# Optimal Intrinsic Mode Function Based Detection of Motor Bearing Damages

^{1}

^{2}

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## Abstract

**:**

## 1. Introduction

## 2. Hilbert–Huang Transform

#### 2.1. Empirical Mode Decomposition (EMD)

- (1)
- In a whole data set, the number of zero-crossing must either equal or differ at most by one.
- (2)
- At any point, the mean value of the envelope defined by local maxima and minima is zero.

- Step 1.
- Identify all the local maxima and minima of $x(t)$.
- Step 2.
- Obtain mean envelope ${m}_{ik}$ by connecting upper and lower envelopes.
- Step 3.
- $x(t)$ subtracts ${m}_{ik}$ to obtain a new signal ${h}_{ik}$.
- Step 4.
- Determine ${h}_{ik}$ whether the IMF, such as the establishment of its deposit in the IMFs ${c}_{i}(t)$, otherwise repeat Step 1 to Step 4.
- Step 5.
- Calculate the tendency ${r}_{i}(t)$ by ${r}_{i}(t)=x(t)-{c}_{i}(t)$.
- Step 6.
- Complete decomposition if the tendency is a monotonic function or constant. Otherwise, repeat Step 1 to Step 6.

#### 2.2. Hilbert Transform (HT)

## 3. Greedy Algorithm Based on Empirical Mode Decomposition Selector

#### 3.1. Energy Distribution Model

#### 3.2. Shortest Path Cost

## 4. Measurement and Analysis

#### 4.1. Experimental Measurements

#### 4.2. Signal Analysis

_{1}to c

_{9}are IMFs from high frequency to low frequency, respectively, and the layer c

_{10}shows the tendency function. The IMFs energy can be calculated to the corresponding detection accuracy by using the BPNN, as shown in Table 2. The selected nodes $\Delta {E}_{i}\text{}\text{}0$ are ${E}_{1}$, ${E}_{3}$, ${E}_{4}$, ${E}_{6}$ and ${E}_{10}$, as nodes A, B, C, D, and E and the layers 1, 3, 4, 6, and 10, respectively, are shown in Figure 9. The distance between each of these nodes are shown in Table 3.

- (Rule 1) each node should be the start node,
- (Rule 2) the start node connects to next nearest node,
- (Rule 3) all remaining nodes should be sequentially connected by Rule 2,
- (Rule 4) compare all costs of the shortest close paths formed by each start node in Rule 1.

## 5. Results and Discussion

#### 5.1. HHT Spectrum and GEMD-HHT Spectrum

#### 5.1.1. Healthy

#### 5.1.2. Seal Damage

#### 5.1.3. Race Surface Damages

#### 5.2. Discussion

- Classify damage types: The paper focuses on three types of gearing which are healthy, seal damage, and race surface damage. The main frequency of GEMD-HHT spectrums of the healthy, seal damage, and race surface damage types are 400, 350, and 200 Hz, respectively. The specific damage type can be detected easily by using the proposed GEMD model.
- Realize damage range/size: The proposed GEMD model can realize the size of the race surface damage. We found that the sub-frequency bands of the 0.5 mm and 1.0 mm damage types are at 25–75 Hz and 20–100 Hz, respectively, no matter whether the damages are located on the inner, outer, or both, of the race surface. Thus, by using the proposed GEMD model, the severity of the damaged bearing can be realized by observing the sub-frequency signals.

#### 5.3. Damage Detection

## 6. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 1.**Structure of bearing damage detection using the proposed greedy empirical mode decomposition (GEMD).

**Figure 6.**(

**A**) Healthy bearing, (

**B**) 1.0 mm holes on both inner and outer race, (

**C**) one 1.0 mm hole on inner race, (

**D**) one 1.0 mm hole on outer race, (

**E**) 0.5 mm holes on both inner and outer race, (

**F**) one 0.5 mm hole on inner race, (

**G**) one 0.5 mm hole on outer race, and (

**H**) seal damage.

Bearing Model | Bearing Size (mm) | ||
---|---|---|---|

Inner | Outer | Thickness | |

6001 | 12 | 28 | 8 |

IMF (i) | 1 | 2 | 3 | 4 | 5 |

Energy (%) | 58.8 | 12.5 | 41.9 | 34.4 | 28.9 |

IMF (i) | 6 | 7 | 8 | 9 | 10 |

Energy (%) | 33.1 | 23.8 | 18.4 | 13.8 | 33.88 |

Node Number | A | B | C | D | E |
---|---|---|---|---|---|

IMF Layer | 1 | 3 | 4 | 6 | 10 |

Axis (X,Y) | (1, 58.8) | (3, 41.9) | (4, 34.4) | (6, 33.1) | (10, 33.8) |

A | 0 | 17.02 | 24.58 | 26.18 | 26.57 |

B | 17.02 | 0 | 7.57 | 9.30 | 10.71 |

C | 24.58 | 7.57 | 0 | 2.39 | 6.03 |

D | 26.18 | 9.30 | 2.39 | 0 | 4.06 |

E | 26.57 | 10.71 | 6.03 | 4.06 | 0 |

Model | Accuracy % | ||
---|---|---|---|

SNR | HHT | GEMD-HHT | |

$\infty $ dB | 97.9 | 98.2% | |

30 dB | 97.4% | 97.6% | |

20 dB | 93.1% | 93.9% | |

10 dB | 69.5% | 74.6% |

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## Share and Cite

**MDPI and ACS Style**

Lee, C.-Y.; Huang, K.-Y.; Hsieh, Y.-H.; Chen, P.-H. Optimal Intrinsic Mode Function Based Detection of Motor Bearing Damages. *Appl. Sci.* **2019**, *9*, 2587.
https://doi.org/10.3390/app9132587

**AMA Style**

Lee C-Y, Huang K-Y, Hsieh Y-H, Chen P-H. Optimal Intrinsic Mode Function Based Detection of Motor Bearing Damages. *Applied Sciences*. 2019; 9(13):2587.
https://doi.org/10.3390/app9132587

**Chicago/Turabian Style**

Lee, Chun-Yao, Kuan-Yu Huang, Yu-Hua Hsieh, and Po-Hung Chen. 2019. "Optimal Intrinsic Mode Function Based Detection of Motor Bearing Damages" *Applied Sciences* 9, no. 13: 2587.
https://doi.org/10.3390/app9132587