# Remaining Useful Life Prediction of Rolling Element Bearings Using Supervised Machine Learning

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## Abstract

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## 1. Introduction

- Avoiding catastrophic failure, unscheduled maintenance and production loss.
- Reducing maintenance costs by minimizing the number of unnecessary interventions and machine overhauls.
- Increasing the lifespan of components by providing advance information on the severity of the fault to be maintained.

## 2. Methodology

#### Contributions

- It improves the fitting of the features extracted from vibration measurements through the use of appropriate regression models.
- It explores the possibility of combining regression models with ANNs to improve the predictive accuracy of regression models.
- A test rig was designed and experimental tests were conducted to generate bearing failure data in order to validate the proposed prognostic model. The model was also validated through industrial data provided by a commercial company.

## 3. Statistical Condition Indicators

#### 3.1. Kurtosis

#### 3.2. Root Mean Square

## 4. Regression Analysis

^{2}. The RMSE is defined as the square root of the variance of the residuals between the predicted and the actual RUL. RMSE measures how close the measured data is to the predicted values. The R

^{2}is defined as the ratio between the difference between the sum square total (SST) and sum square error (SSE) to the SST. SST measures the data deviation from the sample mean, and SSE measures the deviation of the data from the model’s predicted values. One of the disadvantages of the R

^{2}metric is that it does not indicate if a regression model provides an adequate fit to the data. Therefore, the adjusted R

^{2}was instead used in this research as the third performance metric. Adjusted R

^{2}is defined as the ratio between the residual mean square errors to the total mean square error (which is the variance of the predicted values).

## 5. Multilayer Artificial Neural Network

_{h}and b

_{o,}respectively. φ

_{h}and φ

_{o}denote the activation functions of the nodes in the hidden and output layers, respectively. Feedforward neural network models also take the form of

## 6. Data Collection

#### 6.1. Dataset 1

#### 6.2. Dataset 2

## 7. Results

#### 7.1. Signal Features Regression

#### 7.2. Artificial Neural Network

## 8. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 7.**Fitted condition indicators for dataset 1: (

**a**) Fitted condition indicators using exponential functions; (

**b**) Fitted condition indicators using polynomial functions.

**Figure 8.**Fitted condition indicators for dataset 2 (exponential and polynomial functions): (

**a**) Actual and fitted root mean square (RMS); (

**b**) Actual and fitted Kurtosis (KU).

**Figure 11.**Remaining useful life (RUL) results (dataset 1): (

**a**) Regression Model RUL results; (

**b**) Artificial neural network RUL results.

**Figure 12.**Remaining useful life (RUL) results (dataset 2): (

**a**) Regression Model RUL results; (

**b**) Artificial neural network RUL results.

Machine State | Increasing Inner Race Bearing Fault |
---|---|

Power rating | 2 MW flux |

Nominal speed | 1800 rpm |

Measurement Channel | Sensor |

Sample rate | 97,656 Hz |

Record length | 6 s |

Sensor type | Accelerometer |

Parameter | Measurement |
---|---|

External Diameter (Pitch) | 84.14 mm |

Internal Diameter (Bore) | 40.00 mm |

Pitch Circle Diameter | 62.71 mm |

Roller Diameter | 11.91 mm |

Number of Rollers | 10 |

Weight of the Specimen | 1.2 kg |

Condition Indicators | Dataset 1 | Dataset 2 | ||||||
---|---|---|---|---|---|---|---|---|

Model Constants | RMSE | Adj. R2 | Model Constants | RMSE | Adj. R2 | |||

a | b | a | b | |||||

RMS | 2.235 | 0.0511 | 0.05248 | 0.957 | 0.003835 | 0.3797 | 0.000717 | 0.995 |

KU | 3.439 | 0.1121 | 0.9469 | 0.975 | 7.87 | 0.2548 | 0.2494 | 0.990 |

Condition Indicators | Dataset 1 | Dataset 2 | ||||||||
---|---|---|---|---|---|---|---|---|---|---|

Model Constants | RMSE | Adj. R2 | Model Constants | RMSE | Adj. R2 | |||||

a0 | a1 | a2 | a0 | a1 | a2 | |||||

RMS | 2.19 | 0.117 | 0.0044 | 0.1644 | 0.5947 | 0.000552 | 0.001365 | 0.003602 | 0.0007735 | 0.853 |

KU | 3.24 | 0.5718 | 0.3004 | 0.2172 | 0.881 | 0.244 | 1.971 | 7.786 | 0.3851 | 0.792 |

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**MDPI and ACS Style**

Li, X.; Elasha, F.; Shanbr, S.; Mba, D.
Remaining Useful Life Prediction of Rolling Element Bearings Using Supervised Machine Learning. *Energies* **2019**, *12*, 2705.
https://doi.org/10.3390/en12142705

**AMA Style**

Li X, Elasha F, Shanbr S, Mba D.
Remaining Useful Life Prediction of Rolling Element Bearings Using Supervised Machine Learning. *Energies*. 2019; 12(14):2705.
https://doi.org/10.3390/en12142705

**Chicago/Turabian Style**

Li, Xiaochuan, Faris Elasha, Suliman Shanbr, and David Mba.
2019. "Remaining Useful Life Prediction of Rolling Element Bearings Using Supervised Machine Learning" *Energies* 12, no. 14: 2705.
https://doi.org/10.3390/en12142705