Abstract—This study presents a method of diagnosing failures in rotary machines using Machine Learning techniques. In this study, a support vector machine- SVM algorithm is proposed for fault diagnosis of the rotational unbalance in the rotor. Recently, support vector machines (SVMs) have become one of the most popular classification methods in technique for Vibration Analysis. Axis unbalance fault is classified using support vector machines. The experimental data are taken from a rotary machine model of a rigid-shaft rotor and flexible bearings, experimental setup for the study of vibration analysis. Several situation of unbalance faults were detected successfully.
Index Terms—Machine Learning; Fault Diagnosis;
Vibration Analysis, Fault Classification.
I. INTRODUCTION
The integration of mechanical, digital and computer systems is constantly growing in modern industry. In turbo machines, the rotors suffer abrasions and fatigue, due to their continuous use, hampering their operation over time.
Although it has a robust structure, any imperfections, minimum that they are, compromise its performance.
However, rotors of this type of machinery move at high speeds, requiring the use of electronic sensors to extract accurate information.
Over time, the mechanical components that make up the rotating machines suffer wear and become more inefficient, gradually reducing the quality of the processes of which they integrate. According to Bently [1], excessive mechanical stress is associated with the rotational movement of the axes and that high torsional loads and radial loads culminate in severe conditions that lead to eventual rotor cracking.
Techniques with the purpose of predicting situations for the purpose of determining the useful life of an equipment or part are increasingly present in the corporate-industrial environment, as this means obtaining the longest time the machine will work efficiently, guaranteeing quality, generating programmed breaks of component exchange and maintenance, and consequently greater financial control of the process. Predictive maintenance is a useful way of minimizing machine downtime and associated costs [2].
Published on February 17, 2019.
Brandao, I. M. is with the Automation and Control Department, Federal Institute of Sao Paulo, SP 01109-010 Brazil (email:
Pinheiro, A. A. is with the Automation and Control Department, Federal Institute of Sao Paulo, SP 01109-010 Brazil (email:
Da Costa, C. is with the Automation and Control Department, Federal Institute of Sao Paulo, SP 01109-010 Brazil (email: [email protected]).
The fault diagnosis and monitoring of rotary machine have been done using traditional techniques in last 20 years.
Often, by using these techniques, motor faults can´t be detected without an expert. Recently, artificial intelligence techniques by another way can be used without an expert, reducing maintenance costs.
Ayhan et al. [3] have proposed Multiple discriminant analysis (MDA) and artificial neural networks (ANNs) method for broken rotor bar faults. Aydin et al. [4] have used support vector machines (SVM) classification methods to detect broken rotor bar faults. Phase currents and Park’s vector component has been used to extract the features for inputs of SVM algorithm in their study. Razavi-Far et al [5], [6] have proposed a study focused on the development of a diagnostic system based on an adaptive incremental ensemble of extreme learning machines. The diagnostic system contains two major units for data processing and decision making. Martin-Diaz et al [7] have performed an experimental comparative evaluation of Machine learning techniques used for the diagnosis of rotor faults in inverter- fed Induction motor. The fault features are computed (in the frequency and time domains) from the stator electric current.
The motor is fed with four different power supplies and loaded at two levels. Souza et al [8] have proposed to identify incipient short-circuit in electrical generators, and it was possible to separate 99.4% of the Normal conditions from faults when using High Order Statistics (HOS) as a feature extraction method and the Bayesian classifier.
Samanta [9] has proposed a study to compare the performance of gear fault detection using artificial neural networks (ANNs) and support vector machines (SMVs).
The time-domain vibration signals of a rotating machine with normal and defective gears are processed for feature extraction.
The contribution of this work is the development of an automatic predictive maintenance model for the diagnosis of incipient failures in rotary machines, by means of a machine learning model, based in support vector machines (SVMs) classification methods, which classifies the existence of one or more unbalance conditions of a rotary machine.
II. BACKGROUND
A. Vibration Analysis
The fundamentals of vibration analysis can be understood by studying the simple mass-spring damper model. In fact, even a complex structure, like an automobile body, can be modeled as a sum of simple mass and spring damper models. The model is an example of a simple harmonic oscillator. Although several sophisticated techniques can be used, two methods used to display vibration signals are the
Vibration Analysis of Rotary Machines Using Machine Learning Techniques
Allan Alves Pinheiro, Iago Modesto Brandao and Cesar da Costa
time waveform (amplitude versus time) and the frequency spectrum (amplitude versus frequency). Based on the characteristics of a system, it is possible to model its vibration spectrum. For a given rotating machine, this would include an expected peak in the fundamental rotational frequency of the shaft, synchronous (harmonic) peaks based on additional components such as fan blades and gears [10].
Fig. 1 shows the Fourier frequency spectrum of the vibration analysis of a rotary machine.
Fig. 1. Fourier frequency spectrum.
B. Feature Extraction
Once there is a consolidated data set representing the vibration signals in the time domain, it is necessary to extract features from these signals into the frequency domain in order to reduce the complexity of the developed classification model. According to Shah and Patel [11], feature extraction can be defined as a process of extracting a new dataset from an initial data set.
The Fourier transform is, in general, a mathematical algorithm that performs the transformations between the variables in the time domain for variables in the frequency domain. The fast Fourier transform is an efficient algorithm for the calculation of the discrete Fourier transform (DFT) and its inverse. FFTs are extremely important, since it is possible to develop applications of digital signal processing, to algorithms for multiplication of large integers [12].
C. Feature Selection
After feature extraction, it is necessary to select these features to verify that all features are relevant and include or exclude them from the model of machine learning to be developed. According to Kursa and Rudnicki [13], data with many variables are increasingly common today in machine learning problems. To extract useful information from these high volumes of data, you need to use techniques to reduce noise or redundant data. This is where feature selection plays an important role. Not only does it help train your model faster, but it also reduces its complexity, facilitates interpretation, and improves accuracy [2]. There are three types of feature selection methods in general: (i) Filter methods: They are generally used as a preprocessing step.
Feature selection is independent of any machine learning algorithm. Instead, features are selected based on their scores in various statistical tests for their correlation with the outcome variable; (ii) Wrapper methods: uses a subset of features and trains a template using them. Based on the
inferences drawn from the previous model, it is decided to add or remove features from the subset; (iii) Embedded methods: are algorithms that have their own internal feature selection methods.
D. Support Vector Machine - SVM
The SVM is a machine learning algorithm supervised or not with associated learning algorithms that analyze the data and recognize patterns, used for classification and regression analysis. The SVM takes the optimal solution in the condition of a small number of samples. Algorithm for the SVM transforms the Sample Space (SS) into the High Dimensional Feature Space (HDFS) by the nonlinear transformation [14]. In addition to performing linear classification, SVMs can efficiently perform a non-linear classification using what is called the kernel trick, implicitly mapping their inputs into high-dimensional feature spaces.
Fig. 2 shows a linear classification between two classes 1 and 2. The line H1 does not separate the classes. H2 does, but only with a small margin. H3 separates them with the maximal margin. The SVM seeks to maximize the distance between the closest points in relation to each of the classes [4].
Fig. 2. Linear classification between two classes 1 and 2.
For n-dimensional space, input data 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 by (1). This equation finds a maximum margin to separate positive class from negative class [15].
( ) T
f X w x b (1) Where:
w is n-dimensional weight vector;
b is scalar multiplier or bias value.
The decision function is shown in (2).
f x( )sgn(w x bT ) (2) If two classes can be separated linearly, the hyper plane that satisfies maximum margin between two classes is found by solving (3). An example for linearly separable data is
shown in Fig. 2. When the parameters of SVM are well tuned, classification performance is increased [4].
.
1 2
2
( ) 0
to i i i
Minimize w y w x b Subject
(3)
SVM training is performed by solving the optimization problem in (4).
1
1 , 0
1
( ) 1 ( )
2 to 0 0 for i=1...k
k k
i j i j i j
i i j
k
i i
i
i
Maximize L y y k x x
Subject y
(4)Where:
( i j)
k x x is kernel function;
i are Lagrange multipliers.
When the data cannot be separated linearly, kernel function mapping changes according to (5).
( ,i j) ( ,i j) 1 ij k x x k x x
C
(5)
Where:
C
is penalize parameter and appropriate value of this parameter increase the classification performance;
ij is Kronecker symbol.In this work, radial based kernel function is used, and this function is given in (6).
2 2
( ,i j) exp( i j / (2 ))
k x x x x
(6) Where:
is kernel parameter and this parameter affects distributing complexity of data in the feature space.III. EXPERIMENTALPROCEDURE
In the experiments the data were collected from an experimental test bench (Fig. 3), which represents in a reduced scale a real turbo machine, based on the Jeffcott model [16]. Its axis being represented by a rotor and a disk with several holes for simulation of unbalance. Fig. 4 illustrates the disk and the holes where the test mass (weights) were inserted for unbalance faults simulations.
Fig. 3. Experimental setup.
Fig.4. Disk Isometric Perspective.
Eleven different types of tests were performed: (i) one not balanced – N/B (test mass not inserted); (ii) two different balanced: BLC1 and BLC2 (test mass inserted in different positions) and (iii) eight different unbalanced: UBLC1 to UBLC4 (test mass inserted in different positions). The tests performed are listed in Table I.
TABLEI:TESTS PERFORMED
Types Description
N/B NOT BALANCED
BLC1 BALANCED 1
BLC2 BALANCED 2
UBLC1 UNBALANCED
UBLC1+ UNBALANCED
UBLC2 UNBALANCED
UBLC2+ UNBALANCED
UBLC3 UNBALANCED
UBLC3+ UNBALANCED
UBLC4 UNBALANCED
UBLC4+ UNBALANCED
The system architecture is based on the data flow, as shown in Fig. 5, comprising from the step of data acquisition from the rotor in operation until the presentation of the results on the health condition of the rotor.
Fig. 5. Machine learning steps for the vibration analysis.
IV. METHODOLOGY AND DISCUSSION
The experiments consist of several modules software, which include data acquisition, feature extraction, feature selection, machine learning algorithm (SVM), training and results presentation. The acquisition of the vibration data from each of the eleven tests, as shown in Table I, produced a set of data corresponding to each of the vibration signals.
The acquisition parameters for these tests were defined by a sampling frequency of 1KHz and 2000 samples. The data acquisition of the experimental setup was performed, so that all possible faults were tested: (i) not balanced, balanced and unbalanced.
We obtained 1000 features from the feature extraction step and used these features as input data for the feature selection step. We obtained 60 features confirmed as important for training the model. After the feature vector is achieved, support vectors of each condition have been constructed. Fig. 6 shows the graphical result of the combined feature. The learning samples and the test samples for the SVM are obtained from the feature extraction and feature selection experimental data in different fault condition.
Fig. 6. Combined featured.
The standard method for evaluating of classification accuracy has now been indices derived from the confusion matrix. The confusion matrix provides the basis for describing the accuracy of the classification and characterizing the errors, helping to refine the classification.
From a confusion matrix can be derived several measures of classification accuracy, with global accuracy being one of the most known [17]. The confusion matrix is formed by a square arrangement of numbers arranged in rows and columns expressing the number of sample units of a relative category inferred by a classifier (or decision rule) compared to the current category found in the field. Normally below the columns is represented the set of reference data that is compared to the data of the classification product that are represented along the lines. The main diagonal elements indicate the level of accuracy, or agreement, between the two. Once the SVM algorithm was trained, the confusion matrix was obtained. Fig. 7 presents the confusion matrix.
Fig. 7. The confusion matrix.
Fig. 8 shows the HMI - Human Machine Interface developed in the LabView software, which indicates which event is most probability to occur. For example, the BLC 2 (Balanced) category has 90% prediction.
Fig. 8. The HMI.
V. CONCLUSION
In this paper we are applying a method of diagnosing failures in rotary machines using Machine Learning techniques. The rotor unbalance fault in an induction motor have been detected using vibration analysis. The SVM algorithm was proposed for fault diagnosis of the rotational unbalance in the rotor. Several situation of unbalance faults were detected successfully. The SVM algorithm has a practical signification for the machine learning in the case of a small number of samples. The vibrations analysis has been taken an actual experimental setup and success results have been obtained.
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Iago M. Brandão was born in São Paulo, SP, Brazil. He received the B.Sc. degree in Automation and Control Engineering from the IFSP – Federal Institute of São Paulo, SP, Brazil in 2018. His research interest includes Artificial Neural Network, machine learning, induction motors, sensors, diagnostic, electrical machines and FPGA..
Allan A. Pinheiro was born in São Paulo, SP, Brazil. He is currently student of Automation and Control Engineering from the IFSP – Federal Institute of São Paulo, SP, Brazil. His research interest includes machine learning, induction motors, sensors, diagnostic, electrical machines.
Cesar da Costa was born in Rio de Janeiro, RJ, Brazil. He received the B.Sc. degree in electronic and electrical engineering from the CEFET-RJ, Federal Center of Technological Education Center Celso Suckow da Fonseca and Nuno Lisboa University in 1975 and 1980 respectively. He received the M.Sc. degree in mechanical engineering from Taubate University, Taubate, SP, Brazil, and the Ph.D.
degree in mechanical engineering from UNESP- Universidad Estadual Paulista Julio de Mesquita Filho, Guaratingueta, SP, Brazil in 2005 e 2011, respectively. He did sandwich doctoral stage, PDEE-CAPES, in the IST-Institute Superior Tecnico, Lisbon, Portugal in 2009. He is currently post-doctoral and professor of automation and control engineering in the IFSP – Federal Institute of Education, SP, Brazil. His research interests include Fuzzy controller, Artificial Neural Network, machine monitoring, diagnostic, electrical machines, FPGA and Industry 4.0.
Author’s formal photo
