Health monitoring of rolling element bearing using a spectrum searching strategy

1. Introduction

As one of the foremost applied components, rolling element bearing plays a crucial role in the whole safety running process of rotating machinery. Their failures or abnormities could generally cause machine breakdowns and even catastrophic consequence during the production process [1, 2], which necessitates the continuous state monitoring in the whole life-cycle of bearings. Vibration analysis is a generally applied technique in bearing fault diagnosis owing to vibration signal carrying abundant information about failure mode and fault location. Recently vibration-based monitoring is becoming a vital measure in prognostic and health management (PHM), which devotes to collecting and presenting the health state information of a target machine component or an overall system [3, 4].

As is pointed out in [4], an effective PHM system should be dedicated to evaluating the health state of a monitored object using the measured data collected from normal condition to abnormal or failure case. Through employing such a system, the health state of the monitored system can be under control so that the scheduling of preventive maintenance and the inventory of spare parts can be reasonably adjusted or optimized. If so, the goal of cost and time savings can be achieved significantly. Health monitoring is a critical procedure in PHM activities of bearings and mainly consists of the early warning or detection of fault, the assessment of deterioration process and the guidance for prognosis of remaining useful life [5]. Some published literatures are focused on assessing the health state of bearings with features extracted through time-domain, frequency-domain and time-frequency domain methods [5-7]. And for fault diagnosis of bearings, it can commonly be divided into fault classification and fault detection. Fault classification contributes to identifying the health state of bearings with features derived from monitoring signals, and there mainly exists two categories: supervised and unsupervised methods. Supervised methods, such as artificial neural networks and support vector machine [8, 9], are devoted to fault classification only upon the labeled data. While unsupervised methods, such as self-organizing map and cluster approaches [10, 11], are dedicated to fault classification only utilizing the unlabeled data. For instance, an optimized $k$-nearest neighbor ($k$-NN) classifier was employed by Tabaszewski in [12] for the state classification of bearings, and Strączkiewicz et al. [13] performed bearing fault classification in different stage of its development using minimal distance, $k$-NN and $k$-mean-based clustering approaches, etc. Fault detection is applied to localize faults of bearing and its main challenge is how to eliminate or reduce the influence of noise and detect faults in incipient stage successfully. Aiming at these issues, some researchers have also investigated fault vibration responses and properties [14, 15] and signal pre-whitening techniques [16, 17] with regard to bearing fault detection.

In failure stage, the bearing defects can be mainly categorized as local and distributed faults [18]. However, it has been noticed that the localized defects occur more frequently than others in bearing raceway [19]. When a localized fault occurs in a bearing such as the surface of inner-race or outer-race, there commonly generates an impact shock for every rotational period. And this impact shock can excite the resonance of the bearing system to cause a change of the structure of the single-sided amplitude spectrum for frequency-domain analysis, especially nearby the bearing characteristic frequencies (BCFs) and their harmonics. Since the BCFs are usually considered as a prominent indication [20], classical spectrum analysis techniques such as fast Fourier transform (FFT) analysis and envelope analysis are applied to perform the fault diagnosis of bearings [21, 22]. Furthermore, if all the harmonics of BCFs can be searched in the FFT spectrum, the impulse generated by bearing fault could be determined as well [23]. To the knowledge of the authors, the impulse signature presents so weak that the fault detection encounters a greater challenge on account of the presence of noise at the early fault stage. However, the harmonics of BCFs can be detected in the spectrum, but it is not possible to determine the BCFs through simply measuring the spacing of the harmonic series. Furthermore, with regard to the crack formation, growth and deterioration, the power magnitude of the BCFs as well as their harmonics generally served as an indicator could make a difference on the degraded degrees of bearing [24]. Therefore, focusing on constructing a novel feature to depict the bearing degradation, the authors propose a vibration-based methodology for health state assessment of bearings using the structural information of spectrum (SIOS) algorithm demonstrated in literature [25].

In this article, a novel health monitoring strategy is presented by deeply digging the context of the single-sided amplitude spectrum in frequency domain. First, vibration signals are acquired with appropriate sampling rate and length and then transformed into frequency domain to acquire the single-sided amplitude spectrum. Then, the SIOS algorithm is adopted to construct the projected spectrum on a predefined frequency grid. Finally, the two-dimensional (2-D) line plot of the frequency grid versus the average power in SIOS is employed to perform fault diagnosis and the sum of the largest six total-power (SLSTP) of the frequency grid in SIOS is regarded as a health indicator to capture the degradation trend. Simulation and experimental studies are presented to evaluate the performance of the proposed method in early fault diagnosis and state assessment of bearings.

The remainder of this paper is organized as follows. Section 2 describes the health monitoring methodology detailly, including the construction of SIOS and health index. Sections 3 and 4 are dedicated to evaluating the proposed monitoring scheme with simulation and experimental data. Finally, some conclusions are drawn in Section 5.

2. Health monitoring methodology

In order to trace the evolutional process of the health state of bearings, we formulate a novel index focusing on the power variability of the spectrum derived in frequency domain. To begin with, the SIOS of the current analyzed signal is constructed with a simple searching and projection strategy. Then the average power and the so-called SLSTP in SIOS are exploited to conduct fault diagnosis and to capture the changing process of bearing health state, respectively. Next the proposed health monitoring scheme will be illustrated in detail.

2.2. Health indicator construction based on SIOS

In order to monitor the running state of bearings immediately, we propose a novel health monitoring strategy with the SIOS obtained in previous subsection. And this monitoring index is called as “SLSTP” in our research. The main procedures of the proposed scheme can be summarized as follows.

Step 1: With a preset sampling rate $F_S$, vibration signal is collected from the monitored bearing with an appropriate length according to ${∆}_S<2F_l{F}_l/F_S$ to satisfy the frequency-resolution condition.

Step 2: The vibration signal is then transformed into frequency-domain using FFT algorithm to acquire the single-sided amplitude spectrum.

Step 3: Determine parameter $\delta$ and $l$, then search local peaks of the spectrum according to inequality (1). Finally, $M$ local peaks are found from the spectrum.

Step 4: Project the $M$ local peaks onto the predefined frequency grid $G$ to construct the SIOS.

Step 5: For each frequency grid $G\left(i\right)$, compute the total number of the projected peaks, i.e. $N\left(i\right)$, and the total energy, i.e. $E\left(i\right)$, of the SIOS.

Step 6: Create the 2-D line plot of $G\left(i\right)$ (frequency grid) versus $E\left(i\right)/(M-N\left(i\right))$ (called “average power” in this paper) for fault diagnosis and compute the SLSTP, i.e., the summation of the largest six amplitudes of $E$, as the degradation index of bearings.

Fig. 1 depicts the framework of the proposed health assessment methodology for bearings detailedly.

Fig. 1The framework of the proposed health assessment methodology

3. Simulation analysis

In this section, a simulation experiment is designed to validate the effectiveness of the proposed methodology for health monitoring. We simulate the vibration signals along the whole degradation process of the bearing. Herein, the flowing parameters are considered in the simulation: pitch diameter $d_p=$ 23 mm, roller diameter $d_r=$ 8 mm, pitch angle $\theta =$ 0° and the number of rollers $n_r=$ 9. The bearing has an outer-race defect, its shaft rotational frequency $f_r=$ 30 Hz (i.e., the corresponding shaft rotational speed $v_r=$ 1800 rpm) and the bearing-induced resonant frequency $f_s=$ 3500 Hz. Then the ball-pass frequency of the outer raceway can be calculated as:

The sampling frequency $F_S=$ 12000 Hz, and each sample consists of 18000 data points, i.e. 1.5 s, and the sampling is triggered every 10 minutes. To simulate the whole degeneration process of the bearing, vibration samples in normal stage are repeated 400 times and the vibration samples in failure stage are repeated 200 times with the increasing fault severity. That is to say, an incipient outer-race fault occurs in the 401st sample (about at the time of 2.4×10⁵ second). And the vibration signal produced by the out-race fault in failure stage is generated according to the simulation model presented in [26]. The simulated vibration signals of the whole lifetime and the zoomed-in views of the normal and failure stage are shown in Fig. 2.

Fig. 2The simulated vibration signals of the whole lifetime

In this simulation analysis, we predefined the frequency grid as $G=$ [70 Hz, 170 Hz). Then the resolution of the FFT spectrum must satisfy:

Hence, the signal length can be set as 2¹⁴ to carry out sampling due to the resolution ${∆}_S=$ 12000/2¹⁴ $=$ 0.7324, which satisfies the above limiting condition. Moreover, the resolution of the frequency grid is assigned as ${∆}_G=$ 0.25 ${∆}_S$. The SLSTP of the simulated signals is presented in Fig. 3.

Fig. 3The SLSTP evolution of the simulated vibration signals

Examining the SLSTP process in Fig. 3, an explicit change is detected at the time of 2.4×10⁵ second (the 401st data sample), which means that a bearing defect may occur in that monitoring sample. Therefore, the fault detection is triggered after monitoring an anomaly warning during runtime. The time waveform of the 401st simulated sample is shown in Fig. 4, where periodic characteristics cannot be observed directly due to the heavy noise. With the proposed method, the corresponding diagnostic spectrum is plotted in Fig. 5.

Fig. 4The time waveform of the 401st simulated sample

Fig. 5The spectrum of E(i)/(M-N(i)) versus Gi of the 401st simulated sample

From the spectrum in Fig. 5, it can be seen that there exists a large-amplitude at 88.06 Hz, which corresponds to the ball-pass frequency of the outer raceway of the bearing thanks to utilizing the proposed fault detection approach. This illustrates that the proposed method can be applied to the bearing fault detection in weak defect stage.

The simulation results show that the proposed strategy seems a very promising approach for the health monitoring of bearings. Next, bearing vibration data sets obtained from a run-to-failure test are employed to further evaluate the performance of our methodology.

4. Experimental analysis

4.1. Experimental setup

To assess the capability of our proposed methodology, vibration data sets provided by the NSFI/UCR Center for Intelligent Maintenance Systems (IMS) [27], are applied to perform the experimental validation. As shown in Fig. 6, four testing bearings support one shaft which was loaded with 6000 lbs in the radial direction. The rotation speed was set to 2000 rpm with assistance from an AC motor and all bearings were lubricated during the experiments. Vibration signals were acquired using acceleration transducers that installed on the bearing housings. In order to guarantee the safe running of the mechanical system, a magnetic plug mounted in the oil feedback pipe was utilized to collect metal debris produced by the bearing system so that the bearing run-to-failure tests could be stopped until the debris accumulated to a certain level. More detailed instructions on this test rig and can be found in [27].

Fig. 6Accelerated degradation test bench of breaings

In this research, two vibration data sets (testing 1 and testing 2) are applied for the validation of the proposed health monitoring strategy. Vibration data in testing 1 and 2 were collected every 10 minutes with data-acquisition equipment. The sampling frequency was set to 20000 Hz and each signal with 20480 data points was sampled and stored in an ASCII file. At the end of testing 1, an inner race failure and a roller element failure occurred in bearing 3 and bearing 4 respectively; and as for testing 2, an outer race failure was found in bearing 1 after the life test. Next the above-mentioned vibration data sets are applied to validate the performance of our proposed scheme.

4.2. Health monitoring with the proposed methodology

4.2.1. Degradation assessment based on the health indicator

To investigate the capability of SLSTP in assessing degradation of bearings, the SLSTP in SIOS is calculated as an indicator using the collected vibration signals in our investigation. According to the data sets, the sampling rate $F_S=$ 20000 Hz. Moreover, the frequency grid is selected as $G=$ [200 Hz, 300 Hz), which covers the BCFs of common defects, however the resolution of the FFT spectrum must meet the following condition:

${∆}_S<\frac{2F_l{F}_l}{F_S}=\frac{2\times 200\times 200}{20000}=4.$

Therefore, the sampling length is set as 2¹⁴, and ${∆}_S=$ 20000/2¹⁴ $=$ 1.2207, which satisfies the above restriction.

In addition, the resolution of the frequency grid is assigned as ${∆}_G=$ 0.5 ${∆}_S$. The SLSTP of bearing 3 and bearing 4 in testing 1 are computed and plotted in Fig. 7 and Fig. 8, respectively. Meanwhile, the SLSTP of bearing 1 in testing 2 is presented in Fig. 9.

Intuitively, our proposed health monitoring indicator, SLSTP, shows a statistical monotonically increasing trend, which can track the degradation process of the bearing instantly. From Figs. 7-9, some remarks can be concluded that: (1) the proposed SLSTP can illustrate different health stage of bearings from health, early degradation, severe degradation to failure. Notably, the SLSTP increases as bearing performance degenerates continuously until failure; (2) a relative stable period of SLSTP is consumed so that the buffer time is sufficient for condition-based maintenance, which is pretty significant in PHM activities; (3) the proposed SLSTP is capable of prognosticating the weak or early anomaly of bearing and it is sensitive to fault development.

Fig. 7The SLSTP evolution of bearing 3 in testing 1

Fig. 8The SLSTP evolution of bearing 4 in testing 1

Fig. 9The SLSTP evolution of bearing 1 in testing 2

To depict the monotonic trend of the SLSTP and compare its performance, we draw a comparison between SLSTP and root mean square (RMS), and kurtosis in bearing health assessment. First, brief mathematical descriptions on these two time-domain indexes are given as follows. For a discrete signal $x\left(i\right)$ with $n$ points, the RMS is defined as:

$RMS=\sqrt{\frac{{\sum }_{i=1}^n{\left[x\left(i\right)\right]}^2}{n}}.$

And the kurtosis is defined as:

$Kurtosis=\frac{\frac{1}{2}{\sum }_{i=1}^n{[x\left(i\right)-\stackrel{-}{x}]}^4}{{\left(\frac{1}{n}{[x\left(i\right)-\stackrel{-}{x]}}^2\right)}^2},$

where $\stackrel{-}{x}$ denotes the mean value of the discrete series.

Figs. 10-12 present the tracking curves of the aforementioned bearings by plotting RMS and kurtosis. Compared Figs. 10-12 with those derived previously, the SLSTP draws a better performance in tracing the changes of the health state of bearings, especially for the bearing 4 of testing 1 and the bearing 1 of testing 2. Therefore, the health indicator presented in this paper can highlight the bearing degradation behavior preferably and can be utilized for its health assessment.

Fig. 10Bearing 3 in testing 1: a) RMS curve; b) kurtosis curve

a)

b)

Fig. 11Bearing 4 in testing 1: a) RMS curve; b) kurtosis curve

a)

b)

Fig. 12Bearing 1 in testing 2: a) RMS curve; b) kurtosis curve

a)

b)

4.2.2. Fault assessment with the average power of SIOS

In order to demonstrate the ability of the proposed health monitoring method in fault detection, the vibration signals of bearing 1 in testing 2 is applied to further test our method. Three different-stage statuses shown in Fig. 13 corresponding to serious defect, early defect and weak defect (statuses A, B and C), are taken into consideration for fault detection analysis.

Fig. 13Three degeneration stages of bearing 1 in testing 2

Examining the SLSTP degenerative process, we can observe that the degradation trend begins to be emerged by about the 500th record. Next the performances of our method in three health states are presented separately.

4.2.2.1. Bearing at serious defect stage (status A)

From the change trend of the proposed health indicator, the vibration data at serious defect stage (the 923rd record) is employed to analyze. Fig. 14 shows the vibration measurements of status A which was collected nearby the end of the bearing test and the corresponding spectrum generated with the proposed method is presented in Fig. 15. From the spectrum in Fig. 15, an obvious local peak related to the ball pass frequency on bearing outer race (BPFO) at 230.7 Hz is highlighted and detected, which illustrates that a local fault has existed in the outer ring of the monitored bearing. It is clear that the fault of bearing is detected successfully when serious defect appears.

Fig. 14The time waveform of the 923rd record at serious defect stage

Fig. 15The spectrum of E(i)/(M-N(i)) versus Gi of the 923rd record

4.2.2.2. Bearing at early defect stage (status B)

Fig. 16 displays the vibration signals of status B (the 616th record) sampled near two more days before status A. From Fig. 16, the periodical impulses generated by the early fault could not be observed from the time-domain waveform due to the heavy background noise, which leads to a low signal-to-noise ratio. To investigate its performance in early fault diagnosis, the proposed diagnostic scheme is utilized to process the measured signals and the corresponding diagnostic spectrum is depicted in Fig. 17.

Fig. 16The time waveform of the 616th record at early defect stage

Fig. 17The spectrum of E(i)/(M-N(i)) versus Gi of the 616th record

In spite of the low signal-to-noise ratio, a dominant peak at 230.7 Hz, which corresponds to BPFO, is also accentuated, thus bearing fault in this phase can be effectively diagnosed using our monitoring method as well. Therefore, the proposed monitoring methodology is suitable for bearing fault detection in early defect stage.

4.2.2.3. Bearing at weak defect stage (status C)

Here a more complicated monitoring time-point is considered, i.e. the weak defect stage. Examining the degradation curve shown in Fig. 13, the health index, SLSTP, begins into rising trend around 5000 minutes (namely about the 500th record). Hence, we take the 500th record as a representative at the weak defect stage. Compared with status A at the serious defect stage, the weak fault characteristics are almost totally inundated by the noise so that periodic characteristics cannot be intuitively observed in Fig. 18. After processing with the proposed method, we present the diagnostic result in Fig. 19.

Fig. 18The time waveform of the 500th record at weak defect stage

Although a local component round 247 Hz dominates the spectrum, the outer race fault frequency of the bearing as another dominant component is found at 230.7 Hz thanks to utilizing the average power of the SIOS, which is of great importance for fault warning in practical applications.

In this experimental case, vibration signals at three degeneration phases are employed to explain the effectiveness of the health monitoring scheme proposed in this study. All the presented monitoring and diagnostic results prove that it cannot only detect the fault at an early deteriorated phase, but also track the degenerative process of bearings.

Fig. 19The spectrum of E(i)/(M-N(i)) versus Gi of the 500th record

5. Conclusions

A novel health monitoring approach for rolling element bearings is presented in this paper. The purpose of this investigation is to put forward an approach for bearing fault diagnosis and its health assessment so as to provide advanced anomaly warning during runtime. Firstly, the SIOS is constructed using a searching algorithm based on the FFT spectrum of the original vibration signals. Then the 2-D line plot of the frequency grid versus the average power in SIOS is employed to perform fault detection. Finally, a health index is computed as the summation of the largest six total-power of the predefined frequency grid in SIOS to assess the degradation severity. Simulation data and bearing life-test data are applied to validate the performance of the proposed monitoring scheme. It is shown that the proposed method could exhibit strong behaviors in detecting the weak local defect and tracing the degeneration process of rolling bearings.

Otherwise, the SLSTP seems a promising monitoring indicator for remaining useful life prediction of bearings, on which we will pay more attention in the future.