# ANN-Based Pattern Recognition for Induction Motor Broken Rotor Bar Monitoring under Supply Frequency Regulation

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## Abstract

**:**

## 1. Introduction

_{7}]) of DWT under a steady-state frequency regulation. Furthermore, a three-layer ANN of both feed-forward backdrop type and cascade forward backdrop type is examined using different algorithms to design an effective and fast ANN using pattern recognition and curve fitting. The proposed study is carried out in MATLAB/Simulink using 5.5 kW SCIM. The LabVIEW-based real-time implementation is also done as a validation of the proposed fault detection scheme. This proposed approach’s execution requires a minimum instrumentation system compared to the schemes and algorithms used in the available and presented literature [11,12,13,14,15,16,17,18,19,20,21,22,23,24,25], which is highly desirable for the scheme’s reliable working under dusty and hazardous mine environments.

## 2. Modelling of Rotor Bar Crack Fault

#### 2.1. Winding Function Theory-Based Modelling of SCIM

#### 2.2. Modelling of SCIM Subjected to Frequency Regulation

#### 2.3. Modelling of Rotor Bar Crack

_{inc}) with the number of cracked bars can be mathematically expressed as [31]:

_{b}) is considerably small compared to the number of rotor bars (N). Hence, (1) can be approximated as [32,33]:

_{b}<<N and the machine are not run in the underground mining setup, it is sent for maintenance as soon as even one damaged bar is detected, hence, (2) is quite applicable for the modelling of cracked rotor bars in the present work.

## 3. Simulation Results

#### 3.1. FFT-Based Analysis

_{sb}) around the higher-order slot harmonics can be obtained as [35]:

#### 3.1.1. Choice of Sampling Frequency

#### 3.1.2. Analysis of Stationary Current Signal Using FFT

_{lsb}and f

_{usb}appearing at 45 and 54 Hz, respectively) with 3.49 and 3.65% amplitudes w.r.t fundamental (i.e., 50 Hz). According to (14), dominant fault side-band magnitudes A

_{lsb}and A

_{usb}must occur within 45–47 and 53–55 Hz, respectively, depending on the 3–5% variation in the machine slip. Therefore, MCSA using FFT produces precise and expected outcomes under a constant frequency operation.

#### 3.1.3. Analysis of Non-Stationary Current Signal

#### 3.2. DWT-Based MULTI-Resolution Analysis

_{n}] and [d

_{n}] are the approximated and detailed coefficients, respectively that correspond to different frequency bands (in the present work) depending upon the scaling function and the mother wavelet defined as:

#### 3.2.1. Choice of Sampling Frequency for DWT Analysis

_{7}] and [d

_{6}] coefficients, respectively. This corresponds to the sampling frequencies in the range of 6100 to 6350 Hz. Isolation of fault frequency components in different detailed coefficients is highly desirable in contention with ambiguity-less fault detection. In practice, the sampling frequency may not remain fixed due to the sampler’s variation of parameters. Hence, the analysis reveals that any sampling frequency within the specified range is suitable for the proposed fault detection scheme’s satisfactory execution. However, in the present work, a 6250 Hz sampling frequency is used.

#### 3.2.2. Choice of Mother Wavelet and Number of Decomposition Levels

#### 3.2.3. Analysis of Stationary and Non-Stationary Current Signals by DWT for a Motor operating at Variable Load

_{1}]-[d

_{5}], [d

_{8}], and [a

_{8}] do not contain any substantial ripple in any case (Figure 4a–d), since the magnitudes of the other fault side-band frequencies around the other higher-order slot harmonics are progressively smaller and hence, are not reflected in [d

_{1}]-[d

_{5}], while [d

_{8}] and [a

_{8}] represent the low-frequency bands (less than the fundamental frequency).

_{6}] and [d

_{7}], respectively, during the cage fault. The amplitudes of variations in such cases are appreciably higher than those for the healthy cases, as shown in Figure 4a,c due to the presence of both the upper side-band and principal slot harmonics. Furthermore, Figure 4a,c shows the nonexistence of any variation of [d

_{7}], which indicates the absence of the lower side-band frequency around the principle slot harmonic under the healthy motor condition. In contrast, the variation as reflected in [d

_{6}] is similar (having lesser magnitude) to the faulty one (Figure 4b,d) owing to the presence of principal slot harmonics only.

_{7}] for the healthy and the faulty conditions of the SCIM (Figure 4). Therefore, the point-to-point standard deviation of [d

_{7}] is considered for the fault detection algorithm’s edifice in the present work.

#### 3.3. ANN-Based Analysis

_{7}] detailed coefficient are a good indicator of the broken/cracked rotor bar damage. Hence, the instantaneous values of the [d

_{7}] detailed coefficient are used for the training of the ANN. A three-layered ANN having 10 neurons in each layer is designed in the present work. Two types of ANN are designed and tested in the present work using cascaded forward backdrop and feed-forward backdrop-based designs, as shown in Figure 5a,b, respectively [14,27,29,31,40,41,42,43,44,45].

#### 3.4. Modelling of DWT-Based Fault Detection Scheme

_{a}) is used for MRA in the simulation study. In addition, ‘dB34’ is used for scrutinising stationary signals in the ‘wavelet analysis’ block. The point-to-point standard deviation of [d

_{7}] obtained from the ‘wavelet analysis’ block is compared with the pre-fed values of the standard deviation of [d

_{7}] obtained by analysing the healthy motor state in the ‘comparator’ block. The standard deviation of [d

_{7}] obtained from the motor with a faulty cage running in real-time is consistently higher than that of the motor in a healthy state, which indicates the presence of a fault. Furthermore, the instantaneous values of the [d

_{7}] detailed coefficient are fed to the ‘ANN’ block, wherein the cascaded forward backdrop-based design has been adopted, and the execution is done using the Levenberg-Marquardt algorithm. The value of the coefficient of correlation (R) obtained from the ANN block is fed to a comparator block which checks whether the value of R value is more than 0.94. A value greater than 0.94 indicates damaged rotor bars, whereas a lesser value indicates a healthy rotor bar. This is justified based on the values obtained in Table 2.

## 4. Real-Time Validation

#### 4.1. LabVIEW-Based Laboratory Prototype

#### 4.2. Results of Fault Detection

_{7}] coefficient for SCIMs operating at a rated load torque under healthy conditions. The [d

_{7}] components in these cases show significantly lesser variations from the pre-fed values, a characteristic of the healthy machine. Furthermore, Figure 12b shows the [d

_{7}] coefficient for SCIMs operating at a rated load torque having broken rotor bars. It is evident that the deviation of the [d

_{7}] coefficient is much greater than those shown in Figure 12a.

## 5. Conclusions

_{7}] alone is sufficient to detect the rotor bar crack provided the analysing mother wavelet and working sampling frequency are selected accurately. In the present work, it is found that ‘db41’ is suitable for analysing the stationary current signal, whereas ‘sym34’ is the proper choice for the non-stationary current signal in the MRA. Furthermore, it is also observed that the use of cascaded forward backdrop type ANN using the Levenberg-Marquardt algorithm gives highly satisfactory results for the process of fault detection.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Nomenclature

Symbol | Description |

s | Slip of the machine (%) |

f_{1} | Supply frequency (Hz) |

p | Number of pole pairs |

Ω_{r} | Rotor speed (rad/s) |

R_{b},L_{b} | Rotor bar resistance (Ω), inductance (H) |

R_{inc} | Increase in rotor resistance ($\mathsf{\Omega}$) |

R_{e}, L_{e} | End-ring resistance ($\mathsf{\Omega}$), inductance (H) |

N_{1} | Turn number of one stator winding |

N | Total number of rotor bars |

N_{b} | Contiguous number of cracked bars |

f_{sb} | Higher-order slot harmonics |

[V_{s}][I_{r}] | Stator voltage, rotor loop current matrices |

[R_{r}][L_{r}] | Rotor resistance, inductance matrices |

Φ_{s}, Φ_{r} | Total flux linkages of stator and rotor winding |

θ_{r} | Angular rotor position |

Φ | Particular point along the air-gap |

l | Effective length of the motor |

N_{tsp}, N_{spp} | Number of turns/slot/phase, number of slots/pole/phase |

N_{k} (θ_{r}, φ) | Winding function of rotor windings |

L_{a}, L_{b}, L_{c}, L_{ab}, L_{bc}, L_{ca} | Elements of $\left[{L}_{s}\right]$ |

L_{k1}……L_{kk} | Elements of $\left[{L}_{r}\right]$ |

L_{ak}, L_{bk}, L_{ck} | Elements of $\left[{L}_{sr}\right]$ |

θ_{k} | Angular position of bar ‘k’ |

A_{lsb}, A_{usb} | Lower, upper fault side-band amplitude (%) |

v_{a}, v_{b}, v_{c} | Voltages of phase-a, phase-b, phase-c (V) |

i_{a}, i_{b}, i_{c} | Currents of phase-a, phase-b, phase-c (A) |

F_{s} | Sampling frequency (Hz) |

t | Time (s) |

L | Number of decomposition levels |

n_{f} | Detailed coefficient containing 50 Hz |

f_{lsb}, f_{usb} | Lower, upper side-band frequency (Hz) |

[I_{s}] | Stator current vector |

[R_{s}] | Stator winding resistance matrix |

[L_{s}] | Stator winding inductance matrix |

[L_{sr}] | Stator to rotor mutual inductance matrix |

T_{em}, T_{L} | Electromagnetic, load torques (Nm) |

J | Rotor inertia (Kg-m^{2}) |

F | Coefficient of friction |

μ_{0} | Permeability of air |

r | Air-gap average radius (mm) |

N_{s}, N_{s1} | Effective, the actual number of turns of the stator winding |

g | Air-gap length (mm) |

N_{1} (θ_{r}, φ), N_{j} (θ_{r}, φ) | Winding function of circuit $I$ and $J$ |

K_{p}, K_{d}, K_{s} | Pitch, distribution, skew factors |

N_{a}, N_{b}, N_{c} | Winding function of stator windings |

α_{r} | Angle between any two adjacent bars |

## Appendix A. Motor Parameters

Parameters | Ratings |

Shaft power | 5.5 kW |

Rated voltage | 415 V |

Frequency | 50 Hz |

Synchronous speed | 1500 rpm |

Stator resistance/phase | 1.83 Ω |

Stator inductance/phase | 0.0074 H |

Rotor resistance referred to stator/phase | 1.26 Ω |

Rotor inductance referred to stator/phase | 0.007 H |

Mutual inductance | 0.198 H |

Number of stator slots | 36 |

Number of rotor slots | 28 |

Number of poles | 4 |

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**Figure 1.**Simulation and modelling of SCIM: (

**a**) Current distribution in rotor loops using the winding function theory, and (

**b**) block diagram of MATLAB/Simulink model of variable frequency voltage fed SCIM.

**Figure 2.**Analysis of rotor bar crack fault of a 5.5 kW SCIM (1 faulty bar) in stationary regime: (

**a**) Phase-a current (i

_{a}) with 50 Hz frequency, and (

**b**) FFT spectrum of stationary i

_{a}.

**Figure 3.**Analysis of rotor bar crack fault of a 5.5 kW SCIM (1 faulty bar) in non-stationary regime: (

**a**) Phase-a current (i

_{a}) with variable frequency, and (

**b**) FFT spectrum of non-stationary i

_{a}.

**Figure 4.**Approximated $[{a}_{n}]$ and detailed $[{d}_{n}]$ coefficients obtained by the DWT-based MRA of phase-a current of 5.5 kW SCIM running at a rated load torque: Under constant frequency operation: (

**a**) In the absence of cage fault, (

**b**) in the presence of cage fault, and under frequency regulation: (

**c**) In the absence of cage fault, (

**d**) in the presence of cage fault.

**Figure 5.**Artificial neural network design based on (

**a**) cascaded forward backdrop and (

**b**) feed-forward backdrop based design.

**Figure 6.**Pattern recognition-based regression diagram for cascaded forward backdrop using (

**a**) Bayesian Regulation, (

**b**) Polak-Ribiere Restarts, (

**c**) Gradient Descent with momentum and adaptive learning rate, and (

**d**) Levenberg-Marquardt Algorithm.

**Figure 7.**Mean square error diagram for cascaded forward backdrop using (

**a**) Bayesian Regulation, (

**b**) Polak-Ribiere Restarts, (

**c**) Gradient Descent with momentum and adaptive learning rate, and (

**d**) Levenberg-Marquardt Algorithm.

**Figure 8.**Pattern recognition based regression diagram for feed-forward backdrop using (

**a**) Bayesian Regulation, (

**b**) Polak-Ribiere Restarts, (

**c**) Gradient Descent with momentum and adaptive learning rate, and (

**d**) Levenberg-Marquardt Algorithm.

**Figure 9.**Mean square error diagram for feed-forward backdrop using (

**a**) Bayesian Regulation, (

**b**) Polak-Ribiere Restarts, (

**c**) Gradient Descent with momentum and adaptive learning rate, and (

**d**) Levenberg-Marquardt Algorithm.

**Figure 12.**The [d

_{7}] coefficient for SCIMs operating at a rated load torque obtained using the LabVIEW-based laboratory prototype under (

**a**) healthy state, and (

**b**) faulty state.

**Figure 13.**ANN-based pattern recognition diagram for the detection of broken rotor bars using the stator current for SCIM: (

**a**) With broken rotor bars and (

**b**) without broken rotor bars.

[d_{n}]/[a_{n}] | Sampling Frequency F_{s} (Hz) | |||||
---|---|---|---|---|---|---|

6100 | 6150 | 6200 | 6250 | 6300 | 6350 | |

d_{1} | 1525–3050 | 1537–3075 | 1550–3100 | 1562–3125 | 1575–3150 | 1588–3175 |

d_{2} | 762–1525 | 769–1537 | 775–1550 | 781–1562 | 788–1575 | 794–1588 |

d_{3} | 381–762 | 384–769 | 388–775 | 390–781 | 394–788 | 397–794 |

d_{4} | 191–381 | 192–384 | 194–388 | 195–390 | 197–394 | 198–397 |

d_{5} | 95–191 | 96–192 | 97–194 | 98–195 | 97–197 | 99–198 |

d_{6} | 48–95 | 48–96 | 48–97 | 49–98 | 49–98 | 49–98 |

d_{7} | 24–48 | 24–48 | 24–48 | 25–49 | 25–49 | 25–49 |

d_{8} | 12–24 | 12–24 | 12–24 | 13–25 | 13–25 | 13–25 |

a_{8} | 0–12 | 0–12 | 0–12 | 0–13 | 0–13 | 0–13 |

Correlation Coefficient Value (R) | Mean Square Error Epoch Value | |||
---|---|---|---|---|

Cascaded Forward Backdrop | Feed-Forward Backdrop | Cascaded Forward Backdrop | Feed-Forward Backdrop | |

Bayesian Regulation | 0.95127 | 0.94955 | 6 | 8 |

Polak-Ribiere Restarts | 0.945 | 0.95373 | 24 | 5 |

Gradient Descent with momentum and adaptive learning rate | 0.94557 | 0.95264 | 231 | 233 |

Levenberg-Marquardt | 0.94935 | 0.94925 | 5 | 5 |

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## Share and Cite

**MDPI and ACS Style**

Sinha, A.K.; Hati, A.S.; Benbouzid, M.; Chakrabarti, P.
ANN-Based Pattern Recognition for Induction Motor Broken Rotor Bar Monitoring under Supply Frequency Regulation. *Machines* **2021**, *9*, 87.
https://doi.org/10.3390/machines9050087

**AMA Style**

Sinha AK, Hati AS, Benbouzid M, Chakrabarti P.
ANN-Based Pattern Recognition for Induction Motor Broken Rotor Bar Monitoring under Supply Frequency Regulation. *Machines*. 2021; 9(5):87.
https://doi.org/10.3390/machines9050087

**Chicago/Turabian Style**

Sinha, Ashish Kumar, Ananda Shankar Hati, Mohamed Benbouzid, and Prasun Chakrabarti.
2021. "ANN-Based Pattern Recognition for Induction Motor Broken Rotor Bar Monitoring under Supply Frequency Regulation" *Machines* 9, no. 5: 87.
https://doi.org/10.3390/machines9050087