Unbalance detection in rotating machinery based on support vector machine using time and frequency domain vibration features

Abstract

The automated diagnostics of the unbalance in a rotor system has been presented in this study based on an artificial intelligence technique called support vector machine. In order to develop a support vector machine–based unbalance diagnosis, first the raw vibration signals in time and frequency domain are measured experimentally from healthy and unbalanced rotor installed on machine fault simulator. Then, three critical statistical features, namely, standard deviation, skewness, and kurtosis are extracted from the time and frequency domain vibration signals. Further, the features are used for training and testing of the support vector machine for building the automated diagnostic system for unbalance in a rotating system. The results from the present study show that the unbalance fault diagnosis can be effectively done based on the developed support vector machine–based methodology. The automated diagnosis of unbalance is possible with the time domain as well as frequency domain features. The results are better with time domain features than frequency domain features. In addition, the diagnosis is performed and found to be robust at most of the operating speeds of the rotor; however, the diagnosis should be avoided to attempt using the present methodology at very lower operating speeds.

Keywords

Rotating machinery unbalanced rotor time domain and frequency vibration signals artificial intelligence technique support vector machine algorithm

Introduction

Rotating machinery is the heart of all kind of industries like power, production, and manufacturing. Faults in the machinery cannot be avoided due to the error in the manufacturing process or the extreme working conditions. This may result in excessive heat generation, looseness, and other unwanted wears and tears of the rotating parts. Because of the unexpected rotor failures, industries have to bear huge financial losses and sometime serious human injuries. Therefore, rotating machinery needs to be continuously monitored for avoiding any upcoming or already developed fault. Early diagnosis of fault is a big challenge in the area of condition monitoring.

Various rotor-related faults like unbalanced rotor, misaligned rotor, bent rotor, and rotor rub are most likely to occur in the rotatory machines. Many monitoring techniques have been developed to detect these faults.^1,2 In a study, Li et al.³ used the hidden Markov model–based fault diagnostic method for various rotor faults like rotor unbalance, rotor-to-stator rub, oil whirl, and pedestal looseness in a rotating machinery under speed-up and speed-down conditions. In other study, Surendra et al.⁴ worked on diagnosis of unbalance in a rotating system by using operating deflection shapes (ODSs). The emphasis is on correlating changes in the ODS at the machine harmonics with various amounts and locations of unbalance weight. The results of this work provide a new method for detecting machinery unbalance and offer a simplified approach for on-line fault detection in operating machinery. Meng et al.⁵ worked on the feature extraction of rotating machinery by introducing one kind of the classic feature source called shaft orbit, which is widely used in traditional failure diagnosis. Result showed that the shaft orbit feature can be used in identifying different early fault stages of a rotor unbalance.

Reddy and Sekhar⁶ worked on the identification of unbalance and looseness in the rotor bearing systems by using artificial neural networks (ANNs). They proposed two different methods; one is based on statistical features and the second is based on amplitude in frequency domain. They observed that the statistical features are giving better results over frequency domain amplitudes. Kumar et al.⁷ worked on determination of unbalance in a rotating machine by using vibration analysis. The spectrum analysis and phase analysis were successfully carried out to determine the cause of high vibrations in the machine. Singh and Kumar⁸ presented rotor fault diagnosis based on the support vector machine (SVM) and ANN. They used time domain vibration features and concluded that the present methods can be used for fast and reliable diagnosis of rotor fault.

Deng et al.⁹ presented work on the three-dimensional identification for unbalanced mass of rotor system. They developed a noncontact method to identify unbalanced mass of rotor systems in 3D space. A stereo video system with a pair of synchronized high-speed cameras is established, and a feature point is employed to replace the traditional contact transducer for measurement. Saleem et al.¹⁰ worked on detection of unbalance in a rotating machine using shaft deflection measurement during operation. In this, deflected shape of shaft was successfully used for detecting unbalance in the rotating components. In a study, Sen et al.¹¹ worked on polar and orbit plot analysis for unbalance identification in a rotating system. They presented a detailed analysis of polar and orbit plots considering a non-faulty shaft and one with an unbalanced mass attached to it. Chouksey et al.¹² used a finite element model–based approach for prediction of unbalance and balancing of a single-disc rotor system, where the authors used the updated finite element model obtained on the basis of experimental modal data.

Algule and Hujare¹³ worked on experimental study of various faults in a rotor system using vibration signature analysis. The vibrations were measured at different speeds, and then, the fast Fourier transform–based detection was performed for three rotor faults, namely, unbalance, misalignment, and crack. Toyoto et al.¹⁴ proposed failure detection in a rotating machinery based on an orthogonal expansion coefficient of a probability density function. They presented a hypothesis, that is, if the machine is in good condition, then its probability density function of the vibration signal follows the normal distribution in time domain.

Dwi et al.¹⁵ worked on the ANN-based identification system for abnormal vibration of the motor rotating disc system. The ANN system was trained with the time domain and frequency domain features. The present detection system was able to identify the motor rotating disc conditions with 90% accuracy. Thobiani and Tinga¹⁶ presented an approach in diagnosis of rotating machinery faults (misalignment, faulty bearing, and mass unbalance). They combined the second-order statistical features of thermal images and simplified fuzzy ARTMAP and found very effective for this study. Moosavian et al.¹⁷ explored the SVM and the K-nearest neighbor for unbalanced fault detection. They concluded that the proposed intelligent approaches can be used for detecting unbalance. Chen et al.¹⁸ presented self-organizing map (SOM) and SVM-based diagnosis of rotor system faults. They successfully used the SOM for feature extraction in frequency domain and then SVM for diagnosis of unbalanced rotor and bearing faults.

Hsu et al.¹⁹ presented a detail overview of the SVM where they provided a guideline to obtain good SVM performance in different applications. Widodo and Young²⁰ presented the application of SVM in machine condition monitoring and fault diagnosis. They reported that the SVMs have been gaining popularity in the machine learning community because of excellence of generalization ability as compared to traditional methods such as neural networks. In a study, Bordoloi and Tiwari²¹ illustrated SVM-based multi-fault classification in a gear system with evolutionary algorithms from the time domain vibration signal. In other studies, Gangsr and Tiwari^22,23 and Rapur and Tiwari²⁴ successfully developed SVM-based fault diagnosis for the induction motor and the centrifugal pump, respectively. After reviewing a number of studies in this field, it is found that the AI techniques such as SVM and deep learning have been evolving rapidly, and their applications are bringing better performance to many fields including condition monitoring and fault diagnosis of various mechanical and electrical machines.^6,8,21,24,25

This study presents a new strategy to improve the unbalance fault diagnosis performance in rotating machines using a new machine learning strategies called SVM with time and frequency vibration features. This work is of practical significance because unbalance fault detection in rotating machineries is always done by the experts and engineers in the industry by analyzing vibration spectrum; however, with the rapid increase in industrial machineries, it is not always possible to have expert and engineers all the time. Developing an automatic on-line condition monitoring system for unbalance detection based on a machine learning technique such as the SVM is the possible solution of this problem. Automatic diagnostic techniques allow comparatively unskilled operators to take important decisions in emergency. In this work, the experiments are conducted on machine fault simulator (MFS) in the vibration laboratory, SGSITS Indore, for generation of the vibration signals for both healthy and unbalanced rotor. The critical statistical features (standard deviation, skewness, and kurtosis) are then extracted from the time domain vibration signal which is further used as an input to the SVM. Thereafter, the fault diagnosis methodology is developed and used for the detection of the unbalance fault. The present methodology is checked on various operating speeds of the rotor. The results from this study are added and discussed in the results and discussion section.

Support vector machine

For machine learning and predictive technique, many classifiers have been used such as SVM, ANN, genetic programming, fuzzy logic, and hidden Markov models.²⁵

The original SVM algorithm was developed by Vladimir Vapnik; then, current standard incarnation (soft margin) was developed by Corinna Cortes and Vladimir Vapnik. However, from the middle of 1990s, the algorithms used in the SVMs started emerging with having greater computing power availability and also paving the way for the applications of numerous practical problems. Basic SVMs deal with a two-class problem.^19,20

A set of input data belonging to two possible classes are used for training of the SVM. Figure 1 shows a series of points for the two different classes of data. The squares represent the class A and the circles represent the class B. The SVM maps these data into a space where it tries to separate the two classes’ data with a large gap as wide as possible. For this, the SVM creates a number of hyperplanes and then finds an optimal separating hyperplane. The hyperplane which is having maximum margin, that is, the distance between it and the nearest data point of each class is called optimal separating hyperplane (shown in Figure 1). The nearest data points are called the support vectors (SVs). The nearest data points are used to define the margin and called SVs (represented by gray square and circle). The basic aim of the SVM is to maximize the margin. When the SVs are chosen, the remaining feature points set can be rejected because the SV contains all of the useful information for the classifier. Then, the new examples called the testing data are mapped into the same space and are predicted to belong to the category based on the side of gap they fall on.^21,22

Figure 1.

Data classifications by the support vector machine.

The boundary is expressed as below

(wx) + b= 0, w ε R^{N}, b ε R

(1)

where the vector w is the boundary, x is defined the input vector of dimension N, and b is the scalar threshold. On the margins, where the SVs are placed, for the classes A and B, respectively, the equation is as below

(wx) + b= 1

(2)

(wx) + b= −1

(3)

Now, let us consider the above classification task with data point $x_{i}, i = 1,2, \dots, n .,$ belong to class A or class B and their associated labels $y_{i} = \pm 1$ . For the given class as SVs correspond to the extremities of the data, the decision function may be used for the classification of any data point in the class A or class B as follows^19,20

f (x) = sign (w . x + b)

For the linearly separable case, the following condition should be satisfied

y_{i} (w . x + b) > 0 \forall_{i}

where

w

is a normal vector to the hyperplane which is used to describe the boundary and b is the bias which is used to show the distance of the hyperplane from the origin. The optimal separating hyperplane may be obtained by solving the following optimization technique^19,20

min, Φ (w) = \frac{1}{2} {‖ w ‖}^{2}

(6)

subject to, y_{i} (w . x_{i} + b) \geq 1, i = 1,2, ..., n

(7)

The above equation is useful only for linear separable data. In order to solve the problem of nonlinear separable data, the following optimization problem is used^19,20

\min Φ (w) = \frac{1}{2} {‖ w ‖}^{2} + C \sum_{i = 1}^{n} ξ_{i}

(8)

subject to, y_{i} (w . x_{i} + b) \geq 1 - ξ_{i} ξ_{i} \geq 0, i = 1,2, \dots, n

(9)

where

ξ_{i}

is the positive slack variable, which is used to allow misclassification for some data points in order to reduce the complexity in the problem. “

C

” is the generalization parameter, which is a trade-off between the misclassification and boundary complexity. This formulation is called as the soft-margin SVM. The above complex problem can be solved by following equivalent Lagrange dual problem^19,20

Max {D (α)} = \sum_{k = 1}^{n} α_{k} - \frac{1}{2} \sum_{i, j = 1}^{n} {y_{i} α_{i} y_{j} α_{j} (x_{i}, x_{j})}

(10)

Constraint, \sum_{j = 1}^{n} y_{j} α_{j} = 0 and α_{i} \geq 0, i = 1,2, \dots, n

(11)

The kernel function, $k (x, x^{'})$ , is used to handle nonlinear separable data. It uses a nonlinear mapping function, $ϕ (x)$ , to map the data from an input space to a higher dimension space. After that a linear separable hyperplane is obtained in the higher dimension space for separating two classes. The following decision function is obtained by soling the above optimization problem with the kernel functions^19,20

f (x) = \sum_{i = 1}^{m} {y_{i} α_{i} K (x, x_{i})} + b

(12)

Experimental setup

The experiments were performed on the MFS™ which has capability to simulate a range of machine faults, such as unbalance, misalignment on the shaft, gearbox faults, induction motor faults, and bearing faults.

The experimental setup which includes MFS used in this study is shown in Figure 2. In the MFS, a three-phase induction motor is connected to the rotor through a flexible coupling. The rotor consists of a circular disc which is mounted in the middle of it. The rotor is supported on two rolling element bearings. The rotor system considered in the present study is supported on rolling element bearings, which generally exhibit the same stiffness in the vertical and horizontal planes. The shaft is made of steel and its length between the bearings is 0.43 m, whereas the mass of the centrally mounted disc is 0.68 kg. The mass density of the steel shaft and Young’s modulus have been considered as 7800 kg/m³ and 210 GPa, respectively. The schematic diagram of the MFS is shown in Figure 3. This setup allows the study of unbalance of the rotating shaft having a circular disc at its middle. The unbalance in the rotor is artificially produced by inserting the screw (or eccentric mass) in one of the holes of the disc at a particular radial distance and angle. The rotor disc has 24 holes/slots where the eccentric mass can be inserted to produce the unbalance. Figures 4 and 5 show the rotor in healthy and unbalanced condition, respectively.

Figure 2.

Machine fault simulator setup.

Figure 3.

Schematic diagram of machine fault simulator setup.

Figure 4.

Healthy rotor.

Figure 5.

Unbalanced rotor.

The present study mainly includes experimental work for unbalance identification. However, it is important to know the critical speed of the rotor system, before operating it at different speeds. The schematic of the rotor system has been given in Figure 3. Critical speed for the rotor system has been calculated analytically. For this purpose, maximum deflection of the rotor shaft has been calculated, which is then used to calculate the natural frequency of the rotor shaft in its fundamental mode. The rotor shaft is considered to be simply supported. The critical speed of the rotor shaft corresponding to its first bending mode is found out to be 5766 r/min. Therefore, it is decided to operate the rotor system at subcritical frequencies to avoid any unwanted conditions.

A triaxial accelerometer (Make: PCB; Model No.:352A73) is mounted on the top surface of the bearing housing (as shown in Figure 6). It is used to acquire vibration signals in time as well as frequency domain in the three orthogonal directions x, y, and z. In the present work, a National Instrument (NI)–based hardware and software system is used for the experimental data collection and analysis. Chasis (NI’s 4-slot USB chassis (DAQ – 9174) with 4-channel C Series dynamic signal acquisition module sound and vibration (NI 9234) along with NI’s LabVIEW software has been used for the data collection and analysis.

Figure 6.

Triaxial accelerometer in the machine fault simulator.

A variable frequency drive is attached with the motor to run it at different speeds. Vibration data are acquired for the rotational speeds starting from 10 Hz to 40 Hz in the interval of 5 Hz for each fault conditions. In total, 1000 samples were acquired with a sampling frequency of 1000 Hz. In total, 30 datasets (30,000 data points) have been collected in all three directions x, y, and z for all the speeds and rotor conditions.

Figures 7 and 8 show the plots of vibration signals in x, y, and z directions in the time domain data for healthy and unbalanced rotor, respectively. The signals are found to be nonstationary in all the directions for both healthy as well as unbalanced rotor. The amplitude of vibration is found to be increasing in the unbalanced rotor as compared to healthy rotor. The variation of frequency domain vibration signals in x, y, and z directions is added in Figures 9 and 10 for healthy and unbalanced rotor, respectively. In frequency domain signals, many important peaks are observed in all the directions. The harmonic peaks in Figure 10 are at the multiple frequencies of rotor spin speeds due to presence of unbalance which is artificially created in this work. These harmonics also appear in Figure 9 which may be attributed to the presence of residual unbalance in the rotor system. Other minor peaks are due to external noise in measurement of vibration data.

Figure 7

. Time domain data for 40 Hz in the healthy condition.

Figure 8

. Time domain data for 40 Hz in the faulty condition.

Figure 9

. Frequency domain data for 40 Hz in the healthy condition.

Figure 10

. Frequency domain data for 40 Hz in the faulty condition.

Unbalance fault diagnosis using SVM

Feature extraction

Feature extraction is a critical step in any fault diagnosis process because it reduces unwanted noise in the signals. In addition, this reduces the dimensionality of data by reducing the data size. The vibration data from healthy and faulty conditions obtained in the time domain as well as frequency domain in the x-direction, y-direction, and z-direction are now used to extract the critical features. Three statistical features, namely, standard deviation, skewness, and kurtosis are extracted here. Figures 11 and 12 show the plot of the three features obtained from time domain signals in x, y, and z directions at 40 Hz for healthy and faulty condition, respectively. The three features are obtained for all the considered operating speeds of the rotor for both time and frequency data. These features are further classified for training and testing data required in the SVM-based classification.

Figure 11

. Feature extraction for the healthy condition at 40 Hz speed in x, y, and z directions.

Figure 12.

Feature extraction for the faulty condition at 40 Hz speed in x, y, and z directions.

SVM-based unbalance fault detection

After the feature extraction, the SVM is trained by using 80% of the feature data and then tested by using 20% of feature data. The flowchart of the present methodology is represented by Figure 13. Diagnosis is performed for various operating conditions of the motor starting from 10 Hz to 40 Hz in the interval of 5 Hz.

Figure 13.

Flowchart of the present methodology.

Initially, the fault diagnosis is performed by using time domain data, and the results are summarized in Table 1. It is observed from the table that the detection rate is 100% for the healthy condition at all the considered speeds except 10 Hz where rate is 83.33%. At 10 Hz, speed prediction accuracy is not very good, but it is in the acceptable range. Detection rate for the faulty condition is found to be 50% (at 10 Hz), 83.33% (at 25 Hz), and 100% at all other speeds. So, it is clear that for the speed of 15 Hz, 20 Hz, 30 Hz, 35 Hz, and 40 Hz, respectively, prediction capability is very accurate. The overall detection rate is 66.66% at 10 Hz, 91.66% at the speed 25 Hz, and 100% at 15 Hz, 20 Hz, 30 Hz, 35 Hz, and 40 Hz speed, respectively. It can be observed from the results that the overall results obtained are very effective for the speed of 15 Hz, 20 Hz, 25 Hz, 30 Hz, 35 Hz, and 40 Hz, respectively, except 10 Hz. From here, it can be concluded that the unbalance in the rotor system can be detected effectively at all operating speeds. However, it is not suggested to perform the SVM-based unbalance detection using time domain vibration features at very lower speeds.

Table 1.

Support vector machine–based unbalance detection using time domain vibration features.

Training speed (Hz)	Testing speed (Hz)	Individual detection rate		Overall detection rate (%)
Training speed (Hz)	Testing speed (Hz)	Healthy rotor (%)	Unbalanced rotor (%)	Overall detection rate (%)
10	10	83.33	50	66.66
15	15	100	100	100
20	20	100	100	100
25	25	100	83.33	91.665
30	30	100	100	100
35	35	100	100	100
40	40	100	100	100

Now, the unbalance detection is attempted using frequency domain vibration features for various operating speeds of the motor and results are summarized in Table 2. It is observed from the table that for the healthy condition, detection rate is found to be 83.33% at 10 Hz and 25 Hz, 66.66% at 30 Hz, 33.33% at 40 Hz, and 100% at 15 Hz, 20 Hz, and 35 Hz, respectively. It should be noted that the detection rate is better at speed of 15 Hz, 20 Hz, and 35 Hz, respectively, than the speed of 10 Hz, 25 Hz, 30 Hz, and 40 Hz, respectively. For the faulty condition, detection rate is 50% at 10 Hz speed, 83.33% at 30 Hz and 35 Hz, and 100% at 15 Hz, 20 Hz, 25 Hz, and 40 Hz, respectively. The overall detection rate is 66.66% at 10 Hz and 40 Hz, 74.99% at 30 Hz, 91.66% at 25 Hz and 35 Hz, and 100% at 15 Hz and 20 Hz. The overall detection rate is found to be very accurate at 15 Hz and 20 Hz speed and satisfactory at the speed of 25 Hz and 35 Hz. However, detection rate is not in acceptable range at 10 Hz and 40 Hz. From here, it can be concluded that the unbalance in the rotor system can be detected based on the frequency domain vibration features; however, it is suggested to perform the detection for more than one speed.

Table 2.

Support vector machine–based unbalance detection using frequency domain vibration features.

Training speed (Hz)	Testing speed (Hz)	Individual detection rate		Overall detection rate (%)
Training speed (Hz)	Testing speed (Hz)	Healthy rotor (%)	Unbalanced rotor (%)	Overall detection rate (%)
10	10	83.33	50	66.66
15	15	100	100	100
20	20	100	100	100
25	25	83.33	100	91.66
30	30	66.66	83.33	74.99
35	35	100	83.33	91.66
40	40	33.33	100	66.66

Figure 14 shows the comparison of the overall detection rate in time domain and frequency domain. It is clear from the graph that overall prediction accuracy is the same in both time and frequency domain at 10 Hz, 15 Hz, 20 Hz, and 25 Hz. At 10 Hz speed, overall prediction accuracy is 66.66% in both time and frequency domain. At the speeds of 15 Hz and 20 Hz, overall prediction accuracy is 100% in time domain as well as in the frequency domain. Prediction accuracy is 91.66% for 25 Hz speed in the time domain and in the frequency domain.

Figure 14.

Comparison of overall detection rate with time domain and frequency domain vibration features.

It is also shown in the graph that overall detection rate is different in time domain and frequency domain for the rotating speeds of 30 Hz, 35 Hz, and 40 Hz. For 30 Hz, it is 100% in time domain, while 74.99% in the frequency domain. For 35 Hz rotating speed, it is 100% in time domain and 91.66% in the frequency domain. For 40 Hz, it is 100% in time domain and 66.66% in the frequency domain graph. So, it is clear from the above discussion that detection rate is the same in 10 Hz, 15 Hz, 20 Hz, and 25 Hz speeds in both time and frequency domain, but for the speeds of 30 Hz, 35 Hz, and 40 Hz, the prediction accuracy is greater in time domain than frequency domain. It is also observed that detection rate is very less at 10 Hz speed in both time domain and frequency domain; therefore, it is not suggested to perform the diagnosis at very lower rotational speeds. In addition, it can be said that SVM-based unbalance detection is better and more accurate with time domain vibration features than the frequency domain vibration features.

Conclusions

The main focus of this work is to develop an automated system for diagnosing unbalance in the rotor system based on the SVM algorithm using vibration signals. For this, the time and frequency domain vibration signals are acquired from the healthy and faulty rotors using MFS. Then, three critical statistical features (namely, the standard deviation, the skewness, and the kurtosis) are extracted from both the domain and used as inputs to the algorithm. The present work examines the SVM detection performance when the training and testing done at same rotational speeds of the rotor. The detection is performed for a range of operating speeds of the rotor, and results show a near perfect prediction accuracy which is found at higher speeds and somewhat lower, but acceptable accuracy is found at lower speeds. It is because at the higher rotational speed, the noise does not affect so much due to better signal-to-noise ratio in signals. It also shows a better fault prediction accuracy with time domain features than the frequency domain features.

Footnotes

Acknowledgments

The experimental work was carried out on the machine fault simulator (MFS), which is purchased by using TEQIP funds (TEQIP is a Technical Education Quality Improvement Program of World Bank in India) provided to Mechanical Engineering Department, Shri G S Institute of Technology and Science (SGSITS) Indore, India. We are thankful to the World Bank to provide such facility in SGSITS Indore.

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) received no financial support for the research, authorship, and/or publication of this article.

ORCID iD

Purushottam Gangsar

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