# An Experimental Study on Condition Diagnosis for Thrust Bearings in Oscillating Water Column Type Wave Power Systems

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## Abstract

**:**

## 1. Introduction

## 2. Strategy of Diagnosis of Bearing Condition

#### 2.1. Target Selection Using Failure Mode and Effects Analysis (FMEA)

#### 2.2. Analysis of Thrust Bearing Failure Modes

#### 2.3. Construction of the Test Equipment

#### 2.4. Procedure for Health Monitoring using Classification Algorithms

## 3. Strategy of Diagnosis of Bearing Condition

#### 3.1. Sensor Signal Acquisition

#### 3.2. Feature Extraction

#### 3.3. Dimensionality Reduction

#### 3.4. Classifier Learning

#### 3.4.1. Naïve Bayes (NB)

#### 3.4.2. k-Nearest Neighbor (k-NN)

#### 3.4.3. Multi-Layer Perceptron (MLP)

## 4. Results of Machine Learning using the Classification Algorithms

#### 4.1. Learning Results of the Classification Algorithms

#### 4.2. Verification of the Classification Algorithms

## 5. Conclusions

- -
- An outer ring rotating test equipment setup was developed that can ensure the abnormal and fault data by reproducing the operation environment of the bearing in use. Using the developed test equipment, the vibration data in the normal operation state and false brinelling state were measured, and the characteristics of the data were extracted by analyzing the vibration spectrum.
- -
- As a result, features were extracted by applying a feature extraction scheme based on statistical values in the frequency and time domains of the vibration data in the normal and abnormal state acquired in the test equipment. At this time, a total of 45 features are created for the three-axis vibration sensor. In this study, features with more than 50% correlation were applied to three classification algorithms: NB, k-NN, MLP.
- -
- The learning accuracy for each algorithm was 98.1% for NB, 99.1% for k-NN and 99.1% for MLP, with high accuracy calculated for all algorithms. By applying the test data sets to the three classifier algorithms proposed in this study, it was confirmed that the accuracy of all algorithms was approximately 99%.
- -
- Finally, the subject of this study is a unique field of wave power system, and its application to this field is considered to be of great value. By accumulating data using the test equipment of this study, this study is considered to be a cornerstone for the failure reproduction of the wave power system. In addition, it is possible to conduct a study to diagnose a failure in connection with a simulation using the accumulated data.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 1.**Conceptual diagram of OWC [13].

**Figure 4.**Configurations of test equipment of thrust bearing for simulating the operating condition: (

**a**) Design drawing; (

**b**) Real appearance; (

**c**) Measuring scene.

Mode No. | Operation Condition | Operation RPM | Fault |
---|---|---|---|

1 | Normal state | 400 | No fault |

2 | Abnormal state 1 | 400 | No grease |

3 | Abnormal state 2 | 400 | No grease + fault |

Feature Index | Description |
---|---|

Mean | $T1=\frac{{\sum}_{n=1}^{N}x\left(n\right)}{N}$ |

Variance | $T2={\left(\frac{{\sum}_{n=1}^{N}\sqrt{\left|x\left(n\right)\right|}}{N}\right)}^{2}$ |

Standard deviation | $T3=\sqrt{\frac{{\sum}_{n=1}^{N}{\left(x\left(n\right)-T1\right)}^{2}}{N-1}}$ |

RMS | $T4=\sqrt{\frac{{\sum}_{n=1}^{N}{\left(x\left(n\right)\right)}^{2}}{N}}$ |

Skewness | $T5=\frac{{\sum}_{n=1}^{N}{\left(x\left(n\right)-T1\right)}^{3}}{\left(N-1\right){\sigma}^{3}}$ |

Kurtosis | $T6=\frac{{\sum}_{n=1}^{N}{\left(x\left(n\right)-T1\right)}^{4}}{\left(N-1\right){\sigma}^{4}}$ |

Peak value | $T7=\frac{1}{2}\left[\mathrm{max}\left(x\left(n\right)\right)-\mathrm{min}\left(x\left(n\right)\right)\right]$ |

Crest factor | $T8=\frac{T7}{T4}$ |

Shape factor | $T9=\frac{T4}{\frac{{\sum}_{n=1}^{N}\left|x\left(n\right)\right|}{N}}$ |

Feature Index | Description |
---|---|

Mean | $F1=\frac{{\sum}_{m=1}^{M}y\left(m\right)}{M}$ |

Variance | $F2=\frac{{\sum}_{m=1}^{M}{\left(y\left(m\right)-F1\right)}^{2}}{M-1}$ |

Third moment | $F3=\frac{{\sum}_{m=1}^{M}{\left(y\left(m\right)-F1\right)}^{3}}{M{\left(\sqrt{F2}\right)}^{3}}$ |

Fourth moment | $F4=\frac{{\sum}_{m=1}^{M}{\left(y\left(m\right)-F1\right)}^{4}}{M{\left(F2\right)}^{2}}$ |

Grand mean | $F5=\frac{{\sum}_{m=1}^{M}{f}_{m}y\left(m\right)}{{\sum}_{m=1}^{M}y\left(m\right)}$ |

Standard deviation | $F6=\sqrt{\frac{{\sum}_{m=1}^{M}{\left({f}_{m}-F5\right)}^{2}y\left(m\right)}{M}}$ |

Dataset No. | Description | Mode Combination |
---|---|---|

1 | Normal state (100 sec) + Abnormal state 1 (100 sec) | Mode 1 & Mode 2 |

2 | Normal state (50 sec) + Abnormal state 1 (50 sec) + Normal state (50 sec) + Abnormal state 1 (50 sec) | Mode 1 & Mode 2 |

3 | Normal state (100 sec) + Abnormal state 1 (50 sec) + Abnormal state 2 (50 sec) | Mode 1 & Mode 2 & Mode 3 |

Data Set No. | Naïve Bayes | k-Nearest Neighbor | Multi-Layer Perceptron |
---|---|---|---|

1 | 99.5% | 99.0% | 100% |

2 | 98.0% | 100% | 100% |

3 | 99.5% | 99.5% | 99.5% |

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**MDPI and ACS Style**

Kim, T.-W.; Oh, J.; Min, C.; Hwang, S.-Y.; Kim, M.-S.; Lee, J.-H.
An Experimental Study on Condition Diagnosis for Thrust Bearings in Oscillating Water Column Type Wave Power Systems. *Sensors* **2021**, *21*, 457.
https://doi.org/10.3390/s21020457

**AMA Style**

Kim T-W, Oh J, Min C, Hwang S-Y, Kim M-S, Lee J-H.
An Experimental Study on Condition Diagnosis for Thrust Bearings in Oscillating Water Column Type Wave Power Systems. *Sensors*. 2021; 21(2):457.
https://doi.org/10.3390/s21020457

**Chicago/Turabian Style**

Kim, Tae-Wook, Jaewon Oh, Cheonhong Min, Se-Yun Hwang, Min-Seok Kim, and Jang-Hyun Lee.
2021. "An Experimental Study on Condition Diagnosis for Thrust Bearings in Oscillating Water Column Type Wave Power Systems" *Sensors* 21, no. 2: 457.
https://doi.org/10.3390/s21020457