- Original Article
- Open Access
An Intelligent Harmonic Synthesis Technique for Air-Gap Eccentricity Fault Diagnosis in Induction Motors
- De Z. Li^{1},
- Wilson Wang^{1}Email authorView ORCID ID profile and
- Fathy Ismail^{2}
https://doi.org/10.1007/s10033-017-0192-3
© The Author(s) 2017
- Received: 15 June 2017
- Accepted: 29 September 2017
- Published: 21 November 2017
Abstract
Induction motors (IMs) are commonly used in various industrial applications. To improve energy consumption efficiency, a reliable IM health condition monitoring system is very useful to detect IM fault at its earliest stage to prevent operation degradation, and malfunction of IMs. An intelligent harmonic synthesis technique is proposed in this work to conduct incipient air-gap eccentricity fault detection in IMs. The fault harmonic series are synthesized to enhance fault features. Fault related local spectra are processed to derive fault indicators for IM air-gap eccentricity diagnosis. The effectiveness of the proposed harmonic synthesis technique is examined experimentally by IMs with static air-gap eccentricity and dynamic air-gap eccentricity states under different load conditions. Test results show that the developed harmonic synthesis technique can extract fault features effectively for initial IM air-gap eccentricity fault detection.
Keywords
- Air-gap eccentricity
- Current signal
- Fault detection
- Induction motor
1 Introduction
Induction motors (IMs) are commonly used in various industrial applications. Furthermore, IMs consume about 50% of the generated electrical energy in the world [1]. IM defects will lead to low productivity and inefficient energy consumption. Endeavors have been put, for decades, to improve IM operation accuracy and IM driven industrial process efficiency. In industrial maintenance applications, for example, an efficient and reliable IM condition monitor is very useful to detect an IM defect at its earliest stage to prevent malfunction of IMs and reduce maintenance cost.
In general, air-gap eccentricity is classified as static eccentricity, dynamic eccentricity, as well as mixed eccentricity of these two types [2]. In static air-gap eccentricity, geometric axis of rotor rotation is not the geometric axis of the stator, and position of the minimal radial air-gap length is fixed in space. In dynamic air-gap eccentricity, the rotor rotates around the geometric axis of the stator, where the position of the minimum air-gap length rotates with the rotor. In a particular case of static air-gap eccentricity, rotor geometric axis is not parallel to stator geometric axis; the degree of eccentricity gradually changes along stator axis, which is inclined static eccentricity [3]. IM air-gap eccentricity defects could result in unbalanced magnetic pull, bearing damage, excessive vibration and noise, and even stator-rotor rub failure [4]. Correspondingly, this work will focus on initial IM fault detection of static eccentricity and dynamic eccentricity.
Recently, many research efforts have been undertaken to diagnose IM air-gap eccentricity fault using stator current signals due to their low cost and ease of implementation [5, 6]. For example, Blödt et al. [7] presented a Wigner distribution method to analyze stator current signals and diagnose IM eccentricity fault. Akin et al. [8] conducted real-time eccentricity fault detection using reference frame theory. Bossio et al. [9] employed additional excitation to reveal information about air-gap eccentricity fault. Alarcon et al. [10] applied notch finite-impulse response filter and Wigner-Ville Distribution to study rotor asymmetries and mixed eccentricities. Faiz et al. [11] employed instantaneous power harmonics to detect mixed IM eccentricity defect. Huang et al. [12] applied an artificial neural network for the detection of rotor eccentricity faults. Esfahani et al. [13] utilized the Hilbert-Huang transform to detect IM eccentricity fault. Nandi et al. [14] studied the eccentricity fault related harmonics with different rotor cages. Riera-Guasp et al. [15] applied Gabor analysis for transient current signals to detect eccentricity fault. Park and Hur [16] analyzed specific frequency patterns of the stator current to detect dynamic eccentricity fault. Mirimani et al. [17] presented an online diagnostic method for static eccentricity fault detection. Some intelligent tools based on soft computing and pattern classification were also used for motor fault diagnosis in Refs. [18–20], in order to explore patterns of the features. These aforementioned techniques, however, cannot thoroughly explore the relations among massive fault harmonic series in the current spectrum, which may degrade fault detection accuracy.
To tackle the aforementioned problems with IM fault detection using current signals, a harmonic synthesis (HS) technique is proposed in this work for incipient IM eccentricity fault detection. The contributions of the proposed HS technique lie in the following aspects: 1) a novel synthesis approach is proposed to integrate several fault harmonic series to recognize fault related features; 2) fault indicators are properly derived from local spectra for IM health condition monitoring. The effectiveness of the proposed HS technique for IM eccentricity defect detection is verified experimentally under different IM conditions.
The remainder of this paper is organized as follows. The proposed HS technique is discussed in Section 2. Effectiveness of the HS technique for IM air-gap eccentricity fault detection is examined experimentally in Section 3. Finally, some concluding remarks of this study are summarized in Section 4.
2 The Proposed HS Technique for IM Eccentricity Fault Detection
The proposed HS technique is composed of two procedures: harmonic series processing (HSP) and local spectra analysis (LSA). The HSP is to synthesize the fault related features in the spectrum, whereas LSA is to extract fault indicators for incipient IM air-gap eccentricity fault detection.
2.1 Harmonic Series Processing
2.2 Local Spectra Analysis
The local spectra of the first Q harmonics in Eq. (12) will be transformed to the discrete-point domain, and then synthesized into one spectrum in RMS form using Eq. (7). The mean value of the synthesized spectrum is considered as a fault indicator denoted by F _{ d1}. The fault indicator derived from Eq. (13) will be denoted by F _{ d2}.
3 Performance Evaluations
3.1 Overview
Factors and their levels
f _{ s }/Hz | P | u _{ f } | Q | M | d/Hz |
---|---|---|---|---|---|
50 | 8 | 3 | 10 | 5 | 2 |
To derive F _{ m } for eccentricity fault detection, the coefficient \(\alpha\) = 0 in Eq. (3) is set for static eccentricity detection and \(\alpha\) = 1 for dynamic eccentricity analysis. To evaluate the effectiveness of the HS technique, the power spectral density (PSD) is used for comparison. To implement PSD, the mean values of ten local bands are used as fault indicators, whose half bandwidth is set as 2 Hz. Eight of ten center frequencies of the local bands are calculated using Eq. (1) with k = 1 and \(\beta\) = 1, 2, …, 8. The other two center frequencies are computed using \(f^{\prime}_{e1}\) with k = 1 and \(f^{\prime}_{e2}\) with k = 2. In addition, a variant of the HS technique is employed for comparison, in which the center characteristic frequencies in the synthesized local spectra rather than the mean values are utilized as fault indicators, and is denoted by CHS. The frequency components in Eq. (9) with m = 1, 2, …, 8, and the two center frequencies of the synthesized local spectra derived from Eqs. (12) and (13), respectively, are used as fault indicators of the CHS method. The Hilbert-Huang transform (HHT) based fault indicators [13] will be used for comparison. Since this work focuses on the analysis of the current signal based fault indicators, only the current signal related fault indicators provided in Ref. [13] will be used for comparison. The HHT is applied to current signal analysis to generate fault indicators. The mean values of four local bands centered at \(f^{\prime}_{e1}\) with k = 1, 2, and \(f^{\prime}_{e2}\) with k = 2, 3, and averaged Hilbert marginal spectrum in local bands centered at \(f^{\prime}_{e1}\) with k = 1, and \(f^{\prime}_{e2}\) with k = 2, in the first two intrinsic mode functions (IMF), and averaged instantaneous amplitudes of the first two IMFs are used as fault indicators. The half bandwidth of these local bands in HHT is set as 2 Hz.
The HHT, CHS and the proposed HS technique generate fault indicators from the PSD spectrum. To examine if the fault indicators could be used for different classifiers, both the support vector machine (SVM) [23] and linear discriminant analysis (LDA) [24] are utilized to test the accuracy of different fault detection techniques. A series of tests have been conducted for this verification; however, the test results corresponding to five load conditions (i.e., 0, 20%, 50%, 70% and 100% load levels) will be used for demonstration. In data preparation, 200 data sets are collected for each IM condition (healthy, static air-gap eccentricity fault, and dynamic air-gap eccentricity fault) in each of five load conditions. The sampling frequency is f _{ p } = 20000 Hz and the time span of each data set is 3 s. The fault indicators of PSD, HHT, CHS and the proposed HS are extracted from these totally 3000 data sets.
3.2 Experiment Setup
Motor specifications
Phase | Poles | HP | Connection | Rotor bars | Stator slots |
---|---|---|---|---|---|
3 | 2 | 1/3 | Y | 34 | 24 |
3.3 Static Air-gap Eccentricity Fault Detection
Averaged successful rates (SR) of ten runs three-fold cross validation in terms of static air-gap eccentricity fault diagnosis using SVM (%)
Load level | 0 | 20 | 50 | 70 | 100 |
---|---|---|---|---|---|
PSD training SR | 69.71 | 65.84 | 68.23 | 65.38 | 60.46 |
PSD test SR | 65.97 | 61.49 | 65.52 | 61.66 | 53.57 |
HHT training SR | 99.26 | 72.30 | 53.20 | 52.20 | 77.27 |
HHT test SR | 98.41 | 71.59 | 48.76 | 51.20 | 74.99 |
CHS training SR | 96.18 | 81.47 | 96.68 | 96.14 | 96.17 |
CHS test SR | 94.54 | 78.92 | 95.79 | 94.73 | 95.77 |
HS training SR | 100 | 100 | 99.56 | 100 | 97.87 |
HS test SR | 100 | 100 | 99.20 | 100 | 97.28 |
Averaged successful rates (SR) of ten runs three-fold cross validation in terms of static air-gap eccentricity fault diagnosis using LDA (%)
Load level | 0 | 20 | 50 | 70 | 100 |
---|---|---|---|---|---|
PSD training SR | 73.09 | 69.41 | 68.37 | 71.07 | 68.47 |
PSD test SR | 71.63 | 67.95 | 66.60 | 69.88 | 66.32 |
HHT training SR | 93.13 | 72.94 | 66.87 | 67.92 | 77.96 |
HHT test SR | 92.42 | 71.62 | 66.05 | 66.50 | 77.15 |
CHS training SR | 95.98 | 80.79 | 96.69 | 94.47 | 93.57 |
CHS test SR | 95.78 | 79.05 | 95.90 | 93.97 | 92.83 |
HS training SR | 99.99 | 100 | 99.41 | 100 | 95.73 |
HS test SR | 99.83 | 100 | 99.10 | 100 | 95.17 |
3.4 Dynamic Air-gap Eccentricity Fault Detection
Averaged successful rates (SR) of ten runs three-fold cross validation in terms of dynamic air-gap eccentricity fault diagnosis using SVM (%)
Load level | 0 | 20 | 50 | 70 | 100 |
---|---|---|---|---|---|
PSD training SR | 84.14 | 63.21 | 60.68 | 65.44 | 61.28 |
PSD test SR | 81.82 | 60.13 | 57.11 | 60.94 | 58.41 |
HHT training SR | 82.60 | 64.22 | 58.73 | 56.52 | 60.38 |
HHT test SR | 79.99 | 60.23 | 53.67 | 52.66 | 59.30 |
CHS training SR | 94.02 | 91.14 | 85.97 | 78.27 | 75.92 |
CHS test SR | 92.30 | 88.66 | 85.71 | 75.23 | 74.66 |
HS training SR | 99.47 | 97.69 | 98.50 | 94.74 | 93.72 |
HS test SR | 98.96 | 97.13 | 97.73 | 94.53 | 92.47 |
Averaged successful rates (SR) of ten runs three-fold cross validation in terms of dynamic air-gap eccentricity fault diagnosis using LDA (%)
Load level | 0 | 20 | 50 | 70 | 100 |
---|---|---|---|---|---|
PSD training SR | 83.95 | 66.93 | 67.17 | 68.22 | 66.40 |
PSD test SR | 82.73 | 64.75 | 65.02 | 66.87 | 63.45 |
HHT training SR | 79.40 | 67.89 | 67.57 | 68.24 | 68.06 |
HHT test SR | 78.75 | 60.30 | 65.73 | 65.42 | 65.20 |
CHS training SR | 93.51 | 89.00 | 89.45 | 80.79 | 79.59 |
CHS test SR | 92.88 | 87.73 | 88.82 | 79.67 | 78.17 |
HS training SR | 99.02 | 95.99 | 96.27 | 94.67 | 91.78 |
HS test SR | 98.98 | 95.43 | 95.47 | 93.87 | 91.35 |
4 Conclusions
A harmonic synthesis (HS) technique is proposed in this work for initial IM air-gap eccentricity fault detection. In the HS, the fault harmonic series are synthesized to enhance fault characteristic features. The local spectra statistical analysis is employed to extract representative features. The SVM classifier and the LDA classifier are utilized to evaluate the performance of different fault detection techniques. The effectiveness of the proposed HS technique is verified by a series of experimental tests under five load conditions: 0%, 20%, 50%, 70% and 100%. Test results show that the proposed HS technique is an effective fault detection tool, and it outperforms the other techniques in all five load conditions. It is able to process massive fault related information, analyze fault features statistically, and enhance representative features for static eccentricity and dynamic eccentricity fault diagnosis based on the current signals. Future research will be undertaken on classification of health state, static eccentricity state and dynamic eccentricity state altogether, as well as the analysis of stochastic resonance based fault detection.
Notes
Declarations
Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
Authors’ Affiliations
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