Identification of acoustic spectra for fault detection in induction motors

Identification of acoustic spectra for fault detection in induction motors Hüseyin Akçay and Emin Germen Department of Electrical and Electronics Engineering, Anadolu University Eskisehir 26470, Turkey

Abstract— In this paper, we study fault detection problem for induction motors by using a recently developed cross-power spectral density estimation algorithm from sound measurements. In a test rig, from multiple experiments the sound data were collected by an array of five-microphones placed hemispherically around motors in a reverberant and noisy room. After an experiment was performed, each motor was removed from the test rig and was reinstalled for the next experiment to verify the consistency of the experimental procedure. The mechanical and electrical faults frequently encountered in induction motors were isolated by the identification algorithm, which is a non-iterative high resolution spectral estimator. The estimated acoustic spectra, or more compactly statistics extracted from them, can be used in the development of preventive maintenance programs for induction motors in service. Index Terms— power spectrum; subspace identification; fault detection; sound; induction motor.

I. I NTRODUCTION In industry, induction motors are widely used and are considered as critical components for electric utilities and process industries. In order not to interrupt processes, which depend on the regular operation of induction motors, the recognition of potential faults in advance has a crucial importance. There is a substantial amount of research work devoted to the fault detection and condition monitoring of induction motors [1], [2], [3], [4]. The aim is to track the diagnostic of incipient faults for preventive maintenance. Among all fault detection methods, the motor current signature analysis (MCSA) method is the most popular one, which provides an effective way to detect incipient faults [1], [5]. The MCSA method mainly focuses on the analysis of the current data supplied from the AC network to the induction motor utilizing the time-frequency analysis techniques, i.e., the fast Fourier transform (FFT), the shorttime Fourier transform (STFT), the wavelet transform, and the wavelet packet transform [1]. The MCSA method is difficult to implement on induction motors in their working environment since additional circuitry such as isolators and data acquisition cards are to be added between the supply and the test motor. In addition, it may not be possible to detach the load from the motor and run the motor under no load condition. Fault diagnosis methods based on vibration analysis have been developed to detect bearing faults [2], [4], [6]. These methods use the Fourier or the wavelet transforms and E-mail: [email protected]. Fax: +90 222 335 0580. Tel: +90 222 323 9501. Corresponding author. E-mail: [email protected].

circumvent the disadvantages of the current based fault diagnosis methods since the former do not require detaching test motor from its working environment. Acoustic techniques [2], [4], [7], [8] as well do not require intervention to either the test motor or the environment; transducers can simply be placed around the motor without altering its working condition.They are based on the principle that each failure of a specific part in the motor has its own signature in the acoustic spectrum. Ambient noise and complicated relationship between the motor and the surrounding make it difficult to evaluate the signatures of the fault. Unlike the vibration or the current based signature analysis, there are few works dealing with the fault diagnosis of induction motors based on the sound analysis. Acoustic emission produces valuable information for identifying the bearing faults [8]. In [4], the acoustic emission, the sound pressure, and the sound intensity methods for the detection of defects in rolling element bearings were surveyed. In the surveyed works, acoustic experiments were performed in completely clean rooms, i.e., in non-reverberant and noisefree environments. As a result, analysis of the sound data collected in these experiments is hardly useful for real life applications, especially for industrial processes. Cross-spectral analysis is a fundamental and powerful technique to investigate an unknown relationship between two time series in frequency-domain. It is widely used in many engineering problems [9]. This paper is concerned with the identification of fault signatures frequently encountered in the motor industry from the sound measurements collected by microphone arrays by using the cross-spectral analysis. The outline of this paper is as follows. In Section 2, the experimental set-up and the acoustically identifiable and important motor fault types are described. In Section 3, the frequency-domain subspace-based cross-power spectrum estimation algorithm introduced by Akçay [10] is outlined. Then, in Section 4 this algorithm is used to identify both healthy and faulty motors. Section 5 concludes the paper. II. E XPERIMENTAL SETUP AND THE FAULT TYPES STUDIED

In order to obtain acoustic data, which are representative of the faults most commonly seen in the motor industry, induction motors of the same type with different loading conditions were used in the experiments. The test motors were three-phase two-pole squirrel cage induction motors rated at 2.2 kW and 380 Volts supply voltage. To effectively load the test motors, the test bed was designed so that

a single-phase permanent magnet synchronous generator was coupled to them. The generator was also connected to an adjustable resistive load to simulate different loading conditions. In the experiments, the motors were driven by 3.6 Amperes through 5.4 Amperes stator current, ranging from almost no load condition to a heavily loaded condition. The variation in the load level produces a deviation in the speed with respect to the synchronous speed due to the slip. Thus, the different loading condition is the different artifact in the sound spectrum. The test rig used in the experiments is shown in Figure 1.

Fig. 2.

Fig. 1.

The test rig.

The mechanical faults such as formal defects in the rotational parts and cracks in the rotor cage bars form the two common fault types which can be tracked by the acoustic analyzing techniques. More specifically, the defective bearing fault is the foremost fault type encountered in the industry [3]. The second most commonly encountered fault is that of broken rotor cage bars. In the experimental analysis of the rotor cage bars, broken rotor cage bars were synthetically created by drilling holes into either the 3rd or 5th rotor bar (18 bars in total) as illustrated in Figure 2. This fault causes rises in the magnitude of the acoustic spectrum around the main frequency which the stator coils are supplied [2]. The frequencies of the rises are shifted by even integral multiplicities of the slip frequency. Monitoring increases in the magnitude values at the predicted sideband frequencies alone may mislead the fault classification since different fault types may have the same frequency components. Also, when the slip is small, these sidebands come close to the fundamental frequency and it becomes difficult to identify them by inspecting the spectral information due to the dominance of the fundamental component. The bearing faults are the most common faults since the friction between the surfaces and the alignment problems in motor coupling produce defects in different parts of the bearings. Also, corrosion, contamination, and improper lubrication cause residual artifacts on the ball surfaces, resulting in imperfections. The inner surface or the outer surface defects produce different sideband frequency components and the defect frequency characteristics can be monitored. However, in the industry, the bearing defects, in general, have

A broken rotor bar synthetically created by drilling holes.

a much more complex nature caused by several mechanisms at work. As a result, abnormal noise and vibration are produced. In order to simulate prevailing conditions in the industry, two of the bearings were replaced by two broken bearings. Both bearings had been in service until they broke. One of the bearings had an alignment problem, and the other had defects in the ball surfaces. The bearings are the NSK 6205 brand, commonly used in the industry. In the test bed, a three-phase, 25 kVA, ∆-Y connected isolation transformer was located between each motor and the network. The acoustic data were collected by an array of 5 directional cardioid type microphones placed around the motor hemispherically (see Figure 1). The sound data were acquired by a mastering level A/D converter and a professional sound card with the full transparent amplifier where the microphones are connected to. For each fault type, three experiments were carried out by removing the motors from the test rig and reinstalling them in order to simulate dissimilar working conditions. Since the test rig contains mechanical components to fix the motor and the generator, small discrepancies in the assemblage process create different artifacts in the sound data and consistency of the acoustic spectrum models yielded by the subsequent signal processing stage validates the experimental procedure. The fault types studied in this paper are listed in Table 1. Approximately 30 seconds after the motor and the generator unit reached the steady state, the sound data were collected in each experiment. For each fault type listed in Table 1 and each load factor, three experiments were performed. The sound data were sampled at 44.1 kHz. It should be borne in mind that all experiments were deliberately performed in a noisy and reverberant environment. The ambient sound pressure level was recorded as 53.2 dB on average. The sound pressure levels are shown in Table 2 for each experiment and each motor type for the maximum

TABLE I

and wM [n] is an appropriately chosen spectrum window. The Welch cross-PSD estimator is then defined as

T HE FAULT TYPES STUDIED . Motor # Motor 1 Motor 2 Motor 3 Motor 4

Fault type Healthy motor Bearing fault (misalignment) Bearing fault (ball defect) Broken rotor bars (3 out of 18)

jω SW xy (e ) =

TABLE II

Load Factors 3.6 A 5.4 A 73.8 79.4 74.9 75.4 73.8 72.6 86.2 84.2 83.7 82.0 83.2 82.0 84.6 83.2 83.2 83.2 83.2 83.2 75.0 77.1 76.0 74.5 75.0 73.8

Motor 1

Motor 2

Motor 3

Motor 4

dB dB dB dB dB dB dB dB dB dB dB dB dB

and the minimum values of the stator current. III. C ROSS - POWER SPECTRUM ESTIMATION BY A HYBRID

Ykl = sˆxy [k + l − 1] + sˆxy [M + k + l − p − r − 1]

ALGORITHM

Let x ∈ ℜmx and y ∈ ℜmy be two jointly stationary zeromean discrete-time processes. Their cross-covariance and the cross-power spectral density (PSD) matrices are defined by Rxy [τ] = E x[k + τ]yT [k] , ∞

Sxy (z) =

∑

Rxy [τ]z−τ

with z, XT and E(X) denoting respectively the unit-shift operator, the transpose and the expected value of a given (random) matrix X. Welch introduced a nonparametric method [11] to estimate a cross-power spectrum from the samples x[k] and y[k] using the fast Fourier transform. In his method, the data records are divided into L disjoint segments of M samples each so that N = LM, i.e., for 0 ≤ k < M and 0 ≤ i < L the segments x(i) [k] = x[k + iM], y(i) [k] = y[k + iM] are formed and the modified periodograms (i)

1 T X (ω; M)Y(i) (−ω; M) MU (i)

are computed where M−1

X(i) (ω; M) =

∑ wM [n]x(i) [n]e− jωn ,

n=0 M−1

Y(i) (ω; M) = U

=

∑

sˆxy [i] =

1 M−1 i W ∑ zn Sxy (zn ). M n=0

where Σ] contains at most nx + ny nonzero largest singular values. 4) With U] defined in Step 3 and Ju and Jd by Ju = 0(p−1)mx ×mx I(p−1)mx Jd = I(p−1)mx 0(p−1)mx ×mx where In and 0m×n denote respectively the n by n identity matrix and the m by n matrix of zeros, calculate A] = (Jd U] )† Ju U] where X† = (XT X)−1 XT denotes the Moore-Penrose pseudo inverse of a given full-column rank matrix X. 5) Put A] into the following Jordan canonical form: " # −1 Σc 0n0x ×n0y ] Πc Πac A = Πc Πac 0n0y ×n0x Σac 0

(i)

− jωn

wM [n]y [n]e n=0 1 M−1 2 w [n], M n=0 M

∑

2πi

for k = 1, · · · , p; l = 1, · · · , r where with zi = e j M ,

3) Calculate the singular-value decomposition ] h i ] Σ 0 V ] 0 Y = U U 0 Σ0 V0

τ=−∞

Sxy (ω; M) =

M 2πn , n = 0, · · · , (2) M 2 with a rectangular window, i.e., a window with the property wM [n] = 1 for all n in the support of the window function. The following subspace type algorithm was proposed in [10] to estimate a parametric model for Sxy (z) from the data in Eq. (1) at the frequencies in Eq. (2). The consistency properties of this algorithm were discussed there. Algorithm 3.1: jωn ) according to SW (e− jω ) = SW (e jω ) 1) Expand SW xy xy (e xy to obtain samples of the length M where X denotes the complex conjugate of a given complex matrix X. 2) Let nx and ny be respectively upper bounds on the number of the poles of Sxy (z) inside and outside the unit circle. Fix p and r as p > nx + ny , r ≥ nx + ny , p + r ≤ M. Compute the Hankel matrix Y defined blockwise by ωn =

SPL: 53.2 dB

Exp1 Exp2 Exp3 Exp1 Exp2 Exp3 Exp1 Exp2 Exp3 Exp1 Exp2 Exp3

(1)

We assume that the Welch cross-PSD estimator in Eq. (1) is calculated at the equidistantly spaced frequencies:

T HE MEASURED SOUND PRESSURE LEVELS . Environment

1 L−1 (i) ∑ Sxy (ω; M). L i=0

,

0

0

0

where the eigenvalues of Σc ∈ ℜnx ×nx and Σac ∈ ℜny ×ny are respectively inside and outside the unit circle. Let ˆc A ˆ ac A

= Σc , = Σ−1 ac ,

ˆ c = Jf U] Πc C ˆ ac = Jl U] Πac C

where Jf Jl

= Imx 0mx ×(p−1)mx , = 0mx ×(p−1)mx Imx .

(3) (4)

6) Solve the linear least-squares problem:

2 M−1 Bˆ c W

min ∑ S (z ) − E − χ(z ) n xy n Bˆ ac F ˆ B ˆ c ,B ˆ ac n=0 E, where χ(z) = Cc (zI − Ac )−1 Cac (z−1 I − Aac )−1 and 1 kXkF = [trace(XH X)] 2 denotes the Frobenius norm of a given complex matrix X with XH denoting the complex conjugate transpose of X. 7) As the cross-PSD estimator, set b c (zI − A ˆ c )−1 B ˆ ac (z−1 I − A ˆ ac )−1 Bˆ ac . ˆc +C Sˆ xy (z) = Eˆ + C

Motor faults may be detected by monitoring changes in the estimated cross-power spectrum around modal natural frequencies. In structural vibration monitoring, a plethora of fault detection methods is based on monitoring changes in eigenstructures. IV. FAULT DETECTION BY CROSS - SPECTRAL ANALYSIS We first examine the results of applying the cross-spectral analysis to fault-free motors. A. Fault-free motor identification We consider Motor 1 for the minimum and the maximum values of the load factor and repeated experiments. We divided the data equally into two disjoint sets: the estimation and the validation data sets, and calculated the Welch estimator in Eq. (1) with M = 5000 and L = 50 for both data sets. In Algorithm 3.1, p and r were both selected as 200 and in Step 3 the sum of nx and ny was estimated 60. In Figure 3, the largest singular value of the five-microphone array autoPSD matrix estimated by the Welch method and the hybrid algorithm with y = x are plotted for both the estimation and the validation data sets obtained from Experiment 1 with the load factor 3.6 Amperes.

Figure 3 shows that all but two harmonics at multiplicities of the supply frequency, which coincides with the rotor rotating frequency, are captured with a great precision. The ball bearing defects normally show up in the frequency band [0, 500 Hz] [3]. The results for the estimation and the validation data sets overlap; meaning that the stationarity over the data segments of size 250, 000 has prevailed in the experiment. At each frequency, examination of the remaining four singular values showed that they are rather small in comparison to the largest singular value. Hence, the rank of the estimated auto-PSD matrix can be assumed one for all frequencies. Thus, the microphone measurements are nearly correlated. In the rest of the paper, results will be displayed only for the largest singular values. This experiment was repeated twice by decoupling and reinstalling the same motor from the generator and increasing the load factor up to the maximum value. It was observed that in Experiments 1–3 and both on the simulation and the validation data for the same fixed load factor, the identification results were almost identical. Only the number of the harmonics present in the data varied with the load factor. Hence, the proposed experimental procedure is consistent. B. Bearing fault detection In Figure 4, the estimation results for the five-microphone array auto-PSD matrix using the Welch method and Algorithm 3.1 on both the estimation and the validation data sets are plotted for Motor 3 with M = 5000, L = 50, p = r = 200, nx +ny = 60, and 3.6 Amperes. The ball bearing of this motor had been in service until it broke. Comparing Figure 4 with Figure 3, we can draw two important conclusions as follows.

Fig. 4.

The largest singular values of the five-microphone array auto-PSD matrix: the Welch estimate on the estimation (x) and the validation (+) data sets; Algorithm 3.1 on the estimation (-) and the validation (-.) data sets.

Fig. 3. The largest singular values of the five-microphone array auto-PSD matrix: the Welch estimate on the estimation (x) and the validation (+) data sets; Algorithm 3.1 on the estimation (-) and the validation (-.) data sets.

First, at the multiplicities of the supply frequency, some harmonics in the fault-free motor, if not all, change their locations as well as their magnitudes. As a result, it is hard to explain the changes in the auto-PSD matrix completely by the bearing damage showing up itself at the vibration frequencies. There might have been other failure mechanisms in force to end the service time of this bearing. For example, any air gap eccentricity produces anomalies in the air gap

flux density. Since ball bearings support the rotor, any bearing defect will produce a radial motion between the rotor and the stator of the machine. Second, the sound pressure levels dramatically increase due to the broken ball bearing. While the minimum of the sound-pressure level has a value 0.3 × 10−3 in Figure 3, it increases to 10−3 in Figure 4 uniformly over the frequencies. Next, we studied eccentricity defects of ball bearings. In Figure 5, the estimation results for the five-microphone array auto-PSD matrix using Algorithm 3.1 on the estimation data obtained from Motor 2 is presented along with the results for Motor 1. The number of the data used in the estimation was 250, 000 and the data were divided into 50 blocks resulting in the half frequency range [0, 220.5 Hz]. The load factor was 3.6 Amperes. In Algorithm 3.1, we selected p = r = 200, and nx + ny = 60. Figure 5 reveals that the harmonics of the healthy motor are slightly shifted and new harmonics are created. Furthermore, the sound pressure level increases significantly over all frequencies. In summary, the crossspectral analysis of the acoustic spectra appears to be an effective tool in detecting ball bearing faults.

Fig. 6. The largest singular value of the five-microphone array auto-PSD matrix estimated by Algorithm 3.1 on the estimation data from Motor 5 and the largest singular value of Motor 1 redrawn from Figure 5.

The consistency of the experimental procedure with respect to several factors was also investigated. A recently developed subspace type cross-PSD estimation algorithm, which uses the Welch estimates constructed from time-domain measurements, was used to identify the acoustic spectra. Then, this algorithm was applied to motors with misaligned or defected ball bearings, broken rotor cage bars, and short circuit in the stator winding. The algorithm was capable of isolating faulty motors from healthy motors in all acoustically identifiable occasions. Moreover, one microphone was enough to identify a healthy motor or to distinguish it from faulty motors. The estimation algorithm can easily be integrated into fault diagnosis procedures for induction motors. This subject warrants further work. R EFERENCES

Fig. 5.

The largest singular value of the five-microphone array auto-PSD matrix estimated by Algorithm 3.1 on the estimation data from Motor 2 and the largest singular value of Motor 1.

C. Rotor fault detection Lastly, we study the fault detection problem in induction motors with broken rotor cage bars. In Figure 6, the estimation results for the five-microphone array auto-PSD matrix using Algorithm 3.1 on the estimation data obtained from Motor 3 for 3.6 Amperes load factor is presented along with the results for Motor 1. The parameter values of Algorithm 3.1 were chosen as in Figure 5. As in Figure 5, the harmonics are shifted and new harmonics are created with respect to the healthy motor. Nevertheless, amounts of the shift are less in comparison to Motor 2. Again, the crossspectral analysis of the acoustic spectrum isolates a faulty motor with broken rotor cage bars from a healthy motor. V. C ONCLUSIONS In this paper, we studied identification of induction motors from sound measurements collected by a microphone array placed around the motor in a noisy and reverberant room.

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