# Fault Detection and Diagnosis with Imbalanced and Noisy Data: A Hybrid Framework for Rotating Machinery

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## Abstract

**:**

## 1. Introduction

## 2. Review of Current Models

## 3. Background Theory

#### 3.1. WGAN-GP

#### 3.2. CLSTM

#### 3.3. W-ELM

## 4. The Proposed FDD Model

#### 4.1. Sample Generation Model Design

Algorithm 1: WGAN-GP |

Input: $\gamma ,{n}_{critic},m,\alpha ,{\beta}_{1},{\beta}_{2},{\omega}_{0},{\theta}_{0}$ |

#### 4.2. Fault Diagnosis Model Design

#### 4.3. General Procedure of the Proposed Model

**Step 1**: The sensory signals are collected from the accelerometers mounted on the rotating machinery.**Step 2**: The training, the test, and the validation datasets are constructed from the raw signals to separate bursts by resampling.**Step 3**: The training dataset is augmented using WGAN-GP introduced in Section 3.1 on the minority classes. The fake samples are added to the real samples to make the training dataset balanced.**Step 4**: By employing FFT and CWT techniques the model can extract fault signatures which were hidden in the raw signals. The extracted Fourier and Wavelet transform-based diagrams are concatenated to form three-dimensional tensors (such as Figure 5) which will be given in input to the deep learning blocks.**Step 5**: These pre-processed samples go through two different paths of deep learning blocks: (1) a one-dimensional convolutional layer followed by an LSTM block, and (2) three blocks of CNN architectures followed by flatten and dense layers.**Step 6**: After concatenating the outputs of the two deep learning paths, a W-ELM technique is used to classify the extracted deep features and diagnose the fault type.

## 5. Results

#### 5.1. Dataset Description

#### 5.2. GAN Model Selection

#### 5.3. The Sensitivity Analysis

#### 5.4. Model Performance Evaluation

## 6. Discussion and Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 6.**Two-horsepower (

**left**), a torque transducer and encoder (

**center**) and a dynamometer (

**right**) used to collect the dataset.

**Figure 10.**Some random synthesized samples associated with different running conditions made by WGAN-GP.

**Figure 11.**Accuracy (

**left**) and Recall (

**right**) performances of GAN-CLSTM-ELM in different SNR and $\alpha $ levels.

**Figure 12.**AUC (

**left**) and ${f}_{1}$ score (

**right**) performances of GAN-CLSTM-ELM in different SNR and $\alpha $ levels.

**Figure 13.**Confusion matrices and ${f}_{1}$-scores of the comparison panel with classic augmentation in different scenarios (t represents true labeled samples).

**Figure 14.**Confusion matrices and ${f}_{1}$-scores of the comparison panel with WGAN-GP augmentation in different scenarios (t represents true labeled samples).

Block | Layer | Specifications |
---|---|---|

CNN Block1 | 1D-Convolutinoal | filters: 16; kernel size: 5; stride: 2; padding: 0 |

Batch Normalization | momentum: 0.99; epsilon: 0.001 | |

1D-Max Pooling | pool size: 2, padding: 0, stride: 1 | |

CNN Block2 | 1D-Convolutinoal | filters: 32; kernel size: 3; stride: 1; padding: 0 |

Batch Normalization | momentum: 0.99; epsilon: 0.001 | |

1D-Max Pooling | pool size: 2, padding: 0, stride: 1 | |

CNN Block3 | 1D-Convolutinoal | filters: 64; kernel size: 3; stride: 1; padding: 0 |

Batch Normalization | momentum: 0.99; epsilon: 0.001 | |

1D-Max Pooling | pool size: 2, padding: 0, stride: 1 | |

Convolutional LSTM | 1D-Convolutinoal | filters: 20; kernel size: 8; stride: 3; padding: 0 |

Embedding | input dimension: 200; output dimension: 64 | |

LSTM | units: 64; activation function: tanh; | |

ELM unit | WELM | #nuerons: 150; activation function: sigmoid; |

Minority Share (%) | Percentage of Training Samples in Each Condition | |||||
---|---|---|---|---|---|---|

Health | Inner | Ball | Out1 | Out2 | Out3 | |

$\alpha =4$ | 76% | 5% | 5% | 5% | 5% | 4% |

$\alpha =2$ | 78% | 5% | 5% | 5% | 5% | 2% |

$\alpha =1$ | 79% | 5% | 5% | 5% | 5% | 1% |

$\alpha =0.5$ | 79.5% | 5% | 5% | 5% | 5% | 0.5% |

$\alpha =0.25$ | 79.75% | 5% | 5% | 5% | 5% | 0.25% |

Framework | Preprossecing | Description | References |
---|---|---|---|

CLSTM | FFT + CWT + Statistical features | Its architecture comprises two CNN blocks (containing 1D-Convolutional layers, Batch Normalization, ReLU and Max Pooling), a LSTM block, a Logarithmic SoftMax, a concatenation which adds statistical features and three fully connected neural networks for the classification. | [46] |

CLSTM-ELM | FFT + CWT + Statistical features | Its CNN and LSTM architecture are the same as in CLSTM; yet, the fully connected layers are substituted for W-ELM with 150 nodes. | N/A |

df-CNN | raw signals | It is proposed to make an abstract 2-dimensional image out of raw signals. Its architecture comprises two CNN blocks (containing 2D-Convolutional layers, Batch Normalization, ReLU and Max Pooling), and three fully connected neural networks for the classification. df-CNN works directly on the raw vibration signals. | [48] |

sdAE | raw signals | It is a multilayered architecture composed of four auto-associative neural network layers, which contain one input layer and three AEs. The input of this framework are raw signals. | [14] |

CNN | FFT | The architecture consists of three CNN blocks (containing one 1D-Convolutional layer and a Pooling layer), two fully connected layers, and a SoftMax classification layer. It takes short-term Fourier transform (STFT) form of the signals as its input. | [16,31,33] |

W-ELM | FFT + VMD + Statistical features | It takes a combination of FFT, VMD [49] and some statistical features. | [20] |

SVM | Statistical features | SVM with polynomial kernel and degree of 2 is selected | N/A |

ANN | Statistical features | 3 fully connected layers with a grid search to find optimal number of neurons per layer and the activation functions | N/A |

RF | Statistical features | A grid search is designed to find the optimal number of estimators, and criteria (between ‘gini’ and ‘entropy’) parameters | N/A |

Algorithm | Runtime/Step (ms) | #Epochs to Converge | Batch Size | Learning Rate |
---|---|---|---|---|

CLSTM-ELM | 104.7 ± 8.6 | 10 | 64 | ${10}^{-3}$ |

CLSTM | 116.4 ± 10.5 | 12 | 64 | ${10}^{-3}$ |

df-CNN | 12.1 ± 1.8 | 8 | 64 | ${10}^{-3}$ |

sdAE | 43.3 ± 4.1 | 6 | 64 | ${10}^{-4}$ |

CNN | 21.8 ± 1.7 | 7 | 64 | ${10}^{-4}$ |

WELM | 17.2 ±1.4 | 7 | 32 | ${10}^{-3}$ |

Algorithm | Training Time (min) | |||
---|---|---|---|---|

$\mathbf{SNR}={\mathbf{10}}^{\mathbf{2}}\parallel \mathbf{\alpha}={\mathbf{2}}^{\mathbf{2}}$ | $\mathbf{SNR}={\mathbf{10}}^{\mathbf{2}}\parallel \mathbf{\alpha}={\mathbf{2}}^{-\mathbf{2}}$ | $\mathbf{SNR}={\mathbf{10}}^{\mathbf{1}}\parallel \mathbf{\alpha}={\mathbf{2}}^{\mathbf{2}}$ | $\mathbf{SNR}={\mathbf{10}}^{\mathbf{1}}\parallel \mathbf{\alpha}={\mathbf{2}}^{-\mathbf{2}}$ | |

SVM | 8.73 ± 0.45 | 8.90 ± 0.37 | 18.67 ± 1.32 | 19.40 ± 1.49 |

ANN | 1.97 ± 0.22 | 1.72 ± 0.31 | 2.06 ± 0.38 | 2.17 ± 0.42 |

RF | 2.13 ± 0.40 | 1.55 ± 0.36 | 3.06 ± 0.33 | 3.21 ± 0.26 |

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## Share and Cite

**MDPI and ACS Style**

Jalayer, M.; Kaboli, A.; Orsenigo, C.; Vercellis, C.
Fault Detection and Diagnosis with Imbalanced and Noisy Data: A Hybrid Framework for Rotating Machinery. *Machines* **2022**, *10*, 237.
https://doi.org/10.3390/machines10040237

**AMA Style**

Jalayer M, Kaboli A, Orsenigo C, Vercellis C.
Fault Detection and Diagnosis with Imbalanced and Noisy Data: A Hybrid Framework for Rotating Machinery. *Machines*. 2022; 10(4):237.
https://doi.org/10.3390/machines10040237

**Chicago/Turabian Style**

Jalayer, Masoud, Amin Kaboli, Carlotta Orsenigo, and Carlo Vercellis.
2022. "Fault Detection and Diagnosis with Imbalanced and Noisy Data: A Hybrid Framework for Rotating Machinery" *Machines* 10, no. 4: 237.
https://doi.org/10.3390/machines10040237