Rotating machine fault detection using principal component analysis of vibration signal

Tristan Plante, Lucas Stanley, Ashkan Nejadpak, Cai Xia Yang Department of Mechanical Engineering

University of North Dakota Grand Forks, United States

ABSTRACT — Current vibration based maintenance methods can be improved by using principle component analysis to identify fault patterns in rotating machinery. The intent of this paper is to study the effects of using principle component analysis in a vibration based fault detection process and to understand the capability of this method of maintenance. Because vibration-based maintenance practices are capable of identifying motor faults based on their respective vibration patterns, principle component analysis observed in frequency domain can be used to automate the fault detection process. To test this theory, an experiment was set up to compare health conditions of a motor and determine if their patterns could be grouped using principle component analysis. The result from this study demonstrated that the proposed method successfully identified healthy, unbalance and parallel misalignments of rotary rotor. Therefore, it is capable of detecting faults in early stages and reducing maintenance costs.

Keywords—Principal Component Analysis; FFT; Fault Detection; Vibration Analysis; Severity

I. INTRODUCTION

Within the modern day industrial and energy sectors, basic electric motors are the backbone in a large variety of applications. Thus, the maintenance and upkeep of these machines are an essential component to keeping up with production demands. When plants experience an unexpected shutdown due to motor failure, the costs associated with lost production time can be astronomical. It would be ideal if shutdowns are kept to a minimum if not avoided entirely. Because of this, it is common practice to hire vibration analysts to perform both preventive and predictive maintenance [1]. These forms of maintenance are considered to be highly informative and beneficial when performed correctly.

Typically, vibration analysts use Fast Fourier Transformation (FFT) to process and interpret vibration data from motors and other rotating systems. During this process, most of their time is spent observing data and identifying patterns. The skill of an analyst is usually dependent on their past experience and training. While relatively effective, these costs are still considerably high and greatly depend on the analyst’s training, experience and

equipment. Even when analysts have the capability and means to promote effective maintenance practices, mistakes can still be made that affect production. This highlights the limitations of traditional vibration analysis and outlines the need for improvements in predictive maintenance. One such improvement is the application of principal component analysis (PCA) to FFT data. This process is explored in [2].

Due to substantial improvements in computer processing, the concept of autonomous pattern recognition has become more effective. As mentioned earlier, PCA has an application to this process. Applying PCA would reduce the training needed by analyst and hopefully increase the accuracy of predictive maintenance. Rather than analyze vibration data manually, PCA can be used computationally to find the patterns associated with mechanical faults. For example, a motor that is misaligned can be grouped with other motors that share the same fault condition. The same applies for mechanical faults of other types. This notion points towards the automation of the vibration analysis process. This would reduce a large portion of the costs associated with the maintenance industry. For this reason, an experiment was conducted to apply PCA towards fault detection and determine if this method could be deemed both efficient and reliable enough to merit further study and perhaps see an application within an industrial setting.

The tests conducted involved three operating conditions of a typical axle system connected to an induction motor. The axle itself was under load supported by two bearing couples whose respective vibration data was recorded using a set of accelerometers mounted at four locations. Resultant FFT data was processed using PCA which helped outline any patterns that emerged from the experimental data. The validity of these patterns were tested using several unknown data sets to determine if they could be identified correctly.

The remainder of this paper is structured as follows. Section II introduces the fundamentals of fault detection and principal component analysis. Experiment setup, including data collection process, experimental system faults, PCA experiment conditions, and Matlab program process will be discussed in section III. Experiment data displacement and analysis using PCA method will be described in sections, IV and V, respectively. The paper

concludes with future work and a summary recapping the main advantages of the proposed method in Sections IV and V.

II. BACKGROUND INFORMATION

A. Fault detection

In short, fault detection is the common practice of identifying machine faults before they become severe enough to cause harm to itself or the surrounding area. Experiments performed in previous work show that vibration analysis can be used to detect faults in motors [3]. Like most practices, there are a number of methods to do this. However, vibration analysis is the most common. It is capable of detecting the widest range of mechanical faults. It can identify faults from mechanical looseness, to bearing faults, to misaligned rotors and shafts [4]. Vibration analysis can be used to determine the type and severity of faulty systems. This is possible because mechanical faults produce patterns in vibration data that are considered to be specific to their identity. For instance, unbalanced rotors resonate a large amplitude peak in FFT at the same frequency of the running speed also known as the 1X peak [1]. Additionally, mechanical looseness responds with several peak multiples of the running speed 1X, 2X, 3X etc. Of course, these are just a few examples of faults that can be detected using vibration analysis.

B. Principal Component Analysis (PCA)

Principal component analysis is a statistical approach to identifying and isolating large amounts of data with multiple variables. In other words, PCA is a feature extraction technique capable of distinguishing data values based on their respective variance to the rest of the data set [5]. This is done by calculating the amount of variance between several data sets and assigning each variable its own dimension to determine which variables have the largest impact on the variance within the data [6]. By doing this, data of different types are separated into “groups” which can be recognized by identifying one data set within that group. This is commonly used to find patterns in statistical information as seen in [7] which explains the application of PCA to organize a large number of cells into groups based on the genes they possess.

Fault detection, in its nature, involves the identification of vibration patterns. This paper explores how PCA could be applied to determine these patterns computationally without the need of manual data analysis. By comparing large numbers of data sets, PCA can be used to group known FFT vibration patterns based on their relevant trends. At which point, unknown data can be introduced so it can be grouped into their respective fault categories. If successful, this paper may provide a new method of maintenance within industrial applications and could stand as the foundation for future research regarding this application.

III. EXPERIMENT SETUP

A. Data Collection Process

Three health conditions of a motor were studied in a series of experiments: healthy, unbalanced and parallel misalignment. Each of these experiments were conducted using the Machinery Fault

Simulator (MFS) purchased from SpectraQuest Inc. Operating at 25Hz (1500 RPM), data was recorded using four PCB Piezotronics’ IMI model 603C01 accelerometers. Fig. 1 shows an image of this setup.

Data acquired from the accelerometers were processed using a PCI-4498 data acquisition device (DAQ) purchased from National Instruments. This device’s output was then analyzed using the “Sound and Vibration Assistant” software produced by National Instruments set up to read 2000 samples at a rate of 20,000 Hz. The raw time-based vibration data was then converted into an FFT using the zoom power spectrum function, and a Hanning window with a magnitude based setting. This was set up to record data over a 15 second period. Throughout this period, the FFT used a root mean squared average to acquire a reliable estimate of the vibration condition. Because most vibration analysts use the low frequency spectrum for fault detections, the frequency range was limited from 0 Hz to 1000Hz and the number of line set to 1000 to produce an adequate spectrum resolution of 1 Hz.

Fig.1: Machinery Fault Simulator setup

Two accelerometers were placed on each bearing housing in the horizontal and vertical axis, perpendicular to the direction of the shaft. Fig. 2 shows the placement of the two accelerometers on the rear bearing housing. This placement is identical to the placement of the accelerometers on the bearing housing closest to the motor used to operate the system. In fig. 2, the shaft is going into the page. For the experiments conducted in this paper, no accelerometers were placed in the axial direction because data taken in that direction produced results that were less informative than their radial counterparts.

Fig. 2: Placement of accelerometers on the rear bearing housing

B. PCA Experiment Conditions

For any health condition of a motor, a change in spectral patterns can be observed in FFT when a system experiences varying degrees of fault severity. To account for the variance in vibration data in the PCA method, fault severity was altered for every test. Since a healthy motor cannot experience different degrees of healthiness, additional load was added to the motor under healthy conditions in order to change the response of the spectral pattern, thus simulating changing circumstances. Although load does not directly create a larger fault severity, for the purpose of this experiment it was assumed that an increased severity or load would intensify the response in the vibration data.

For the series of healthy system tests, washers were added uniformly around the rotor to increase the amount of load applied to the system. This was done in multiples of four, starting zero and going until there were a total of 20. Unbalanced tests were conducted by adding washers in sets of two, starting at zero and going to 20. Fig. 3 shows the rotor used to add load and simulate unbalance. Misalignment was simulated via the misalignment dial in place on the MFS (see fig. 4). These tests increased by five milli-inches (mils) starting at 10 mils and ending at 35 mils. The unknown healthy test was taken with nine washers arranged uniformly the rotor. The unknown unbalanced test was taken with seven washers. The unknown misalignment test was conducted at 27 mils.

Fig. 3: Rotor used to add load and simulate unbalance

Fig. 4: Dial used for introducing parallel misalignment

By changing the severity of the faults and the load of the healthy condition, the robustness of the PCA method was tested. This was done to determine if PCA could correctly group faults of the same type together that had different operating conditions. This concept was represented in test set seven which was recorded in a similar fashion. The only difference was that the severity/load of the unknown data set lied between the severities of the known faulty test sets. This allowed for the possibility of trend mapping the data set and approximating the severity of an unknown fault.

C. Experimental System Faults

As mentioned earlier, the health conditions of the motor that were tested were healthy, parallel misalignment, and rotor unbalance. The healthy data set was taken to act as a control group for the other test sets. The fault conditions studied were tested to determine if the PCA method could correctly group health conditions by type and identify fault severity. With that said, the severity of one fault cannot be accurately compared with that of another. Instead, the intention of this experiment was to evaluate the trend of each fault group individually. For example, the most severe instance of misalignment cannot be compared with the most severe instance of unbalanced because the systems were operating under different conditions. Rather, it was intended that for each fault, a trend in fault severity would emerge. This would allow for an unknown test set to have the severity of its fault estimated.

D. Matlab Program Process Once data was collected from each experiment, text files were

created for each data set displaying the running speed and amplitude values at each frequency. For the majority of the experiment, data was left unedited for the purpose of distinguishing the application of PCA towards vibration based fault identification. However, for comparison purposes, this paper also explains the benefits/limitations of adjusting data sets to improve fault groupings. This process is explained further in the “Experimental Data” and “Analysis” sections of this report.

After being formatted, the data associated with their respective accelerometers was assigned to a cell containing similar data from other data sets. Once each data set was organized, the program processed them using Matlab’s “pca” function to produce a PCA using the correlation matrices. This process was repeated for each accelerometer.

Because each recorded test was controlled, the location of unknown tests could be compared to that of each known test by creating a region in which the fault was known. By doing this, unknown tests could be identified by determining if the test lied within the proximity of the region specific to that fault condition.

IV. EXPERIMENT DATA

A. Three Fault Spectrum Results

Figs. 5-7 displays three examples of the FFT data recorded during the experiment. Each graph shows the FFT of a healthy rotor, misaligned rotor, and an unbalanced rotor. Traditionally, these are the types of graphs vibration analysts used to identify faults and their corresponding severities.

Fig. 5: Healthy Rotor Data in FFT

Fig. 6: Parallel Misaligned Rotor in FFT

Fig. 7: Unbalanced Rotor Data in FFT

While it is easy to identify the differences between each graph from a broad perspective, it is quite difficult to identify the specific peaks that represent the fault as a whole. With the exception of unbalance, which has a 1X peak that dominates the graph by a significant margin, it becomes increasingly difficult to identify the more subtle differences between the healthy and misaligned FFT data set. These subtle changes are what make vibration analysts training and experience so important. PCA presents an alternative approach to this method, which may be advantageous to analyzing such subtle differences.

B. PCA of Fault data PC 1 and PC 2 (2D)

The processed data sets for each accelerometer are represented in figs. 8-11. Each data set displays both the scores (red) and loadings plot of the PCA. In short, the square plot is represented by a large number of points each of which represents a single frequency value in the graph. On the other hand, the points representing the loadings portion of the graph are each a single test (unbalance, healthy, etc.). Additionally, each point in the loadings portion of the graph are marked with either an “H” (healthy), a “U” (unbalanced), or an “M” (misalignment) as well as the test number for that fault type in order of occurrence.

Fig. 8: Accelerometer 1 PCA

Fig. 9: Accelerometer 2 PCA

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Fig. 11: Accelerometer 4 PCA

C. PCA of Fault data PC 1, PC 2, and PC 3 (3D)

Figs. 12 through 15 represent the same data presented in the previous section of this report. The only difference is that a third dimensions was added by including the third principal component reference to the graph. Besides this, the data is presented in the same manner with both the loadings and score plot displayed in each graph.

Fig. 12: Accelerometer 1 PCA

Fig. 13: Accelerometer 2 PCA

Fig. 14: Accelerometer 3 PCA

Fig. 15: Accelerometer 4 PCA

D. PCA of Adjusted Data

Fig. 16 displays the results of vibration data that has been scaled and ordered before being processed in PCA. This adjusted data set was created by subtracting a spectrum produced by averaging each of the healthy data sets. Amplitudes that were left with negative values were set to zero to standardize the data set. After this process, each data set was put in terms of order by assigning the amplitude at a certain frequency to that of the nearest order multiple of the running speed. This was done so that data sets operating at different speeds could be compared more readily with controlled tests. Next, data was scaled and

standardized using a square-root operation and computing the z-score of the resultant amplitudes. Both these processes were done to make larger peaks more distinct.

Fig. 16: Accelerometer 1 Adjusted PCA

Unknown data sets are represented with a square box surrounding an “X” and are labeled in order of intended fault grouping. That is “1” relating to healthy, “2” for parallel misalignment, and “3” for an unbalanced rotor.

V. ANALYSIS

A. Fault Grouping in Two Dimensions

Based on the data presented in figs. 8 through 11, it can be stated that PCA is capable of detecting mechanical faults based on processed FFT vibration data. Within the loadings plot of each graph, each of the fault conditions can be seen grouped together with other points of the same fault type. However, there are some exceptions to this. As seen in figs. 12 -15, there is some overlap between the healthy and misaligned loading points. Because of this, it would be difficult to correctly identify an unknown point that lied within this region. This highlights the advantage of using more than one accelerometer as well as the addition of another PC dimension. Should one accelerometer produce a PCA graph that does not clearly identify an unknown test set, other accelerometers can help clarify the results by providing alternative views on its fault type.

As for the score plot, there is less clarity about the information shown compared to the loading plot. This is because each point represents a single amplitude value with respect to each data set. Many of these frequencies experience little change and are thus destined to lie within the same area. The points located near the x-axis of each graph could depict some type of trend. These points may represent the increase in fault severity for unbalance or misalignment. However, due to the setup of the experiment and Matlab code, it is not possible to verify such a trend. Even if the points were identified as a certain fault group, this is, in fact, the only trend readily identified by the graph meaning the other two conditions could not be identified based on score plot alone.

Needless to say, the loadings plot offers much more clear and precise information.

B. Fault Grouping in Three Dimensions

Within figs. 12-15, the addition of a third PC dimension shows a distinct improvement in the grouping of each fault condition. Compared to the previous graphs involving only two PC dimensions, the misaligned and healthy groups in figs. 12-15 do not lie within the same region. Instead, each fault group becomes more distinct with the addition of a third PC dimension and would be easier to recognize computationally. This concept is explained further by the incorporation of unknown data sets in each fault grouping.

C. Unknown Data Representation

Looking once again at fig. 8 through 11, the unknown data sets, represented by an (X), can be seen near or within each fault group. Despite the fact that not every unknown data point lies within the immediate proximity of each fault group, a simple observation suggests that a point lying near a specific fault group can be considered that same fault.

Whether or not user intuition can identify the unknown data set is irrelevant. The purpose of this program is to determine the type of fault computationally. To do this, the program was written to incorporate an algorithm that judged the proximity of an unknown data point with each of the fault groups. Each fault group would be assigned a score based on the proximity of the unknown to the fault group. The fault group with the highest score would be assigned to the unknown data point.

Severity Trend

In most of the graphs displayed previously, the points within the healthy region typically form a tighter cluster than that of the other faults. Both the unbalance and misaligned data sets appear to form more narrow regions that resemble a linear function. This can be explained by looking at one of the fault groups in closer detail as shown in fig. 17.

Fig. 17: Example of fault severity trend showing Accelerometer 1’s Misaligned Fault Group

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This figure displays how the data sets are in the same order as when they were read by the program. While only the fault trend for misalignment is shown, each of the faults in the other graphs display a similar pattern. For the purposes of this paper, fig. 17 is analyzed to shed further light on this subject.

The severity levels of fig. 17’s specific fault cluster are shown in points 1 through 6 starting at 10 mils and proceeding to 35 mils in increments of 5 mils respectively. This arrangement is significant because as each data set was collected, the severity of that specific fault condition was increased. Meaning that data with higher severity levels were located further from the healthy cluster as seen in fig. 5. This concept holds true for each of the PCA graphs and outlines the potential for PCA to determine the type of fault present, and its approximate severity.

D. Adjusted PCA Interpretation

As mentioned earlier, fig. 16 corresponds to the results of a loading graph whose respective FFT data has been scaled, ordered, and standardized in an attempt to improve the fault identification process. Based on the figure, each of the fault groupings appear to be more independent of each other. That is, each group is more distinct than the PCA graph produced without adjusting the data set. With that said, it may beneficial to adjust the data set before processing it in PCA and may provide a better result; however, the downside to this method is that, based on this figure, no trend line can be readily plotted and no estimate of the severity can be determined.

VI. FUTURE WORK

In addition to actual identification of an unknown data set, future work needs to be done on the relationship between data sets from other motors. Specifically, if data from a variety of motors can be processed in PCA to produce a program capable of identifying the type of fault present in any type of motor running at a certain speed. In principle, so long as the data was scaled and filtered correctly, this concept would hold true for most motors because of the fault based vibration patterns described in [1] and proven in [3]. Engineers could then construct a large database in which to refer to for machine maintenance for, potentially all industrial applications involving rotating equipment. Therefore, this concept should be studied in future experiments to reveal more about the limitations and benefits of this process.

VII. CONCLUSION

In summary, PCA can be used to distinguish between motor faults of varying types. This, of course, is done in conjunction with several accelerometers as the use of supplementary data can provide a more in-depth look at the data. By comparing data from multiple accelerometers, steps can be taken towards automating the fault identification process. This is further supported by the

similarities between the unknown data set and the other fault tests. Additionally, when dealing with a system running at a constant speed, the data has shown a correlation between the faulty data set’s severity and its respective position in the PCA graph. Meaning that the fault severity of an unknown data set could be potentially estimated. With that said, PCA provides a simple and inexpensive alternative to current maintenance techniques. Not only can industries become more efficient by reducing production costs, but they may also see an increase in productivity by avoiding unplanned plant shutdowns thus improving the industry as a whole.

ACKNOWLEDGEMENT

The work reported in this paper was funded by ND EPSCoR New Faculty Start-up Award UND0019805 and ND EPSCoR Advanced Undergraduate Research Awards UND0020387 and UND0021402.

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