# A Self-Learning Fault Diagnosis Strategy Based on Multi-Model Fusion

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Fault Diagnosis Method

_{1}, m

_{2}, …, m

_{n}and the classification models M

_{1}, M

_{2}, …, M

_{N}.

_{1}, M

_{2}, …, M

_{N}. Then, according to the results of each model, a Fusion operator Fi is used to make a decision. Then according to the requirement of self-learning, if the results of the classification models meet the requirement of self-learning, it will use the real-time data sample to update them.

#### 2.1. Fault Detection

- ➢
- The detection models we choose are different from each other, or they can be complementary, in order to decrease false alarms and missing alarm rates.
- ➢
- The detection models need to have a high detection accuracy to avoid a cumulative error.
- ➢
- As the detection models will run in parallel, judicious implementation approaches can be used in combination with a multi-core and graphics processing unit (GPU)-based system to reduce the computational time.

#### 2.2. Fault Classification

- ➢
- The classification models are different from each other, in order to increase the classification accuracy.
- ➢
- The classification models need to have a high classification accuracy to avoid the occurrence of cumulative error.
- ➢
- The computational time of each classification model must be as short as possible. Indeed, for fault classification, the time constraint is less.

_{i}for classifier i) and the accumulated vote for each class is calculated as follows:

_{i}is the weight value of the ith classifier and y is the result of the fusion.

## 3. Case of Complex Condition

#### 3.1. Fault Detection

^{2}statistics [13,30]. The second one is based on the KICA [31] and the I

^{2}statistic [33]. The third model uses the SVDD and the distance between the test sample, and the center of a hypersphere is used as the fault detection feature [27,34]. The flowchart is described in Figure 2.

_{cl}

^{2}is the confidence limit of T

^{2}statistic. The details of this method can be found in Reference [13].

_{cl}

^{2}is the confidence limit of the I

^{2}statistic. The details of this method can be found in Reference [34].

_{i}= 1, (i = 1, 2, 3) or healthy if y

_{i}= -1, (i = 1, 2, 3). r is the radius of the high dimensional sphere and d is the distance from the detection point to the center of the high dimensional sphere.

_{1}, y

_{2}, y

_{3}], and the fusion operator is F

_{e}= [ω

_{1},ω

_{2},ω

_{3}] where $\sum _{i=1}^{n}{\mathsf{\omega}}_{i}}=1$.

_{e}= 1, a fault is detected. If Re = 0 or −1, the sample is used to update the model(s) that have detected that no fault has occurred.

#### 3.2. Fault Classification

_{vote}(x) is fault type of the final decision, g

_{i}(x) is the voting time of ith fault by these classification models and K is the number of fault types.

## 4. Experimental Results and Analysis

#### 4.1. Fault Detection

^{2}statistic. The result showed that fault 2 can be detected with good performance. However, the KPCA failed to detect fault 1 and fault 3, and there were many false alarms. Moreover, the insufficient historical healthy sample also contributed to the poor fault detection results.

^{2}statistic monitoring with the KICA. The results showed that fault 1 and fault 3 were clearly detected, while fault 2 was not detected. Figure 4c shows the fault detection result with the SVDD. The red line is the radius of the hypersphere obtained with the healthy data samples. Despite a high false alarm rate, the fault detection performances were fairly good.

^{2}and square predictive error (SPE) statistic, respectively. The performances were obviously very poor. Significant improvements were obtained when the SVDD was used to analyze the features extracted with the PCA. The results are plotted in Figure 6.

#### 4.2. Fault Classification

## 5. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

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Files Sections | Healthy/Faulty |
---|---|

1–80 | Normal |

81–160 | Fault 1: Outer race failure in bearing 1 |

161–240 | Normal |

241–320 | Fault 2: Outer race failure in bearing 3 |

321–400 | Normal |

401–480 | Fault 3: inner race failure in bearing 3 |

Approach | False Alarm Rate (%) | Missing Alarm Rate (%) | |
---|---|---|---|

KPCA | 1.04 | 33.33 | |

KICA | 3.13 | 17.08 | |

SVDD | 19.17 | 0.0 | |

PCA | T^{2} | 0.0 | 47.50 |

SPE | 0.0 | 49.17 | |

PCA-SVDD | 0.0 | 27.92 | |

Multi-model Detection | 19.38 | 0.0 | |

Proposed Strategy | 2.29 | 0.0 |

Approach | Classification Accuracy | |||
---|---|---|---|---|

Fault 1 | Fault 2 | Fault 3 | Overall | |

ELM | 40.5/80 | 60/80 | 80/80 | 75.20% |

SVDD | 44/80 | 74/80 | 73/80 | 79.58% |

BP | 22/80 | 80/80 | 77/80 | 74.58% |

RVM | 56/80 | 74/80 | 79/80 | 87.08% |

Multi-model | 62/80 | 80/80 | 80/80 | 92.50% |

Proposed Strategy | 78/80 | 80/80 | 80/80 | 99.17% |

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**MDPI and ACS Style**

Wang, T.; Dong, J.; Xie, T.; Diallo, D.; Benbouzid, M.
A Self-Learning Fault Diagnosis Strategy Based on Multi-Model Fusion. *Information* **2019**, *10*, 116.
https://doi.org/10.3390/info10030116

**AMA Style**

Wang T, Dong J, Xie T, Diallo D, Benbouzid M.
A Self-Learning Fault Diagnosis Strategy Based on Multi-Model Fusion. *Information*. 2019; 10(3):116.
https://doi.org/10.3390/info10030116

**Chicago/Turabian Style**

Wang, Tianzhen, Jingjing Dong, Tao Xie, Demba Diallo, and Mohamed Benbouzid.
2019. "A Self-Learning Fault Diagnosis Strategy Based on Multi-Model Fusion" *Information* 10, no. 3: 116.
https://doi.org/10.3390/info10030116