This paper presents an improved gearbox fault diagnosis approach by integrating complementary ensemble empirical mode decomposition (CEEMD) with permutation entropy (PE). The presented approach identifies faults appearing in a gearbox system based on PE values calculated from selected intrinsic mode functions (IMFs) of vibration signals decomposed by CEEMD. Specifically, CEEMD is first used to decompose vibration signals characterizing various defect severities into a series of IMFs. Then, filtered vibration signals are obtained from appropriate selection of IMFs, and correlation coefficients between the filtered signal and each IMF are used as the basis for useful IMFs selection. Subsequently, PE values of those selected IMFs are utilized as input features to a support vector machine (SVM) classifier for characterizing the defect severity of a gearbox. Case study conducted on a gearbox system indicates the effectiveness of the proposed approach for identifying the gearbox faults.
Gears can be considered as significant subassembly in machines for power or rotation transmission from one shaft to another. Their fault may cause unexpected breakdown of the machine systems and lead to significant economic loss or even personnel casualties [
Aiming at avoiding restrictions of conventional techniques, permutation entropy (PE) is used to characterize vibration signals for the purpose of fault diagnosis. The PE only uses the order of entropy for signal characterization and can overcome nonlinear distortion which existed in the signal. It has been applied in various applications. For instance, permutation entropy is proved to offer an efficient evaluation to monitor rolling bearings [
Empirical mode decomposition (EMD), as an approach of adaptive signal treatment in the field of time frequency analysis, can decompose a signal into sets of intrinsic mode functions (IMFs) based on its features [
By making full use of characteristics of the PE and CEEMD, this paper proposes a hybrid approach to diagnose gearbox faults. The CEEMD is utilized as the preprocessing to filter signals and extract IMFs that are closely associated with the filtered signal. Subsequently, PE value of each chosen IMF would be calculated. The PE value of the chosen IMFs is utilized as the feature vector to a classifier in which the support vector machine (SVM) is applied for identifying gearbox defect. The remaining parts of this paper are arranged as follows. Overview of the gearbox fault diagnosis approach is shown in Section
CEEMD is developed based upon EEMD. Originally, the EMD approach deals with a given signal
Later, Huang et al. have proposed a noise-guided statistical approach to resolve the mode mixture issue, which is the ensemble empirical mode decomposition. However, the effect of the additional noise could only be restricted by a large amount of ensemble mean computation, causing high computational load.
Complementary ensemble mode decomposition, as an improved and noise enhanced data analysis approach, has been developed for reducing computational burden [
A pair of white Gaussian noises with the same amplitude is added to
Decompose
The final IMF which is the ensemble of
Specifically, a simulated signal
The simulated signal.
The decomposition result by CEEMD.
Through comparing the result in Figure
PE is a nonlinear dynamic parameter that characterizes a signal’s complexity. Based on the principle of Takens-Maine, the phase space of time series
If
If all the symbol sequences appear with the same possibility distribution as
To demonstrate the validity of the PE algorithm, sample vibration signals of a gearbox under three different conditions are shown in Figure
Gearbox vibration signals under various operating conditions.
Boxplot of PE values on normal condition (NC), slight fault condition (SC), and catastrophe fault condition (CC).
In this study, a gearbox fault diagnosis method has been developed using the CEEMD and PE, and Figure
Flow chart of the proposed method.
The sampled vibration signal measured on gearbox is decomposed using CEEMD.
The product
The correlation coefficients between each IMF and filtered signal are calculated by (
The PE values of all the chosen IMFs are calculated to generate a feature vector which can be utilized to train the SVM for identification of gearbox operating condition.
The PE feature vector from test gearbox vibration signal is extracted and utilized as input to the well-trained SVMs. In this way, the result of classification can be realized [
A series of gearbox fault signals acquired from LC5T81 type transmission were used to verify the effectiveness of the presented approach. The data was measured from the testbed presented in Figure
The automobile transmission gearbox.
Structure of the gearbox
The gearbox setup
The waveforms of the vibration signals collected from the test gearbox under three conditions are shown in Figure
Vibration signal waveforms of the gearbox under different conditions.
Normal condition
Light fault condition
Severe fault condition
Figure
Correlation coefficients between filtered signals and each IMF.
Correlation coefficient | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|
IMF 1 | IMF 2 | IMF 3 | IMF 4 | IMF 5 | IMF 6 | IMF 7 | IMF 8 | IMF 9 | IMF 10 | |
Normal condition | 0.5235 | 0.7648 | 0.4783 | 0.4284 | 0.4036 | 0.1092 | 0.0971 |
|
|
|
Light fault condition | 0.8594 | 0.4635 | 0.3582 | 0.2347 | 0.1921 | 0.0925 |
|
|
|
|
Severe fault condition | 0.9219 | 0.2578 | 0.2215 | 0.1937 | 0.1625 | 0.0859 |
|
0.0008 |
|
0.0007 |
The decomposition result by CEEMD under different conditions.
Normal condition
Light fault condition
Severe fault condition
It can be seen from the table that correlation coefficients for the first 5 IMFs are all more than 0.1. They can describe the main features of the signal and thus are selected for further analysis. According to the main steps of the presented fault diagnosis approach, the permutation entropy values of these IMFs are calculated, as listed in Table
Permutation entropy values of IMF 1
Permutation entropy value | |||||
---|---|---|---|---|---|
IMF 1 | IMF 2 | IMF 3 | IMF 4 | IMF 5 | |
Normal condition | 0.958 | 1.239 | 0.782 | 0.837 | 0.5036 |
Light fault condition | 0.710 | 0.859 | 0.518 | 0.421 | 0.8421 |
Severe fault condition | 0.539 | 0.709 | 0.876 | 0.659 | 0.2625 |
In the experiment, 120 feature vectors in total were gained from three different circumstances. 50% of the feature vectors were applied into classifier training, while the rest of them were used in classification of fault. Table
Fault diagnosis using improved approach based on CEEMD and PE.
Fault type | Test sample | Classification results |
Classification |
Overall classification | ||
---|---|---|---|---|---|---|
Normal condition | Minor fault condition | Serious fault condition | ||||
Normal condition | 20 | 20 | 0 | 0 | 100 | |
Light fault condition | 20 | 1 | 18 | 1 | 90 | 95 |
Severe fault condition | 20 | 0 | 1 | 19 | 95 |
For purpose of comparison, the values of approximate entropy (ApEn) from the chosen IMFs are also calculated and applied in the SVM classifier. Table
Fault diagnosis using the approach based on CEEMD and ApEn.
Fault type | Test sample | Classification results |
Classification |
Overall classification | ||
---|---|---|---|---|---|---|
Normal condition | Minor fault condition | Serious fault condition | ||||
Normal condition | 20 | 19 | 0 | 1 | 95 | |
Light fault condition | 20 | 1 | 17 | 2 | 85 | 88.3 |
Severe fault condition | 20 | 1 | 2 | 17 | 85 |
To further study the effectiveness of the developed approach, a 10 × 10-fold cross validation procedure is employed with the selected 120 samples. The average classification rate of the 10 × 10-fold cross validation is 94.82%. The result is close to the classification result in Table
This study develops an integrated approach by combining PE algorithm with CEEMD to diagnose gearbox faults. With the CEEMD, gearbox vibration signals can be decomposed into sets of IMFs with low computational load. Then PE method can efficiently extract fault characteristic from the selected IMFs. Without mathematical model and the study of the fault mechanism of the system, this developed approach can directly recognize gearbox fault severity. Furthermore, the CEEMD, as a preprocessing step, can be utilized to purify the signal for PE calculation, leading to increased classification rate (e.g., 95% for experimental data). It is envisioned that the approach developed in this study could be used in a wide range of applications in the field of fault diagnosis.
The authors declare that there is no conflict of interests regarding the publication of this paper.
This paper is supported by the Nature Science Foundation of Jiangsu Province of China (no. BK2012739) and the National Natural Science Foundation of China (no. 61101163 and no. 51175080).