Stator Current Bi-Spectrum Patterns for Induction

Stator Current Bi-Spectrum Patterns for Induction Machines Multiple-Faults Detection L. Saidi (1), (2),

F

Fnaiech (1),

G-A

Capolino (2) and H, Henao (2)

(I)

University of Tunis, Ecole Superieure des Sciences et Techniques de Tunis, 5, Avenue Taha Hussein, 1008 Tunis - Tunisia (2) University of Picardie "Jules Verne", Department of Electrical Engineering, 7, rue du Moulin Neuf, 80000 Amiens - France E-mail: fnaiech@ieee, org

Ahstract- Inspecting the literature, the most used techniques proposed for induction machines diagnosis are focused

on

detecting single faults. There is a lack of works dealing with the diagnosis and identification of multiple combined faults. In this framework, this paper presents the stator current bi-spectrum analysis to detect two types of faults mixed together which may appear

in

three

phase

induction

motors.

Based

on

real

experimental data, the detection study concerns isolated rotor broken bars and damage in the bearing's inner race rolling element.

For

multiple

faults

detection,

and

for

lack

of

experimental data, only synthetic data are used. To deal with the frequency analysis, a mathematical model of the stator current has been derived and used into the bi-spectrum formulas. The main

contribution

of

this

paper

is

the

development

of

a

theoretical method which may help the user to assess the presence of fault frequencies in induction motors in both settings namely single or multiple combined faults. To highlight the superiority of the bi-spectrum tool over the spectrum, receiver operating characteristics (ROC) analysis has been carried out. Therefore,

simulation

results

are

performed

in

noisy

environment showing that the bi-spectrum is able to detect frequency faults better.

Index Terms--Bearings, bi-spectrum analysis, receiver operating characteristics (ROC), rotor broken bars, higher order spectra, multiple-fault diagnosis.

I.

INTRODUCTION

Condition monitoring (CM) of induction motors (IMs) have been a challenging task for the engineers and researchers mainly in industrial applications [1], There are many CM techniques, including vibration monitoring, chemical and wear debris monitoring, thermal monitoring, acoustic emission monitoring but all these monitoring methods require expensive sensors or specialized tools and not always simple to be performed; whereas current monitoring out of all does not require additional sensors [1], [2], Current monitoring techniques called motor current signature analysis (MCSA) are usually applied to detect various types of IMs faults such as broken rotor bars (BRBs), short winding, air gap eccentricity, bearing defects (BDs), and unbalance or gearboxes failures. Among of MCSA techniques, spectral analysis is highlighted due to the low cost-to benefit rate obtained from its implementation [3].

978-1-4673-2421-2/12/$31.00 ©2012

IEEE

Moreover, in most cases these failures are treated separately. For instance, in [4], a method based on multiple signal classification (MUSIC) has been proposed to improve diagnosis of BRBs fault in IMs, by detecting a large number of frequencies in a given bandwidth. This method is called zoom-MUSIC. In [5], because the accurate slip estimation needs advance signal processing, in order to localize the side­ band frequencies around the fundamental in the stator current spectrum. A new technique of broken bar fault detection based on discrete wavelet transform without slip estimation is proposed. In [6] a new method for detecting BDs based on the exploitation of the instantaneous power factor that varies according to torque oscillations, is presented. However, in many applications, the harmful characteristics of the stator current to be analyzed (e.g., nonlinearity, low signal-to-noise ratio (SNR), etc.) may affect the obtained power spectrum results. In addition, the main drawback of power spectrum analysis is the removal of all phase information. Hence, it cannot handle the identification of sets of phased-coupled signals [3], All these proposed methods have been used and restricted to isolated fault detection of a single stator current or a mechanical signal. In order to analyze mixed signals and to overcome the problem of phase information removal, advanced signal processing techniques are required such as higher-order statistics. For instance, the bi-spectrum tool is a bi-dimensional frequency representation capable of detecting nonlinear harmonic interactions and its corresponding phase. Indeed the bi-spectrum is one of the recent signal processing techniques, through which better practical results have been recorded in CM of IMs [7]-[10]. Then, the amplitude or frequency modulation processes that exhibits in the analysis of stator current produced by bar breakages in IMs or defective bearing's rolling element makes possible to deduce that bi­ spectrum is suitable to be applied [3]. Recently, the bi-spectrum and its diagonal slice for the detection of bar breakages in IMs are successfully used in [7]. These techniques are compared with the power spectrum

5132

showing their superiority in induction motor diagnosis when the machine operates at low level of shaft load. In [8] the twice slice of cyclic bi-spectrum (CBS) is used for the detection of BDs. This method inherits the advantage of the CBS, and is not sensitive to noise. In addition, twice slice of CBS is more direct and clearly to show the features for diagnosis purpose. In [9], an amplitude-modulation detector using bi-coherence (normalized bi-spectrum) is developed to detect incipient defects in the outer race before their characteristic fault frequencies become significant in the power spectrum. In [10], a new promising technique to detect generalized roughness BDs seems to be the spectral kurtosis (SK) applied to both vibration and current analyses. The SK is a spectral descriptor that is able to detect and characterize transients in a signal, to discover the presence of hidden nonstationarities, and to identify in which frequency ranges these occur. In [11], the combination of cyclostationary and higher order statistics analysis methods is presented. This combination exhibits better results, in terms of bearing status identification. In real IMs two or more faults can occur in the same time. In the literature, a reduced number of works deal with the diagnosis and identification of multiple combined faults. For instance, in [12], neural networks and fuzzy logic are combined together for the detection of stator inter-turn insulation and bearing wear faults in single-phase induction motor. In [13], a hardware methodology implementation method is proposed, which merges information entropy analysis with fuzzy logic inference to identify faults like BDs, unbalance, BRBs, and combinations of faults by analyzing induction motor current signal. In [14], a condition­ monitoring strategy for accurate assessments of the presence of specific fault conditions in induction motors with single or mixed faults is proposed. This method combines a finite impulse response filter bank with high-resolution spectral analysis based on MUSIC for an accurate identification of the characteristic frequencies fault. In. [15], the authors present a diagnosis method for detecting four combined faults (rotor asymmetries, mixed eccentricities, interturn, and intercoil stator short circuits) based on the application of the discrete wavelet transform to the startup current, requiring the interpretation of the current signature along the wavelet decomposition. This paper attempts to present recent results on the application of higher-order spectra (HaS) based on signal processing techniques, namely the bi-spectrum exploited in CM. Particular emphasis is placed on the development of analytical models used for the interpretation and the identification of fault frequency pairs characteristics (called bi-frequency patterns). The stator current is thus used to build the bi-spectrum, in single and multiple-faults conditions. Such bi-frequency information is necessary to classify different faults in IMs. This paper is organized as follows: Section II provides the

Dc

Fig.I. Geometry of rolling element bearing [6].

BRBs and BDs current signature analysis and Section III gives a brief development of the basic bi-spectrum theory. Theoretical and experimental results are discussed in section IV. In Section V we introduce ROC curves for comparing the two HaS techniques namely the power spectrum and the bi­ spectrum. Section VI presents the conclusions and further proposed works regarding this method. II.

FAULTS SIGNATURES

Two different electromechanical faults are considered in this paper; BRBs, and inner race BDs. 1.

Broken rotor bars fault signatures

Rotor failures account for 5-10% of total IMs failures [1], [2]. The detection of BRBs faults can be done by the inspection of the frequency components (tEREs) in the current spectrum as a fault indicator, fliNlis

=

[(; J

(I

-

s) ± s

]

II

(1)

where f.. is the supply frequency, p is the number of pole pairs, k is an integer and s is the rotor slip. By considering the speed ripple effects, it has been reported that other frequency components, may be observed in the stator current spectrum and may be determined by the following additional equation [1], [2]: fEREs = (1± 2ks )II (2) 2.

Bearing defects signatures

BDs represent about 40% among the most frequent faults in IMs [I], [2]. The bearings consist mainly of the outer and inner raceways, the balls, and the cage as shown in Fig. I. BDs can be classified into two classes: single-point defects and generalized roughness [17]. Single-point defects are localized and classified into, • Outer raceway defect; • Inner raceway defect; • Ball defect. Generalized roughness is a type of fault where the condition of a bearing surface has degraded considerably over a large area and become rough, irregular, or deformed. These faults may enhance vibration and noise level [2]. Moreover, there are internal operating stresses caused by vibration, eccentricity, and bearing current. Additionally, bearings can also be affected by other external causes such as: • Contamination and corrosion;

5133

Lack of lubrication causing heating and abrasion; • Defect of bearing's mounting, by improperly forcing the bearing onto the shaft or in the 1M's stand. The single-point defect may be seen by fault frequencies appearing in the machine vibration spectrum record. The frequencies at which these components occur are predictable and depend on the surface on which the bearing contains the fault. Therefore, there are different fault frequency characteristics associated with each component among the four parts of the bearing [15], [16]. These frequencies are: ft: inner race fault frequency, fo: outer race fault frequency,fc: cage fault frequency andftl: ball fault frequency, their mathematical equations are as follows: •

1. = o

1r 2

N

b (1

Db

cos fJ)

D

(3)

c

(4) (5)

correlation of the data and is given by * B(!; , 12) = E { X (j;)X (f2)X (j;+ f2)}

(8)

fl h are the frequency indices. ' where X denotes the complex conjugate of X and X (f) is .•.

the Fourier transform of the discrete signal x(n) and E {.} is an average over an ensemble of realizations of a random signal. For deterministic signals, the relationship holds without an expectation operation with the third order correlation being a time-average. In the sequel, the bi-spectrum plots are depicted in 2D space of coordinates lfl h) and the amplitude will be represented in ' dB scale by a color-bar. The bi-spectrum exhibits many symmetries including Blfl, h)= Blf2, fl); therefore, it is not necessary to compute every frequency pair. For interested readers, a good review of bi-spectrum symmetries and its region of computation are provided in [18]-[19]. In addition, for reasons of simplicity, bi-spectra matrixes are plotted as an image scale. In the next section, a set of simulated signals is firstly considered and then validated by experimental results to identify the bi-frequency faults patterns. IV.

(6)

SIMULATION AND EXPERIMENTAL TESTS: SINGLE

FAULT BROKEN ROTOR BARS AND BEARINGS DEFECTS

In this section, the bi-spectrum stator current signal is theoretically presented. In particular, the cases regarding current signals with single fault (BRBs, BDs) and multiple combined faults (BRBs and BDs) are considered. This theoretical analysis will be also confirmed by the some experimental results.

where, fe

Nb

Db Dc

fJ

rotor shaft frequency number of rolling elements ball diameter pitch diameter ball contact angle

The torque oscillations generate stator current components at predictable fault bearing frequencies. The bearing fault frequencies ftlng are related to the oscillations and electrical supply frequency by [17] f nng = I I ,

± mfv

I

(7)

Where J, is the power supply frequency, fv is one of the characteristic vibration frequencies lfe, fo, flY fs), and m= 1, 2, 3, ... III.

THE Bl-SPECTRUM OVERVIEW

The bi-spectrum belongs to the class of HOS, or used to represent the frequency content of a signal. HOS provides higher order moments and nonlinear combinations of the higher order moments called cumulants [18], [19]. Thus, HOS consist of moment and cumulant spectra. An overview of the theory on HOS can be found in [18], [19]. Bi-spectral techniques show its effectiveness in quadratic phase coupling peak detection, and because it's a third order moment function noise background is eliminated in the estimation procedure [18]-[20]. Third order statistics of the stator current signal "the bi­ spectrum" is used in this work, it has the advantage of reduced computation time than the other HOS analysis, but it gives fully play of the advantages of the HOS analysis [8]. The bi-spectrum is the Fourier transform of the third order

1.

Single-Fault Condition: BRBs

The synthetic rotor fault was obtained by drilling a small hole of 3-mm diameter in all the rotor bar depth, without harming the rotor shaft. Let consider that the stator current is given by equation (9). This signal is similar to the measured current for one broken bar at rated load, and it is generated at a sampling rate of 5 1 2 Hz. Assume the simplest case of a stator current signal, where only the first sideband frequencies associated with the BRBs (fi=48.87 Hz. andi';.==51. 13 Hz) are considered. iaCt) = if cos(2JrIJ-cp)+il cos(2Jrht-CPI)

polyspectra

+ir cos(2Jr frt-CPr)

(9)

: RMS value of the supply phase current : RMS value of the lower current component at (1- 2s)/, , and its phase angle respectively ir , CPr

cP

: RMS value of the upper current component at (1 + 205)/" and its phase angle respectively

: Phase angle at the supply frequency By ignoring contributions of negative frequencies which fall outside the useful region of interest, the bi-spectrum of the stator current signal generated by bar breakages is theoretically calculated using the Fourier transform of

5134

60

expression (9) and substituted in the bi-spectrum formula given by (8), is given by (10) * BUpf2)=laU))1"U2)1,, (f; =J., +f2)

[ [ [

, � irJ(J., - fs)eJ