Bearing damage assessment using Jensen-Rényi Divergence based on EEMD
Introduction
Rolling element bearing forms an integral and vital part of any modern rotating machinery. Over a period of time due to variety of reasons faults may develop in them that may cause overheating, friction torque, increased clearance leading to drop in performance and if undetected can cause breakdown. Based on vibration data, a number of signal processing techniques in time domain, frequency domain and time-frequency domain have been proposed in the past for an early and accurate fault detection [1]. However, the traditional methods can have some drawbacks and limitations that hinder the development of a robust online bearing degradation assessment tool. For example, in practice whenever data is acquired over the entire life span of a bearing, the signals are usually exposed to interference by the effect of background noise, presence of outliers, unexpected variation in operating parameters such as load variation and speed fluctuation. It can become challenging to accurately assess the bearing health status over its lifetime and timely forewarning of failure. The accurate estimation of current health status may reduce economic losses, decrease production downtime and improve efficiency.
Many researchers have attempted to address this problem in the past. Enough literature on variety of fault features is available in the field of bearing degradation assessment. Different features are sensitive to different faults and degradation severity [2]. Statistical moments such as RMS and kurtosis have been frequently used in many works as features for machine health condition monitoring [3], [4]. Qiu et al. [5] and Peter et al. [6] showed that the sensitivity of the RMS feature, in terms of identifying an incipient defect, is very low. Gebraeel et al. [7] chose the average of the amplitudes of the defective frequency and its first six harmonics, as the degradation index over the full cycle life of a bearing. However, it is difficult to detect and track the weak signals at an early stage using only time domain and frequency domain parameters [8].
Qiu et al. [5] developed a robust degradation assessment method based on optimal wavelet filter and self-organizing map (SOM). Huang et al. [9] further predicted the degradation condition using SOM and back propagation neural network on the basis of the methodology given by Qiu et al. [5]. Pan et al. [10] proposed a methodology for bearing performance assessment based on an improved wavelet packet-support vector data description. Suggesting further improvements in the past work, Pan et al. [2] proposed a new health assessment index based on lifting wavelet packet decomposition and fuzzy c-means. Pan et al. [11] proposed spectral entropy as a health index and the results of both simulations and experiments showed that spectral entropy effectively reflects the bearing degradation process. Yu [12], [13] proposed dimension reduction and feature extraction approach based on locally preserving projections for bearing degradation assessment, and further quantified the performance of bearings by the integration of the exponential weighted moving average statistic and the negative log likelihood probability based on Gaussian mixture model. He proposed a hybrid-learning-based feature selection method for fault diagnosis and machine health assessment [14]. Mi et al. [15] proposed a method to achieve multi-step bearing degradation prediction based on an improved back propagation neural network model using features extracted by principle component analysis. Wang [16] trained the features extracted from Empirical Mode Decomposition (EMD) using SVM and further used Mahalanobis distance as a fault indicator. Li et al. [17] used autoregressive model to separate the original vibration signal into random parts and deterministic parts and used the energy ratio between the random parts and the original signal as a fault indicator. Hong et al. [18] combined wavelet packet and EMD for feature extraction and derived a confidence value through SOM to assess bearing health states. Shakya et al. [19] applied Chebyshev׳s inequality to the Mahalanobis distance for online monitoring and damage stage detection for naturally progressing defect. Ali et al. [20] combined traditional statistical features and EMD energy entropy and estimated the degradation condition with the back propagation neural network for online bearing fault diagnosis. Hu et al. [21] used Mahalanobis–Taguchi system and SOM network to track the dynamic degradation trend of the bearing from real-time vibration data.
Many a times the fault information in vibration signals of the bearings is weak due to strong background noise. For such signals the time–frequency methods are considered to be an effective way for extracting the features from the noisy data. In recent years, EMD which is a widely used time-frequency domain analysis technique has been successfully used to decompose a signal into a set of intrinsic mode functions (IMFs) for fault diagnosis using the concept of energy entropy [8], [22], [23], [24]. Boškoski and Juričić [25], [26] further extended the concept of energy entropy to evaluate an information index known as Jensen-Rényi Divergence (JRD) based on Rényi entropy. JRD evaluated the relative change in the energy distribution of coefficients derived from wavelet packet transform of a defective signal with reference to a base distribution in order to quantify mechanical faults. But it is well established that diagnosis approach based on EMD energy entropy identifies roller bearing fault patterns effectively and is superior to that based on wavelet packet decomposition and reconstruction [22]. In addition in all the above studies the appropriate IMFs to be selected for evaluating entropy have been chosen randomly or based on visual inspection. The choice of appropriate IMFs is crucial not only to monitor the health of the bearing but also for fault classification.
Studies reveal that though the importance of bearing degradation assessment has prompted many researches in this field, yet there are challenges in accurately assessing the health status of a bearing.
- 1)
The first major challenge is to devise a robust and a stable condition monitoring parameter that can be used to detect incipient damage for any degradation mode. The parameter should be sensitive enough to detect any change in the level of degradation during early part of damage propagation rather than showing changes close to the complete failure to raise an alarm. Most of the proposed methods use SOM, ANN, SVM etc. which rely on prior knowledge of the domain wherein training data from all classes of specific bearing defects is required during the training phase. These methods provide reasonably good results for those particular defects only. For practical bearing health assessment, it may be quite difficult to have a complete prior knowledge about the type of failure mode. A large amount of training data is also needed for accurate modelling. Moreover a change in the operating parameters or bearing type will change the vibration characteristics, hence the machine learning operator needs to be trained for the new set of conditions.
- 2)
Whenever data is acquired over the entire life cycle of the bearing, the measured vibration signals are often disturbed by uncertain impulsive changes and random fluctuations. The overall effect of such changes is a confusing trend of the condition monitoring parameter involving false positives. Such trends have been observed from the bearing life test data reported by Shakya et al. [19]. It is necessary to filter out the effects of these disturbances as they can cause false indication of abrupt rise in the value of condition monitoring parameter.
- 3)
A generalized health indicator is necessary that allows to judge the health of different bearings, having different defect types on a common platform. The performance degradation assessment methodology should be independent of the physical characteristics of the bearing or the operating conditions, for it to be more general.
- 4)
The method should be capable of accurately classifying the type of defect as soon as it develops. Identifying the point of defect initiation is essential for accurate prognosis of bearing.
- 5)
In order to automate the degradation assessment methodology, the approach should be non-parametric in nature.
- 6)
The condition monitoring parameter should be insensitive to background noise and temporal variability in operating conditions during the full life cycle of the in-service bearing.
To address all these issues for better bearing degradation assessment, a divergence (Jensen Rényi divergence) based feature as a condition monitoring parameter is implemented in this work. Ensemble Empirical Mode Decomposition (EEMD) is employed to decompose the signal into a set of IMFs. A new sensitive IMF selection methodology is proposed where IMFs are clustered into two groups of sensitive and redundant (not-so-sensitive) IMFs. Using the selected IMFs a probability distribution of their energies is evaluated. Presence of any kind of defect in a rolling element bearing is expected to alter the probability distribution. Jensen Rényi divergence (JRD) measures and quantifies the deviation between probability distributions and is used here as an indicator of change of bearing condition. The presence of outliers in the trended JRD parameter is detected and removed with the help of an algorithm based on Chebyshev's inequality. Finally a Confidence value (CV) which will act as a generalized quantification index to assess current health state of the bearing is proposed.
The paper is organised as follows. Section 2 introduces the components of the proposed methodology based on EEMD, a procedure for selecting the sensitive IMFs, Rényi entropy, Jensen Rényi divergence, Chebyshev's inequality and fault classification methodology. Section 3 explains the proposed methodology. Section 4 discusses verification of the methodology as applied on simulated vibration signals and experimental data. Experimental data consists of seeded defect data measured on an industrial test setup and run-to-failure bearing life data sourced from Prognostics Centre of Excellence through prognostic data repository contributed by Intelligent Maintenance System (IMS), University of Cincinnati [27].
Section snippets
Degradation assessment framework
The proposed methodology for bearing degradation assessment is subdivided into two broad parts: 1. Monitoring the bearing health and 2. Fault identification. The subcomponents of these two parts are summarized in the flowchart given in Fig. 1.
Monitoring the bearing health uses an integral approach that uses EEMD for IMF generation followed by an automatic selection of sensitive IMFs. The EEMD will help to achieve higher degree of damage detection and particularly enhance the fault type
Proposed methodology
The flowchart explaining the complete methodology is given in Fig. 6(a) and (b). Initially at the start of the acquisition process, EEMD will be applied on the raw time domain vibration data to decompose the signal into a set of IMFs. Thereafter, sensitive IMF cluster will be identified, which will be used to construct the probability distribution. For any new acquired signal, Jensen Rényi divergence is evaluated by calculating the distance between the probability distribution of healthy and
Fault diagnosis based on simulated signal
The proposed approach is tested on simulated vibration signal using a mathematical model. In this section, vibration signal of a bearing under healthy state, bearing with outer race defect and bearing with inner race defect are simulated. The modelling includes most of the practical issues encountered in the measured data such as rotor unbalance, radial load variation, speed variation and signal noise. The simulations aim to test the following-:
- a)
The robustness of the proposed EEMD energy
Fault diagnosis method on experimental data
The previous section explored application and effectiveness of the proposed JRD measure on simulated vibration signal for both inner and outer race defects. In order to check its performance on actual test data, two experimental case studies are undertaken.
- a)
In the first study, the proposed JRD measure is tested on experimental bearing vibration signals with artificially seeded damage. The aim is to validate its effectiveness in correlating to the severity of the fault (outer race and inner
Conclusions
In this work, it is demonstrated that EEMD based Jensen Rényi divergence (JRD) as a degradation parameter has the potential to accurately monitor the bearing health. The JRD measures the change in the energy probability distribution of IMF's through Rényi entropy. Only a selected few IMFs are expected to contain the bearing fault related information, hence a new IMF selection approach proposed in this work clusters IMFs in two groups of sensitive and not so sensitive IMFs. Evaluating JRD by
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