An improved combination of Hilbert and Park transforms for fault detection and identification in three-phase induction motors

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Abstract

In this work we propose an original fault signature based on an improved combination of Hilbert and Park transforms. Starting from this combination we can release two fault signatures: Hilbert modulus current space vector (HMCSV) and Hilbert phase current space vector (HPCSV). These two signatures are subsequently analyzed using the classical fast Fourier transform (FFT). The effects of HMCSV and HPCSV spectrums are described and the related frequencies are determined. A comparative study is presented of the suggested signature (HPCSV) and the MCSA which is the signature more recently proposed in the literature. The proposed signature shows its effectiveness and its robustness in both electrical and mechanical fault detection. The magnitudes of spectral components relative to the studied faults are extracted in order to develop the input vector necessary for the pattern recognition tool based on support vector machine (SVM) approach with an aim of classifying automatically the various states of the induction motor. This approach was applied to a 1.1 kw induction motor under normal operation and with the following faults: unbalanced voltage, broken rotor bar, air-gap eccentricity and outer raceway ball bearing defect.

Highlights

► Original fault signature using an improved combination of Hilbert and Park transforms is proposed. ► The proposed fault signature shows its effectiveness and its robustness in both electrical and mechanical fault detection. ► Support vector machine approach is used in order to classify automatically the various machine conditions.

Introduction

Induction motors are nowadays extensively used in all types of industry applications due to their simple construction, reliability, and the availability of power converters using efficient control strategies. In this way, early fault detection and diagnosis allow preventative and condition-based maintenance to be arranged for the electrical machines during scheduled downtimes and prevent an extended period of breakdown due to extensive system failures. For the fault detection problem, it is interesting to know if a fault exists in the system via online measurements. For the fault diagnosis one, it is not only worthwhile to detect if the system has a fault but also to insulate the fault and to find its origin [1].

Although induction machines are failures subjected which are inherent to the machine itself or due to external environment. The origins of inherent failures are due to the mechanical or electrical forces acting in the machine enclosure. Researchers have studied a variety of machine faults, such as winding faults [2], voltage unbalance [3], [4], broken rotor bars [5], eccentricity [6], and bearing faults [7].

Various methods for induction motor fault detection have been reported in the literature. In [8], an online induction motor diagnosis system using motor current signature analysis (MCSA) with advanced signal processing algorithms is proposed. In [9], authors propose a method based on monitoring certain statistical parameters estimated from the analysis of the steady state stator current. The approach is based on the extraction of the signal envelop by Hilbert transformation, pre-multiplied by a Tukey window to avoid transient distortion. In [10], authors use a sliding window constructed by Hilbert transform of one current phase and the fault severity is diagnosed by motor current signature analysis (MCSA) of the stored Hilbert transform of several periods.

Besides the traditional current signature analysis based on one-phase current spectrum lines, the procedures based on the analysis of the harmonics at fault frequency in the spectrum respectively of instantaneous power, space vector current modulus and electromagnetic torque are presented in [11]. In [12], a method based on Park’s vector approach for bearing fault detection using three-phase stator current analysis is presented. In [13], author describes the use of the Extended Park’s Vector Approach (EPVA) for diagnosing the occurrence of stator winding faults in operating three-phase induction motor. In [14], the authors take the initial step to investigate the efficiency stray flux monitoring for induction motor fault diagnosis. The effects of stray flux spectrum are described and the related frequencies are determined.

Several researchers have used the artificial intelligence tools in order to classify faults in electrical power systems. In [15], authors propose an approach to obtain objective function using the Hebb’s learning rule. The continuous genetic algorithm optimization method is used to estimate the fault section making use of the objective function. A comparison with artificial neural network approach is also presented. In [16], the pattern classification technology and linear discrimination principle of pattern recognition theory are used in order to identify the fault components and fault sections, and eventually accomplish fault isolation.

In this work we propose an original fault signature based on an improved combination of Hilbert and Park transforms. Starting from this combination we can release two fault signatures: Hilbert modulus current space vector (HMCSV) and Hilbert phase current space vector (HPCSV). These two signatures are subsequently analyzed using the classical fast Fourier transform (FFT). A comparative study is presented of the suggested signature (HPCSV) and the MCSA which is the signature more recently proposed in the literature. The magnitudes of the HPCSV spectral components relative to the studied faults are extracted in order to develop the input vector necessary for the pattern recognition tool based on support vector machine (SVM) approach with an aim of classifying automatically the various states of the induction motor.

This approach was applied to a 1.1 kw induction motor under normal operation and with the following faults: unbalanced voltage, broken rotor bar, air-gap eccentricity and outer raceway bearing defect.

Section snippets

Basic theory of the proposed fault signature

The basic idea is instead of using directly the three lines currents to calculate the park vector, we only employ useful information immersed in these currents. For this reason we apply the Hilbert transform to the three line currents. Indeed Hilbert transform is used to acquire the instantaneous frequency and instantaneous amplitude. It reveals modulation in signals caused by faulty components. In addition, it removes carrier signals and this will reduce the influence of irrelevant information

Basic theory of the SVM

The basic concept of the SVM is detailed in [17]. SVM analysis seeks to find an optimal separating hyper-plane by maximizing the margin between the separating data.

The regression approximation estimates a function according to a given data set T={xk,yk}km, where xk denotes the input vector, yk ϵ {−1; 1} denotes the corresponding output value and m denotes the total number of data patterns, the SVM regression function is:f(x)=w.x+b=k=1mwk.xk+b=0where w denotes the weight vector and b denotes the

Test bench description

The test motor used in the experimental investigation was a three-phase 50-Hz, four-pole, 28 rotor bars, 1.1-kW induction machine (Fig. 2a). The induction machine shaft is mounted with a powder brake in order to simulate different level of load torque during the tests.

The studied faults are: broken rotor bar, unbalanced voltage, one air-gap eccentricity and the outer raceway ball bearing defect.

The machine with broken rotor bar is faulted by drilling a hole on all its depth. Stator voltages

Conclusions

An original fault signature based on an improved combination of Hilbert and Park transforms has been proposed. Starting from this combination, two fault signatures have been realized: Hilbert modulus current space vector (HMCSV) and Hilbert phase current space vector (HPCSV). These two signatures are subsequently analyzed using the classical fast Fourier transform (FFT). The effects of HMCSV and HPCSV spectrums are described and the related frequencies determined. A fault sensitivity

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