# Broken Bar Diagnosis for Squirrel Cage Induction Motors Using Frequency Analysis Based on MCSA and Continuous Wavelet Transform

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## Abstract

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## 1. Introduction

## 2. Related Works

## 3. Proposed Approach

_{s,τ}is the mother wavelet, and s and τ are the mother wavelet scale and translation, respectively. Note that a signal must meet certain conditions before it can be considered to be mother wavelet. The signal has to be properly located in time (i.e., admissibility), its average energy should be null, and it should behave as a band-pass filter with fast decay on ω

_{s}= 0 and when ω

_{s}→ ∞ [25,26], ω

_{s}being the angular frequency.

_{0}is a non-dimensional frequency. Note that a value of ω

_{0}= 6 is considered in this work to satisfy the admissibility condition [26].

_{0}= 6. This implies that the Morlet wavelet scale is equal to the Fourier period.

_{0}= 6, this relationship is expressed as λ = 1.03∙s. The utilization of the CWT technique allows the use of variable scales to perform the analysis. This way, the identification of information localized at different frequencies is identified. In contrast to other wavelet analysis, which use a scale power of two (e.g., Daubechies scales are 2

^{n}). The Morlet mother wavelet scale is defined as follows [26]:

_{j}is the Morlet wavelet scale, s

_{0}= 2dt is the smallest resolvable scale, dt = 1/F

_{s}is the inverse of the sampling frequency F

_{s}, and d

_{j}is an empirical value less than 0.5. For the Morlet wavelet, values of d

_{j}of about 0.5 give adequate sampling at scale, whereas lower values give a finer resolution. According to [50], this study considers a value of d

_{j}= 0.15.

## 4. Experimental Validation Results and Comparison

#### 4.1. Motor Test Bench Configuration

^{−6}) = 600,000 samples, with N being the number of samples in 24 s). Note that Morlet-CWT generates distortion at the edges of the motor current signal spectrum, since the calculation algorithm (i.e., Fourier space) considers that the studied signals are periodic. To overcome this drawback, the motor is started after a time interval of 2 s, as shown in Figure 4.

^{®}environment. The tests are performed at different speeds with full- and non-load using both a healthy motor and a faulty motor with one, two, and three broken bars. The current signal processing and the fault detection technique are developed in Matlab

^{®}(Version 9.1, MathWorks, Natick, MA, USA).

#### 4.2. Results

## 5. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

- Glowacz, A.; Glowacz, Z. Diagnosis of stator faults of the single-phase induction motor using acoustic signals. Appl. Acoust.
**2017**, 117, 20–27. [Google Scholar] [CrossRef] - Puche-Panadero, R.; Pineda-Sanchez, M.; Riera-Guasp, M.; Roger-Folch, J.; Hurtado-Perez, E.; Perez-Cruz, J. Improved Resolution of the MCSA Method Via Hilbert Transform, Enabling the Diagnosis of Rotor Asymmetries at Very Low Slip. IEEE Trans. Energy Convers.
**2009**, 24, 52–59. [Google Scholar] [CrossRef] - Nandi, S.; Toliyat, H.A.; Li, X. Condition monitoring and fault diagnosis of electrical motors—A review. IEEE Trans. Energy Convers.
**2005**, 20, 719–729. [Google Scholar] [CrossRef] - Cusidó, J.; Romeral, L.; Ortega, J.A.; Garcia, A.; Riba, J. Signal injection as a fault detection technique. Sensors
**2011**, 11, 3356–3380. [Google Scholar] [CrossRef] [PubMed] - Delgado, M.; Garcia, A.; Ortega, J.A.; Urresty, J.; Riba, J.R. Bearing diagnosis methodologies by means of common mode current. In Proceedings of the IEEE 13th European Conference on Power Electronics and Applications, Barcelona, Spain, 8–10 September 2009; pp. 1–10. [Google Scholar]
- Ceban, A.; Pusca, R.; Romary, R. Study of Rotor Faults in Induction Motors Using External Magnetic Field Analysis. IEEE Trans. Ind. Electron.
**2012**, 59, 2082–2093. [Google Scholar] [CrossRef] - Bellini, A.; Filippetti, F.; Tassoni, C.; Capolino, G.-A. Advances in Diagnostic Techniques for Induction Machines. IEEE Trans. Ind. Electron.
**2008**, 55, 4109–4126. [Google Scholar] [CrossRef] - Mustafa, M.O.; Nikolakopoulos, G.; Gustafsson, T. Broken bars fault diagnosis based on uncertainty bounds violation for three-phase induction motors. Int. Trans. Electr. Energy Syst.
**2015**, 25, 304–325. [Google Scholar] [CrossRef] - Moussa, M.A.; Boucherma, M.; Khezzar, A. A Detection Method for Induction Motor Bar Fault Using Sidelobes Leakage Phenomenon of the Sliding Discrete Fourier Transform. IEEE Trans. Power Electron.
**2017**, 32, 5560–5572. [Google Scholar] [CrossRef] - Thomson, W.T.; Fenger, M. Current signature analysis to detect induction motor faults. IEEE Ind. Appl. Mag.
**2001**, 7, 26–34. [Google Scholar] [CrossRef] - Gyftakis, K.N.; Spyropoulos, D.V.; Kappatou, J.C.; Mitronikas, E.D. A Novel Approach for Broken Bar Fault Diagnosis in Induction Motors Through Torque Monitoring. IEEE Trans. Energy Convers.
**2013**, 28, 267–277. [Google Scholar] [CrossRef] - Talhaoui, H.; Menacer, A.; Kessal, A.; Kechida, R. Fast Fourier and discrete wavelet transforms applied to sensorless vector control induction motor for rotor bar faults diagnosis. ISA Trans.
**2014**, 53, 1639–1649. [Google Scholar] [CrossRef] [PubMed] - Glowacz, A.; Glowacz, Z. Diagnosis of the three-phase induction motor using thermal imaging. Infrared Phys. Technol.
**2017**, 81, 7–16. [Google Scholar] [CrossRef] - Gaeid, K.S.; Ping, H.W.; Khalid, M.; Salih, A.L. Fault diagnosis of induction motor using MCSA and FFT. Electr. Electron. Eng.
**2011**, 1, 85–92. [Google Scholar] - Kliman, G.B.; Stein, J. Methods of motor current signature analysis. Electr. Mach. Power Syst.
**1992**, 20, 463–474. [Google Scholar] [CrossRef] - Elbouchikhi, E.; Choqueuse, V.; Trachi, Y.; Benbouzid, M. Induction machine bearing faults detection based on Hilbert-Huang transform. In Proceedings of the 2015 IEEE 24th International Symposium on Industrial Electronics (ISIE), Buzios, Brazil, 3–5 June 2015; pp. 843–848. [Google Scholar]
- Mehala, N.; Dahiya, R. Rotor faults detection in induction motor by wavelet analysis. Int. J. Eng. Sci. Technol.
**2009**, 1, 90–99. [Google Scholar] - Nau, S.L.; Schmitz, D.; de Lima Pires, W. Methods to evaluate the quality of stator and rotor of electric motors. In Proceedings of the 2015 IEEE 10th International Symposium on Diagnostics for Electrical Machines, Power Electronics and Drives (SDEMPED), Guarda, Portugal, 1–4 September 2015; pp. 64–70. [Google Scholar]
- Keskes, H.; Braham, A. Recursive Undecimated Wavelet Packet Transform and DAG SVM for Induction Motor Diagnosis. IEEE Trans. Ind. Inform.
**2015**, 11, 1059–1066. [Google Scholar] [CrossRef] - García-Escudero, L.A.; Duque-Perez, O.; Morinigo-Sotelo, D.; Perez-Alonso, M. Robust condition monitoring for early detection of broken rotor bars in induction motors. Expert Syst. Appl.
**2011**, 38, 2653–2660. [Google Scholar] [CrossRef] - Chikouche, D.; Boukazzoula, N.; Rezki, M.; Ayad, M. Search of a robust defect signature in gear systems across adaptive Morlet wavelet of vibration signals. IET Signal Process.
**2014**, 8, 918–926. [Google Scholar] - Garcia-Perez, A.; Romero-Troncoso, R.J.; Cabal-Yepez, E.; Osornio-Rios, R.A. The Application of High-Resolution Spectral Analysis for Identifying Multiple Combined Faults in Induction Motors. IEEE Trans. Ind. Electron.
**2011**, 58, 2002–2010. [Google Scholar] [CrossRef] - Corral-Hernandez, J.A.; Antonino-Daviu, J.; Pons-Llinares, J.; Climente-Alarcon, V.; Frances-Galiana, V. Transient-Based Rotor Cage Assessment in Induction Motors Operating with Soft Starters. IEEE Trans. Ind. Appl.
**2015**, 51, 3734–3742. [Google Scholar] [CrossRef] - Pons-Llinares, J.; Antonino-Daviu, J.A.; Riera-Guasp, M.; Lee, S.B.; Kang, T.; Yang, C. Advanced Induction Motor Rotor Fault Diagnosis Via Continuous and Discrete Time-Frequency Tools. IEEE Trans. Ind. Electron.
**2015**, 62, 1791–1802. [Google Scholar] [CrossRef] - Farge, M. Wavelet Transforms and their Applications to Turbulence. Annu. Rev. Fluid Mech.
**1992**, 24, 395–458. [Google Scholar] [CrossRef] - Torrence, C.; Compo, G.P. A Practical Guide to Wavelet Analysis. Bull. Am. Meteorol. Soc.
**1998**, 79, 61–78. [Google Scholar] [CrossRef] - Cusido, J.; Rosero, J.A.; Cusido, M.; Garcia, A.; Ortega, J.A.; Romeral, L. On-Line System for Fault Detection in Induction Machines based on Wavelet Convolution. In Proceedings of the 2007 IEEE Power Electronics Specialists Conference, Orlando, FL, USA, 17–21 June 2007; pp. 927–932. [Google Scholar]
- Mehrjou, M.R.; Mariun, N.; Marhaban, M.H.; Misron, N. Evaluation of Fourier and wavelet analysis for efficient recognition of broken rotor bar in squirrel-cage induction machine. In Proceedings of the 2010 IEEE International Conference on Power and Energy, Kuala Lumpur, Malaysia, 2–4 November 2010; pp. 740–743. [Google Scholar]
- Ece, D.G.; Başaran, M. Condition monitoring of speed controlled induction motors using wavelet packets and discriminant analysis. Expert Syst. Appl.
**2011**, 38, 8079–8086. [Google Scholar] [CrossRef] - Haji, M.; Toliyat, H.A. Pattern recognition-a technique for induction machines rotor broken bar detection. IEEE Trans. Energy Convers.
**2001**, 16, 312–317. [Google Scholar] [CrossRef] - Da Silva, I.N.; Godoy, W.F.; Lopes, T.D.; Goedtel, A.; Palácios, R.H.C. Application of intelligent tools to detect and classify broken rotor bars in three-phase induction motors fed by an inverter. IET Electr. Power Appl.
**2016**, 10, 430–439. [Google Scholar] - Karmakar, S.; Chattopadhyay, S.; Mitra, M.; Sengupta, S. Induction Motor Fault Diagnosis Approach through Current Signature Analysis; Springer: Singapore, 2016; p. 182. [Google Scholar]
- Hernandez, J.C.; Antonino-Daviu, J.; Martinez-Gimenez, F.; Peris, A. Comparison of different wavelet families for broken bar detection in induction motors. In Proceedings of the 2015 IEEE International Conference on Industrial Technology (ICIT), Sevilla, Spain, 17–19 March 2015; pp. 3220–3225. [Google Scholar]
- Rangel-Magdaleno, J.; Ramirez-Cortes, J.; Peregrina-Barreto, H. Broken bars detection on induction motor using MCSA and mathematical morphology: An experimental study. In Proceedings of the 2013 IEEE International Instrumentation and Measurement Technology Conference (I2MTC), Minneapolis, MN, USA, 6–9 May 2013; pp. 825–829. [Google Scholar]
- Tallam, R.M.; Habetler, T.G.; Harley, R.G. Stator winding turn-fault detection for closed-loop induction motor drives. IEEE Trans. Ind. Appl.
**2003**, 39, 720–724. [Google Scholar] [CrossRef] - Devi, N.R.; Sarma, D.V.S.S.S.; Rao, P.V.R. Diagnosis and classification of stator winding insulation faults on a three-phase induction motor using wavelet and MNN. IEEE Trans. Dielectr. Electr. Insul.
**2016**, 23, 2543–2555. [Google Scholar] [CrossRef] - Menacer, A.; T-Said, M.S.d.N.; Benakcha, A.H.; Drid, S. Stator current analysis of incipient fault into asynchronous motor rotor bars using Fourier fast transform. J. Electr. Eng.
**2004**, 55, 122–130. [Google Scholar] - Ahamed, S.K.; Sarkar, A.; Mitra, M.; Sengupta, S. Detection of Induction Motor Broken Bar Fault through Envelope Analysis Using Start-Up Current. Procedia Technol.
**2012**, 4, 646–651. [Google Scholar] [CrossRef] - Spyropoulos, D.V.; Gyftakis, K.N.; Kappatou, J.; Mitronikas, E.D. The influence of the broken bar fault on the magnetic field and electromagnetic torque in 3-phase induction motors. In Proceedings of the 2012 20th International Conference on Electrical Machines, Marseille, France, 2–5 September 2012; pp. 1868–1874. [Google Scholar]
- Picazo-Rodenas, M.J.; Antonino-Daviu, J.; Climente-Alarcon, V.; Royo-Pastor, R.; Mota-Villar, A. Combination of Noninvasive Approaches for General Assessment of Induction Motors. IEEE Trans. Ind. Appl.
**2015**, 51, 2172–2180. [Google Scholar] [CrossRef] - Singh, G.; Kumar, C.A.; Naikan, V.N.A. Effectiveness of Current Envelope analysis to detect broken rotor bar and inter turn faults in an inverter fed induction motor drive. In Proceedings of the 2015 International Conference on Power and Advanced Control Engineering (ICPACE), Bengalooru, India, 12–14 August 2015; pp. 191–194. [Google Scholar]
- Gyftakis, K.; Antonino-Daviu, J.; Garcia-Hernandez, R.; McCulloch, M.; Howey, D.; Cardoso, A. Comparative Experimental Investigation of the Broken Bar Fault Detectability in Induction Motors. In Proceedings of the 2015 IEEE 10th International Symposium on Diagnostics for Electrical Machines, Power Electronics and Drives (SDEMPED), Guarda, Portugal, 1–4 September 2015; pp. 461–467. [Google Scholar]
- Sapena-Bano, A.; Perez-Cruz, J.M.J.; Pineda-Sanchez, M.; Roger-Folch, J.; Riera-Guasp, M.; Puche-Panadero, R. Harmonic order tracking analysis: A novel method for the diagnosis of induction generators. In Proceedings of the 2014 International Conference on Electrical Machines (ICEM), Berlin, Germany, 2–5 September 2014; pp. 1765–1771. [Google Scholar]
- Kia, S.H.; Henao, H.; Capolino, G.-A. Diagnosis of broken-bar fault in induction machines using discrete wavelet transform without slip estimation. IEEE Trans. Ind. Appl.
**2009**, 45, 1395–1404. [Google Scholar] [CrossRef] - Mehrjou, M.R.; Mariun, N.; Karami, M.; Noor, S.B.M.; Zolfaghari, S.; Misron, N.; Kadir, M.Z.A.A.; Radzi, M.A.M.; Marhaban, M.H. Wavelet-Based Analysis of MCSA for Fault Detection in Electrical Machine. In Wavelet Transform and Some of Its Real-World Applications; InTech: Rijeka, Croatia, 2015. [Google Scholar]
- Ngote, N.; Ouassaid, M.; Guedira, S.; Cherkaoui, M. On the Detection of Induction-Motor Rotor Fault by the Combined ‘Time Synchronous Averaging-Discrete Wavelet Transform’ Approach. J. Electr. Eng. Technol.
**2015**, 10, 2315–2325. [Google Scholar] [CrossRef] - Li, D.Z.; Wang, W.; Ismail, F. A Spectrum Synch Technique for Induction Motor Health Condition Monitoring. IEEE Trans. Energy Convers.
**2015**, 30, 1348–1355. [Google Scholar] [CrossRef] - El Bouchikhi, E.H.; Choqueuse, V.; Benbouzid, M. Induction machine faults detection using stator current parametric spectral estimation. Mech. Syst. Signal Process.
**2015**, 52–53, 447–464. [Google Scholar] [CrossRef] - Pons-Llinares, J.; Antonino-Daviu, J.A.; Riera-Guasp, M.; Pineda-Sanchez, M.; Climente-Alarcon, V. Induction Motor Diagnosis Based on a Transient Current Analytic Wavelet Transform via Frequency B-Splines. IEEE Trans. Ind. Electron.
**2011**, 58, 1530–1544. [Google Scholar] [CrossRef] - Komorowski, D.; Pietraszek, S. The Use of Continuous Wavelet Transform Based on the Fast Fourier Transform in the Analysis of Multi-channel Electrogastrography Recordings. J. Med. Syst.
**2016**, 40, 10. [Google Scholar] [CrossRef] [PubMed]

**Figure 2.**Broken fault detection algorithm through Motor Current Signature Analysis (MCSA) method and Morlet-CWT (Continuous Wavelet Transform) technique.

**Figure 6.**Signal data acquired using the MCSA method for a faulty motor with one broken bar operating at non- and full-load.

**Figure 7.**Current signal spectrum obtained using the Fast Fourier Transform (FFT) technique for a faulty motor with one broken bar: (

**a**) FFT spectrum for motor starting interval; (

**b**) FFT spectrum for non-load operation interval; and (

**c**) FFT spectrum for full-load operation interval.

**Figure 8.**Spectrum of the current signal obtained using the CWT technique for a faulty motor with one broken bar operating at non- and full-load.

**Figure 9.**Spectrum of the current signal obtained using the CWT technique for a motor operating at non-load (

**a**) healthy motor; (

**b**) faulty motor with three broken bars; and (

**c**) spectrum of the current signal obtained through the FFT technique of a faulty motor with three broken bars operating at non-load.

**Figure 10.**Spectrum of the current signal obtained using the CWT technique for a motor operating at full-load (

**a**) healthy motor and (

**b**) faulty motor with three broken bars.

Description | Value | Unit |
---|---|---|

Brand | ABB | – |

Rated power | 1 | Hp |

Rated current | 3.4 | A |

Conection type | Delta | – |

Rated voltage | 220 | V |

Supply frequency | 60 | Hz |

Nominal speed | 1705 | Rpm |

Torque | 4.2 | Nm |

Moment of inertia | 0.00174 | kg·m^{2} |

Pole pairs | 2 | – |

Number of bars | 22 | – |

**Table 2.**Frequency bands associated with motor failures caused by broken bars when operating at full-load.

Number of Broken Bars | Frequency Bands | |||
---|---|---|---|---|

56–58.5 Hz | 52.8–54.8 Hz | 50.5–52.5 Hz | 48.5–50 Hz | |

0 | 56.98 < f < 57.55 | 53.34 < f < 53.85 | 51.12 < f < 51.5 | 48.9 < f < 49.3 |

∆f = 0.57 | ∆f = 0.51 | ∆f = 0.42 | ∆f = 0.41 | |

1 | 57.41 < f < 58.35 | 53.5 < f < 54.5 | 51.2 < f < 51.8 | 48.9 < f < 49.5 |

∆f = 0.94 | ∆f = 0.98 | ∆f = 0.58 | ∆f = 0.59 | |

2 | 57.02 < f < 58.43 | 53.2 < f < 54.6 | 51 < f < 51.9 | 48.7 < f < 49.6 |

∆f = 1.41 | ∆f = 1.40 | ∆f = 0.93 | ∆f = 0.89 | |

3 | 56.23 < f < 58.35 | 52.82 < f < 54.79 | 50.7 < f < 51.2 | 48.5 < f < 49.8 |

∆f = 2.08 | ∆f = 1.97 | ∆f = 1.41 | ∆f = 1.32 |

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**MDPI and ACS Style**

,, D.G.; Aguilar, W.G.; Arcos-Aviles, D.; Sotomayor, D.
Broken Bar Diagnosis for Squirrel Cage Induction Motors Using Frequency Analysis Based on MCSA and Continuous Wavelet Transform. *Math. Comput. Appl.* **2017**, *22*, 30.
https://doi.org/10.3390/mca22020030

**AMA Style**

, DG, Aguilar WG, Arcos-Aviles D, Sotomayor D.
Broken Bar Diagnosis for Squirrel Cage Induction Motors Using Frequency Analysis Based on MCSA and Continuous Wavelet Transform. *Mathematical and Computational Applications*. 2017; 22(2):30.
https://doi.org/10.3390/mca22020030

**Chicago/Turabian Style**

,, Danilo Granda, Wilbert G. Aguilar, Diego Arcos-Aviles, and Danny Sotomayor.
2017. "Broken Bar Diagnosis for Squirrel Cage Induction Motors Using Frequency Analysis Based on MCSA and Continuous Wavelet Transform" *Mathematical and Computational Applications* 22, no. 2: 30.
https://doi.org/10.3390/mca22020030