EffiMultiOrthoBearNet: An Efficient Lightweight Architecture for Bearing Fault Diagnosis

Abstract

Amidst the advent of Industry 4.0 and the rapid advancements in smart manufacturing, the imperative for developing resource-efficient condition monitoring and fault prediction technologies tailored for industrial equipment in resource-limited settings has become increasingly evident. This study puts forward EffiMultiOrthoBearNet, an innovative, lightweight, deep learning model specifically designed for the accurate identification and classification of bearing faults. Central to EffiMultiOrthoBearNet’s architecture is the integration of multi-scale convolutional layers and orthogonal attention mechanisms—key innovations that significantly enhance the model’s performance. Leveraging advanced feature extraction capabilities, EffiMultiOrthoBearNet meticulously processes Continuous Wavelet Transform (CWT) images from the CWRU dataset, ensuring the precise delineation of essential bearing signal traits through its multi-scale and attention-enhanced mechanisms. Optimized for supreme operational efficiency in resource-deprived environments, EffiMultiOrthoBearNet achieves unmatched classification accuracy—up to 100% under ideal circumstances and consistently above 90% amidst significant noise and operational complexities. Demonstrating remarkable adaptability and efficiency, EffiMultiOrthoBearNet provides a pioneering and practical fault diagnosis solution for industrial machinery across a wide range of application scenarios, even under stringent resource limitations.

1. Introduction

As the Industry 4.0 era unfolds, the manufacturing sector is undergoing an unprecedented transformation, marked by the extensive digitalization and integration of intelligence. At the heart of this revolution lies the goal of significantly enhancing production efficiency and product quality through the application of real-time monitoring and predictive analytics of equipment conditions [1,2,3,4]. In this context, bearings, as critical components of rotating machinery, play a pivotal role in the overall reliability and fault tolerance of the system. Importantly, a substantial portion of rotating machinery failures can be directly attributed to bearing malfunctions. Bearing malfunctions not only jeopardize system stability but also lead to diminished production efficiency and heightened safety risks. Therefore, in the highly automated and intelligent landscapes of Industry 4.0, the swift and accurate detection and prediction of bearing failures become imperative [5,6,7]. In the realm of smart manufacturing, the deep integration of artificial intelligence technology, a hallmark of the Industry 4.0 era, has emerged as a key strategy to boost production efficiency and achieve high levels of automation. This technological synthesis not only optimizes production processes but also significantly enhances the predictive and maintenance capabilities for equipment malfunctions. Specifically, in smart manufacturing contexts, monitoring the performance and health status of bearings as key components of mechanical systems is critically important. With the widespread deployment of intelligent devices, the demand for identifying mechanical failures, especially bearing defects, has become more pressing [8,9,10]. For instance, the bearing dataset developed by Case Western Reserve University represents one of the standard public datasets for assessing such models [11,12,13]. The effectiveness of traditional bearing fault diagnosis methods, which rely heavily on feature extraction and signal processing techniques, is often constrained by the complexity of the signals and an overreliance on expert knowledge [14,15,16,17]. Despite constraints related to model complexity, computational demands, and data-processing costs, deep learning algorithms, particularly convolutional neural networks (CNNs), have demonstrated significant potential in analyzing images to detect bearing faults. Consequently [18,19], research has shifted towards reducing the scale and complexity of models while maintaining their classification accuracy. The real-time monitoring of bearing health is crucial for ensuring the stable operation of rotating equipment. The diagnosis of bearing failures has evolved to integrate advanced AI-based systems, incorporating multi-channel sensor data fusion, time-frequency analysis, feature extraction, and supervised learning techniques at their core [20].

Current methodologies for bearing fault diagnosis often face challenges in high-noise settings and under varied operational conditions. Moreover, in resource-constrained industrial settings, the utility of most models is compromised by limited computational and data processing capabilities. Addressing these challenges, this study puts forward EffiMultiOrthoBearNet, an efficient network that utilizes multi-scale convolutional layers and orthogonal attention mechanisms for bearing fault diagnosis. This novel deep learning model is specifically designed to enhance diagnostic accuracy and efficiency in identifying bearing faults. EffiMultiOrthoBearNet combines multi-scale convolution with orthogonal attention mechanisms, excelling in diverse conditions, including high-noise environments, and demonstrating exceptional diagnostic accuracy in complex scenarios. Its design is lightweight and ideally suited for use in resource-limited industrial contexts, offering an efficient and adaptable solution for real-time monitoring. EffiMultiOrthoBearNet achieves up to 100% classification accuracy under consistent conditions and maintains performance above 90% in variable and high-noise environments, striking an effective balance between high performance and computational efficiency. The deployment of this model in bearing fault diagnosis heralds a significant technological breakthrough, providing an efficient, highly adaptable solution for real-time monitoring. The main contributions of this paper include:

1. Development of EffiMultiOrthoBearNet: We introduce EffiMultiOrthoBearNet, a novel, lightweight, deep learning model optimized for bearing fault diagnosis. This model enhances fault feature recognition through the integration of multi-scale convolution and orthogonal attention mechanisms, ensuring efficient real-time detection in computer-constrained environments.

2. Advanced Feature Extraction and Learning: EffiMultiOrthoBearNet employs Continuous Wavelet Transform and an image classification framework to extract precise time-frequency features from bearing signals. The model utilizes multi-scale feature fusion and orthogonal attention to improve diagnostic accuracy and robustness.

3. Performance Validation: Extensive testing on the CWRU dataset demonstrates EffiMultiOrthoBearNet’s effectiveness, showing superior performance under high-noise conditions and diverse operational settings, confirming its practical applicability.

The remainder of the paper is organized as follows: Section 2 reviews related work, Section 3 details the proposed method, Section 4 discusses experiments and results, and finally, Section 5 concludes the paper.

2. Related Work

Bearing fault diagnosis methods can be broadly categorized into two main approaches: those based on vibration signal analysis and those leveraging deep learning techniques [21].

2.1. Vibration Signal Analysis in Bearing Fault Diagnosis

Current research on signal analysis primarily focuses on time, frequency, and time-frequency domain analyses and the decomposition of signals. Bao et al. utilized the short-time Fourier transform to convert one-dimensional fault signals into two-dimensional images, which were then classified using transformer models. This method underscores the innovative application of the technique, despite its inherent limitations [22]. However, the efficacy of the short-time Fourier transform is limited by the selection of time windows and parameters, which may lead to information loss or blurring, adversely affecting classification accuracy. Sun et al. introduced a novel approach for bearing fault diagnosis that combines empirical mode decomposition with an enhanced Chebyshev distance, using the latter as a unique diagnostic feature [23]. Nonetheless, the reliance on enhanced IMF Chebyshev distance limits its applicability across various fault modes or datasets, requiring tailored adjustments and validations. Grover et al. developed a time-domain bearing fault diagnosis method based on Hjorth parameters [24]. It constructs feature vectors from the Hjorth parameters of intrinsic mode functions obtained through empirical mode decomposition of vibration signals and employs four standard classifiers for data classification. However, by focusing solely on time-domain Hjorth parameters and omitting frequency or time-frequency features, this method might fail to capture the complex nature of bearing faults fully, resulting in critical information loss. H.S. Kumar utilized empirical mode decomposition to decompose bearing vibration signals into various intrinsic mode functions (IMFs), extracting statistical features from the first three IMFs to characterize different bearing conditions [25]. These features served as inputs for the K-NN classifier, aiding in the differentiation of bearing states. However, by focusing only on the first three IMFs, this method might overlook crucial fault features or frequency domain information, failing to capture the full spectrum of bearing fault characteristics. Guo et al. developed a methodology employing complementary ensemble empirical mode decomposition (CEEMD) and permutation entropy for anomaly detection, further enhancing signal analysis through CEEMD [26]. Subsequently, Hilbert envelope spectrum analysis is applied to IMF components with high correlation coefficients to extract fault features. Although this technique reduces reconstruction errors by incorporating white noise, modal aliasing issues may arise during decomposition, potentially affecting the accuracy of fault feature extraction. Although effective in certain scenarios, methods based on vibration signal analysis frequently face challenges in complex industrial environments, constrained by the need for precise parameter tuning and the difficulty in capturing all essential fault characteristics. Kiakojouri et al. [27] introduced a hybrid approach that enhances early detection of bearing faults. Their method combines improved Cepstrum Pre-Whitening with high-pass filtering to optimize signal-to-noise ratios in vibration data, providing a significant step forward in automated fault diagnosis despite challenges in handling variable resonant frequencies.

2.2. Application of Deep Learning Techniques in Bearing Fault Diagnosis

Compared to traditional signal analysis methods, bearing fault diagnosis techniques based on deep learning can directly learn complex feature representations from data without relying on specialized signal processing and domain knowledge. Che et al. introduced a bearing fault diagnosis approach utilizing a domain-adaptive deep belief network (DBN) [28]. The method involves pre-training the DBN with labeled samples of vibration signals and their time-frequency indicators. In the domain adaptation phase, model parameters are optimized by evaluating the MK-MMD loss function and classification error. However, the complexity of domain adaptation makes choosing suitable loss functions and parameter adjustment strategies a challenge. Du et al. [29] propose an Integrated Gradient-based Continuous Wavelet Transform (IG-CWT) approach for bearing fault diagnosis, which enhances diagnostic accuracy by optimizing feature selection and focusing on critical frequency components. In this method, the parameter λ is set between 0.25 and 0.35 to select the appropriate frequency range. While the Continuous Wavelet Transform is the primary tool for time-frequency transformation, other methods such as the S-transform may also be applicable. A limitation of this technique is the requirement for dual training of the neural network model—once for data preprocessing and once for fault diagnosis, making the process time-consuming. Chen et al. created an automatic feature learning network that processes raw vibration signals directly. The network uses two CNNs with different kernel sizes to extract a range of frequency features, and an LSTM to identify fault types based on these features [13]. The core of this method lies in using convolutional layers with different kernel sizes to automatically extract features on multiple scales, effectively capturing various frequency characteristics in the raw vibration signals. In a recent advancement, Ding et al. [30] proposed S-AlexNet, a parameter transplantation CNN designed for edge intelligence in fault diagnosis. This approach seeks to optimize resource efficiency by reducing the model complexity and computational needs. However, the challenge lies in ensuring robust performance across diverse operating conditions without extensive parameter tuning. Song et al. proposed a WKCNN model that employs wide convolutional kernels to broaden the receptive field, targeting efficient feature extraction [31]. This architecture enhances the extraction of time-domain features, rapidly processing vibration signals in the early layers to generate an enriched input dataset. However, its reliance on extensive time-domain data for training necessitates larger datasets and potentially extends training durations. Luis A. Pinedo-Sánchez et al. introduced a CNN-based methodology for assessing wear levels in roller bearing components such as the inner race, outer race, and rolling elements [32]. This approach converts raw vibration data into square images for classification and diagnostics using an AlexNet-based CNN, focusing on rotary system analysis. However, this image conversion may result in information loss and spatial distortion, potentially impacting the model’s accuracy and generalizability. Spyridon Plakias et al. unveiled the ADCNN, which merges dense convolutional blocks with an attention mechanism to improve temporal consistency and reduce dependency on large datasets [33]. Although it enhances temporal consistency, ADCNN’s accuracy and generalizability still require a diverse and sufficient dataset.

In the field of bearing fault diagnosis, traditional methods such as vibration signal analysis and empirical mode decomposition are effective under specific conditions but often falter due to stringent requirements for parameter tuning. This often results in substantial information loss, diminishing the accuracy of fault classifications. Deep learning techniques, while adept at extracting complex features directly from data, face significant challenges, including the complexities of domain adaptation, constraints on computational resources, and the need for intricate parameter tuning, limiting their effectiveness in dynamic industrial environments.

To address these prevalent challenges, this study introduces EffiMultiOrthoBearNet, an advanced, lightweight, deep learning model engineered for the precise identification and classification of bearing faults. Unlike traditional methods that struggle with parameter tuning and information loss and deep learning techniques hindered by computational demands, EffiMultiOrthoBearNet introduces a hybrid approach that combines the Continuous Wavelet Transform (CWT) with advanced neural network features to offer a more robust and efficient solution. This model leverages CWT for detailed fault information extraction and processing and refines feature extraction through the integration of multi-scale convolutional layers, effectively capturing a comprehensive spectrum of fault signatures. The incorporation of orthogonal attention mechanisms enhances the model’s performance by focusing on salient features, crucial in noisy industrial settings. The lightweight architecture of EffiMultiOrthoBearNet ensures its suitability for deployment on resource-constrained devices within industrial environments, providing an optimal balance of computational efficiency and diagnostic precision.

3. Method

3.1. Multi-Scale Convolution

In this study, we utilize multi-scale convolution technology to perform feature fusion, integrating features obtained from convolutional kernels of different sizes [34]. Convolutional kernels with sizes of 3 × 3 and 5 × 5 operate simultaneously, extracting features across different dimensions and scales. Larger kernels, such as 5 × 5, capture low-frequency characteristics and attenuate high-frequency noise, thereby enhancing perception. Smaller kernels, such as 3 × 3, focus on high-frequency details, enhancing the model’s capability to detect subtle signal variations. By combining features from different scales, our approach comprehensively captures signal characteristics, thereby enhancing the model’s recognition capability.

$${\mathrm{Y}}_1=\left[{\mathrm{K}}_1\left(\mathrm{X}\right),{\mathrm{K}}_2\left(\mathrm{X}\right)\right]$$

(1)

$${\mathrm{Y}}_2={\mathrm{P}}_{\mathrm{m}}\left(\mathrm{Act}\left(\mathsf{\delta }\left({\mathrm{Y}}_1\right)\right)\right)$$

(2)

In the formula, $K_1$ and $K_2$ represent convolutional kernels of different sizes, $\left[,\right]$ denotes the concatenation operation, Act denotes an activation function, $\delta$ represents Batch Normalization (BN), and $P_m$ stands for max pooling.

This method of multi-scale convolution significantly enhances the capability to capture essential features of localized bearing faults, surpassing the limitations of conventional feature extraction confined to a single temporal scale. By employing this approach, the model substantially improves its effectiveness in identifying bearing fault characteristics, consequently enhancing the precision and sensitivity of fault diagnosis.

3.2. OrthoNet

OrthoNet introduces a novel orthogonal channel attention mechanism specifically designed for deep convolutional neural networks [35]. It achieves filter orthogonalization through the Gram–Schmidt process, thereby enhancing channel attention. At the heart of OrthoNet lies its orthogonal filters, which amplify the channel attention mechanism and effectively emphasize crucial features. OrthoNet has exhibited superior performance across diverse datasets and application contexts, emphasizing the significance of orthogonal filters in crafting efficient attention mechanisms. The architecture of OrthoNet is depicted in Figure 1.

3.3. Continuous Wavelet Transform (CWT)

The Continuous Wavelet Transform (CWT) is a sophisticated mathematical technique employed for the time-frequency analysis of signals. It decomposes a signal into wavelets—small waves localized in both time and frequency. The CWT offers distinct advantages over the Fourier Transform by providing variable resolution at different frequencies, making it exceptionally suitable for analyzing non-stationary and transient signals, which are typical in industrial diagnostic applications. The CWT is integrally formulated into the product of the signal and scaled, and the wavelet function ψ(t) is shifted, as defined as follows:

$$CWT\left(s,\mathsf{\tau }\right)={\displaystyle \frac{1}{\sqrt{\left|s\right|}}}{\int }_{-\mathrm{\infty }}^{\mathrm{\infty }}x\left(t\right)\cdot \overline{\mathsf{\psi }}\left({\displaystyle \frac{t-\mathsf{\tau }}{s}}\right)dt$$

(3)

where $\mathrm{x}\left(t\right)$ represents the signal to be transformed; $\mathsf{\psi }\left(t\right)$ is the mother wavelet function. s denotes the scale factor, influencing the wavelet’s width; $\mathsf{\tau }$ is the translation parameter, shifting the wavelet along the signal timeline; and $\overline{\mathsf{\psi }}$ indicates the complex conjugate of the wavelet function.

For the purpose of analyzing bearing fault data in the EffiMultiOrthoBearNet model, the Complex Morlet wavelet, denoted as cmor100-1, is selected. This wavelet is particularly effective due to its Gaussian-shaped envelope and oscillatory component, which align well with the spectral characteristics of mechanical vibrations in bearings. The Complex Morlet wavelet is mathematically expressed as seen in the following formula:

$$\mathsf{\psi }\left(t\right)={\mathsf{\pi }}^{-1/4}\cdot e^{i{\mathsf{\omega }}_{0}t}\cdot e^{-t^2/2}$$

(4)

Here, ${\omega }_0$ represents the central frequency of the wavelet. For the cmor100-1 configuration, ${\omega }_0$ is set to 100, optimizing the resolution at the frequency crucial for detecting mechanical anomalies.

The application of CWT to the dataset involves transforming each time-domain signal from the bearing data using the CWT with the cmor100-1 wavelet. This transformation produces a two-dimensional time-frequency representation known as a scalogram, which illustrates the evolution of different frequency components of the signal over time. These scalograms serve as input features for the EffiMultiOrthoBearNet, enabling the network to effectively learn and identify patterns associated with various types of bearing faults. Utilizing CWT, particularly with the cmor100-1 wavelet, significantly augments the model’s capability to discern subtle frequency-domain changes indicative of bearing defects. This enriched, multi-scale time-frequency analysis of vibration signals provides a more detailed and precise fault diagnosis, crucial for optimizing operational efficiency and preventing unforeseen equipment failures.

3.4. EffiMultiOrthoBearNet Model

EffiMultiOrthoBearNet is an advanced deep learning model specifically crafted for the precise identification and diagnosis of bearing faults within industrial machinery. This model integrates custom-designed modules, namely the DepthOrthoBlock and OrthoConvBlock, to optimize feature extraction processes and enhance adaptability and efficiency in handling complex diagnostic scenarios. The structural designs of these blocks, depicted in Figure 2a and Figure 2b, respectively, underscore their unique functionalities within the network architecture.

(1)

DepthOrthoBlock

The DepthOrthoBlock, as shown in Figure 2a, is a crucial component of the EffiMultiOrthoBearNet architecture. It incorporates depthwise separable convolutions paired with the OrthoNet layer, a configuration aimed at maximizing feature extraction while minimizing computational demands. The block begins with a 1 × 1 convolution that refines channel-wise features, followed by a 3 × 3 depthwise convolution. This arrangement effectively decomposes the convolutional process into simpler, more manageable operations, ensuring detailed feature capture with reduced redundancy. The integration of OrthoNet within this block enhances the orthogonality of features, ensuring robust and distinctive feature representations crucial for accurate fault detection.

(2)

OrthoConvBlock

Complementing the DepthOrthoBlock, the OrthoConvBlock, shown in Figure 2b, utilizes standard 3 × 3 convolutions to capture broader contextual information from the input data—essential for recognizing diverse fault patterns. Each convolution layer in this block is augmented by an OrthoNet layer, which recalibrates and optimizes the outputs to improve representational efficiency. This module is vital for the network’s ability to integrate and analyze multi-scale data, thereby enhancing overall sensitivity to various fault indications.

(3)

Overall Architecture Integration

EffiMultiOrthoBearNet exemplifies cutting-edge integration of advanced deep learning modules tailored specifically for the efficient and effective diagnosis of bearing faults. As depicted in Figure 3: Architecture of EffiMultiOrthoBearNet, the model’s architecture skillfully combines sophisticated DepthOrthoBlock and OrthoConvBlock units. This intricate arrangement allows for a dynamic interplay between depthwise and standard convolutions, further enhanced by the precision adjustments offered by OrthoNet layers. The strategic deployment of these components ensures that EffiMultiOrthoBearNet can process complex datasets with remarkable efficiency and accuracy. By leveraging both depthwise separable and standard convolutional layers, the model excels in extracting nuanced features essential for fault diagnosis across various operational contexts. The incorporation of OrthoNet layers further refines the feature maps, optimizing the network’s performance by increasing the orthogonality and distinctiveness of the extracted features. This architecture does more than just streamline the learning process; it significantly reduces computational overhead. This efficiency makes EffiMultiOrthoBearNet particularly suitable for deployment in environments where computational resources are limited but where high diagnostic accuracy is paramount. The model’s design not only facilitates rapid training and inference times but also enhances the system’s reliability and robustness in real-world industrial applications.

3.5. Diagnosis Procedure

Figure 4 illustrates the flowchart of the EffiMultiOrthoBearNet system for bearing fault diagnosis. The general process unfolds as follows:

Step 1: Data Acquisition. Utilizing the Case Western Reserve University Bearing Data Center’s experimental setup, signals are acquired from the motor bearings under various health conditions. These signals are collected through sensors that monitor vibrations, which effectively capture the operational state of the bearings.

Step 2: Data Preprocessing and Multi-Scale Feature Fusion. The raw vibration signals are initially preprocessed to remove noise and normalize the data. Each processed signal is then segmented into smaller, manageable frames. These frames undergo a transformation through Continuous Wavelet Transform (CWT), enhancing their suitability for input into deep learning models by highlighting essential time-frequency components.

Step 3: Feature Extraction Using EffiMultiOrthoBearNet. The preprocessed data frames are fed into the EffiMultiOrthoBearNet, which employs an architecture consisting of DepthOrthoBlock and OrthoConvBlock modules for robust feature extraction. The DepthOrthoBlock utilizes depthwise convolutions combined with orthogonal attention mechanisms to optimize feature space and enhance model responsiveness to subtle signal variations. Simultaneously, OrthoConvBlock handles broader feature integration using standard convolutions augmented by OrthoNet adjustments, ensuring comprehensive multi-scale feature recognition.

Step 4: Fault Diagnosis. Once trained, the EffiMultiOrthoBearNet evaluates test samples to classify the health status of bearings. The model’s output includes detailed classifications across different fault types, such as ball, inner raceway (IR), outer raceway (OR), and normal conditions. These diagnostic results are displayed alongside a custom t-SNE visualization and a confusion matrix, providing clear and interpretable insights into the model’s performance and accuracy.

Figure 4 further showcases the sophisticated design of EffiMultiOrthoBearNet, illustrating how each component contributes to a holistic fault diagnosis approach. This approach leverages advanced deep learning techniques to offer a highly accurate, resource-efficient solution for real-time bearing fault monitoring.

4. Experimental Validation

In this study, we conduct a thorough validation of the EffiMultiOrthoBearNet model using the CWRU dataset, a recognized benchmark in the field of bearing fault diagnosis. We employ key performance metrics, such as accuracy, precision, recall, and F1 score, to rigorously assess the model’s effectiveness. The validation process is methodically executed across three distinct experimental setups: consistent operating conditions, varied signal-to-noise ratio conditions, and diverse operating conditions. These experiments systematically evaluate the robustness and adaptability of EffiMultiOrthoBearNet.

4.1. Experimental Setup and Evaluation Metrics

The experiments were conducted using a high-performance computing system outfitted with an Intel(R) Core(TM) i9 10900K CPU at 3.70 GHz, an Nvidia GeForce GTX 3090 GPU, and 32 GB of RAM. Supported by Ubuntu 18.04.6 LTS, this configuration provided a stable and compatible platform to meet our computational demands. The development and testing phases were facilitated through the Pytorch framework, with Pycharm utilized as the development environment, ensuring an efficient and robust setup for our deep learning experiments.

To rigorously assess the performance of the EffiMultiOrthoBearNet model, we employed four primary metrics: accuracy, precision, recall, and F1 score. These metrics play a crucial role in evaluating the model’s accuracy in identifying and classifying faults, and they are widely recognized across various research domains. The formulas for each metric are presented as follows:

Accuracy is the ratio of correctly classified samples (both true positives and true negatives) to the total number of samples.

$$\mathrm{A}\mathrm{c}\mathrm{c}\mathrm{u}\mathrm{r}\mathrm{a}\mathrm{c}\mathrm{y}={\displaystyle \frac{\mathrm{T}\mathrm{P}+\mathrm{T}\mathrm{N}}{\mathrm{T}\mathrm{P}+\mathrm{T}\mathrm{N}+\mathrm{F}\mathrm{P}+\mathrm{F}\mathrm{N}}}$$

(5)

Precision is the ratio of correctly classified positive examples (true positives) to the total number of examples classified as positive (both true positives and false positives).

$$\mathrm{P}\mathrm{r}\mathrm{e}\mathrm{c}\mathrm{i}\mathrm{s}\mathrm{i}\mathrm{o}\mathrm{n}={\displaystyle \frac{\mathrm{T}\mathrm{P}}{\mathrm{T}\mathrm{P}+\mathrm{F}\mathrm{P}}}$$

(6)

Recall is the ratio of correctly classified positive examples (true positives) to all actual positive examples (both true positives and false negatives).

$$\mathrm{R}\mathrm{e}\mathrm{c}\mathrm{a}\mathrm{l}\mathrm{l}={\displaystyle \frac{\mathrm{T}\mathrm{P}}{\mathrm{T}\mathrm{P}+\mathrm{F}\mathrm{N}}}$$

(7)

F1 Score is the harmonic mean of precision and recall, offering a balance between them, especially when their values vary widely.

$$\mathrm{F}1=2\times {\displaystyle \frac{\mathrm{P}\mathrm{r}\mathrm{e}\mathrm{c}\mathrm{i}\mathrm{s}\mathrm{i}\mathrm{o}\mathrm{n}\times \mathrm{R}\mathrm{e}\mathrm{c}\mathrm{a}\mathrm{l}\mathrm{l}}{\mathrm{P}\mathrm{r}\mathrm{e}\mathrm{c}\mathrm{i}\mathrm{s}\mathrm{i}\mathrm{o}\mathrm{n}+\mathrm{R}\mathrm{e}\mathrm{c}\mathrm{a}\mathrm{l}\mathrm{l}}}$$

(8)

where TP (True Positive) indicates the number of correctly classified positive samples, TN (True Negative) represents the number of correctly classified negative samples, FP (False Positive) denotes the number of negative samples incorrectly classified as positive, and FN (False Negative) signifies the number of positive samples incorrectly classified as negative.

Using these metrics, we quantitatively evaluate EffiMultiOrthoBearNet’s accuracy in diagnosing bearing faults under diverse conditions. These metrics offer a comprehensive assessment of the model’s effectiveness and practical applicability. The combination of accuracy and recall provides insights into the model’s inclusiveness and sensitivity in fault identification, while precision and F1 score further reflect the model’s ability to distinguish between fault types. Overall, these evaluation results not only validate the technical advancements of EffiMultiOrthoBearNet but also demonstrate its potential value in real-world applications.

4.2. CWRU Bearing Dataset

This study utilizes the publicly accessible bearing fault dataset provided by Case Western Reserve University (CWRU) in the United States to validate the effectiveness and feasibility of the proposed diagnostic approach. The experimental setup comprises 1.47 kW motors, a central torque sensor, and a dynamometer, as illustrated in Figure 5. The SKF model 6205-2RSJEM test bearing supports the motor shaft and is subjected to testing under various load conditions. The dataset includes faults such as ball defects (BF), outer race defects (OF), and inner race defects (IF). These faults are induced using electric discharge machining, resulting in diameters ranging from 0.007 mm to 0.021 mm. Vibration data under different loads are collected using an accelerometer with a 12 kHz sampling rate.

4.3. Data Preprocessing

Prior to analyzing the CWRU dataset, crucial data preprocessing steps were carried out. These steps primarily involved the application of Continuous Wavelet Transform (CWT) to convert one-dimensional time-domain vibration signals into two-dimensional time-frequency images. This transformation accurately captures bearing fault characteristics, thereby enhancing the model’s accuracy and robustness for complex tasks. Applying CWT enables a detailed analysis of transient features within the signal, particularly variations across different time and frequency scales, thereby enhancing the precision of bearing fault detection. Figure 6 illustrates this conversion process from signal to image in detail.

4.4. Model Performance Analysis under Consistent Operating Conditions

To substantiate the effectiveness of our proposed methodology, we meticulously analyzed bearing data from the Case Western Reserve University (CWRU) dataset under zero horsepower (0 hp) load conditions. This in-depth analysis targeted the drive-end bearings, covering ten distinct operational states, with each state comprising 1000 samples, totaling 10,000 samples analyzed. The sample length was established at 2048 data points to ensure comprehensive coverage of at least two rotations of the bearing, thereby capturing essential fault-specific information. The dataset was strategically divided into an 80:20 split for training and testing sets, respectively, to rigorously assess EffiMultiOrthoBearNet’s diagnostic proficiency across a variety of bearing faults under consistent conditions. Through the application of Continuous Wavelet Transform (CWT), these samples were converted into time-frequency images, capturing the full spectrum of signal characteristics.

Table 1. Division of dataset.

Fault Diameter	Fault Type	Lable Type
0	Normal	0
0.007	InnerRace	1
0.007	OuterRace	2
0.007	Ball	3
0.014	InnerRace	4
0.014	OuterRace	5
0.014	Ball	6
0.021	InnerRace	7
0.021	OuterRace	8
0.021	Ball	9

outlines the distribution of these samples, detailing fault diameter, type, and the associated label for each category, ensuring a balanced evaluation. This structured framework allows for a thorough investigation of EffiMultiOrthoBearNet’s diagnostic capabilities under steady operating conditions, offering a clear insight into its potential applications in industrial settings.

In this study, EffiMultiOrthoBearNet was benchmarked against a diverse range of diagnostic models, from established architectures like VGG16 and ResNet152 to more recent advancements such as ConvNeXt-S, VIT-S, and Swin-S, all meticulously fine-tuned for fault diagnosis on the CWRU dataset. The tuning involved adapting the final layers of each model to enhance their specificity for bearing fault diagnosis and calibrating their training parameters—adjustments to learning rates and epochs—to optimize performance metrics, specifically precision, recall, F1 score, and accuracy. Figure 7 presents a heatmap of the diagnostic results, offering a visual comparison of performance across different models as detailed in

Table 2. Diagnostic results of different diagnostic models on CWRU dataset.

Methods	Precision	Recall	F1 Score	Accuracy
VGG16	0.9124	0.8941	0.8927	0.8948
Resnet152	0.9496	0.9354	0.9294	0.9364
Resnet152-Senet [36]	0.9685	0.9521	0.9675	0.9300
VIT-S	0.9813	0.9783	0.9778	0.9781
ConvNeXt-S	0.9833	0. 9825	0.9822	0.9823
Swin-S	0.9938	0. 9937	0.9936	0.9936
EffiMultiOrthoBearNet	1.00	1.00	1.00	1.00

. Table 2 presents a detailed comparison of the results, revealing that traditional models like VGG16 and ResNet152, while achieving respectable accuracies of 89.48% and 93.64%, respectively, fell short in comparison to newer models on other critical diagnostic metrics. This shortfall is largely attributed to their older architectural designs, which are less effective at managing the complex feature interactions characteristic of the fault diagnosis domain. In contrast, newer models like ConvNeXt-S, VIT-S, and Swin-S showed remarkable improvements in diagnostic capabilities, with F1 scores up to 98.22%, 97.78%, and 99.36%, respectively, underscoring the advantage of incorporating modern neural network architectures and attention mechanisms that better capture subtle fault indicators. EffiMultiOrthoBearNet stood out significantly, achieving perfect scores of 100% across all metrics, a testament to its sophisticated design that integrates multi-scale convolutional feature fusion with DepthOrthoBlock and OrthoConvBlock modules. These modules harness advanced residual learning and orthogonal attention mechanisms, significantly boosting the model’s efficiency in processing complex features across varied scales and orientations. Such enhancements not only improve computational efficiency but also ensure unparalleled diagnostic accuracy in intricate bearing fault scenarios. EffiMultiOrthoBearNet’s exceptional performance highlights its transformative potential for advancing diagnostic imaging and machine fault analysis, paving the way for its application in next-generation intelligent manufacturing and automation technologies.

Figure 8 presents a t-SNE visualization of the features derived from the data analyzed in Table 2, offering a comparative view of how various models cluster these features under different fault conditions. Additionally, Figure 9 displays confusion matrices that provide a direct visual representation of the diagnostic accuracy for each model, as detailed in Table 2. These matrices distinctly delineate precision and recall for various fault categories, underscoring the superior diagnostic performance of EffiMultiOrthoBearNet.

Table 3. Performance comparison of different diagnostic models on the CWRU dataset.

Methods	Params (M)	MAdd (G)	FLOPs (G)
VGG16	134.302	7.733	15.466
Resnet152	58.164	5.801	11.602
ConvNeXt-S	49.419	4.341	8.683
VIT-S	21.593	2.124	4.248
Swin-S	48.797	4.272	8.544
EffiMultiOrthoBearNet	2.321	1.060	2.121

showcases a performance comparison of various diagnostic models, emphasizing EffiMultiOrthoBearNet’s supremacy in the field. When juxtaposed with traditional models like VGG16 and ResNet152, EffiMultiOrthoBearNet showcases dramatic reductions in parameters, Multiply-Adds (MAdd), and Floating Point Operations Per Second (FLOPs), illustrating its ability to achieve high diagnostic accuracy while significantly minimizing the demand for computational resources. This efficiency underscores EffiMultiOrthoBearNet’s suitability as an ideal diagnostic solution for industrial environments with constrained computational capacities. As shown in Figure 10a, EffiMultiOrthoBearNet significantly reduces the number of model parameters. Figure 10b illustrates its lower Multiply-Add operations, and Figure 10c depicts the decreased Floating Point Operations Per Second (FLOPs). These figures collectively underscore the model’s capability to maintain high diagnostic performance with reduced computational requirements.

4.5. Model Performance Analysis under Varied Signal-to-Noise Ratio Conditions

In the domain of bearing fault diagnostics, the ability of a model to withstand noise interference is a crucial indicator of its performance. This study meticulously evaluates the performance of EffiMultiOrthoBearNet and other cutting-edge models under diverse signal-to-noise ratio (SNR) settings, with a special focus on noise-free scenarios, and the −10 dB and −5 dB SNR levels. These particular testing environments are deliberately designed to reflect the wide range of operational conditions encountered in industrial settings, from relatively quiet to highly noisy situations.

The findings, as depicted in Figure 11, unequivocally highlight EffiMultiOrthoBearNet’s outstanding noise resilience across a vast spectrum of SNR levels. Notably, in environments free from noise, all models tested showcased commendable diagnostic accuracy. However, as the SNR decreased to −5 dB—a level indicative of a realistic yet challenging noise environment in numerous industrial applications—EffiMultiOrthoBearNet remarkably outshone its competitors by maintaining high diagnostic precision. Moreover, even under the extreme noise condition of −10 dB, EffiMultiOrthoBearNet displayed extraordinary performance stability, maintaining a diagnostic accuracy above 90%. This is in stark contrast to other models, which showed a significant decline in diagnostic accuracy under the same condition. EffiMultiOrthoBearNet’s ability to consistently deliver exceptional diagnostic performance, even in the harshest noise environments, not only emphasizes its formidable noise-counteracting capabilities but also confirms its significant potential as an efficient and reliable tool for bearing fault diagnosis in complex, high-noise industrial environments.

4.6. Model Performance Analysis across Diverse Operating Conditions

To delve into the adaptability and generalization capabilities of EffiMultiOrthoBearNet, a series of experiments were conducted using the Case Western Reserve University (CWRU) dataset across different operating conditions. This dataset includes four subsets (A, B, C, and D), symbolizing a variety of load conditions from 0 hp to 3 hp, designed to emulate real-world industrial scenarios. The experimentation involved pairwise testing (A-B, B-C, A-C, A-D), with one set designated for training and the other for testing, aiming to thoroughly evaluate EffiMultiOrthoBearNet’s diagnostic precision and its adaptability to shifting operational states.

The accuracy of several models across operating conditions is presented in

Table 4. Comparison of the accuracy of different methods across operating conditions.

Methods	Accuracy
	A-B	A-C	A-D	B-A	B-C	B-D	C-A	C-B	C-D	D-A	D-B	D-C
VGG16	0.8655	0.8755	0.8405	0.8701	0.8430	0.8163	0.8515	0.8332	0.8311	0.8319	0.7906	0.8215
Resnet152	0.9203	0.9127	0.8894	0.9278	0.8822	0.8506	0.9195	0.8897	0.8853	0.8804	0.8196	0.8876
VIT-S	0.9657	0.9593	0.9145	0.9566	0.9077	0.8777	0.9448	0.9138	0.9111	0.9083	0.8885	0.9159
ConvNeXt-S	0.9699	0.9647	0.9248	0.9638	0.9180	0.8861	0.9555	0.9255	0.9212	0.9159	0.8557	0.9233
Swin-S	0.9799	0.9724	0.9292	0.9652	0.9204	0.8867	0.9606	0.9293	0.9260	0.9167	0.8998	0.925
EffiMultiOrthoBearNet	0.9864	0.9791	0.9343	0.9734	0.9278	0.8956	0.9652	0.9348	0.9310	0.9254	0.9050	0.9330

, highlighting EffiMultiOrthoBearNet’s dominance in navigating diverse operational landscapes with exceptional adaptability and stability under varying load conditions. Figure 12 illustrates the heatmap of diagnostic model accuracy across different operating conditions, effectively summarizing these comparative performances. EffiMultiOrthoBearNet consistently achieved accuracy levels exceeding 90% in all tested scenarios, peaking at 98.64% in the A-B configuration, demonstrating unmatched diagnostic proficiency across different loads and operational parameters. This performance starkly contrasts with other models like VGG16 and Resnet152, which, while demonstrating commendable accuracy, do not reach the high standards set by EffiMultiOrthoBearNet, especially in more challenging scenarios such as A-D and B-D, where operational variances are most pronounced. Models such as ConvNeXt-S and VIT-S show significant advancements in handling variable conditions, with accuracies consistently above 85%, yet still fall short of EffiMultiOrthoBearNet’s benchmark. This illustrates EffiMultiOrthoBearNet’s superior capability not only in maintaining high diagnostic accuracy in stable conditions but also in its remarkable adaptability to changing environments—a crucial attribute for applications within smart manufacturing and industrial automation realms, where operational conditions frequently vary.

EffiMultiOrthoBearNet’s standout performance, particularly its ability to maintain elevated accuracy across a broad spectrum of conditions, robustly validates its potential for widespread industrial application, emphasizing its crucial role in the advancement of intelligent manufacturing and automation technologies. In contrast, while other models such as Swin-S exhibit noteworthy adaptability and performance, EffiMultiOrthoBearNet’s consistency and resilience under varying and challenging conditions underline its pre-eminence in adaptive and generalizable bearing fault diagnosis. This comprehensive analysis lays a solid foundation for EffiMultiOrthoBearNet’s broader future applications and deployments, highlighting its indispensable role in navigating the complexities of modern industrial processes.

5. Conclusions

In conclusion, this study successfully proposes EffiMultiOrthoBearNet, a groundbreaking, lightweight deep learning model tailored for the challenges of bearing fault diagnosis in resource-constrained industrial environments. The integration of innovative DepthOrthoBlock and OrthoConvBlock mechanisms enables this model to effectively manage multi-scale convolution and orthogonal attention, significantly enhancing its diagnostic capabilities. Our experimental validations, conducted with the CWRU dataset across diverse operating conditions and signal-to-noise ratios, confirm EffiMultiOrthoBearNet’s superior performance, achieving classification accuracies up to 100% in ideal conditions and consistently above 90% amidst significant operational complexities.

Despite its high performance, EffiMultiOrthoBearNet may encounter limitations when applied in environments drastically different from those in the CWRU dataset. Additionally, achieving optimal performance in extremely resource-limited settings might require further simplification or targeted optimizations.

Future research will focus on enhancing the model’s adaptability and efficiency. This will involve refining algorithms to perform reliably across a broader range of operational conditions and incorporating a wider range of scenario simulations during training. Additionally, exploring more efficient neural network architectures and employing techniques such as model pruning and quantization will help reduce the computational demands, making the model viable in environments with limited hardware capabilities.