Advanced Diagnosis of Air Gap Eccentricity in Three-Phase Induction Motor Using DWT Decomposition and AI Techniques

Electrical machines, like any mechanism, are prone to undesirable sudden breakdowns that may hinder the industrial process from functioning properly. This could lead to critical economic losses and, in some cases, may endanger the operating personnel due to hazardous threats that the breakdowns may cause.

The importance of three-phase induction motors (IM) across various industries is due to their ability to generate high motive power, their durability, and their low maintenance costs. These motors serve as the primary mover in about 90% of industrial equipment worldwide, highlighting their crucial role in industrial operations [1].

Induction machine faults have been diagnosed using various frequency analysis methods, including fast Fourier transform (FFT), power spectrum estimation, and envelope spectrum analysis [2]. The disadvantage of this technique is based on the fact that it requires that the signal being processed is stationary and linear and that the rotational speed has transient mode, which represents a limitation by this technique. Therefore, to mitigate this obstacle a Time-Frequency analysis is performed such as Short Fast Fourier Transform (STFT) [3], the premise of this technique is based on the FFT method with applying a sliding window to enhance the frequency resolution. However, the limitation of this method is the fixed size of the window which is not practical with the transient nature of the signal. Another method is being applied for this regard, Wigner-Ville distribution (WVD) [4] which delivers better frequency resolution under the same conditions, another drawback of this approach is the generation of undesirable large frequencies. Empirical mode decomposition (EMD) [5-7] on the other hand, is a self-adaptive approach, which produce a series of intrinsic mode functions (IMFs) and with the help of the Hilbert Transform (HT) [8], it can estimate instantaneous frequencies, but its limitation resides on the generation of undesirable negative frequencies. Wavelet Transform (WT) delivers an enhanced frequency resolution results thanks to its local frequency-time domain properties [9].

This work’s focus orbits around the combination of signal processing through Discrete Wavelet Transform (DWT) decomposition of the stator current signal and an Artificial Intelligence (AI) driven model that utilizes the denoised data signal and through a meticulous study of the decomposed levels, the most suitable frequency detail band level was chosen to be used for feature extraction by using both of energy distribution analysis and RMS values, both of these factors will be introduced as inputs for machine learning algorithms such as Support Vector Machine (SVM) and Decision Trees (DT).

1.1 Related works

Widagdo et al. [10] mentioned that failures due to air gap eccentricity are predicted by decomposing the leakage flux spectrum waveform using discrete wavelet transform. This method was tested using the leakage flux data from a 1.5 Kw induction motor. Experimental results validated the effectiveness of this approach in detecting eccentricity failures.

Nikhil et al. [11] used various indices to detect eccentricity are introduced, along with their boundary conditions and potential areas for future research. Finally, the merits and demerits of each index are discussed, and a comparison is made between them.

Rouaibia et al. [12] introduced two methods for diagnosing and detecting eccentricity faults, as well as evaluating their severity, by monitoring stator current signals. The approaches use the Park vector method and DWT to differentiate between healthy and faulty machine conditions. The simulation results obtained through these techniques enable the detection and diagnosis of eccentricity faults and their severity.

Laala et al. [13] presented a contribution in the classification of a vibration signal for bearing fault, where wavelet packet decomposition (WPD) and multi-layer perceptron (MLP) were combined. At first, the most suitable component to bearing defect was used as a fault indicator. Then, feature extraction was used for the classification by MLP algorithm.

To mitigate the limitation of FFT technique when dealing with non-stationary signal, WT delivers a robust time-frequency domain analysis for both stationary and non-stationary signals, and among its tools DWT is the most efficient technique in terms of computational capabilities which gives more accuracy when dealing with non-stationary signal and especially at low frequency [22, 23]:

$D W T(J, k)=\frac{1}{\sqrt{2^J}} \int_{-\infty}^{+\infty} x(t) \psi^*\left(\frac{t-k \cdot 2^J}{2^J}\right) \mathrm{d} t=2^{\frac{-J}{2}} \psi\left(2^{-J} \cdot t-k\right)$                   (2)

DWT relies on the decomposition of the raw signal back to its constituent point (scales), which give us an information about the frequency band at a particular time frame.

DWT is conducted through a sequential operation using a high-pass filters H (details) and through a series of low-pass filters L (approximations).

Figure 4 shows the decomposition process of DWT starting from raw signal until getting subsignals.

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Figure 4. DWT decomposition process

Raw signal x(t) is devided into two ports, the first one contain the high frequency band, and the second one low frequency band, both of them are combined for the decomposition and the reconstruction of the original signal [24, 25].

The low frequency part called approximations (A_j) contains the low-frequency information of the original signal belong to [0, fs×2–(j+1)]. The high-frequency part called detail (D_j) contains high frequency information included in the interval [fs×2–(j+1), fs×2–j]. Practically, the DWT decomposition at level N of signal x(t), giving rise to one approximation coefficient vector AN and N detail coefficient vectors D_j are expressed by [26, 27]:

$x(t)=A_N(t)+\sum_{j=1}^N D_j(t)$            (3)

It can be shown that the approximation and detail coefficients can be recursively calculated by:

$A_{j, k}=\sqrt{2} \sum_{-\infty}^{+\infty} L[n] A_{j-1,2 k+n}$             (4)

$D_{j, k}=\sqrt{2} \sum_{-\infty}^{+\infty} H[n] A_{j-1,2 k+n}$                (5)

Before getting into the mother wavelet function selection, it is mandatory to choose the number of decomposition levels that are suitable to cover all of the details and approximations frequency range, which can be determined by the following equation:

$\frac{f_s}{2^{N+1}} \leq f_e$               (6)

where, f_e which is the fundamental frequency, and f_s is the sampling frequency set to f_s=10KHz.

3.1 Time-frequency domain analysis

The first step of the research is to perform a full decomposition of the stator raw current signal, and to achieve this 1-D DWT decomposition was used up to 12 levels to cover all the ranges of frequency bands of both approximations and details by using debauchees -24 as the mother wavelet function and the sampling frequency was set to 10KHz. Full decomposition results for both healthy and air gap irregularity current signals were collected to be compared later on (Figure 5).

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Figure 5. DWT signal decomposition and reconstruction

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(a) Decomposition levels of a healthy signal

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(b) Decomposition levels of a faulty signal

Figure 6. Full decomposition of stator current

Till the present day, there’s no specific rule that dectates the choice of a specific mother wavelet. However, through various deep studies it was noticed that Debauchees mother wavelet povides more stability and a robust reconstruction of the original signal with maintaining information since it locates less in time with less oscillation due to its dilation nature, which makes it practical for the diagnosis of induction machine [28]. Figure 6 shows the complete decompostion usnig DWT of raw current signal for healthy and faulty machines.

After analyzing the obtained results of the full decomposition for both approximation and detail frequencies in healthy and faulty condition, we can notice that air gap irregularity manifests some changes in high frequency (detail frequency) band [1000-5500Hz] and they’re more visible in levels 4, 5 and 6, which can deliver a promising comparison opportunity, further results are discussed thoroughly in the next section.

Three decomposition levels were selected since they show promising characteristic comparison and contain inherent frequency that characterize air gap defect which are levels 4, 5 and 6th level of detail decomposition illustrated in Figure 7.

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(a) Healthy detail frequency levels

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(b) Faulty detail frequency levels

Figure 7. Detail levels 4, 5 and 6

5.1 Support vector machine (SVM)

SVM branches out from machine learning models under supervised learning algorithms by performing a linear classification for a multiclass dataset. It provides great generalization abilities even when dealing with a small number of dataset samples [29]. Its architecture is shown in the Figure 9 [30], the margin in this structure is the distance between the decision boundaries and the support vectors, while the latter contains the group of data samples that are approximate to decision boundary which represents a hyperplane of the linear classification [31].

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Figure 9. SVM basic architecture

The decision boundary is determined by the following equation:

$\mathrm{d}(\mathrm{x})=\mathrm{w} x_i+\mathrm{b}$            (8)

where, w is the weight vector, x_i is the input data and b is the bias.

The distance of the margin can be obtained as follows:

$\operatorname{margin}=\frac{2}{\|w\|}+\mathrm{C} \sum_{i=1}^n \xi_i$                 (9)

In case of misclassification where the data can’t be linearly classified ξ is the variable slack that can adjust the rate of misclassification, C is a parameter defined by the user, the higher this parameter’s value, the lower the degree of misclassification.

5.2 Decision trees

Decision Trees (DT) is one of the strongest classification algorithms and used in many fields [32], it effectively unites a series of basic test, the construction of conceptual rules are easier in comparison with the numerical weights which are used in neural networks of connections between nodes [33, 34]. Each one of the trees compose the branches and the nodes, those nodes each one of them represents a feature that would be classified, the value taken by the node is defined by each subset. Figure 10 shows how decision trees algorithm works starting with the root node responsible for dividing into decision nodes 

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Figure 10. DT process

After applying the proposed methodology, it becomes evident that using DWT decomposition for the purpose of employing energy dissipation levels and RMS values as fault indicators combined with machine learning, proved reliable for the classification of air gap eccentricity and can serve quite effectively the purpose of monitoring task for this type of defects in induction machine.

The task for choosing the best classifier for the detection of air gap irregularity went through training various models and the best models in terms of accuracy of detection were SVM with an overall 70% accuracy and DT classifier with 100% accuracy.

The main challenge lies in providing more complex data in terms of harmonics and noise in the signal which would render the detection more challenging and would require introducing other models with more specific settings for the hyperparameters. Therefore, the upcoming work will focus on using more features for fault classification and introducing more severity degrees in hope of achieving a global diagnosis process with maintaining a strong monitoring capability.