# A Multi-Model Diagnosis Method for Slowly Varying Faults of Plunger Pump

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## Abstract

**:**

## 1. Introduction

## 2. SVM-MM Algorithm Framework

#### 2.1. State Model

#### 2.2. Conditional Probability of the MM

#### 2.3. Posterior Probability of the SVM

#### 2.4. Probabilistic Fusion

#### 2.5. State Assessment

## 3. Research Object

#### 3.1. The Plunger Pump Mechanism Model

#### 3.2. Fault Simulation and State Model Establishment

## 4. Simulation Results

#### 4.1. Single Fault

#### 4.2. Multiple Faults

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Appendix A

## References

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**Figure 5.**Probability calculated by four methods (MM, SVM, SVM-MM1, and SVM-MM2, ${\alpha}_{p}$ in SVM-MM1 is 0.98, and ${\alpha}_{p}$ in SVM-MM2 is 0.95) during fault diagnosis: (

**a**) Fault ${S}_{1}$ diagnosis results; (

**b**) Fault ${S}_{2}$ diagnosis results; (

**c**) Fault ${S}_{3}$ diagnosis results; (

**d**) Fault ${S}_{4}$ diagnosis results.

Parameter | Value |
---|---|

rotation speed | 5000 r/min |

outlet pressure rating | 16 MPa |

oil return pressure | 0.3~0.55 MPa |

inlet pressure | 0.25~0.3 MPa |

egress traffic | 7 L/min |

return oil flow | <0.4 L/min |

Fault Type | Symbol | Parameter Change |
---|---|---|

shaft displacement | ${S}_{1}$ | swash plate inclination $\gamma -2$ |

pipeline leakage | ${S}_{2}$ | discharge pressure ${p}_{o}-2$ |

piston sticking | ${S}_{3}$ | number of plungers $z-1$ |

spring breakage | ${S}_{4}$ | piston stroke $S-0.02$ |

Fault Type | Method | ${\mathit{\epsilon}}_{\mathit{d}}$ | ${\mathit{\epsilon}}_{\mathit{i}}$ |
---|---|---|---|

MM | 0.545 | 0.625 | |

${S}_{1}$ | SVM-MM1 | 0.345 | 0.585 |

SVM-MM2 | 0.010 | 0.565 | |

MM | 0.790 | 1.14 | |

${S}_{2}$ | SVM-MM1 | 0.265 | 0.790 |

SVM-MM2 | 0.220 | 0.635 | |

MM | 0.565 | 0.645 | |

${S}_{3}$ | SVM-MM1 | 0.420 | 0.610 |

SVM-MM2 | 0.010 | / | |

MM | 0.430 | 1.135 | |

${S}_{4}$ | SVM-MM1 | 0.325 | 1.025 |

SVM-MM2 | 0.009 | 0.995 |

Fault Type | Method | First Fault | Second Fault | ||
---|---|---|---|---|---|

${\mathit{\epsilon}}_{\mathit{d}}$ | ${\mathit{\epsilon}}_{\mathit{i}}$ | ${\mathit{\epsilon}}_{\mathit{d}}$ | ${\mathit{\epsilon}}_{\mathit{i}}$ | ||

${S}_{1}+{S}_{2}$ | MM | 0.545 | 0.620 | 0.760 | 1.060 |

SVM-MM | 0.380 | 0.580 | 0.250 | 0.785 | |

${S}_{3}+{S}_{4}$ | MM | 0.560 | 0.645 | 0.475 | 0.535 |

SVM-MM | 0.425 | 0.610 | 0.380 | 0.510 |

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## Share and Cite

**MDPI and ACS Style**

Yu, C.; Yan, H.; Zhang, X.; Ye, H.
A Multi-Model Diagnosis Method for Slowly Varying Faults of Plunger Pump. *J. Mar. Sci. Eng.* **2022**, *10*, 1968.
https://doi.org/10.3390/jmse10121968

**AMA Style**

Yu C, Yan H, Zhang X, Ye H.
A Multi-Model Diagnosis Method for Slowly Varying Faults of Plunger Pump. *Journal of Marine Science and Engineering*. 2022; 10(12):1968.
https://doi.org/10.3390/jmse10121968

**Chicago/Turabian Style**

Yu, Changli, Haodong Yan, Xingming Zhang, and Hua Ye.
2022. "A Multi-Model Diagnosis Method for Slowly Varying Faults of Plunger Pump" *Journal of Marine Science and Engineering* 10, no. 12: 1968.
https://doi.org/10.3390/jmse10121968