( , red) defective bearing Fig.26 The projection of the training data on the first three axes Fig 27 Classification results of the conventional k-NN (-, square) and proposed k-NN ( , triangle) according to k; (a) evaluated with three, (b) four, (c) five, (d) six, and (e) seven features (vertical axis is the average accuracy, horizontal axis is k) Fig 28 Decision tree without feature extraction Fig 29 PCA-based decision tree with new features Fig 30 PCA-based decision tree with new features Fig 31 Decision tree with all features Fig 32 Decision tree with selected features Fig 33 RF classification result of case The test data classification error is 7.506% Fig 34 RF classification result of case The test data classification error is 7.748% Fig 35 RF classification result of case The test data classification error is 4.843% Fig 36 RF classification result of case The test data classification error is 4.358% Fig 37 RF classification result of case The test data classification error is 5.327% Fig 38 Some bearing training patterns, defective (-) and normal ( ) Fig 39 Input membership functions (training with 150 epochs) (a) before training, (b) after training, and (c) targets and ANFIS system output Fig 40 Input membership functions (training with 80 epochs), (a) before training, (b) after training, and (c) targets and ANFIS system output vi 5.3.5 ANFIS In this part, vibration training data are processed in both time signal and FFT spectra The maximum amplitude of time signal and the sum of bearing frequency amplitudes are preferred as input of the ANFIS model Only one output is used to detect bearing conditions: normal or damage, corresponding to binary values or Bearing frequency amplitudes are calculated with a Hz frequency band around them By collecting the vibration data of defective and normal bearings to create a training database, this part investigates a way to optimize the fuzzy system based on that data Combining fuzzy logic and neural network in the ANFIS archives a neuro-fuzzy system that can optimize the system model from the given input-output data The GA is also used to optimize the construction of the ANFIS system Each set of vibration data has 10000 samples at 20000Hz sampling rate The time-domain feature considered is maximum value of the amplitude of vibration signal N −1 xmax = max (d (n)) (30) n =0 FFT transform is performed to extract the frequency features of vibration signal, and each basic bearing frequency is considered in the Hz frequency band ⎛ F FFT ⎜⎜⎜ ⎜⎝ Δf F = f −2.5 f + 2.5 xFFT = ∑ ⎞⎟ ⎟⎟, Δf = Ts ⎠⎟ (31) where, Ts is sampling time Spectrum feature referred to as input of ANFIS is the sum of all bearing basic frequencies As a result, the bearing condition can be detected whether it is good or not, but it is impossible to find out what type of bearing fault it is - 65 - The bearing used in this part has basic frequencies: BPOF (ball pass outer race frequency) = 3.57 x rps (revolutions in second), BPIF (ball pass inner race frequency) = 5.429 x rps, BSF (ball spin frequency) = 4.632 x rps, and FCF (fundamental cage frequency) = 0.396 x rps Fig 38 shows sets of features extracted from vibration data in both defect and normal conditions 150 35 Bearing frequencies magnitude Time-domain signal amplitude 30 100 50 25 20 15 10 10 20 30 Samples 40 50 60 140 40 120 35 Bearing frequencies magnitude Time-domain signal amplitude 100 80 60 40 20 0 10 20 30 Samples 40 50 60 10 20 30 Samples 40 50 60 30 25 20 15 10 10 20 30 Samples 40 50 60 Fig 38 Some bearing training patterns, defective (-) and normal ( ) The GA algorithm has a 50-chromosome population size, and uses 50 generations to search for optimal ANFIS configuration The training and simulation were performed by Matlab software The training data set has about 1200 samples extracted from measured bearing vibration data Table 12 shows the local optimum results obtained from the genetic program, which chooses the local optimal number of input membership functions, a type of input-output membership function (MF) corresponding to each averaging training error - 66 - Table 12: Local optimum parameters are obtained from GA algorithm Training Average Number of Number of MF type MF type MF type epochs training MFs (input 1) MFs (input 2) (input 1) (input 2) (output) error 10 0.0168 5 gbellmf gaussmf linear 40 0.0140 5 gbellmf trimf linear 60 0.0129 5 gbellmf gbellmf linear 80 0.0097 5 gbellmf gaussmf linear 100 0.0086 gbellmf gbellmf linear 110 0.0068 gbellmf gbellmf linear 120 0.0040 5 gbellmf gbellmf linear 130 0.0022 5 gbellmf trimf linear 150 0.0000 trapmf trapmf constant 0.5 0 50 100 input 1: TimeSignal (before training) 150 0.5 0 10 15 20 25 30 35 input 2: Spec (before training) (a) - 67 - 40 45 50 0.5 0 50 100 input 1: TimeSignal (after training) 150 0.5 0 10 15 20 25 30 35 input 2: Spec (after training) 40 45 50 (b) Target Output Target/Output 0.8 0.6 0.4 0.2 0 50 100 150 200 Sample 250 300 350 400 (c) Fig 39 Input membership functions (training with 150 epochs) (a) before training, (b) after training, and (c) targets and ANFIS system output The model in Fig 39 is trained with the prepared data and terminated at the 150th epochs with 100% training accuracy The initial membership functions {trapmf (5), trapmf (3)} are shown in Fig 39(a), and Fig 39(b) presents post-training Output membership function is constant type, and the comparison between target output and predicted output is also indicated in Fig 39(c) - 68 - 0.5 0 50 100 input 1: TimeSignal (before training) 150 0.5 0 10 15 20 25 30 35 input 2: Spec (before training) 40 45 50 (a) 0.5 0 50 100 input 1: TimeSignal (after training) 150 0.5 0 10 15 20 25 30 35 input 2: Spec (after training) (b) - 69 - 40 45 50 Target Output Target/Output 0.8 0.6 0.4 0.2 0 50 100 150 200 Sample 250 300 350 400 (c) Fig 40 Input membership functions (training with 80 epochs), (a) before training, (b) after training, and (c) targets and ANFIS system output The same explanation can be applied to Fig.35, but, in this case, the model used input membership function set {gbellmf (5), gaussmf (5)} is trained till 80 epochs, and training error is 0.0097 The output membership function used in this case is linear type From Table 12, the best training accuracy obtained with the given training data when input membership is {trapmf (5), trapmf (3)} and output membership is {constant} after 150 epochs training Other structures are also acquired with smaller number of epochs but larger averaging training error, which is perhaps appropriate for systems that need to update the training database frequently to reduce time Tests are performed in two of the above mentioned models and the accurate predictions are achieved, which are almost the same as the targets in case of Fig 39 Once the optimal parameters have been found, such a fuzzy system can be supposed as an optimal model for bearing diagnosis This selection is done offline and can be used for online diagnosis once the parameters are available The new parameters are also reselected easily using GA if the data is updated or modified Therefore, it can be concluded that using GA for selecting the optimal configuration of ANFIS is a powerful technique; where the GA program can search for the optimal structure of the fuzzy modeling based on the given training data - 70 - Conclusions This part investigated a way to optimize the fuzzy modeling on ANFIS architecture applied to bearing diagnosis Parameters and structure of the model are obtained on the base of neural network and genetic algorithm Averaging error of ANFIS is selected as fitness function of the genetic program, and the model can get a local optimal design with each of the selected training epochs The structure results may not suitable for another machine Training data have to be collected with different types and levels of bearing conditions to achieve better predictions because the model can obtain the suitable structure based on those extracted data features A rich and reliable database can improve the reliability of the proposed model 5.4 Summary In this work, the signal processing based methods are studied for diagnosing the induction motor conditions to prove the efficiency of the proposed feature selection The optimal feature selection method is applied for evaluating the features, which are based on the distance criterion, and then the classification algorithms are used to monitor the motor conditions with the selected features The classification results demonstrate that the methods with optimal feature selection have better performance compared to methods without feature selection The performance of classifiers which are studied in this work is summarized in Table 13 As shown in Table 13, it is clear that the performances are improved much better if the proposed feature selection is applied Especially, the performance is improved remarkably in case of k-NN, where the accuracy increases from 78% (78.5% of the conventional k-NN) to 98.1% Decision tree and random forest also work well with the proposed selection But SVM has the best performance (99.67% classification accuracy) even its improvement is not the highest Each classifier has its advantages and disadvantages that can be recommended in some specific case For diagnostic problems with small data set, simple algorithm likes k-NN is suggested For two-class classification problems (normal and defective), ANFIS is recommended SVM performs well on problems that are non-linear, sparse, and high dimensional therefore it is suitable for multiclass fault diagnosis problems Also, this algorithm (as well as ANFIS) has many parameters that - 71 - make it difficult to use and choose the best ones K-NN algorithm is a simple and good classifier that relies on a distance function, but is sensitive to noise and irrelevant features Meanwhile, decision tree can be easily understood and explained but may be suffered from over-fit problem Constructing from many decision trees, random forest shows better stability but has more parameters than a single decision tree Table 13: Performance comparison on multi faults diagnosis Method Test Performance (% classification accuracy) Before feature selection Proposed feature selection Decision tree 90.1 95.9 (3 features) Random forest 92.5 95.6 (3 features) The conventional k-NN 78.5 98.1 (5 features) 78 98.1 (5 features) 94.14 99.67 (5 or features) The weighted k-NN SVM The main advantages and disadvantages of the classifiers using in this work can be summarized in Table 14 Table 14: The main advantages and disadvantages of classifiers Method Decision tree Advantage Simple, the tree structure is Disadvantage Over-fit, sensitive to noise easy to understand Random forest Using with large data set and Many parameters input variables k-NN Simple, has good performance Sensitive to noise and for small data set irrelevant data, only suitable for small data set SVM Has high performance for nonlinear and high dimensional - 72 - Many parameters to choose data set ANFIS Useful for non-linear data set Has only one output and many parameters In summary, there is no method with superior features comparing to the others Therefore, in order to get the reliable and accurate condition of induction motor, these methods are suggested to use simultaneously with different input feature sets, and then the results are combined together to yield the final classification decision That makes the classification system adapt with many situations in practical applications - 73 - Conclusions These signal processing based algorithms with the proposed optimal selection features are both highly accurate and have a high performance due to its removal of redundant and irrelevant information Importantly, the proper feature selection can significantly improve the classification performances as well as reducing the system computation time In case of the online diagnosis, once the optimal features are selected, the selection need not be activated again Therefore, the time to perform the fault detection algorithm can be reduced significantly The experimental results of this study verify that the signal processing based methods with the proposed optimal feature selection are the efficient way to improve diagnosis performance In this study, it proves that vibration data can be sufficient as a diagnostic indicator for induction motor fault diagnosis because most of faults can be reflected directly by vibration The features extracted from time domain vibration signals also show the effect in fault diagnosis of induction motor using signal processing based methods Much research work needs to be done in future in order to develop a reliable system for the practical use The dataset needs to be enriched with many operating conditions of induction motor Moreover, the severity of faults also needs to be considered to increase the accuracy of the diagnosis These will help to improve the performance and stability of the classification - 74 - References [1] V Sugumaran, V Muralidharan, K I Ramachandran, Feature selection using Decision 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Quinlan, C4.5: Programs for Machine Learning, Morgan Kaufmann Publisher, Inc., 1993 [42] The C4.5 code comes from the Internet (http://rulequest.com/personal/c4.5r8.tar.gz) [43] J S Rao, Vibratory Condition Monitoring of Machines, Alpha Science International Ltd., 2000, 361-382 [44] C T Leondes, Fuzzy Theory Systems: Techniques and Applications, Academic Press, 1999, Volume 1, 205-221 [45] A Dimarogonas, S Haddad, Vibration for Engineers, Prentice Hall, Inc., 1992, 675-705 [46] R K Mobley, Root Cause Failure Analysis, Butterworth-Heinemann, 1999 - 78 - Publications N T Nguyen, H H Lee, Improvement of induction motor fault diagnosis performance by using genetic algorithm-based feature selection, Proc IMechE, Part C: J Mechanical Engineering Science 222, 2008, 1613-1619 N T Nguyen, H H Lee, J M Kwon, Optimal feature selection using genetic algorithm for mechanical fault detection of induction motor, Journal of Mechanical Science and Technology 22, 2008, 490-496 N T Nguyen, H H Lee, Decision Tree with Optimal Feature Selection for Bearing Fault Detection, Journal of Power Electronics 8, 2008, 101-107 H H Lee, N T Nguyen, J M Kwon, Bearing Fault Diagnosis Using Fuzzy Inference Optimized by Neural Network and Genetic Algorithm, Journal of Electrical Engineering & Technology 2, 2007, 353-357 N T Nguyen, J M Kwon, H H Lee, A Study on Machine Fault Diagnosis using Decision Tree, Journal of Electrical Engineering & Technology 2, 2007, 461-467 H H Lee, N T Nguyen, J M Kwon, Bearing Diagnosis Using Time-Domain Feature and Decision Tree, LNAI 4682, 2007, 952-960 N T Nguyen, H H Lee, An Application of Support Vector Machines for Induction Motor Fault Diagnosis with Using Genetic Algorithm, LNAI 5227, 2008, 190-200 H H Lee, N N Tu, K J Min, M J Yi, M Y Chung, B Y Lee, Expert System for Induction Motor Online Fault Diagnostics, in KIPE 2005, S Korea, 2005, 643-646 H H Lee, N N Tu, K J Min, A Study on Decision Tree for Induction Motor Diagnostic System, in ISEE 2005, Vietnam, 2005 N T Nguyen, H H Lee, Bearing Fault Diagnosis using Adaptive Network based Fuzzy Inference System, in ISEE 2007, Vietnam, 2007, 280-285 N T Nguyen, J M Kwon, H H Lee, Fault Diagnosis of Induction Motor using Decision Tree with An Optimal Feature Selection, in ICPE 2007, S Korea, 2007, 729-732 N T Nguyen, H H Lee, Fault Diagnosis of Induction Motor using k-Nearest Neighbors, in ICMT 2007, S Korea, 2007, 430-433 - 79 - ... 진단 Fault Diagnosis of Induction Motors using Signal Processing based Methods and Optimal Feature Selection 지도교수 이홍희 이 논문을공학박사학위 논문으로 제출함 2008 년 12 월 울산대학교 대학원 전기전자정보시스템공학부 웬옥투 Fault Diagnosis of. .. Diagnosis of Induction Motors using Signal Processing based Methods and Optimal Feature Selection Ngoc-Tu Nguyen A thesis submitted to the School of Electrical Engineering in fulfillment of the thesis... faults, signal based processing methods for monitoring the condition of induction motor, the optimal feature selection using distance based criterion is considered to remove the irrelevant and redundant