Knowledge-driven subdomain adaptation for bearing fault diagnosis

Abstract

Bearing fault diagnosis is crucial for ensuring the reliability and safety of rotating machinery in industrial settings. Machine learning-based diagnostic models offer powerful solutions, but their effectiveness is challenged by substantial domain shifts caused by variations in operating conditions, such as changes in motor load. To address this challenge, a novel domain adaptation framework that combines physical domain knowledge with deep learning techniques is proposed. The framework employs envelope spectrum analysis to generate reliable pseudo-labels for unlabeled target domains. By incorporating local maximum mean discrepancy into the training process, the framework aligns feature distributions between source and target domains while preserving class-specific information. This method enhances the adaptability of diagnostic models to real-world industrial conditions, reducing the need for extensive labeled data and improving predictive reliability across different operating scenarios. Experimental results performed on the Case Western Reserve University bearing dataset demonstrate that our method outperforms baseline models, achieving superior classification accuracy under significant domain shifts. By improving fault detection under varying load conditions, this approach contributes to more efficient predictive maintenance, reducing unexpected failures and operational downtime in industrial machinery. This approach highlights the potential of combining physics-based insights with deep learning to enhance fault diagnosis in diverse and complex industrial scenarios.

Keywords

bearing fault fault diagnosis subdomain adaptation transfer learning

Introduction

Bearings play a critical role as key components in rotating machinery, responsible for supporting loads and reducing friction between moving parts.¹ The condition of bearings directly influences the efficiency, reliability, and safety of industrial systems.² Undetected bearing faults can lead to catastrophic equipment failure, significant financial losses, and safety hazards.^3,4 As a result, precise and prompt bearing fault diagnosis has emerged as a crucial focus in both research and industrial practices.

Traditionally, bearing fault diagnosis has relied on signal processing techniques and statistical methods to extract time, frequency, and time-frequency domain characteristics from vibration signals.^5–7 These handcrafted features were then analyzed using methods like envelope detection and spectral analysis. However, these methods often face limitations due to their reliance on expert knowledge and their lack of adaptability to complex fault patterns.^8,9 Machine learning methods, including support vector machines (SVMs) and random forests (RFs), have been utilized to automate the processes of feature selection and classification, offering improved accuracy and scalability.^1,10 For example, Zhou et al.¹¹ proposed a model, combining the whale gray wolf optimization algorithm with variational mode decomposition (VMD) and SVM, achieving 100% fault diagnosis accuracy by effectively optimizing VMD decomposition and SVM parameters. Wang et al.¹² introduced an SVM-based diagnostic model optimized with particle swarm optimization and used features derived from singular value decomposition of Hilbert spectra and permutation entropy for accurate fault detection. Roy et al.¹³ developed an RF classifier using features extracted from autocorrelation of vibration signals and refined through recursive feature elimination, achieving high diagnostic accuracy across varying operating conditions. Wan et al.¹⁴ improved the RF model by removing low-performance and redundant trees, and parallelizing it on the Spark platform to enhance fault diagnosis accuracy and speed for large-scale datasets.

In recent years, deep learning approaches have shown exceptional performance by automatically extracting hierarchical features from raw signals, thereby removing the need for handcrafted feature engineering.^15–17 Ruan et al.¹⁸ introduced a physics-guided convolutional neural network (PGCNN) where the input size and convolution kernel were optimized based on bearing acceleration signal characteristics. The PGCNN, validated on two benchmark datasets, demonstrated improved accuracy and efficiency compared to traditional CNNs with standard parameters. Wang et al.¹⁹ proposed a 1D-CNN-based multi-modal approach that fuses vibration and acoustic signals for bearing fault diagnosis. By combining features from multiple sensors, the method achieved higher accuracy and robustness under varying signal-to-noise ratios compared to single-modal methods. Qiao et al.²⁰ developed a dual-input CNN-LSTM model for end-to-end fault diagnosis using time and frequency domain features. The model, tested under varying noise and load conditions, showed high fault recognition accuracy and adaptability due to its combination of spatial and sequential feature extraction. Khorram et al.²¹ designed a convolutional RNN model using raw time-domain vibration data without preprocessing. The method achieved state-of-the-art accuracy in bearing fault detection, emphasizing speed and end-to-end learning for practical application. He et al.²² proposed RTSMFFDE-HKRR for train-bearing fault diagnosis in noisy environments, improving feature extraction but not addressing domain adaptation. He et al.²³ developed AGFCN for high-speed train bogie bearings, enhancing fault detection under noise but relying on labeled target data. Yao et al.²⁴ introduced an attention-based neural network for wheelset axle faults, improving efficiency but lacking domain adaptation. Despite these advancements, deep learning models often encounter challenges in real-world applications due to the lack of sufficient real-world training data.^25,26

To tackle the challenges posed by domain shift, researchers have developed transfer learning, a method in which models are trained on one dataset and then applied to real-world observational data.²⁷ However, domain shift remains a major obstacle in transfer learning, as differences between the source and target domains can hinder model performance.²⁸ These differences often result from variations in operating conditions, such as load, speed, or temperature, between the training data (source domain) and the testing data (target domain).²⁹ Such discrepancies can significantly affect the ability of features learned from the source domain to generalize to the target domain.^30,31 To address these challenges, several domain adaptation techniques have been proposed to align the distributions between the source and target domains.⁹ Figure 1 illustrates the domain adaptation problem and its two main solutions: global and local adaptation. For the global approach, Wan et al.²⁸ introduced a deep convolutional multi-adversarial domain adaptation model that utilizes an enhanced ResNet for feature extraction. This model integrates multi-kernel maximum mean discrepancy (MMD) with domain discriminators to achieve effective alignment between domains, demonstrating superior performance in cross-domain fault diagnosis. Similarly, Liu et al.³² introduced a simulation-driven domain adaptation approach using a domain adversarial neural network (DANN). By utilizing simulated vibration signals, their model achieved high fault diagnosis accuracy with minimal reliance on real-world data, making it suitable for industrial applications. Furthermore, Chen et al.³³ developed a joint attention adversarial domain adaptation framework that integrates both local and global attention mechanisms with MMD-based feature region weighting. This approach demonstrated superior accuracy across multiple fault datasets, outperforming state-of-the-art models and proving its robustness in addressing domain shifts. Figure 1 illustrates the domain adaptation problem and highlights its two primary solutions: global and local adaptation.

Figure 1.

Illustration of the domain adaptation problem (left) and solutions (right).

For the local domain adaptation approach, local maximum mean discrepancy (LMMD) has been widely used.³⁴ The LMMD method reduces distributional discrepancies between the source and target domains in a localized manner by aligning both marginal and conditional distributions. This approach enhances fault classification performance across varying working conditions.³⁵ While other methods focus on global adaptation, LMMD outperforms them all due to its ability to adapt at the class level, known as subdomain adaptation. This allows LMMD to achieve higher classification accuracy. However, LMMD-based methods have limitations when the domain shift is large. In such cases, the predictions made by the model for the target domain data may be unreliable. Since LMMD relies on these predictions to guide the adaptation process, incorrect predictions can propagate errors and hinder the model’s performance.³⁶ This highlights the need for a more robust approach to address large domain shifts.

While machine learning and deep learning have significantly advanced bearing fault diagnosis, their effectiveness is often hindered by domain shifts caused by varying operating conditions. Transfer learning techniques have been introduced to mitigate this issue, yet existing methods struggle with effectively balancing global and local adaptation. LMMD-based approaches have improved feature alignment across domains, but their reliance on pseudo-labels can lead to error propagation when domain shifts are large. In such cases, inaccurate predictions in the target domain compromise the adaptation process, ultimately degrading model performance. These challenges highlight the need for a more robust adaptation framework that can enhance reliability under substantial domain shifts while preserving class-specific information.

To overcome this limitation, we propose a knowledge-driven subdomain adaptation framework for bearing fault diagnosis. Our approach leverages prior knowledge of fault frequencies to generate guided labels for the target domain. These guided labels serve as a reliable reference for the LMMD process, enabling more accurate alignment of the source and target domain distributions, even under significant domain shifts. By integrating domain knowledge into the deep learning framework, our method enhances the model’s robustness and diagnostic accuracy across varying working conditions.

The key contributions of this paper are as follows.

(i) We identify the limitations of existing LMMD-based domain adaptation methods for bearing fault diagnosis under large domain shifts.

(ii) We propose a novel knowledge-driven subdomain adaptation framework that integrates fault frequency information to generate guided labels for LMMD.

(iii) We validate the effectiveness of the proposed framework through extensive experiments, achieving improved fault classification performance across diverse working conditions.

Problem formulation

Bearing fault diagnosis under varying operating conditions is a complex problem, often requiring the adaptation of machine learning models to handle the differences in data distributions between training (source) and testing (target) datasets. These variations in operating conditions such as changes in load, speed, or temperature can significantly impact the signals collected from vibration sensors, which are commonly used for fault diagnosis.

Let the source domain D_s be represented as D_s = {x_s,y_s}, where x_s are the input features (e.g., vibration signals) and y_s are the corresponding fault labels for the source domain data. The source domain data is labeled, and we use this data for training our initial fault diagnosis model. On the other hand, the target domain D_t is represented as D_t = {x_t}, where x_t are the input features from the target domain, which are unlabeled. In practice, the target domain data comes from a different operating condition than the source data. The distributions of x_s and x_t are not identical, which poses a challenge for accurate fault classification in the target domain.

The goal of domain adaptation is to overcome the discrepancy between the source domain distribution P_s(x_s) and the target domain distribution P_t(x_t), which arises due to differences in working conditions. This distributional shift can lead to poor performance of the trained classifier when applied to the target domain, as the feature space and fault characteristics in the target domain may not directly match those in the source domain.

To tackle this challenge, the goal is to learn a classifier F that can effectively classify faults in the target domain, despite the domain shift between the source and target domains. This can be achieved by minimizing the domain shift through a process known as domain alignment, where we align the feature distributions between the source and target domains. Figure 1 illustrates the domain adaptation problem (left) and solutions (right).

Methodology

The methodology for this study combines domain knowledge of fault frequencies with advanced neural network-based domain adaptation techniques to achieve robust fault diagnosis across varying working conditions. This approach consists of three main components: data preprocessing, pseudo-label generation using fault frequency information, and a neural network architecture enhanced with LMMD. Figure 2 illustrates the proposed methodology. In the first step, data preprocessing involves extracting features from vibration signals in both the source and target domains, which are represented as the envelope spectrum. These extracted features serve as crucial inputs for the subsequent stages. The next step focuses on the pseudo-label generation, where fault frequency features from the envelope spectrum are used to create pseudo-labels. These labels provide fault-related guidance for the unlabeled target domain data. Finally, the neural network is trained using two loss functions: cross-entropy loss and LMMD loss. The cross-entropy loss aids in fault classification by using the envelope spectrum and true labels from the source domain, while the LMMD loss reduces the distribution mismatch between predictions from the source and target domains. By utilizing pseudo-labels, LMMD supports domain adaptation, enabling the model to effectively classify target domain data. Additional details of each component are provided in the following sections.

Figure 2.

The proposed method for cross-condition bearing fault diagnosis.

Data preprocessing

In this stage, the raw vibration signals are processed to extract meaningful features that are sensitive to bearing faults. A widely adopted approach, envelope spectrum analysis, is employed to highlight fault-specific frequency components buried within complex signals. This process begins with band-pass filtering of the raw vibration signals to isolate the frequency range that typically contains fault-related features. The filtered signals are then demodulated using the Hilbert transform to compute the signal envelope:

e (t) = | x (t) + j H (x (t)) |

(1)

where H is the Hilbert transform of the raw signal x(t). Finally, the envelope spectrum is obtained by applying the Fast Fourier transform (FFT) to the envelope of the vibration signal.

X_{e v e} (f) = F F T (e (t))

(2)

This transformation highlights peaks corresponding to specific fault frequencies, including the ball pass frequency outer race (BPFO), ball pass frequency inner race (BPFI), and ball (roller) spin frequency (BSF). These frequencies are determined using the physical dimensions of the bearing and its operating conditions (as shown in Table 1) and serve as reliable indicators for accurate fault diagnosis.

Table 1.

Roller bearing fault frequencies.

Fault frequency	Formula
BPFO	$N_{b} \times \frac{f_{s}}{2} \times (1 - \frac{D_{b}}{D_{p}} \cos (θ))$
BPFI	$N_{b} \times \frac{f_{s}}{2} \times (1 + \frac{D_{b}}{D_{p}} \cos (θ))$
BSF	$N_{b} \times \frac{D_{p}}{2 D_{b}} \times [1 - {(\frac{D_{b}}{D_{p}} \cos (θ))}^{2}]$

N_b: number of rollers; f_s: fundamental frequency of the rotor; D_b: roller diameter; D_p: pitch diameter; θ: contact angle.

Pseudo-label generation

The fault frequency-guided label generation is a critical step in adapting the model to new domains. Fault frequencies are consistent across varying operating conditions because they are determined by the bearing’s geometry and rotational speed. This property is leveraged to assign pseudo-labels to the unlabeled target domain samples. The process involves calculating theoretical fault frequencies using known machine specifications as shown in Table 1 and comparing them to peaks in the envelope spectrum of the target domain data.

Samples exhibiting prominent peaks at the calculated fault frequencies are pseudo-labeled as belonging to the corresponding fault class. Peaks are identified in the envelope spectrum using signal processing criteria, including peak prominence, height, and distance as in 37. A peak is considered valid if it is within a predefined frequency range associated with the expected fault frequencies (e.g., BPFO, BPFI, and BSF), with tolerances set to account for minor variations in system dynamics.

If a single prominent peak corresponding to a calculated fault frequency or a harmonic is detected, the sample is pseudo-labeled as belonging to the corresponding fault class. In cases where multiple peaks are found, the label is assigned to the fault class whose frequency is closest to the most prominent peak (based on amplitude). If no prominent peaks are detected within the tolerance range of any fault frequency, the sample is pseudo-labeled as “healthy.” This approach ensures that every sample is assigned a single label while leveraging physical phenomena to guide the pseudo-labeling process. By avoiding reliance on uncertain model predictions and directly linking pseudo-labels to fault-related characteristics in the spectrum, this method enhances the reliability of domain adaptation, even under significant domain shifts.

Neural network architecture

This study employs a CNN as the backbone for feature extraction and classification as presented in Table 2. The input to the CNN consists of envelope spectrum features, which contain key information about the bearing’s condition. The network includes multiple convolutional layers to extract hierarchical features from the input, followed by max-pooling layers for dimensionality reduction. Fully connected layers map the extracted features to specific fault classes, and a final softmax layer outputs the probability distribution across these classes.

Table 2.

The neural network architecture for this study.

Layer type	Input dimensions	Output dimensions	Kernel size	Activation
Input layer	L x 1	L x 1	-	-
Conv1D-1	L x 1	(L/2) x 16	16	ReLU
BatchNorm-1	(L/2) x 16	(L/2) x 16	-	-
MaxPooling1D-1	(L/2) x 16	(L/4) x 16	2	-
Conv1D-2	(L/4) x 16	(L/8) x 32	8	ReLU
BatchNorm-2	(L/8) x 32	(L/8) x 32	-	-
MaxPooling1D-2	(L/8) x 32	(L/16) x 32	2	-
Conv1D-3	(L/16) x 32	(L/32) x 64	4	ReLU
BatchNorm-3	(L/32) x 64	(L/32) x 64	-	-
GlobalAvgPooling	(L/32) x 64	64	-	-
Fully Connected-1	64	128	-	ReLU
Dropout-1	128	128	-	-
Fully Connected-2	128	64	-	ReLU
Dropout-2	64	64	-	-
Output layer	64	4	-	Softmax

The unique aspect of this architecture is its integration with a domain adaptation component, where a shared feature extractor is used for both the source and target domains. The LMMD loss function is applied in the shared feature space to align both the marginal and conditional distributions between the two domains. This design facilitates the learning of domain-invariant features, enabling the model to generalize effectively across different working conditions.

Training process

The training process combines supervised learning on the source domain with unsupervised domain adaptation on the target domain. The total loss function comprises two terms: the classification loss, L_cls, for the source domain, and the LMMD loss, L_LMMD, for domain alignment. These are combined as:

L = L_{c l s} + λ L_{L M M D}

(3)

where λ is a hyperparameter balancing the two terms. To suppress noisy activations at the early stages of training and ensure a smooth adaptation process, we employ a progressive schedule for the adaptation factor λ instead of using a fixed value. Specifically, λ is gradually adjusted from 0 to 1 using the following schedule: λ = 2/exp(−γθ)−1, where θ represents the training progress, and γ = 10 is fixed throughout the experiments. This scheduling strategy allows for a controlled increase in the adaptation strength, preventing instability in the early training phase while ensuring effective alignment between the source and target domains as training progresses. The classification loss for the source domain is based on the cross-entropy loss:

L_{c l s} = - \frac{1}{N_{s}} \sum_{i = 1}^{N_{s}} \sum_{k = 1}^{K} y_{i}^{k} \log {\hat{y}}_{i}^{k}

(4)

where Ns is the number of source samples, K is the number of classes, y_i^k is the true label, and

{\hat{y}}_{i}^{k}

is the predicted probability for class k. The LMMD loss aligns the source and target domain feature distributions locally:

L_{L M M D} = \frac{1}{K} \sum_{k = 1}^{K} (\frac{1}{N_{s, k}^{2}} \sum_{x, x^{'} \in D_{s}} k (x, x^{'}) + \frac{1}{N_{t, k}^{2}} \sum_{x, x^{'} \in D_{t}} k (x, x^{'}) - \frac{2}{N_{s, k} N_{t, k}} \sum_{x \in D_{s}, x^{'} \in D_{t}} k (x, x^{'}))

(5)

where N_s,k and N_t,k are the number of samples of class k in source and target domains, respectively, and k(x,x’) is a kernel function measuring pairwise distances in the feature space.

The training process is divided into two phases. In the first phase, the model is trained using labeled source domain data to achieve accurate fault classification within the source domain. In the second phase, the model is fine-tuned using both source and target domain data. During this phase, fault frequency-guided pseudo-labels are utilized to compute the LMMD loss, enabling precise alignment of the feature distributions between the source and target domains. The model parameters Φ in each phase are updated using the Adam optimizer with a learning rate η:

ϕ \leftarrow ϕ - η \frac{\partial L}{\partial ϕ}

(6)

Experiments

The proposed methodology is tested through a series of experiments to evaluate its performance across different operating conditions. The experiments utilize the CWRU bearing dataset,³⁵ which contains vibration signals collected at various motor loads (1HP, 2HP, and 3HP). This dataset includes four fault categories: normal operation, inner race fault (IF), outer race fault (OF), and rolling element fault (RF), with fault diameters of 0.007, 0.014, and 0.021 inches. The vibration signals were captured using accelerometers attached to the motor housing, with a sampling frequency of 48 kHz. These signals are representative of real-world scenarios where domain shifts arise due to variations in machine load or operating conditions. Figure 3 demonstrates the experimental testbed from CWRU bearing dataset.

Figure 3.

Experimental test setup of the CWRU dataset.

For this study, only data corresponding to the smallest fault diameter of 0.007 inches is used to evaluate the model’s capability for early fault detection. The raw vibration data is preprocessed by segmenting it into windows corresponding to five revolutions of the motor shaft with 75% overlap. This ensures that each segment contains five full cycles of rotational data, allowing the model to focus on fault-specific patterns and improving the granularity of fault diagnosis. Examples of the raw vibration signals from the motor under different working conditions are shown in Figure 4.

Figure 4.

Raw vibration signals from different working conditions.

Additionally, envelope spectrum analysis was performed to validate the reliability of fault frequency-based pseudo-labeling in the target domain. The spectral analysis in Figure 5 revealed clear peaks around characteristic fault frequencies, confirming the physical interpretability of the guided labels. Although there may be multiple peaks, our selection algorithm ensures that they are appropriately pseudo-labeled.

Figure 5.

Validation of pseudo-labels created from envelope spectrum analysis.

Three domain adaptation tasks are defined to assess the robustness of the proposed method under varying operating conditions: 1HP → 2HP, 1HP → 3HP, and 2HP → 3HP. These tasks simulate real-world scenarios where the operational conditions of machinery undergo significant changes, requiring the model to generalize effectively across different domains. For each task, 80% of the source data and 80% of the target data are used for training, while 20% of the source data is reserved for model validation during training, and 20% of the target data is used to evaluate the model’s performance. Each task is conducted multiple trials, and the average accuracy is reported to ensure the reliability of the results.

The training process was further analyzed through loss convergence graphs in Figure 6, which demonstrated the effectiveness of the proposed framework in aligning source and target domains. In both two phases, the loss function decreased steadily during training, indicating successful feature alignment, while the validation accuracy converged stably, ensuring reliable performance across tasks. These results emphasize the importance of integrating fault frequency-guided labels into the adaptation process, especially in challenging scenarios with significant domain shifts.

Figure 6.

Loss function and validation accuracy in the training process.

The classification accuracy for each adaptation task is summarized in Table 3. The proposed framework consistently outperformed baseline methods, including no adaptation (NA), MMD-based adaptation,³⁸ DANN,³⁹ CDAN,⁴⁰ and LMMD³⁵ without guided labels. Without adaptation (NA), performance is the lowest, with accuracies of 74.6%, 76.8%, and 70.1% for the three tasks 1HP → 2HP, 1HP → 3HP, and 2HP → 3HP, respectively. Standard domain adaptation methods such as MMD-based, DANN, and CDAN improve accuracy, with CDAN achieving 85.4%, 87.2%, and 83.1%. The LMMD-Based method further improves performance, reaching 86.1%, 88.5%, and 83.6%, demonstrating its effectiveness in aligning source and target domains. However, the proposed framework consistently outperforms all other methods, achieving the highest accuracy of 91.4%, 93.2%, and 89.8%, demonstrating its superior ability to adapt across different working conditions.

Table 3.

The classification accuracy performance and comparisons.

Adaptation task	No adaptation (NA)	MMD-based	DANN	CDAN	LMMD-based	Proposed framework
1HP → 2HP	74.6%	82.3%	83.4%	85.4%	86.1%	91.4%
2HP → 3HP	76.8%	84.7%	86.8%	87.2%	88.5%	93.2%
1HP → 3HP	70.1%	79.2%	81.5%	83.1%	83.6%	89.8%

Table 4 presents the classification accuracy of different domain adaptation methods under varying noise levels (0.2, 0.5, and 1.0). To evaluate model robustness, Gaussian noise was added to the sensor signals, simulating real-world signal interference and measurement uncertainties. This also makes the adaptation process more challenging, allowing the robustness of the models to be evaluated. As expected, increasing noise reduces classification accuracy across all methods. At noise level 0.2, the NA method achieves 69.6% (1HP → 2HP), 72.3% (2HP → 3HP), and 65.1% (1HP → 3HP), while the proposed framework maintains significantly higher accuracy at 91.0%, 92.9%, and 89.4%, outperforming LMMD-based methods by 5.5%, 4.7%, and 5.9%, respectively. As noise increases to 0.5, NA accuracy drops to 64.9%, 68.1%, and 60.9%, whereas even advanced methods like CDAN reach only 82.4%, 84.8%, and 79.8%. The proposed framework remains robust, achieving 90.6%, 92.4%, and 89.3% under these conditions. At the highest noise level (1.0), where classification becomes more challenging, NA accuracy drops further to 60.7%, 63.8%, and 56.7%, while LMMD-based methods achieve 84.8%, 87.0%, and 82.9%. Notably, the proposed framework continues to lead in performance, maintaining 90.0%, 92.0%, and 88.5%, demonstrating its superior resilience to high noise levels.

Table 4.

The classification accuracy performance under different levels of noise.

Adaptation task	No adaptation (NA)	MMD-based	DANN	CDAN	LMMD-based	Proposed framework
Noise level = 0.2
1HP → 2HP	69.6%	78.8%	80.6%	84.1%	85.5%	91.0%
2HP → 3HP	72.3%	81.1%	84.2%	85.9%	88.2%	92.9%
1HP → 3HP	65.1%	75.7%	79.0%	81.6%	83.5%	89.4%
Noise level = 0.5
1HP → 2HP	64.9%	75.3%	78.4%	82.4%	85.4%	90.6%
2HP → 3HP	68.1%	77.9%	81.9%	84.8%	87.4%	92.4%
1HP → 3HP	60.9%	72.3%	76.8%	79.8%	83.3%	89.3%
Noise level = 1.0
1HP → 2HP	60.7%	71.5%	76.4%	81.0%	84.8%	90.0%
2HP → 3HP	63.8%	74.3%	79.2%	83.2%	87.0%	92.0%
1HP → 3HP	56.7%	69.2%	74.7%	78.4%	82.9%	88.5%

The confusion matrices for the three domain adaptation tasks in Figure 7 highlight the effectiveness of the proposed framework compared to baseline methods. For the 1HP → 2HP task, the proposed method significantly reduces misclassifications across all fault classes, particularly resolving ambiguities between inner and roller faults that are prevalent in the NA approach. In the 2HP → 3HP task, the proposed framework demonstrates clear improvements, especially in distinguishing race faults from others, which remain challenging for MMD and LMMD. The largest domain shift, 1HP → 3HP, poses severe challenges for NA and moderate issues for MMD and LMMD, as evidenced by high confusion between normal and faulty classes. However, the proposed method achieves the highest true positive rates across all tasks, effectively addressing inter-class confusion and demonstrating superior robustness under significant domain shifts. These results underscore the reliability and effectiveness of the proposed framework in comparison to traditional and existing domain adaptation techniques.

Figure 7.

The confusion matrices for the three domain adaptation tasks.

To illustrate feature alignment, t-SNE visualizations were used to project the feature space for the 1HP → 3HP task as shown in Figure 8. Without adaptation, source and target features were poorly aligned, resulting in overlapping class boundaries. MMD-based adaptation partially improved alignment, but some classes remained misaligned. In contrast, the proposed framework demonstrated a clear alignment of source and target features, with well-separated class boundaries, enabling accurate classification.

Figure 8.

t-SNE visualizations for the 1HP → 3HP task. (a) No adaptation; (b) MMD method; (c) LMMD; and (d) proposed method.

Discussion

Despite the promising outcomes, the current approach has limitations. Firstly, the reliance on pseudo-label generation based on fault frequency may not fully account for complex fault patterns that are not explicitly linked to specific frequency features, limiting its generalization to more diverse fault types. Additionally, the performance of the model is highly dependent on the quality of the source and target domain data. Variations in data quality or sensor reliability could impact the model’s effectiveness. The method also assumes that the fault frequencies are consistent across different working conditions, which may not always be the case in real-world applications where fault characteristics can change dynamically.

Recent advancements in machine learning and signal processing have introduced various approaches for industrial fault diagnosis. Digital twin methodologies have gained traction for vibration-based monitoring and gear wear prediction, enabling real-time assessment and predictive maintenance by creating virtual replicas of physical systems.⁴¹ Digital twin-driven intelligent assessment of gear surface degradation integrates physics-based and data-driven models to track fault progression and optimize maintenance strategies.⁴² Furthermore, digital twin-enabled domain adversarial graph networks have been explored to enhance cross-domain fault diagnosis by leveraging structured relationships between different operating conditions.⁴³ Another emerging direction is the use of neuro-fuzzy system-guided cross-modal zero-sample diagnostic frameworks, which combine heterogeneous sensing data, such as infrared thermography and acoustic signals, to improve diagnostic accuracy when labeled data is limited.⁴⁴

Conclusion

This paper presented a knowledge-driven subdomain adaptation framework for bearing fault diagnosis, addressing the challenges posed by domain shifts due to varying operating conditions. By leveraging fault frequency-based pseudo-labels and LMMD, the framework aligns source and target domains effectively while minimizing the reliance on model predictions. The integration of physical domain knowledge ensures reliable adaptation even under significant domain shifts, as demonstrated in experiments on the CWRU bearing dataset. Comparative analysis against baseline approaches showed that the proposed method consistently outperforms in terms of accuracy and robustness. This study underscores the importance of combining domain knowledge with advanced machine learning techniques, paving the way for practical and reliable fault diagnosis solutions in real-world industrial applications.

Future work will focus on several areas to enhance the proposed methodology. First, exploring more sophisticated techniques for fault frequency extraction and incorporating additional domain knowledge could help in handling more complex fault patterns. Furthermore, enhancing the robustness of the model to variations in sensor data quality will be crucial for real-world applicability. Future studies could also investigate multi-source domain adaptation to further improve performance when data from multiple sources or varying conditions are available. Finally, incorporating online learning techniques that allow the model to adapt continuously to new, unseen operating conditions would make the system more flexible and capable of handling evolving fault scenarios in industrial environments.

Footnotes

ORCID iD

Nguyen Duc Thuan

Author contributions

All authors contributed to the study conception and design. Material preparation, data collection, and analysis were performed by N.T.H., N.D.T., and H.S.H. The first draft of the manuscript was written by N.T.H. and all authors commented on previous versions of the manuscript. All authors read and approved the final manuscript.

Funding

The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This research is funded by Hanoi University of Science and Technology (HUST) under project number T2023-PC-027.

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Data Availability Statement

The CWRU bearing dataset is available at .

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