# Deep Domain Adaptation with Correlation Alignment and Supervised Contrastive Learning for Intelligent Fault Diagnosis in Bearings and Gears of Rotating Machinery

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## Abstract

**:**

## 1. Introduction

- We propose DCASCL, a novel domain adaptation (DA) framework applied to fault diagnosis of mechanical machinery. DCASCL simultaneously considers domain distribution alignment and class distribution alignment. We experimentally validate that these two aspects complement each other.
- The correlation alignment is used to realize the domain distribution alignment by minimizing the difference between the covariance matrices of the source and target domain features. The supervised contrastive learning loss is combined with classifier discrepancy loss to align the feature distributions class-wisely. Unlike other methods, DCASCL utilizes class label information through the supervised contrastive learning loss term, which makes it possible to align the features of samples of the same class more tightly while pushing apart those of dissimilar classes.
- Three different datasets with distinct transfer tasks are employed to validate the feasibility of DCASCL. Furthermore, extensive comparison experiments are carried out to demonstrate the effectiveness of DCASCL over several popular cross-domain diagnostic methods.

## 2. Methods

#### 2.1. Problem Description

#### 2.2. Model Structure

#### 2.3. Optimization Objectives of DCASCL

**Classification Loss Term**: To enable the model to learn discriminative features of the input fault samples, we first utilize the source domain to train the whole model, including the feature extractor F and the classifiers ${C}_{1}$ and ${C}_{2}$. This training phase aims to minimize the classification loss of both classifiers. The classification loss used is the cross-entropy, which is computed for both classifiers and integrated as follows:

**Correlation Alignment Loss Term**: The correlation alignment (CORAL) loss is a statistical matching-based domain adaptation strategy. Its primary objective is to align the feature distributions of the source and target domains by minimizing the difference in the covariance matrices in the feature space. This aids in extracting domain-invariant feature representations that are robust to the domain shift. The CORAL loss is calculated as follows:

**Discrepancy Loss Term**: Due to the presence of domain shift, global domain alignment can only alleviate it but not entirely remove it. This results in target samples near the class boundaries being prone to mis-classification by the classifier. Therefore, it is imperative to implement class alignment as well. In this work, class alignment is realized by adopting the discrepancy loss between the classifiers ${C}_{1}$ and ${C}_{2}$. Since the classifiers are initialized differently, their predictions for the target samples near class boundaries that fall outside the support of the source domain are inconsistent. By intentionally maximizing this inconsistency in the predictions between ${C}_{1}$ and ${C}_{2}$, the model can effectively identify the target samples situated near class boundaries. We can measure the difference between the predictions of the two classifiers on the target domain samples as follows:

**Supervised Contrastive Learning Loss Term**: In the process of minimizing classifier discrepancy, the class label information is neglected. In order to utilize this information effectively, drawing inspiration from supervised contrastive learning (SCL) [33], we introduce a novel cross-domain supervised contrastive learning loss aimed at learning representations with both intra-class compactness and inter-class separability. Applying this loss, the model is trained to project samples of the identical category nearer in the feature space while pushing apart the samples of distinct categories, whether these samples originate from the source or target domain. We regard the ${\ell}_{2}$-normalized features ${z}_{i}^{t}$ obtained from the i-th sample ${x}_{i}^{t}$ in the target domain as an anchor. It forms a positive pair with a sample from the source domain belonging to the identical category, denoted as ${z}_{p}^{s}$. The cross-domain supervised contrastive learning loss is then defined as follows:

#### 2.4. Training Process

**Step 1**: the feature extractor F and the two classifiers ${C}_{1}$ and ${C}_{2}$ are trained synchronously using the cross-entropy loss term and the CORAL loss term, as shown in Figure 2b. The overall optimization goal is achieved by combining Equations (2) and (6) as follows:

**Step 2**: the feature extractor F is fixed, and the two classifiers ${C}_{1}$ and ${C}_{2}$ are trained using the discrepancy loss term, as displayed in Figure 2c. The objective of this step is to maximize the discrepancy of the prediction distributions between ${C}_{1}$ and ${C}_{2}$ on target samples using Equation (8).

**Step 3**: the two classifiers ${C}_{1}$ and ${C}_{2}$ are fixed, and the feature extractor F is trained using SCL loss term and discrepancy loss term, as depicted in Figure 2d. The objective of this step is to minimize the discrepancy loss along with the SCL loss. Integrating Equations (10) and (14), the training process for F in this step can be expressed as follows:

Algorithm 1: Training process of DCASCL |

Input: the labeled samples ${X}^{s}$ and the corresponding label ${Y}^{s}$, the unlabeled samples ${X}^{t}$, number of epochs (E), number of batch size (B), initial learning rate, and the trade-off parameter $\lambda $Output: Optimal parameters ${\theta}_{F}$ of F, Optimal parameters ${\theta}_{{C}_{1}}$ and ${\theta}_{{C}_{2}}$ of ${C}_{1}$ and ${C}_{2}$1. For epoch = 1 to E do2. $\alpha $ increases from 0 to 1 3. For i = 1 to B do4. #Step 1: Simultaneously update parameters of F, ${C}_{1}$, and ${C}_{2}$,5. Calculate classification loss ${\mathcal{L}}_{C}\left({X}^{s},{Y}^{s}\right)$ and correlation alignment loss ${\mathcal{L}}_{CORAL}$ using Equations (1) and (3) 6. Update parameters of F, ${C}_{1}$, ${C}_{2}$ using the Equation (16) 7. #Step 2: Update parameters of ${C}_{1}$ and ${C}_{2}$, fix parameters of F8. Calculate classifier discrepancy $dis\left({p}_{1}\left(y|{x}^{t}\right),{p}_{2}\left(y|{x}^{t}\right)\right)$ using Equation (7) 9. Update parameters of ${C}_{1}$, ${C}_{2}$ using the Equation (8) 10. #Step 3: Update parameters of F, fix parameters of ${C}_{1}$ and ${C}_{2}$11. Calculate classifier discrepancy $dis\left({p}_{1}\left(y|{x}^{t}\right),{p}_{2}\left(y|{x}^{t}\right)\right)$ and supervised contrastive learning loss using Equations (7) and (12) 12. Update parameters of ${C}_{1}$, ${C}_{2}$ using the Equation (17) 13. End14. End |

## 3. Experimental Results and Discussion

#### 3.1. Dataset Description

**CWRU Bearing Dataset**: The CWRU dataset is commonly utilized for fault diagnosis [36], and its experimental configuration is depicted in Figure 3, which is adapted from [37]. Downloads for it are available at [38]. The dataset was acquired at either 12 kHz or 48 kHz. In this paper, we specifically utilized the data collected at 12 kHz. They contain vibration signals obtained from bearings, covering four distinct operating conditions: 0, 1, 2, and 3 hp. Each operating condition comprises ten distinct health states of the bearings, including normal (N), inner race fault (IF) with defect diameters of 0.007, 0.014, and 0.021 inches, as well as both ball fault (BF) and outer race fault (OF) with the corresponding defect diameters. Twelve different transfer tasks are established based on the distinct operating conditions. In the transfer task 0 hp → 1 hp, it indicates the utilization of 0 hp and 1 hp operating conditions as the source domain and target domain datasets, respectively. Detailed information can be found in Table 2.

**JNU Bearing Dataset**: Jiangnan University provided this dataset [39], which is also commonly used for research in bearing fault diagnosis. Its experimental signal acquisition system is illustrated in Figure 4, which is sourced from [39], and it can be obtained from [40]. The vibration data in the JNU bearing dataset were acquired at three different speeds: 600, 800, and 1000 rpm. Normal health (N), inner fault (IF), outer fault (OF), and ball fault (BF) are the four health states included in each speed. Six transfer tasks were established based on the three different speed conditions, where 600 rpm → 800 rpm indicates that the dataset obtained at the speed condition of 600 rpm is used for the source domain and 800 rpm is employed for the target domain. Table 3 provides comprehensive information.

**SEU Gearbox Dataset**: This dataset is from the Southeast University in China [41], and its experimental setup is depicted in Figure 5, which is adapted from [37]. It can be downloaded from [42]. The dataset is separated into two sub-datasets that provide information on the health of bearings and gearboxes. The data were collected using a Drivetrain Dynamics Simulator (DDS) and included eight vibration information channels. The data from the second channel of the gearbox dataset are used in this work. This dataset contains two operating conditions based on speed and load: 20 HZ-0V and 30 HZ-2V. Each operating condition includes one healthy condition and four faulty conditions, namely Health, Chipped, Root, Miss, and Surface. Based on these two operating conditions, two transfer tasks are created, where 20 HZ-0V → 30 HZ-2V represents the utilization of the 20 HZ-0V dataset for the source domain and the 30 HZ-2V dataset for the target domain. For more comprehensive information, refer to Table 4.

#### 3.2. Data Processes

#### 3.3. Implementation Details

#### 3.4. Comparison Methods

- (1)
- No Domain Adaptation: 1D-CNN serves as a baseline method, utilizing only source domain data to directly train the model for diagnostic tasks in the target domain.
- (2)
- Only Domain Distribution Alignment: Both MK-MMD [43] and CORAL [15] align distributions by matching statistical differences between two domains. DANN [44] introduces a domain discriminator to differentiate between domains and encourages the model to learn representations that are invariant across domains by confusing the discriminator.
- (3)
- Only Class Distribution Alignment: MCD [30] method maximizes discrepancy in predictions on unlabeled target samples between two separate classifiers during optimization. Meanwhile, it minimizes this discrepancy when optimizing the feature extractor to generate target features under the support of the source domain.

#### 3.5. Experimental Results and Analysis

## 4. Model Analysis

#### 4.1. Ablation Studies

#### 4.2. Feature Visualization

#### 4.3. Parameter Analysis

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 1.**The model architecture diagram of DCASCL. The source domain samples ${X}^{s}$ and the target domain samples ${X}^{t}$ act as inputs to the feature extractor F after FFT processing, ultimately obtaining high-dimensional features ${Z}_{s}$ and ${Z}_{t}$. The ${L}_{CORAL}$ is employed to measure the difference in the covariance matrices between ${Z}_{s}$ and ${Z}_{t}$. Pseudo-labels for target domain samples are acquired using the double-confirmation (DC) strategy and are subsequently utilized for supervised contrastive learning (${L}_{SCL}$) alongside labeled source domain samples. The ${L}_{adv}$ represents the classifier discrepancy and is computed from the probability outputs of two classifiers, ${C}_{1}$(F(${X}^{t}$)) and ${C}_{2}$(F(${X}^{t}$)). The ${L}_{C}$ is a classification loss.

**Figure 2.**The detailed training process of the DCASCL model. (

**a**) represents the prediction process, (

**b**) represents Step 1, (

**c**) represents Step 2, and (

**d**) represents Step 3. In the figure, the black arrow indicates the flow of source domain data, while the red arrow indicates the flow of target domain data.

**Figure 3.**CWRU bearing test rig [37].

**Figure 4.**Experimental signal acquisition system for the JNU dataset [39].

**Figure 5.**The experimental setup of SEU dataset [37].

**Figure 9.**Confusion matrix of combinations between different components on the 0 hp → 3 hp transfer task:(

**a**) MCD; (

**b**) MCD+CORAL; (

**c**) MCD+SCL; (

**d**) DCASCL.

**Figure 10.**Confusion matrix of combinations between different components on the 600 rpm → 1000 rpm transfer task: (

**a**) MCD; (

**b**) MCD+CORAL; (

**c**) MCD+SCL; (

**d**) DCASCL.

**Figure 11.**Confusion matrix of combinations between different components on the 20 HZ-0V → 30 HZ-2V transfer task: (

**a**) MCD; (

**b**) MCD+CORAL; (

**c**) MCD+SCL; (

**d**) DCASCL.

**Figure 12.**Feature visualization of combinations between different components in the 20 HZ-0V → 30 HZ-2V transfer task of the SEU dataset: (

**a**) MCD; (

**b**) MCD+CORAL; (

**c**) MCD+SCL; (

**d**) DCASCL.

Module Name | Block Name | Layer Type | In/Out Channel | Kernel Size/Stride | Activation Function |
---|---|---|---|---|---|

Feature extractor | Conv1 | Convolutional | 1/16 | 64/4 | ReLU |

BatchNorm | 16 | / | / | ||

Max Pooling | / | 2/1 | / | ||

Conv2 | Convolutional | 16/32 | 3/2 | ReLU | |

BatchNorm | 32 | / | / | ||

Max Pooling | / | 2/1 | / | ||

Conv3 | Convolutional | 32/64 | 3/2 | ReLU | |

BatchNorm | 64 | / | / | ||

Max Pooling | / | 2/1 | / | ||

Conv4 | Convolutional | 64/64 | 3/2 | ReLU | |

BatchNorm | 64 | / | / | ||

Max Pooling | / | 2/1 | / | ||

Conv5 | Convolutional | 64/64 | 3/1 | ReLU | |

BatchNorm | 64 | / | / | ||

Max Pooling | / | 2/1 | / | ||

Dense1 | Linear | 64 × 56/2048 | / | ReLU | |

BatchNorm | 2048 | / | |||

Dense2 | Linear | 2048/1024 | / | ReLU | |

BatchNorm | 1024 | / | / | ||

Classifier | / | Linear | 1024/512 | / | ReLU |

BatchNorm | 512 | / | / | ||

Dropout | / | / | / | ||

/ | Linear | 512/256 | / | ReLU | |

BatchNorm | 256 | / | / | ||

Dropout | / | / | / | ||

/ | Linear | 256/num classes | / | Softmax |

Fault Type | BF | BF | BF | IF | IF | IF | OF | OF | OF | N |

Fault Size (Inches) | 7 | 14 | 21 | 7 | 14 | 21 | 7 | 14 | 21 | 0 |

Class Label | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |

Load (hp) | 0, 1, 2, 3 | |||||||||

Total number of samples | 4000 | |||||||||

Train and test set ratio | 7:3 |

Fault Type | IF | N | OF | BF |

Class Label | 0 | 1 | 2 | 3 |

Speed (rpm) | 600, 800,1000 | |||

Total number of samples | 2400 | |||

Train and test set ratio | 7:3 |

Fault Type | Chipped | Health | Miss | Root | Surface |

Class Label | 0 | 1 | 2 | 3 | 4 |

RS-LC | 20 HZ-0V, 30 HZ-2V | ||||

Total number of samples | 3000 | ||||

Train and test set ratio | 7:3 |

Tasks Symbol | Tasks | 1D-CNN | MK-MMD | CORAL | DANN | MCD | DCASCL |
---|---|---|---|---|---|---|---|

C0 | 0 hp → 1 hp | 98.67 | 100 | 98.53 | 99.35 | 100 | 100 |

C1 | 0 hp → 2 hp | 97.08 | 100 | 98.54 | 100 | 100 | 100 |

C2 | 0 hp → 3 hp | 90.84 | 94.65 | 93.65 | 92.76 | 93.45 | 100 |

C3 | 1 hp → 0 hp | 94.04 | 99.81 | 100 | 99.78 | 100 | 100 |

C4 | 1 hp → 2 hp | 93.19 | 100 | 100 | 100 | 100 | 100 |

C5 | 1 hp → 3 hp | 95.79 | 99.84 | 100 | 98.43 | 100 | 100 |

C6 | 2 hp → 0 hp | 90.99 | 98.85 | 99.23 | 98.46 | 100 | 100 |

C7 | 2 hp → 1 hp | 95.73 | 99.35 | 99.68 | 100 | 100 | 100 |

C8 | 2 hp → 3 hp | 89.19 | 100 | 100 | 100 | 100 | 100 |

C9 | 3 hp → 0 hp | 91.21 | 94.13 | 92.50 | 93.51 | 92.96 | 100 |

C10 | 3 hp → 1 hp | 94.18 | 99.03 | 92.21 | 94.28 | 100 | 100 |

C11 | 3 hp → 2 hp | 96.24 | 100 | 99.68 | 98.68 | 100 | 100 |

Average | - | 93.93 | 98.81 | 97.84 | 97.94 | 98.87 | 100 |

Tasks Symbol | Tasks | 1D-CNN | MK-MMD | CORAL | DANN | MCD | DCASCL |
---|---|---|---|---|---|---|---|

J0 | 600 rpm → 800 rpm | 83.01 | 89.73 | 93.45 | 95.57 | 98.67 | 99.37 |

J1 | 600 rpm → 1000 rpm | 78.95 | 91.80 | 90.27 | 94.32 | 96.34 | 100 |

J2 | 800 rpm → 600 rpm | 86.09 | 90.36 | 94.05 | 92.51 | 99.07 | 100 |

J3 | 800 rpm → 1000 rpm | 88.65 | 92.63 | 91.25 | 93.83 | 98.12 | 100 |

J4 | 1000 rpm → 600 rpm | 80.49 | 91.27 | 88.14 | 93.67 | 97.81 | 99.68 |

J5 | 1000 rpm → 800 rpm | 90.35 | 93.27 | 92.13 | 92.49 | 97.06 | 100 |

Average | - | 84.59 | 91.51 | 91.55 | 93.73 | 97.85 | 99.84 |

Tasks Symbol | Tasks | 1D-CNN | MK-MMD | CORAL | DANN | MCD | DCASCL |
---|---|---|---|---|---|---|---|

S0 | 20 HZ-0V → 30 HZ-2V | 68.35 | 81.35 | 83.62 | 65.86 | 81.48 | 100 |

S1 | 30 HZ-2V → 20 HZ-0V | 75.43 | 84.52 | 85.17 | 79.32 | 82.93 | 100 |

Average | - | 71.89 | 82.94 | 84.40 | 72.59 | 82.21 | 100 |

Method | 0 hp → 3 hp | 600 rpm → 1000 rpm | 20 HZ-0V → 30 HZ-2V | |||
---|---|---|---|---|---|---|

Accuracy | F1-Score | Accuracy | F1-Score | Accuracy | F1-Score | |

MCD | 91.83 | 89.62 | 96.25 | 96.25 | 81.56 | 81.84 |

MCD+CORAL | 94.33 | 93.84 | 98.19 | 98.19 | 91.44 | 91.52 |

MCD+SCL | 97.25 | 97.20 | 98.75 | 98.75 | 93.89 | 93.88 |

DCASCL | 100.0 | 100.0 | 100.0 | 100.0 | 100.0 | 100.0 |

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## Share and Cite

**MDPI and ACS Style**

Zhang, B.; Dong, H.; Qaid, H.A.A.M.; Wang, Y.
Deep Domain Adaptation with Correlation Alignment and Supervised Contrastive Learning for Intelligent Fault Diagnosis in Bearings and Gears of Rotating Machinery. *Actuators* **2024**, *13*, 93.
https://doi.org/10.3390/act13030093

**AMA Style**

Zhang B, Dong H, Qaid HAAM, Wang Y.
Deep Domain Adaptation with Correlation Alignment and Supervised Contrastive Learning for Intelligent Fault Diagnosis in Bearings and Gears of Rotating Machinery. *Actuators*. 2024; 13(3):93.
https://doi.org/10.3390/act13030093

**Chicago/Turabian Style**

Zhang, Bo, Hai Dong, Hamzah A. A. M. Qaid, and Yong Wang.
2024. "Deep Domain Adaptation with Correlation Alignment and Supervised Contrastive Learning for Intelligent Fault Diagnosis in Bearings and Gears of Rotating Machinery" *Actuators* 13, no. 3: 93.
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