# Comprehensive Learning Particle Swarm Optimized Fuzzy Petri Net for Motor-Bearing Fault Diagnosis

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Fault-Diagnosis Model Architecture Based on CLPSO-FPN

## 3. Continuous Fault Signal Processing Based on EMD

#### Conversion of Fault Classification Information

## 4. The Fault-Diagnosis Method Based on CLPSO-FPN

#### 4.1. Discrete Fault Data Processing

#### 4.2. Fault-Diagnosis Model Optimization Based on CLPSO-FPN

- (1)
- $P=\left\{{p}_{1},{p}_{2},\dots ,{p}_{n}\right\}$; P represents the collection of libraries.
- (2)
- $T=\left\{{t}_{1},{t}_{2},\dots ,{t}_{m}\right\}$; T represents the change set.
- (3)
- I is the input matrix, representing the mapping of the library to the transition.
- (4)
- O is the output matrix, representing the mapping of transitions to the library.
- (5)
- $M=\left({m}_{1},{m}_{2},\dots ,{m}_{n}\right)$, representing the distribution vector identified by the library.
- (6)
- $W=\left({\omega}_{ij}\right)$ is the matrix of library weight n × m, representing the influence degree of the input database on the transition.
- (7)
- $H=\left({\lambda}_{1},{\lambda}_{2},\dots ,{\lambda}_{m}\right)$, representing the transition threshold distribution vector.
- (8)
- $a=\left({a}_{1},a,\dots ,{a}_{n}\right)$, ${a}_{i}\in \left[0,1\right]$ represents the confidence of the event represented by the pi of the library.
- (9)
- $B=\left({b}_{1},{b}_{2},\dots ,{b}_{r}\right)$; b represents the transition influence factor, representing the ability of the transition to influence its output library, where r represents the number of all arcs from the transition to its output library.
- (10)
- S represents the number of particles in the comprehensive learning particle swarm optimization algorithm.
- (11)
- D represents the dimension of the particle in the comprehensive learning particle swarm optimization algorithm.
- (12)
- K represents the number of iterations.

#### 4.2.1. Structure Optimization

#### 4.2.2. Parameter Optimization

^{−3}.The initial parameter set of the system is selected as the particle value with the minimum average error. When the training is to the 11th iteration, the minimum average error E is as follows: E = 2.695 × 10

^{−8}. At this point, the training errors of the four faults are as follows: E

_{1}= 4.074 × 10

^{−9}, E

_{2}= 3.6414 × 10

^{−10}, E

_{3}= 5.034 × 10

^{−8}, E

_{4}= 5301 × 10

^{−8}. It is proven that the integrated particle swarm optimization algorithm has excellent global optimization ability and local optimization ability.

#### 4.3. Reasoning Optimization

- Competition operator ▽: C = ▽A; A is m × n matrix, C is n-dimensional vector, then c
_{ij}= max(a_{ij}), where i = 1, …, m, j = 1, 2, …, n. - Maximum operator ⨁: C = A⨁B; A, B and C are all m × n matrices, then c
_{ij}= max(a_{i}_{j}, b_{ij}), where i = 1, 2, …, m, j = 1, 2, …, n. - Direct multiplication operator: C = A⨂b; A and C are m × n matrices, B is M-dimensional vector, then c
_{ij}= a_{ij}× b_{i}, where i = 1, 2, …, m, j = 1, 2, …, n.

- (1)
- Forward reasoning

_{k}, is the value generated in the kth iteration. This can be demonstrated as follows:

_{i}= 1 is satisfied. When x ≤ λ, S

_{i}= 0, and ${S}_{k}$ is the transition triggering vector generated in the kth iteration.

_{k}is the vector identified by the library generated in the kth iteration, and the change of the vector reflects the change of Token in the library. A represents an n-dimensional row vector with elements of 1.

- (2)
- Reverse reasoning

^{−}= O is the input matrix of reverse reasoning, namely, the output matrix of forward reasoning.

^{−}= I is the output matrix of reverse reasoning, namely, the input matrix of forward reasoning. When ${M}_{k+1}^{-}={M}_{k}^{-}$, the reasoning ends.

## 5. Experiments and Discussion

_{15}and X

_{19}. In this case, if two events occurred at the same time, the event with the largest probability value would be selected as the trigger condition of X

_{20}. According to the trigger rule calculation, the probability value X

_{20}= 0.790 of X

_{20}was derived, and the calculation result was consistent with that of CLPSO-FPN, which proved the effectiveness of the fault-diagnosis method in this paper.

## 6. Conclusions

- (1)
- The EMD method is used to effectively process the acquired fault signals, and discrete fault classification signals are obtained to activate the discrete signal processing system. This addresses the problem that occurs when the traditional quantitative analysis method lacks integrity in fault diagnosis and the qualitative analysis method lacks timeliness in fault diagnosis.
- (2)
- The concept of the transition influence factor is defined, the structure of the fault-diagnosis model is optimized and the space explosion of the fault-diagnosis model of a complex system is restrained. A comprehensive learning particle swarm optimized fuzzy Petri net algorithm is proposed to optimize the parameters of the fault-diagnosis model, improve the adaptability of the fault-diagnosis model, reduce the influence of human subjective factors on the fault-diagnosis results and improve the accuracy of fault identification.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Abbreviations

CLPSO-FPN | comprehensive learning particle swarm optimized fuzzy Petri net |

EMD | empirical mode decomposition |

PCA | principal component analysis |

SVM | support vector machine |

PSO | particle swarm optimization |

IMFs | intrinsic mode functions |

TSHFPNs | time sequence hierarchical fuzzy Petri nets |

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**Figure 6.**The model of bearing fault. (

**a**) Fault-diagnosis model based on FPN; (

**b**) fault-diagnosis model based on CLPSO-FPN.

Possibility of Failure | Probability of Failure | Library Confidence |
---|---|---|

Inevitable | (50–100%) | [0.96, 1.00] |

Easily happened | (40–50%) | [0.81, 0.95] |

Occurs more easily | (30–40%) | [0.76, 0.80] |

May occur | (10–30%) | [0.51, 0.75] |

Not likely to happen | (0–10%) | [0.35, 0.50] |

Libraries | Failure Events | Libraries | Failure Events |
---|---|---|---|

p1 | motor is mixed with impurities | p11 | load overload |

p2 | aging of rotor winding | p12 | low resistance of rotor winding |

p3 | Inter-turn short circuit of rotor | p13 | short circuit of rotor winding |

p4 | interphase rotor short circuit | p14 | bearing wear |

p5 | scanning cage malfunction | p15 | fatigue peeling of bearing |

p6 | rolling body fault | p16 | abnormal motor vibration |

p7 | outer ring fault | p17 | bearing fracture |

p8 | inner ring fault | p18 | rotor current increases |

p9 | sweep the chamber | p19 | bearing temperature rise |

p10 | the rotor broken bar | p20 | bearing fault |

Serial Number | The Cause of the Problem | The Fault Phenomenon | Library Confidence |
---|---|---|---|

1 | p1, p2, p3, p4 | p20 | 0.144 |

2 | p5, p6, p7 | p20 | 0.658 |

3 | p7, p8 | p20 | 0.790 |

4 | p9, p10, p11 | p20 | 0.769 |

Parameter | Weight | Parameter | Weight | Parameter | Weight |
---|---|---|---|---|---|

${\omega}_{1,1}$ | 0.5237 | ${\omega}_{2,1}$ | 0.4763 | ${\omega}_{3,2}$ | 0.2457 |

${\omega}_{4,2}$ | 0.7543 | ${\omega}_{5,3}$ | 0.2146 | ${\omega}_{6,3}$ | 0.2577 |

${\omega}_{7,3}$ | 0.5277 | ${\omega}_{7,4}$ | 0.6497 | ${\omega}_{8,4}$ | 0.3503 |

${\omega}_{9,5}$ | 0.6175 | ${\omega}_{10,5}$ | 0.3825 | ${\omega}_{12,7}$ | 0.3397 |

${\omega}_{13,7}$ | 0.6603 | ${\omega}_{18,11}$ | 0.2083 | ${\omega}_{14,11}$ | 0.7917 |

**Table 5.**The table of fault-diagnosis results. (

**a**) The table of fault causes and diagnosis results; (

**b**) the table of failure probability and accuracy.

(a) | ||||
---|---|---|---|---|

Diagnosis Way | Cause of the Problem | Results of Diagnosis | Terminal Malfunction | |

FPN | p6, p7, p8 p9, p10, p11 | p14, p15, p20 p16, p17, p20, p17 | p20 p20 p20 | |

BP-FPN | p6, p7, p8 p9, p10, p11 | p15, p20, p16 p17, p20, nothing | p20 p20 p20 | |

PSO-FPN | p6, p7, p8 p9, p10, p11 | p14, p15, p20 p16, p17, p20, p17 | p20 p20 p20 | |

CLPSO-FPN | p6, p7, p8 p9, p10, p11 | p14, p15, p19, p20 p16, p17, p20, p17, p20 | p20 p20 p20 | |

(b) | ||||

Diagnosis Way | Actual Failure Probability | Diagnostic Fault Probability | Accuracy | Computation Time |

FPN | 0.790 | 0.611 | 77.4% | 1.5924S |

0.769 | 0.536 | 69.7% | ||

0.590 | 0.182 | 30.9% | ||

BP-FPN | 0.790 | 0.790 | 100% | 1.7049S |

0.769 | 0.601 | 78.2% | ||

0.590 | 0 | 0 | ||

PSO-FPN | 0.790 | 0.771 | 97.6% | 1.7918S |

0.769 | 0.625 | 81.3% | ||

0.590 | 0.6075 | 97.0% | ||

CLPSO-FPN | 0.790 | 0.790 | 100% | 1.4832S |

0.769 | 0.768 | 99.9% | ||

0.590 | 0.583 | 98.8% |

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**MDPI and ACS Style**

Xu, C.; Li, J.; Cheng, X.
Comprehensive Learning Particle Swarm Optimized Fuzzy Petri Net for Motor-Bearing Fault Diagnosis. *Machines* **2022**, *10*, 1022.
https://doi.org/10.3390/machines10111022

**AMA Style**

Xu C, Li J, Cheng X.
Comprehensive Learning Particle Swarm Optimized Fuzzy Petri Net for Motor-Bearing Fault Diagnosis. *Machines*. 2022; 10(11):1022.
https://doi.org/10.3390/machines10111022

**Chicago/Turabian Style**

Xu, Chuannuo, Jiming Li, and Xuezhen Cheng.
2022. "Comprehensive Learning Particle Swarm Optimized Fuzzy Petri Net for Motor-Bearing Fault Diagnosis" *Machines* 10, no. 11: 1022.
https://doi.org/10.3390/machines10111022