# Fault Diagnosis of Mine Truck Hub Drive System Based on LMD Multi-Component Sample Entropy Fusion and LS-SVM

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## Abstract

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## 1. Introduction

## 2. Literature Analysis

- (1)
- A feature extraction method based on LMD multi-component sample entropy fusion is proposed. Aiming at the problems of mode confusion and poor accuracy in LMD decomposition, canonical correlation analysis (CCA) [34,35] is used to discriminate the true and false components of the decomposed PF, and then the multi-component sample entropy fusion sample entropy feature is constructed.
- (2)
- Combining the vibration signal characteristics of the wheel drive system, the LMD multi-component sample entropy fusion feature is introduced into the fault diagnosis of nonstationary and nonlinear vibration signals in the wheel drive system, better characterizing the fault feature information.
- (3)
- In response to the difficulty in obtaining vibration signals from the wheel drive system and the small number of samples, LS-SVM is proposed to classify fault features using LMD multi-component sample entropy fusion features extracted from the vibration signals of the wheel drive system, which improves the accuracy of the algorithm.
- (4)
- The effectiveness of this method has been verified through experiments.

## 3. Theory

#### 3.1. Local Mean Decomposition

_{i}(i = 1, 2, 3…) of signal x(t), and calculate the mean value m

_{i}between adjacent extreme points n

_{i}and n

_{i}

_{+1}and their envelope estimation value a

_{i}.

_{i}and envelope estimation values a

_{i}in turn and use the moving average method to process them respectively to obtain the local mean function m

_{11}(t) and envelope estimation function a

_{11}(t).

_{11}(t) is separated from the original signal x(t) to obtain

_{11}(t) is used to demodulate the obtained h

_{11}(t) to obtain the frequency modulation signal s

_{11}(t).

_{11}(t) is a pure frequency modulation signal, so its corresponding envelope estimation function a

_{12}(t) = 1. If the envelope estimation function a

_{12}(t) ≠ 1, treat s

_{11}(t) as the original signal and repeat the above iterative steps until the pure frequency modulation signal s

_{1n}(t) is obtained, and then −1 ≤ s

_{1n}(t) ≤ 1 can be satisfied, and the corresponding envelope estimation function a

_{1(n+1)}(t) = 1. The specific steps are as follows:

_{1(n+1)}(t) = 1 is the ideal state for obtaining pure frequency modulation signal s

_{1n}(t). In practice, in order to reduce the number of iterations and improve the calculation efficiency, a small deviation Δ (Δ > 0) is introduced without changing the decomposition results. When 1 − Δ ≤ a

_{1(n+1)}(t) ≤ 1+ Δ, s

_{1n}(t) is considered to be a relatively ideal pure frequency modulation signal. With reference to the literature and a large amount of experimental data, deviation Δ is the most appropriate value in the range of [0.001, 0.1]. In this paper, under the condition that the iteration results are correct and meet the needs of feature extraction, deviation Δ is taken as 0.05. Then, the above iteration termination condition is as follows:

_{1}(t) can be obtained by multiplying all envelope functions obtained before the end of iteration.

_{1}(t) and s

_{1n}(t).

_{1}(t) is separated from x(t), and the remaining signals are recorded as u

_{1}(t). Repeat the above steps with signal u

_{1}(t) as a new signal for k times until u

_{k}(t) is a monotone function, and then the extreme point u

_{k}(t) ≤ 1.

_{k}(t), which is shown as follows:

#### 3.2. Sample Entropy

_{m}(i) is constructed according to the serial number.

_{m}(i), X

_{m}(j)] as the maximum difference between the two vectors X

_{m}(i) and X

_{m}(j).

_{m}(i), the number of d[X

_{m}(i), X

_{m}(j)] less than r is recorded as B

_{i}, where r is the similarity threshold. Record the ratio of B

_{i}to the number of vectors as ${B}_{i}^{m}\left(r\right)$.

#### 3.3. Canonical Correlation Analysis

#### 3.4. LMD Multi-Component Sample Entropy Fusion

_{k}(t). The correlation between k PF components and the original signal is analyzed by CCA method. The PF component with large correlation coefficient (the real component in the effective frequency domain) is taken as the analysis object, and then the sample entropy of the effective PF component is calculated. Since the original signal contains false invalid signals, a single PF component can only characterize the fault characteristics in the corresponding frequency domain. Therefore, the sample entropy corresponding to the effective PF component of LMD decomposition is used to construct a feature vector, and this vector is used as the fault feature for analysis. LMD multi-component sample entropy fusion feature extraction model is shown in Figure 1.

#### 3.5. LS-SVM

## 4. Experimental Analysis

#### 4.1. Data Collection

#### 4.2. Vibration Signal Analysis

_{5}(t) fluctuates about three times and the amplitude is very weak and can be regarded as a monotonic function when a small deviation of 0.05 Δ is added.

#### 4.3. Fault Feature Extraction

#### 4.4. Classification of Fault States

## 5. Conclusions

- (1)
- The proposed LMD multi-component sample entropy fusion can effectively extract fault diagnosis features within the wheel drive system, which has significant advantages compared to traditional methods.
- (2)
- Introducing LS-SVM into the fault feature classification of wheel hub drive systems, the RBF kernel function is analyzed to be more suitable for fault classification in this study through two dimensions of training time and testing accuracy.
- (3)
- The method was applied to gear experimental data and achieved good diagnostic results.
- (4)
- The proposed method has been validated through experimental data analysis, but, due to significant differences in vibration characteristics caused by complex working conditions and varying degrees of component damage, further research is needed on the diagnostic effectiveness in actual working environments.

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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Gear Type | Canonical Correlation | |||||
---|---|---|---|---|---|---|

PF_{1} | PF_{2} | PF_{3} | PF_{4} | PF_{5} | u_{5}(t) | |

normal | 0.685 | 0.593 | 0.186 | 0.019 | 0.00023 | 0.00011 |

broken teeth | 0.792 | 0.526 | 0.238 | 0.021 | 0.00017 | 0.00006 |

wear | 0.612 | 0.624 | 0.195 | 0.012 | 0.00030 | 0.00017 |

broken teeth + wear | 0.801 | 0.496 | 0.156 | 0.024 | 0.00013 | 0.00014 |

Type | Normal | Broken Teeth | Wear | Broken Teeth + Wear | |
---|---|---|---|---|---|

linear kernel function | training time | 0.321 s | 0.332 s | 0.340 s | 0.343 s |

precision | 90% | 70% | 80% | 80% | |

Polynomial kernel function | training time | 0.364 s | 0.373 s | 0.387 s | 0.382 s |

precision | 90% | 80% | 80% | 90% | |

RBF kernel function | training time | 0.431 s | 0.457 s | 0.463 s | 0.475 s |

precision | 100% | 100% | 100% | 100% |

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## Share and Cite

**MDPI and ACS Style**

Xu, L.; Li, W.; Zhang, B.; Zhu, Y.; Lang, C.
Fault Diagnosis of Mine Truck Hub Drive System Based on LMD Multi-Component Sample Entropy Fusion and LS-SVM. *Actuators* **2023**, *12*, 468.
https://doi.org/10.3390/act12120468

**AMA Style**

Xu L, Li W, Zhang B, Zhu Y, Lang C.
Fault Diagnosis of Mine Truck Hub Drive System Based on LMD Multi-Component Sample Entropy Fusion and LS-SVM. *Actuators*. 2023; 12(12):468.
https://doi.org/10.3390/act12120468

**Chicago/Turabian Style**

Xu, Le, Wei Li, Bo Zhang, Yubin Zhu, and Chaonan Lang.
2023. "Fault Diagnosis of Mine Truck Hub Drive System Based on LMD Multi-Component Sample Entropy Fusion and LS-SVM" *Actuators* 12, no. 12: 468.
https://doi.org/10.3390/act12120468