# Induction Motor Multiclass Fault Diagnosis Based on Mean Impact Value and PSO-BPNN

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Signal Analysis Method and Classifier

#### 2.1. S-Transform (ST)

#### 2.2. Neural Network

## 3. Methodology

#### 3.1. Mean Impact Value

- Step (1)
- Select all features as feature set $F=\left\{{F}_{1}{,F}_{2},\dots ,{F}_{j}\right\}$
- Step (2)
- Train the model of PSO-BPNN.
- Step (3)
- Assume adjustment rate $\pm R$ and adjust ${F}_{i}$, get ${F}_{i\mathit{1}}=\left\{{F}_{1},{F}_{2},\dots ,{F}_{i}\left(1+R\right),\dots ,{F}_{j}\right\}$ and ${F}_{i\mathit{2}}=\left\{{F}_{1},{F}_{2},\dots ,{F}_{i}\left(1-R\right),\dots ,{F}_{j}\right\}$.
- Step (4)
- Respectively input ${F}_{i1}$ and ${F}_{i2}$ to BPNN.
- Step (5)
- Get the output ${Y}_{i1}$ and ${Y}_{i2}$.
- Step (6)
- Calculate impact value of ${F}_{i}$, $I{V}_{i}={Y}_{i1}-{Y}_{i2}$.
- Step (7)
- Calculate mean impact value, ${MIV}_{i}=mean({\mathit{IV}}_{i})$.

#### 3.2. Particle Swarm Optimization-BP Neural Network

- Step (1)
- Set number of particles i, number of iterations t, the maximum number of iterations t
_{max}, the acceleration constants c_{1}and c_{2}, and the inertia weights w. - Step (2)
- Assume that the coordinates of each particle in space ${X}_{i}=\left({X}_{1i},{X}_{2i},\dots ,{X}_{Di}\right)$, and the speed of each particle in space ${V}_{i}=\left({V}_{1i}{,V}_{2i},\dots {,V}_{Di}\right)$.
- Step (3)
- Calculate the fitness values of all particles by BPNN, and obtain the best solution P
_{best}for individuals and the best solution G_{best}for groups. - Step (4)
- Correct flight speed of the particle ${V}_{i\_new}=w{V}_{i}{+c}_{1}{r}_{1}\left({P}_{best}{-X}_{i}\right){+c}_{2}{r}_{2}\left({G}_{best}{-X}_{i}\right)$
- Step (5)
- Correct the particle position ${X}_{i\_new}={X}_{i}{+V}_{i\_new}$.
- Step (6)
- if $t<{t}_{max}$, $t=t+1$ and repeat step (3) to step (5).
- Step (7)
- Obtain the best position of the groups as the best solution.
- Step (8)
- Get PSO-BP model.

#### 3.3. Feature Selection

- Step (1)
- Select all features to establish feature vector F
_{origin}and set dimension D = 50. - Step (2)
- Use PSO to optimize the initial weights w
_{origin}and bias b_{origin}of BPNN. - Step (3)
- Record the optimized result and evaluate the accuracy Acc
_{remove}of BPNN. - Step (4)
- Calculate MIV of all features.
- Step (5)
- Arrange MIV from the minimum to the maximum and remove a feature corresponding to the smallest MIV. D = D − 1.
- Step (6)
- Select unremoved features to create a new feature vector F
_{new}, and evaluate the accuracy Acc_{remove}. If Acc_{remove}> Acc_{origon}, go back to Step (5). - Step (7)
- Select the features that have not been removed to create a new feature vector ${F}_{new}$, and use PSO to optimize the initial weight w
_{new}and b_{new}bias of BPNN. To evaluate the accuracy Acc_{new}. - Step (8)
- If Acc
_{new}> Acc_{origin}, go back to Step (5).

## 4. Experimental Measurements and Analysis of IM

#### 4.1. Experiment Device

#### 4.2. Experiment Structure

#### 4.3. Analysis Current of IM

#### 4.3.1. Healthy Motor

#### 4.3.2. Bearing Failure Motor

#### 4.3.3. Stator Short Circuit Fault Motor

#### 4.3.4. Rotor Drilling Fault Motor

#### 4.4. Feature Extraction

- (1)
**Tmax**: maximum value of each column of ST matrix.- (2)
**Tmin**: minimum value of each column of ST matrix.- (3)
**Tmean**: average value of each column of ST matrix.- (4)
**Tmse**: mean square error of each column of ST matrix.- (5)
**Tstd**: standard deviation of each column of ST matrix.- (6)
**Fmax**: maximum value of each row of ST matrix.- (7)
**Fmin**: minimum value of each row of ST matrix.- (8)
**Fmean**: average value of each row of ST matrix.- (9)
**Fmse**: mean square error of each row of ST matrix.- (10)
**Fstd**: standard deviation of each row of ST matrix.

#### 4.5. Classifier

## 5. Results

#### 5.1. Motor Current Signal Measurement

#### 5.2. Feature Selection Results

## 6. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

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**Figure 4.**Experiment apparatus (

**a**) power meter platform, (

**b**) power meter platform control panel, and (

**c**) data acquisition system.

**Figure 6.**Healthy motor characteristic diagram (

**a**) spectrum, (

**b**) time domain characteristic curves, (

**c**) frequency domain characteristic curves.

**Figure 7.**Bearing failure motor characteristic diagram (

**a**) spectrum, (

**b**) time domain characteristic curves, (

**c**) frequency domain characteristic curves.

**Figure 8.**Stator short circuit fault motor characteristic diagram (

**a**) spectrum, (

**b**) time domain characteristic curves, (

**c**) frequency domain characteristic curves.

**Figure 9.**Stator short circuit fault motor characteristic diagram (

**a**) spectrum, (

**b**) time domain characteristic curves, (

**c**) frequency domain characteristic curves.

Tmax | Tmin | Tmean | Tmse | Tstd | Fmax | Fmin | Fmean | Fmse | Fstd | |
---|---|---|---|---|---|---|---|---|---|---|

MAX + MIN | F1 | F6 | F11 | F16 | F21 | F26 | F31 | F36 | F41 | F46 |

MAX − MIN | F2 | F7 | F12 | F17 | F22 | F27 | F32 | F37 | F42 | F47 |

Mean | F3 | F8 | F13 | F18 | F23 | F28 | F33 | F38 | F43 | F48 |

Mse | F4 | F9 | F14 | F19 | F24 | F29 | F34 | F39 | F44 | F49 |

Std | F5 | F10 | F15 | F20 | F25 | F30 | F35 | F40 | F45 | F50 |

Classfier | Accuaracy |
---|---|

PNN | 86.12% |

BPNN | 96.3% |

PSO-BPNN | 100% |

Feature Number | Number of Features | Accuracy | Computing Time |
---|---|---|---|

F1, F2, F3, …, F48, F49, F50 | 50 | 100% | 21.03 |

F11, F13, F24, F27, F31, F32, F34, F35, F39, F40, F42, F43, F46, F47, F49, F50 | 16 | 100% | 19.43 |

F24, F31, F32, F39, F40, F43, F46, F47, F49, F50 | 10 | 100% | 19.11 |

F24, F31, F32, F40, F43, F46, F47, F49, F50 | 9 | 99.4% | 19.07 |

Feature Number | Number of Features | Accuracy | Computing Time |
---|---|---|---|

F1, F2, F3, …, F48, F49, F50 | 50 | 86.5% | 21.09 |

F9, F20, F24, F26, F27, F30, F32, F36, F38, F39, F40, F44, F45, F46, F47, F50 | 16 | 88.6% | 19.43 |

F36, F38, F39, F40, F44, F46, F50 | 7 | 86.5% | 19.08 |

F38, F39, F40, F44, F46, F50 | 6 | 86.2% | 18.90 |

Feature Number | Number of Features | Accuracy | Computing Time |
---|---|---|---|

F1, F2, F3,…, F48, F49, F50 | 50 | 64.0% | 21.07 |

F1, F3, F5, F7, F8, F9, F11, F12, F13, F14, F20, F23, F24, F25, F26, F28, F32, F35, F36, F37, F38, F39, F42, F43, F45, F49, F50 | 27 | 71% | 19.95 |

F42, F43, F45 | 3 | 67.3% | 18.71 |

F42, F45 | 2 | 63.2% | 18.76 |

Feature Selection Methods | Number of Features | Accuaracy of Healthy Motor | Accuaracy of Bearing Failure Motor | Accuaracy of Stator Short Circuit Fault Motor | Accuaracy of Rotor Drilling Fault Motor | Total Accuaracy |
---|---|---|---|---|---|---|

All features | 50 | 100% | 100% | 100% | 100% | 100% |

MIV base on PSO-BPNN | 9 | 97.7% | 100% | 99.9% | 100% | 99.4% |

Feature Selection Methods | Number of Features | Accuracy |
---|---|---|

All features | 50 | 100% |

GA | 28 | 100% |

ReliefF | 9 | 98.5% |

MIV base on PSO-BPNN | 9 | 99.4% |

Healthy Motor | Bearing Failure Motor | Stator Short Circuit Fault Motor | Rotor Drilling Fault Motor | Total | |
---|---|---|---|---|---|

Healthy motor | 48.85 | 0 | 0.05 | 0 | 99.8% 0.2% |

Bearing failure motor | 0 | 50 | 0 | 0 | 100% 0% |

Stator short circuit fault motor | 0.1 | 0 | 49.9 | 0 | 100% 0% |

Rotor drilling fault motor | 0.2 | 0 | 0 | 50 | 97.8% 2.2% |

Total | 97.7% 2.3% | 100% 0% | 99.8% 0.2% | 100% 0% | 99.4% 0.6% |

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**MDPI and ACS Style**

Lee, C.-Y.; Ou, H.-Y.
Induction Motor Multiclass Fault Diagnosis Based on Mean Impact Value and PSO-BPNN. *Symmetry* **2021**, *13*, 104.
https://doi.org/10.3390/sym13010104

**AMA Style**

Lee C-Y, Ou H-Y.
Induction Motor Multiclass Fault Diagnosis Based on Mean Impact Value and PSO-BPNN. *Symmetry*. 2021; 13(1):104.
https://doi.org/10.3390/sym13010104

**Chicago/Turabian Style**

Lee, Chun-Yao, and Hong-Yi Ou.
2021. "Induction Motor Multiclass Fault Diagnosis Based on Mean Impact Value and PSO-BPNN" *Symmetry* 13, no. 1: 104.
https://doi.org/10.3390/sym13010104