# A Study of Noise Effect in Electrical Machines Bearing Fault Detection and Diagnosis Considering Different Representative Feature Models

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## Abstract

**:**

## 1. Introduction

## 2. Bearing Fault Detection Workflow, Problem Description and Review

#### 2.1. General Perception of the Bearing Fault Detection Workflow

#### 2.2. A Short Review of Bearing Fault Datasets

#### 2.3. Feature Extraction and Selection

#### 2.4. Machine Learning and Deep Learning Models

## 3. Study of the Noise Effect in Bearing Fault Detection

#### 3.1. Emulation of Different Noisy Environments

#### 3.2. Dataset under Consideration

#### 3.3. Adopted Feature Domains for Evaluation

#### 3.3.1. Statistical Features

#### 3.3.2. Wavelet Packet Decomposition

#### 3.3.3. Continuous Wavelet Transform

#### 3.3.4. Signal-to-Image Conversion

#### 3.4. Adopted Learning Models and Evaluation Study

## 4. Results

#### 4.1. Performance with No Noise

#### 4.2. Performance in Noisy Environments

## 5. Discussion

- No-noise under individual load conditions:
- -
- Preprocessing method: For machine learning candidates, TDA is preferred over WPD. Apart from the better produced performance, TDA typically involves straightforward computations directly in the time domain which is often simpler to implement and computationally less intensive compared to frequency domain methods like Fourier transform. In the deep learning context CWT appears to be a strong approach as it consistently produced high accuracy results across different neural network architectures, including LeNet-5, 1D CNN-2L, 1D CNN-4L, 2D CNN-2L and 2D CNN-4L.
- -
- Training model: It appears that the 1D CNN model with four layers consistently performed very well across the different load conditions. This model is also relatively easier to implement compared to deep 2D convolutional architectures like LeNet-5 and 2D CNNs, making it an attractive choice in terms of both performance and simplicity.

- No-noise with all load conditions considered in a merged dataset:
- -
- Preprocessing method: In this case, TDA is preferred over WPD again, while, in the deep learning context, CWT appears to be again the most dominant approach in all training model cases. It should be noted that, with low deviation from the best performed approach, raw signals can be used in 1D implementations in the case that the lowest computational burden is needed from the signal processing perspective.
- -
- Training model: The most dominant model is 1D CNN-4L, while 1D CNN-2L and both 2D CNNs can also be used. However, the 1D CNN models seem to be more effective at capturing the relevant features of rolling bearing fault data compared with 2D CNNs. Also, 1D CNN architectures are generally simpler than 2D CNN architectures, both in terms of the model architecture and the number of parameters.

- Noisy environment under individual load conditions:
- -
- Preprocessing method: For machine learning candidates, WPD seems to perform slightly better under weak noise conditions only; thus, TDA is preferable in general in this case. For deep learning cases, CWT is clearly the most suitable for all cases with raw signals producing noise resilient forms in the 1D-CNN models.
- -
- Training model: It appears that the 1D CNN model with two layers performs better than 1D CNN-4L for weak noise conditions, but the latter is more resilient to medium and strong noise environments. In the 2D CNN implementations the one with two layers performs consistently better than the one which includes four layers. However, 1D CNN is preferred over 2D CNN in terms of performance and complexity.

- Noisy environment with all load conditions considered in a merged dataset:
- -
- Preprocessing method: In this case, WPD performs slightly better than TDA under strong noise but produces a degraded performance with respect to TDA in all other cases. In deep learning models, CWT provides a reliable preprocessing approach in all cases. However, the most resilient case is to include raw signals in deeper architectures of 1D CNN.
- -
- Training model: From the 2D CNN family, as the number of layers increases a less accurate performance is observed. In general, 1D CNN models seem to be well-suited to processing such data because they are designed to capture patterns along a single dimension, making them a natural choice for time series analysis. Deeper 1D CNN seems to work better with raw data in this generalized scenario under all noisy conditions. Also, this model provides the best choice from the computational burden perspective.

## 6. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## Abbreviations

AE | Auto-Encoder | KNN | k-Nearest Neighbors |

AWGN | Additive White Gaussian Noise | LSTM | Long Short-Term Memory |

BF | Ball Fault | ML | Machine Learning |

CNN | Convolutional Neural Network | MMA | Mayfly Optimization Algorithm |

CWC | Continuous Wavelet Coefficient | ORF | Outer Race Fault |

CWRU | Case Western Reserve University | PCA | Principal Component Analysis |

CWT | Continuous Wavelet Transform | PSO | Particle Swarm Optimization |

DAT | Digital Audio Tape | RMSF | Root Mean Square Frequency |

DBN | Deep Belief Network | RNN | Recurrent Neural Network |

DFT | Discrete Fourier Transform | RUL | Remaining Useful Life |

DL | Deep Learning | RVF | Root Variance Frequency |

DWT | Discrete Wavelet Transform | SIC | Signal-to-Image Conversion |

EMD | Empirical Mode Decomposition | SNR | Signal-to-Noise Ratio |

EEMD | Ensemble Empirical | STFT | Short-Time Fourier Transform |

Mode Decomposition | |||

EWT | Empirical Wavelet Transform | SVD | Singular Value Decomposition |

GAN | Generative Adversarial Network | SVM | Support Vector Machine |

GWO | Gray Wolf Optimization | TDA | Time-Domain Analysis |

FC | Frequency Center | TQWT | Tunable Q-Factor Wavelet Transform |

FFT | Fast Fourier Transform | WOA | Whale Optimization Algorithm |

IMS | Intelligent Maintenance Systems | WPD | Wavelet Package Decomposition |

IRF | Inner Race Fault |

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**Figure 2.**Visual representation of the rolling bearing fault detection process from the CNN perspective using different feature extraction methods.

**Figure 9.**Feature representation for all learning models in their last dense layer under normal conditions (no-noise).

**Figure 10.**Feature representation for all learning models in their last dense layer in noisy environments (SNR = −2).

**Figure 11.**Overall performance for all models with respect to the different SNR values for the merged dataset case (all loading conditions).

Dataset Name | Fault Mode | Sensor Type | Sampling Rate | Fault Type |
---|---|---|---|---|

CWRU [6] | Artificial | Accelerometer (2 sensors) | 12/48 kHz | Inner and outer race, ball fault; 4 fault diameters: 0.007, 0.014, 0.021 and 0.028 inches; 4 load conditions: 0, 1, 2 and 3 (HP) |

IMS [7] | Accelerated aging test | Accelerometer (2 sensors) | 20 kHz | Inner and outer race, ball fault; 3 run-to-failure tests |

Paderborn [8] | Artificial and Accelerated aging test | Accelerometer (1 sensor), Current (2 sensors), Thermocouple (1 sensor) | 64 kHz | 6 undamaged bearings and 12 artificially damaged; 14 bearing faults emerged from accelerated life tests; inner and outer race fault |

PRONOSTIA [9] | Accelerated aging tests | Accelerometer (2 sensors), Thermocouple (1 sensor) | 25.6 kHz | 3 operating conditions; 17 run-to-failure tests |

Class | Fault Type | Fault Diameter (inch) |
---|---|---|

0 | Ball | 0.007 |

1 | Ball | 0.014 |

2 | Ball | 0.021 |

3 | Ball | 0.028 |

4 | Inner | 0.007 |

5 | Inner | 0.014 |

6 | Inner | 0.021 |

7 | Inner | 0.028 |

8 | [email protected] | 0.007 |

9 | [email protected] | 0.007 |

10 | [email protected] | 0.007 |

11 | [email protected] | 0.014 |

12 | [email protected] | 0.021 |

13 | [email protected] | 0.021 |

14 | [email protected] | 0.021 |

15 | Normal | - |

Name | Formula |
---|---|

min value | $min{\left\{{x}_{i}\right\}}_{i=1}^{N}$ |

max value | $max{\left\{{x}_{i}\right\}}_{i=1}^{N}$ |

mean value | $\overline{x}=\frac{{\sum}_{i=1}^{N}{x}_{i}}{N}$ |

standard deviation value | $\sigma =\sqrt{\frac{1}{N}{\sum}_{i=1}^{N}{({x}_{i}-\overline{x})}^{2}}$ |

root mean square value | $rms={\left(\frac{1}{N}{\sum}_{i=1}^{N}{x}_{i}^{2}\right)}^{1/2}$ |

skewness value | $skewness=\frac{1}{N}{\sum}_{i=1}^{N}{\left[\frac{({x}_{i}-\overline{x})}{\sigma}\right]}^{3}$ |

kurtosis value | $kurtosis=\frac{1}{N}{\sum}_{i=1}^{N}{\left[\frac{({x}_{i}-\overline{x})}{\sigma}\right]}^{4}-3$ |

crest factor | $crest=\frac{max\left({x}_{i}\right)}{{\left(\frac{1}{N}{\sum}_{i=1}^{N}{x}_{i}^{2}\right)}^{1/2}}$ |

form factor | $form=\frac{{\left(\frac{1}{N}{\sum}_{i=1}^{N}{x}_{i}^{2}\right)}^{1/2}}{\overline{x}}$ |

Layer No. | Layer Type | Kernel Size | Stride | Filters | Output Shape | Trainable Parameters |
---|---|---|---|---|---|---|

1 | Convolution 1 | $5\times 5$ | 1 | 6 | $28\times 28$ | 156 |

2 | Pooling 1 | $2\times 2$ | 2 | 6 | $14\times 14$ | - |

3 | Convolution 2 | $5\times 5$ | 1 | 16 | $10\times 10$ | 2416 |

4 | Pooling 2 | $2\times 2$ | 2 | 16 | $5\times 5$ | - |

5 | Dense | - | - | - | 120 | 48,120 |

6 | Dense | - | - | - | 84 | 10,164 |

7 | Output | - | - | - | 16 | 1360 |

Layer No. | Layer Type | Kernel Size | Stride | Filters | Output Shape | Trainable Parameters |
---|---|---|---|---|---|---|

1 | Convolution 1 | $3\times 1$ | 2 | 64 | $511\times 64$ | 256 |

2 | Pooling 1 | $2\times 1$ | 2 | 64 | $255\times 64$ | - |

3 | Convolution 2 | $3\times 1$ | 2 | 128 | $127\times 128$ | 24,704 |

4 | Pooling 2 | $2\times 1$ | 2 | 128 | $63\times 128$ | - |

5 | Dense | - | - | - | 100 | 806,500 |

6 | Dense | - | - | - | 50 | 5050 |

7 | Output | - | - | - | 16 | 816 |

Layer No. | Layer Type | Kernel Size | Stride | Filters | Output Shape | Trainable Parameters |
---|---|---|---|---|---|---|

1 | Convolution 1 | $3\times 1$ | 2 | 16 | $511\times 16$ | 64 |

2 | Pooling 1 | $2\times 1$ | 2 | 16 | $255\times 16$ | - |

3 | Convolution 2 | $3\times 1$ | 2 | 32 | $127\times 32$ | 1568 |

4 | Pooling 2 | $2\times 1$ | 2 | 32 | $63\times 32$ | - |

5 | Convolution 3 | $3\times 1$ | 2 | 64 | $31\times 64$ | 6208 |

6 | Pooling 6 | $2\times 1$ | 2 | 64 | $15\times 64$ | - |

7 | Convolution 4 | $3\times 1$ | 2 | 128 | $7\times 128$ | 24,704 |

8 | Pooling 4 | $2\times 1$ | 2 | 128 | $3\times 128$ | - |

9 | Dense | - | - | - | 100 | 38,500 |

10 | Dense | - | - | - | 50 | 5050 |

11 | Output | - | - | - | 16 | 816 |

Layer No. | Layer Type | Kernel Size | Stride | Filters | Output Shape | Trainable Parameters |
---|---|---|---|---|---|---|

1 | Convolution 1 | $3\times 3$ | 2 | 64 | $16\times 16$ | 640 |

2 | Pooling 1 | $2\times 2$ | 2 | 64 | $8\times 8$ | - |

3 | Convolution 2 | $3\times 3$ | 2 | 128 | $4\times 4$ | 73,856 |

4 | Pooling 2 | $2\times 2$ | 2 | 128 | $2\times 2$ | - |

5 | Dense | - | - | - | 100 | 51,300 |

6 | Dense | - | - | - | 50 | 5050 |

7 | Output | - | - | - | 16 | 816 |

Layer No. | Layer Type | Kernel Size | Stride | Filters | Output Shape | Trainable Parameters |
---|---|---|---|---|---|---|

1 | Convolution 1 | $3\times 3$ | 2 | 16 | $16\times 16$ | 160 |

2 | Pooling 1 | $2\times 2$ | 2 | 16 | $8\times 8$ | - |

3 | Convolution 2 | $3\times 3$ | 2 | 32 | $4\times 4$ | 4640 |

4 | Pooling 2 | $2\times 2$ | 2 | 32 | $2\times 2$ | - |

5 | Convolution 3 | $3\times 3$ | 2 | 64 | $1\times 1$ | 18,496 |

6 | Pooling 6 | $2\times 2$ | 2 | 64 | $1\times 1$ | - |

7 | Convolution 4 | $3\times 3$ | 2 | 128 | $1\times 1$ | 73,856 |

8 | Pooling 4 | $2\times 2$ | 2 | 128 | $1\times 1$ | - |

9 | Dense | - | - | - | 100 | 12,900 |

10 | Dense | - | - | - | 50 | 5050 |

11 | Output | - | - | - | 16 | 816 |

Load (Hp) | SVM TDA | SVM WPD | LeNet-5 SIC | LeNet-5 CWT |
---|---|---|---|---|

0 | 80.00 | 80.62 | 74.37 | 99.06 |

1 | 94.68 | 85.41 | 73.75 | 95.31 |

2 | 94.58 | 84.58 | 82.81 | 98.75 |

3 | 94.37 | 84.79 | 81.56 | 98.44 |

Load (Hp) | 2D CNN-2L SIC | 2D CNN-2L CWT | 2D CNN-4L SIC | 2D CNN-4L CWT |
---|---|---|---|---|

0 | 84.06 | 97.50 | 70.31 | 96.56 |

1 | 81.87 | 94.06 | 75.31 | 75.94 |

2 | 83.75 | 97.50 | 77.81 | 89.69 |

3 | 85.93 | 98.12 | 78.75 | 94.68 |

Load (Hp) | 1D CNN-2L Raw | 1D CNN-2L CWT | 1D CNN-4L Raw | 1D CNN-4L CWT |
---|---|---|---|---|

0 | 95.00 | 99.10 | 94.68 | 99.17 |

1 | 93.12 | 98.44 | 97.81 | 98.81 |

2 | 96.87 | 98.75 | 97.82 | 99.06 |

3 | 96.24 | 99.28 | 98.12 | 99.37 |

Models | Data Type | Accuracy |
---|---|---|

SVM | TDA | 92.34 |

SVM | WPD | 89.92 |

Lenet-5 | SIC | 87.42 |

LeNet-5 | CWT | 99.29 |

2D CNN-2L | SIC | 92.81 |

2D CNN-2L | CWT | 98.28 |

2D CNN-4L | SIC | 87.65 |

2D CNN-4L | CWT | 98.00 |

1D CNN-2L | Raw | 98.28 |

1D CNN-2L | CWT | 99.37 |

1D CNN-4L | Raw | 98.76 |

1D CNN-4L | CWT | 99.53 |

Load (HP) | SNR (dB) | SVM TDA | SVM WPD | LeNet-5 SIC | LeNet-5 CWT |
---|---|---|---|---|---|

−2 | 16.87 | 13.43 | 15.31 | 32.18 | |

2 | 21.25 | 20.31 | 21.25 | 53.44 | |

0 | 4 | 47.50 | 37.18 | 29.69 | 59.69 |

10 | 60.93 | 64.68 | 38.44 | 80.00 | |

15 | 77.50 | 80.25 | 47.50 | 92.19 | |

−2 | 14.37 | 15.43 | 18.44 | 26.88 | |

2 | 30.62 | 22.81 | 20.62 | 45.00 | |

1 | 4 | 43.75 | 35.00 | 34.00 | 53.44 |

10 | 65.31 | 61.56 | 44.37 | 67.50 | |

15 | 77.50 | 81.87 | 62.19 | 82.19 | |

−2 | 13.12 | 14.73 | 17.19 | 33.75 | |

2 | 32.50 | 20.62 | 20.31 | 50.31 | |

2 | 4 | 41.56 | 34.06 | 35.00 | 53.43 |

10 | 67.50 | 59.06 | 52.81 | 80.31 | |

15 | 72.18 | 84.06 | 67.19 | 89.37 | |

−2 | 18.12 | 11.56 | 17.50 | 30.31 | |

2 | 32.18 | 20.00 | 24.68 | 49.06 | |

3 | 4 | 48.12 | 33.75 | 26.87 | 60.00 |

10 | 66.87 | 64.37 | 48.12 | 84.06 | |

15 | 70.32 | 83.12 | 68.19 | 95.93 | |

−2 | 20.40 | 23.51 | 17.50 | 37.66 | |

2 | 32.57 | 30.15 | 27.66 | 54.61 | |

0–3 | 4 | 57.34 | 45.93 | 34.45 | 62.66 |

10 | 70.00 | 69.92 | 46.56 | 83.20 | |

15 | 85.00 | 89.14 | 62.73 | 94.61 |

Load (Hp) | SNR (dB) | 2D CNN-2L SIC | 2D CNN-2L CWT | 2D CNN-4L SIC | 2D CNN-4L CWT |
---|---|---|---|---|---|

−2 | 26.56 | 34.06 | 25.00 | 29.06 | |

2 | 38.44 | 50.63 | 31.87 | 42.81 | |

0 | 4 | 49.37 | 54.68 | 35.94 | 49.69 |

10 | 65.93 | 80.31 | 53.75 | 73.12 | |

15 | 73.12 | 91.87 | 60.00 | 86.87 | |

−2 | 23.43 | 29.69 | 16.56 | 30.00 | |

2 | 34.06 | 44.37 | 35.62 | 38.12 | |

1 | 4 | 44.06 | 54.37 | 39.69 | 40.62 |

10 | 65.62 | 76.56 | 60.00 | 59.68 | |

15 | 76.56 | 84.38 | 71.88 | 73.75 | |

−2 | 28.12 | 32.19 | 24.06 | 29.06 | |

2 | 39.69 | 48.75 | 38.12 | 38.44 | |

2 | 4 | 44.69 | 50.31 | 39.38 | 44.69 |

10 | 64.06 | 74.69 | 59.69 | 66.56 | |

15 | 75.31 | 89.37 | 65.68 | 80.32 | |

−2 | 29.37 | 31.56 | 21.25 | 27.81 | |

2 | 44.37 | 52.49 | 32.49 | 42.50 | |

3 | 4 | 47.49 | 57.49 | 36.56 | 45.93 |

10 | 65.31 | 80.31 | 59.87 | 65.93 | |

15 | 82.18 | 94.06 | 82.18 | 64.06 | |

−2 | 37.73 | 39.14 | 28.82 | 37.57 | |

2 | 49.53 | 55.54 | 40.70 | 55.08 | |

0–3 | 4 | 60.00 | 61.56 | 47.65 | 60.46 |

10 | 80.16 | 84.61 | 70.63 | 81.41 | |

15 | 86.89 | 94.14 | 83.44 | 93.91 |

Load (Hp) | SNR (dB) | 1D CNN-2L Raw | 1D CNN-2L CWT | 1D CNN-4L Raw | 1D CNN-4L CWT |
---|---|---|---|---|---|

−2 | 35.62 | 41.20 | 44.37 | 39.06 | |

2 | 50.31 | 59.69 | 60.94 | 57.49 | |

0 | 4 | 57.50 | 65.94 | 69.38 | 66.87 |

10 | 80.62 | 88.75 | 81.25 | 82.81 | |

15 | 89.06 | 96.56 | 94.68 | 93.12 | |

−2 | 32.19 | 33.75 | 56.56 | 32.19 | |

2 | 41.56 | 53.43 | 63.12 | 49.69 | |

1 | 4 | 46.56 | 62.50 | 71.25 | 61.25 |

10 | 80.00 | 85.32 | 88.68 | 82.18 | |

15 | 89.69 | 93.75 | 93.72 | 89.06 | |

−2 | 33.13 | 38.44 | 50.00 | 33.45 | |

2 | 47.50 | 56.25 | 63.75 | 54.37 | |

2 | 4 | 58.44 | 60.62 | 71.25 | 60.94 |

10 | 80.31 | 88.75 | 86.56 | 79.37 | |

15 | 89.38 | 97.50 | 90.62 | 94.38 | |

−2 | 28.44 | 33.75 | 48.12 | 31.56 | |

2 | 40.62 | 54.68 | 59.68 | 55.00 | |

3 | 4 | 52.19 | 65.93 | 73.44 | 61.87 |

10 | 81.25 | 91.87 | 87.19 | 87.18 | |

15 | 90.31 | 99.06 | 92.81 | 96.87 | |

−2 | 40.39 | 41.25 | 54.14 | 44.99 | |

2 | 59.76 | 59.92 | 69.92 | 61.56 | |

0–3 | 4 | 68.59 | 66.56 | 75.58 | 68.59 |

10 | 85.07 | 88.52 | 90.55 | 89.14 | |

15 | 94.06 | 96.64 | 97.11 | 97.19 |

Models | Trainable Parameters | Training Time (s) |
---|---|---|

LeNet-5 | 62,216 | 55.89 |

2D CNN-2L | 131,662 | 55.22 |

2D CNN-4L | 115,918 | 37.95 |

1D CNN-2L | 837,326 | 37.44 |

1D-CNN-4L | 76,910 | 15.87 |

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## Share and Cite

**MDPI and ACS Style**

Moysidis, D.A.; Karatzinis, G.D.; Boutalis, Y.S.; Karnavas, Y.L.
A Study of Noise Effect in Electrical Machines Bearing Fault Detection and Diagnosis Considering Different Representative Feature Models. *Machines* **2023**, *11*, 1029.
https://doi.org/10.3390/machines11111029

**AMA Style**

Moysidis DA, Karatzinis GD, Boutalis YS, Karnavas YL.
A Study of Noise Effect in Electrical Machines Bearing Fault Detection and Diagnosis Considering Different Representative Feature Models. *Machines*. 2023; 11(11):1029.
https://doi.org/10.3390/machines11111029

**Chicago/Turabian Style**

Moysidis, Dimitrios A., Georgios D. Karatzinis, Yiannis S. Boutalis, and Yannis L. Karnavas.
2023. "A Study of Noise Effect in Electrical Machines Bearing Fault Detection and Diagnosis Considering Different Representative Feature Models" *Machines* 11, no. 11: 1029.
https://doi.org/10.3390/machines11111029