 Original Article
 Open Access
IBPSOBased MUSIC Algorithm for Broken Rotor Bars Fault Detection of Induction Motors
 PanPan Wang^{1}Email author,
 XiaoXiao Chen^{1},
 Yong Zhang^{2},
 YongJun Hu^{1} and
 ChangXin Miao^{1}
https://doi.org/10.1186/s1003301802795
© The Author(s) 2018
 Received: 27 June 2016
 Accepted: 11 September 2018
 Published: 21 September 2018
Abstract
In spectrum analysis of induction motor current, the characteristic components of broken rotor bars (BRB) fault are often submerged by the fundamental component. Although many detection methods have been proposed for this problem, the frequency resolution and accuracy are not high enough so that the reliability of BRB fault detection is affected. Thus, a new multiple signal classification (MUSIC) algorithm based on particle swarm intelligence search is developed. Since spectrum peak search in MUSIC is a multimodal optimization problem, an improved barebones particle swarm optimization algorithm (IBPSO) is proposed first. In the IBPSO, a modified strategy of subpopulation determination is introduced into BPSO for realizing multimodal search. And then, the new MUSIC algorithm, called IBPSObased MUSIC, is proposed by replacing the fixedstep traversal search with IBPSO. Meanwhile, a simulation signal is used to test the effectiveness of the proposed algorithm. The simulation results show that its frequency precision reaches 10^{−5}, and the computational cost is only comparable to that of traditional MUSIC with 0.1 search step. Finally, the IBPSObased MUSIC is applied in BRB fault detection of an induction motor, and the effectiveness and superiority are proved again. The proposed research provides a modified MUSIC algorithm which has sufficient frequency precision to detect BRB fault in induction motors.
Keywords
 MUSIC
 Multimodal
 Barebones particle swarm optimization
 Induction motors
 Broken rotor bars
 Fault detection
1 Introduction
Induction motors are essential components and play an irreplaceable role in industrial production process [1]. Although this motor is simplestructure, lowcost, reliable and robust, it is also prone to failure due to reasons, such as harsh working environment, internal incipient defects [2]. Broken rotor bars (BRB) or end ring cracking is one of the most common faults of induction motor, which accounts for about 10% of all failures [3]. This percentage is inconspicuous, but BRB fault will not only reduce the efficiency, but also cause other faults, such as bearing fault, airgap eccentricity [4]. In severe cases, broken pieces of the rotor bar may even damage the stator windings during operation [5]. Therefore, rotor fault detection of induction motor in early stage is essential and significant.
When broken bars occur, new sideband components at f_{brk}= (1 ± 2ks)f_{1} Hz will appear in the stator current spectrum, where k= 1, 2, 3,…, f_{1} is the supply frequency and s is the motor slip [6]. So the sideband components can be regarded as fault characteristics, and their frequency detection is key to identify the BRB fault. However, the strongest faultrelated components at (1 ± 2s)f_{1} Hz are quite close to fundamental component due to small slip value and their amplitudes are relatively small, which make them easy to be submerged by the leakage of fundamental component, reducing the reliability of BRB fault detection. In addition, their signal property differs significantly under various motorworking conditions. When motor runs in steady state, the values of f_{brk} are almost constant, and when motor is running in transient state, such as start up or load change, the values of f_{brk} are variable, that is to say, the faultrelated components are nonstationary signals. For these two different properties of stator current, scholars have adopted many different signal processing methods.
In transient state, promising results have been obtained through approaches based on shorttime Fourier transform [7], continuous or discrete wavelet transform [7, 8], fractional Fourier transform [9], complex empirical mode decomposition [10] and Synchrosqueezing transform [11]. Yet, the frequency resolution and accuracy of these methods are low, which restrict their applications.
For steady state of induction motor, spectrum analysis based on discrete Fourier transform (DFT) is the most popular method for BRB fault detection. However, in this case, the influence of spectrum leakage of fundamental component is more serious due to smaller slip value. To solve this problem, many distinctive methods have been developed, such as instantaneous power [12], particle swarm optimization [13] and Hilbert transform [14]. The main idea of these methods is to filter the fundamental component or convert it into a DC component from current signal. Then DFT is implemented to highlight the fault characteristics. Although these methods based on DFT analysis can eliminate the influence of fundamental component, their performances are restricted by DFT own shortcomings. For example, the frequency resolution is limited by measurement time, namely, high frequency resolution needs to be ensured with a long enough measurement time. If the signal measurement period is too long, the probability of load fluctuations, noise and other interference factors will be increased, which will affect the accuracy of fault detection [15].
As one of the modern spectrum estimation methods, multiple signal classification (MUSIC) algorithm has a capability of original signal extrapolation and high frequency resolution. Therefore, MUSIC has been introduced into the BRB fault detection of induction motor. GarciaPerez et al. [16] applied MUSIC to multiple faults detection of induction motor. On the basis of MUSIC, Fang et al. [17] moved the maximum eigenvector of fundamental component into noise subspace to constitute a new noise space. The results indicate that this method not only eliminates the influence of fundamental component, but also improves the frequency resolution. ZMUSIC method based on the frequency spectrum zooming technique and MUSIC was presented by Kia et al. [18], to further improve the frequency resolution and computational efficiency. A hybrid scheme based on MUSIC and empirical mode decomposition was proposed by CamarenaMartinez et al. [19], to detect multiple faults of induction motor. RomeroTroncoso et al. [20] detected rotor unbalance fault using a hybrid MUSIC method combined with completeensembleEMD. Another method that combined optimization algorithm with MUSIC was presented by Xu et al. [21]. It solved the problem that MUSIC couldn’t compute the amplitudes and phases of components. However, when the MUSIC is used in BRB fault detection, its efficiency of spectrum peak search is low due to fixedstep and traversal search.
Particle swarm optimization (PSO) is an emerging global optimization technology proposed by Kennedy et al. [22], in 1995. Because of the advantages of simple concept, easy realization, effective solution to complex problems, PSO has been widely applied in practical engineering problems, such as structural optimization [23], design optimization, PID controller tuning, stretch force trajectory optimization and parameter optimization [24]. However, the standard PSO and most improved algorithms are designed to deal with the problem which includes only one global optimal solution in search space. They are not suitable for searching multiple extremes, such as searching spectrum peaks in MUSIC. To optimize multimodal problem, scholars have introduced niche technology into evolutionary algorithm, and accordingly presented many strategies [25, 26], such as preselection technique, crowding strategy, fitness sharing, species conservation, but several issues still remain. For instance, low convergence speed and precision, trapped in local optimum and error fluctuation may compromise the optimization results.
This paper tries to improve PSO and take the advantages of PSO and MUSIC for BRB detection in induction motor. Organization of this paper is as follows. In Section 2, the principles of MUSIC are introduced firstly. In Section 3, an improved barebones PSO (IBPSO) is proposed for multimodal optimization problem. In Section 4, a new MUSIC method based on IBPSO is proposed and its simulation analysis is also conducted. In Section 5, the IBPSObased MUSIC is applied in BRB fault detection and its performance is compared with DFT and traditional MUSIC.
2 Multiple Signal Classification
As a kind of frequency estimation technique based on matrix eigenvalue decomposition, multiple signal classification (MUSIC) was proposed by Schmid [27] in the 1980s. Its main idea is described below. Firstly, through eigenvalue decomposition, the information space of observed signal is divided into two orthogonal subspaces, namely, signal subspace and noise subspace. Then the frequency components in observed signal can be estimated by constructing spectrum according to subspaces’ orthogonality.
Then, all eigenvalues decomposed from R_{yy} are sorted in the descending order. The subspace spanned by eigenvectors corresponding to the P largest eigenvalues is the signal subspace S. The subspace spanned by the rest of eigenvectors is the noise subspace G.
For frequency f_{q} included in signal y(n), since D(f_{q})^{T}·G= 0, then PM(f_{q})= 1/D(f_{q})^{T}·G^{2} will take a peak at f_{q}. Therefore, signal frequency estimation can be obtained by searching peaks of PM(f_{q}) with step Δf.
3 Improved BareBones Particle Swarm Optimization
3.1 Particle Swarm Optimization
3.2 BareBones Particle Swarm Optimization
Compared with the standard PSO, BPSO needs less control parameters, and that is more suitable for practical application.
3.3 Improved BPSO
As described above, seed selection strategy is executed in each generation of the evolutionary process. First of all, according to the fitness value, personal best positions of all particles are arranged in descending order to form a set Spbest. Then, the similarity between each individual in Spbest and each existing seed of X_{s} (called seed set) is compared. If the Euclidean distance between them is larger than threshold value σ^{*}, this personal best position will be added to X_{s}.
 Step 1::

Initialize particles’ positions, personal best positions and seed set X_{s}. Set algorithm parameters, including population size α, maximum generation m_{max} and species similarity threshold σ^{*}
 Step 2::

Calculate the fitness of each particle
 Step 3::

Update personal best position p_{i}
 Step 4::

According to the fitness, arrange all p_{i} in descending order
 Step 5::

Update seed set X_{s}
 Step 6::

Assign each particle to the nearest seed by calculating the distance between them
 Step 7::

According to Eq. (8), update particle positions, where p_{g} is the seed found in Step 5;
 Step 8::

If the condition of termination is satisfied (i.e., the fitness error is less than the threshold or the iterative number exceeds the maximum), stop iterative procedure and output all the seed positions and fitness values. Otherwise, return to Step 2
3.4 IBPSO Performance Analysis
A benchmark function, Rastrigin, is used to verify the effectiveness of IBPSO. And the performance of IBPSO is compared with species conserving genetic algorithm (SCGA) [25] and speciesbased PSO (SPSO) [26].
Parameter configurations for the selected optimization algorithms
Parameter  SCGA  SPSO  IBPSO 

Population size α  150  150  150 
Maximum generation m_{max}  50  50  50 
Species similarity threshold σ^{*}  −  −  0.9 
Niche radius r_{n}  1.5  1.25  − 
Crossover probability γ_{c}  0.6  −  − 
Mutation probability γ_{m}  0.05  −  − 
Constriction factor λ  −  0.729844  − 
Learning factor c_{1}, c_{2}  −  2.05  − 
As shown in Figure 3(a) and (b), for the given nine optimal solutions, SCGA finds eight, and SPSO finds only five. Unfortunately, the SPSO also fail to find the global optimal solution (0, 0) with best fitness. The reason is that they adopt fixed niche radius to determine subpopulations, which limits the global search ability of algorithm. On the contrary, IBPSO has an improvement. It can adaptively adjust subpopulations according to the distance between each particle and seed. This behavior makes particles have a larger flight range at the beginning of iteration, which can improve the global search ability. And with the increasing generations, search radius can be reduced automatically to improve the local search ability. Figure 3(c) verifies that IBPSO finds all the optimal solutions with high location accuracy.
In addition, only species similarity threshold σ^{*} needs to be set in IBPSO so that the effect of parameters will be reduced. So the IBPSO is more suitable for application in engineering.
4 IBPSOBased MUSIC and Simulation Analysis
4.1 IBPSOBased MUSIC
 Step 1::

Measure a set of signal data, and construct its autocorrelation matrix R_{yy}
 Step 2::

Generate the signal subspace S and noise subspace G by handling R_{yy} with eigenvalue decomposition.
 Step 3::

Encode the f_{q} of Eq. (1) to form population particles, and select the Eq. (11) as the fitness function.
 Step 4::

Search multiple spectrum peaks in the frequency domain by using IBPSO.
4.2 Simulation Analysis
MUSIC estimation results with different search step
Frequency parameter  True value  Estimation value with different search step  

∆f= 0.1  ∆f= 0.01  ∆f= 0.001  
Fundamental frequency f_{1} (Hz)  50.0000  50.0  50.00  50.000 
Faultrelated frequency (1 – 2s)f_{1} (Hz)  49.5438  49.6  49.54  49.544 
Faultrelated frequency (1 + 2s)f_{1} (Hz)  50.4562  50.5  50.46  50.456 
Estimation results of IBPSObased MUSIC
Frequency parameter  True value  Statistical indices  

Average estimation value  Average estimation error  Maximum estimation error  
Fundamental frequency f_{1} (Hz)  50.0000  50.0000  4.7 × 10^{−7}  4.8 × 10^{−5} 
Faultrelated frequency (1 – 2s)f_{1} (Hz)  49.5438  49.5438  1.1 × 10^{−5}  7.8 × 10^{−4} 
Faultrelated frequency (1 + 2s)f_{1} (Hz)  50.4562  50.4562  6.9 × 10^{−6}  8.4 × 10^{−4} 
Table 2 shows that traditional MUSIC has a very high frequency resolution even with a shorttime data window. Therefore, it has superiority in the stator current spectrum analysis, especially in BRB fault detection of induction motor. However, its estimation accuracy of frequency is limited by search step, that is, the highest accuracy will not exceed ∆f. And the increasing search step results in increasing error of the faultrelated frequencies. Fortunately, it is an exception for fundamental frequency, because 50 Hz is an integer multiple of the search steps like 0.1, 0.01, and 0.001. For the IBPSObased MUSIC, the estimation accuracy of faultrelated frequencies reaches 10^{−5}, even 10^{−7} for fundamental frequency, as Table 3 shown. And the maximum error in 50 times of operation doesn’t exceed 10^{−4}. Therefore, in terms of precision, the proposed algorithm has far exceeded the traditional MUSIC with Δf= 0.001 Hz.
Computation cost comparison for the algorithms
Index  MUSIC with different search step  IBPSObased MUSIC (average time in 50 runs)  

∆f= 0.1  ∆f= 0.01  ∆f= 0.001  
Computation time t (s)  0.101  0.814  7.732  0.339 
Therefore, IBPSObased MUSIC obtains a prominent improvement on solution accuracy and search efficiency contrasting with traditional MUSIC.
5 Application in BRB Fault Detection of Induction Motors
Specifications of the test motor
Rated power P_{N} (kW)  Rated voltage U_{N} (V)  Rated current I_{N} (A)  Rated speed n_{N} (r/min)  Number of rotor bars 

7.5  380  15.4  1440  32 
Figure 7(a) and (b) show that both two algorithms have a high frequency resolution. However, for traditional MUSIC, spectrum peaks can only appear at the integer multiples of ∆f (0.001 Hz) due to usage of fixed step size. As shown in Figure 7(b), three spectrum peaks are only located at 45.861 Hz, 50.023 Hz and 54.224 Hz. Therefore, traditional MUSIC cannot attain a finer frequency resolution. Contrastively, it is obvious that IBPSObased MUSIC can find higher spectrum peaks no matter for fundamental frequency or for fault feature frequencies (under the same signal subspace and noise subspace). Figure 7(a) and (b) prove that the frequency resolution and accuracy of IBPSObased MUSIC are higher than MUSIC. Meanwhile, IBPSObased MUSIC also takes a less computation time. In this experiment, its time cost is only 0.106 s comparing with 4.054 s of MUSIC, which greatly improves the search efficiency. Accordingly, IBPSObased MUSIC is more suitable and reliable for BRB fault detection.
6 Conclusions
 (1)
An improved BPSO (IBPSO) is proposed to make it more suitable for multimodal optimization problem. Compared with SCGA and SPSO, the solution quality and convergence speed are improved greatly.
 (2)
Based on multimodal intelligence search of the IBPSO, a new MUSIC algorithm is proposed for BRB fault detection. Contrasting with traditional MUSIC, the IBPSObased MUSIC obtains a prominent improvement on frequency accuracy and search efficiency.
 (3)
Finally, DFT, MUSIC and IBPSObased MUSIC are compared in BRB fault detection of an actual induction motor. Experimental results show that the proposed algorithm has the best frequency resolution and accuracy, which make it more reliable to detect the BRB fault.
Declarations
Authors’ Contributions
PPW was in charge of the whole trial; PPW, XXC and YZ wrote the manuscript; YJH and CXM assisted with sampling and laboratory analyses. All authors read and approved the final manuscript.
Authors’ Information
PanPan Wang, born in 1982, is currently a lecturer at School of Electrical and Power Engineering, China University of Mining & Technology, China. He received his PhD degree from China University of Mining & Technology, China, in 2013. His research interests include fault diagnosis of induction motor, intelligence optimization, signal processing.
XiaoXiao Chen, born in 1992, is currently a master candidate at School of Electrical and Power Engineering, China University of Mining & Technology, China.
Yong Zhang, born in 1979, is currently an associate professor at China University of Mining & Technology, China. He received his PhD degree from China University of Mining & Technology, China, in 2009. His main research interests include intelligence optimization and its application, optimal control.
YongJun Hu, born in 1963, is currently an associate professor at China University of Mining & Technology, China. He received his master degree from China University of Mining & Technology, China, in 1987. His research interests include signal processing, artificial intelligence, harmonic detection.
ChangXin Miao, born in 1976, is currently an associate professor at China University of Mining & Technology, China. He received his PhD degree from China University of Mining & Technology, China, in 2012. His research interests include intelligence optimization, smart grid, reactive power compensation.
Competing Interests
The authors declare that they have no competing interests.
Funding
Supported by Fundamental Research Funds for the Central Universities (Grant No. 2017XKQY032).
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