An Intelligent Harmonic Synthesis Technique for Air-Gap Eccentricity Fault Diagnosis in Induction Motors

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.

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.

2.2 Local Spectra Analysis

The mth harmonic (\(\beta\) = 2 m–1) of the Kth order fault harmonic series will be derived from Eq. (2),

$$f_{K,m} = f_{o\_K} + \left( {2m - 1} \right)f_{s}$$

(8)

Through the synthesis operation in Eq. (7), the mth fault harmonic over all M harmonic frequency bands is synthesized to form a new fault frequency component. Then the mth synthesized fault frequency component in the discrete-point domain will be derived in the synthesized spectrum by the following representation:

$$v\left\{ {1 + \left( {2m - 1} \right)f_{s} u_{f} } \right\}$$

(9)

The local spectra encompassing the mth synthesized fault frequency component will be

$$\left[ {v\left\{ {1 + \left( {2m - 1} \right)f_{s} u_{f} - du_{f} } \right\}, \, v\left\{ {1 + \left( {2m - 1} \right)f_{s} u_{f} + du_{f} } \right\}} \right]$$

(10)

where d is the half bandwidth of the local spectra in the frequency domain. The mean value of this local spectrum is the fault indicator regarding the mth synthesized fault frequency component, denoted by F _m .

To illustrate the operation of the proposed HSP and LSA processes, a simulated current spectrum with three air-gap eccentricity frequency harmonic series is illustrated in Figure 1. It is normalized by deducting mean and then being divided by its standard deviation. In Figure 1, the black arrow points 50 Hz supply frequency; magenta arrows with number 1, green arrows with number 2 and yellow arrows with number 3 denote three fault harmonic series respectively. The origin frequency components \(f_{o\_K}\) are 114.1 Hz, 142.4 Hz, and 170.7 Hz, respectively. The harmonics of defect features are computed using Eq. (2) with f _s  = 50 Hz and \(\beta\) = 1, 3, 5, 7, 9. Figure 1 shows that some fault characteristic frequency components are buried in the spectrum, and it is difficult to predict which characteristic frequency components will protrude in the spectrum. The extracted frequency bands represented in Eq. (6) of three fault harmonic series, and synthesized spectrum represented in Eq. (7) with fault related local spectra are demonstrated in Figure 2. The dashed vertical lines indicate the boundaries of local spectra encompassing synthesized fault frequency components. Figures 2(a), 2(b) and 2(c) represent three frequency bands computed by Eq. (4) with staring frequencies \(f_{o\_K}\) being 114.1 Hz, 142.4 Hz, and 170.7 Hz, respectively. Figure 2(d) shows results of the synchronization of spectra in Figures 2(a), 2(b) and 2(c) using root-mean-square calculation using Eq. (7). It is seen from Figure 2(d) that the fault characteristic features can be highlighted in the spectrum after the HSP operation, which could be used for IM fault detection. In this simulation, the supply frequency f _s  = 50 Hz; \(f_{o\_K}\) is the starting point of the spectrum in Figure 2(d). Based on Eqs. (2) and (3), the fault frequencies in Figure 2(d) should appear at 50 Hz, 150 Hz, 250 Hz, 350 Hz and 450 Hz. The frequency components outside the boundaries of local spectra are usually caused by the modulation of load variation and supply frequency, and the synchronization of different harmonic series local bands.

If both static and dynamic eccentricities occur simultaneously, the following characteristic frequency components could also be excited [22], given by

$$f^{\prime}_{e} = \left| {kf_{r} \pm f_{s} } \right|,\quad k = 1,{ 2},{ 3}, \, \ldots$$

(11)

The related harmonic series can be expressed as

$$f^{\prime}_{e1} = kf_{r} + f_{s} ,\quad k = { 1},{ 2},{ 3}, \, \ldots$$

(12)

$$f^{\prime}_{e2} = kf_{r} - f_{s} ,\quad k = { 2},{ 3}, \, \ldots$$

(13)

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.

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.