Comparative analysis of deep learning algorithms for rolling element bearing fault classification under variable loads and speeds.

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Learn more: PMC Disclaimer | PMC Copyright Notice Sci Rep . 2026 Apr 11;16:16892. doi: 10.1038/s41598-026-42592-y Comparative analysis of deep learning algorithms for rolling element bearing fault classification under variable loads and speeds Pratyush Vishal 1 , Rohith Nair 2 , Jonathan Jacob 2 , Narendiranath Babu T 2, ✉ , M Pandiyan 2 Author information Article notes Copyright and License information 1 School of Electrical Engineering, Vellore Institute of Technology, Vellore, India 2 School of Mechanical Engineering, Vellore Institute of Technology, Vellore, India ✉ Corresponding author. Received 2026 Jan 23; Accepted 2026 Feb 26; Collection date 2026. © The Author(s) 2026 Open Access This article is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License, which permits any non-commercial use, sharing, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if you modified the licensed material. You do not have permission under this licence to share adapted material derived from this article or parts of it. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by-nc-nd/4.0/ . PMC Copyright notice PMCID: PMC13230911  PMID: 41965751 Abstract This paper presents a comparative study of deep learning methods used to classify roller bearing faults. We obtained experimental vibration data by conducting controlled tests on roller bearings with various faults under different load conditions to simulate real-world industrial conditions. The methodology first evaluates four different time-frequency techniques-STFT, CWT, WPT and CQ-NSGT, establishing CQ-NSGT as the superior method for feature visualization. A novel hybrid transfer learning architecture that integrates pre-trained backbones (EfficientNetB0, MobileNetV2, InceptionV3) with custom residual blocks is proposed. These CNNs are compared to a baseline CNN and a Vision Transformer (ViT). Their performance was rigorously evaluated using fivefold cross-validation and tested against additive white Gaussian noise at Signal-to-Noise Ratios (SNR) of 1 dB, 3 dB, and 5 dB. The EfficientNetB0 hybrid model was able to reach the highest baseline accuracy of 99.83% while also exhibiting excellent robustness-maintaining 98.8% accuracy even at 1 dB SNR. MobileNetV2 is the most computationally efficient model with a training time of only 121.4 s and 0.50 GFLOPS making it perfect for edge deployment. ViT has potential but is less noise stable and lacks the inductive bias of CNNs which is important for this particular application. These results can be used as a guide for trading off accuracy of diagnosis and computational cost in industrial predictive maintenance. Keywords: Bearing fault diagnosis, Deep learning, EfficientNetB0, Transfer learning, Hybrid architecture, CQ-NSGT, Vibration analysis, Predictive maintenance, Condition monitoring, Spectrograms Subject terms: Engineering, Mathematics and computing Introduction Industries heavily emphasize the reliability of rotating machinery since component failures not only halt production but also lead to costly repairs. One of the most crucial parts is rolling element bearings whose failure can be due to wear, fatigue, fracture, and corrosion. Such problems are sometimes caused by assembly errors, misuse, and lack of maintenance 1 . Deep learning (DL) models for fault diagnosis have become quite popular recently. One hybrid approach first transforms the signal into a time-frequency image using Continuous Wavelet Transform (CWT), afterward the transformed image is processed by a 1D convolutional residual network(ResNet), a multi-head self-attention (MHSA) mechanism, and a bidirectional long short-term memory (BiLSTM) network to simultaneously extract spatial, temporal, and hierarchical features 2 . A big challenge in developing these models is data scarcity. To tackle “few-shot learning”, an innovative method uses CWT images but applies a Denoising Diffusion Probabilistic Model (DDPM) to create synthetic, high-quality data. The enhanced dataset was thus fed to a hybrid KANs-CNN model which leveraged the unique learnable activation functions of Kolmogorov-Arnold Networks 3 . One more significant challenge is environmental noise. For a noise-robust model, a lightweight 1D-CNN was developed that operated in the frequency domain and uniquely used both the magnitude and phase parts of a Fast Fourier Transform (FFT) as input. It was able to keep a very high level of accuracy even at extremely low signal-to-noise ratios (-10 dB) 4 by training the model with noise additions. Advanced architectures such as the MLSCA-CW, on the other hand, are intended for extreme noise situations as they combine soft thresholding modules for filtering with a multi-location fusion module to integrate data from different sensor positions 5 . Through its use of vibration envelope spectrum data which extracts peak frequencies and peak intensities as features and classifies them with a basic Naive Bayes algorithm, the method achieves 99% accuracy 6 . A team of scientists developed a complex parallel-path model which unites 1D-LSTM time-series analysis with 2D-CNN CWT image processing to extract data from both temporal and frequency domains 7 . Researchers concentrate their efforts on enhancing one specific metric through their work to improve hybrid CNN-Gated Recurrent Unit (GRU) models by first applying envelope analysis to preprocess signals and then using adaptive mean filtering to reduce noise 8 . Identifying fault severity is also important. A two-layered diagnostic scheme was introduced to address this. A hybrid feature pool was created from time-domain, envelope spectrum, and wavelet energy features and then fed into a sparse stacked autoencoder (SSAE) to classify the specific crack size 9 . The “signal-to-image” pipeline enables the use of powerful, pre-trained 2D-CNNs. Previous work has used 2D-CNN based methods for this task. In one method, the Constant-Q Nonstationary Gabor Transform (CQ-NSGT) is used to create time–frequency images. An Inception-ResNet-V2 model is then applied to these images 10 . In another study, spectrograms were used as input to AlexNet. The model achieved 100% accuracy and required fewer resources compared to newer deep learning architectures 11 . Deep feature extraction can be used together with classical ML techniques. In one approach, a CWT image is fed to a deep CNN such as ResNet50 just to extract features. These features are then classified using Support Vector Machines or Random Forests 12 . A few black-box deep learning models are being re-examined. A researcher applied Hamiltonian Neural Networks to classify a system’s total energy signature while enforcing physics-based constraints 13 . The conversion of signals into images is an important research area. One approach classifies faults under different operating conditions. In the method, one-dimensional motor current signals are first transformed into two-dimensional pictures via Gramian Angular Field technology. A simple two-layer CNN is subsequently adapted for classification 14 . EfficientNetV2 showcases model flexibility as it was architected to harmonize accuracy, training speed, and parameter efficiency 15 . Some use even less complicated techniques like the wavelet envelope power spectrum 16 or add specific modules, such as a multi-feature block, in a custom CNN 17 . Some very recent work has focused on the development of simpler models that can be interpreted more easily. One feature engineering study has demonstrated that frequency band separation techniques, when used together with a Random Forest classifier, yield good results. The method managed to attain very high accuracy at a very low computational cost 18 . Thus deep learning models, which are more complex and involved, may not always be necessary when it is possible to use domain-specific methods. Unfortunately, the majority of these methods have been tested only on clean benchmark datasets, which do not present the same level of complexity as real-world scenarios. A factory-based vibration dataset collected from a pulp mill has revealed the real challenge. Real-world data, in fact, come with variations in symptoms of a failure, changes in the operational conditions and external disturbances, which are not the case with controlled laboratory data 19 . This real challenge from the world has been confirmed by research records that demonstrate simple CNNs alone sometimes reach over 98% accuracy just by being directly applied to raw accelerometer data 20 . CNN-BiLSTM-MHSA hybrid models are needed to effectively deal with the speed variability feature of the air vehicles (UAVs) application 21 . In order to address the issues of limited data and environmental noise, Siddique et al. 22 proposed a hybrid deep learning framework that combines Convolutional Neural Networks (CNNs) with Vision Transformers (ViTs) for milling machine fault diagnosis. Their technique starts with the extraction of clean time-frequency features from vibration signals using logarithmic Continuous Wavelet Transform (log-CWT) scalograms and Canny edge filtering. The researchers then combined the local spatial details captured by ResNet-18 with the global contextual information modeled by ViT and employed a validation-guided stacking ensemble classifier to enhance the accuracy of the diagnosis. This method with two branches demonstrated a high level of robustness against variations in conditions and achieved a classification accuracy of 99.78% on real-world milling datasets, outperforming conventional single-model designs 22 . As a solution to the problem of both accuracy and speed in the diagnosis of centrifugal pump faults, Zaman et al. 23 came up with a hybrid deep learning model that integrates Convolutional Neural Networks (CNNs) with Principal Component Analysis (PCA). The vibration signals of the pump were converted to Stockwell Transform and Continuous Wavelet Transform (CWT) scalograms that were later filtered by the Sobel operator to highlight the fault signature transients. After each individual CNN branch got its essential features and these were combined into a hybrid feature pool, the authors applied PCA to reduce the feature space and therefore, a two-layer Artificial Neural Network (ANN) was trained for the classification of the pump states with high accuracy. The authors’ multi-modal approach outperformed the best state-of-the-art baseline models in terms of noise immunity, reaching a classification accuracy of 95.60% and showing significant improvements in precision and recall metrics 23 . Ullah et al. 24 in their study addressed data efficiency problems and varying operating pressure issues in centrifugal pump fault diagnosis essentially by coming up with a multi-sensor framework based on autoregressive (AR) residual learning. First, the AR observer in the study generates fault-sensitive residuals from vibration signals, which are then statistically and spectrally characterized, followed by a refinement of the features using an Auto-Permutation Feature Importance (Auto-PFI) tool. By utilizing these refined features, the authors constructed a Gaussian Mixture Model (GMM) that provided a powerful probabilistic classification system, capable of handling class imbalance and overlapping fault signatures in an efficient manner. Comparison experiments at different pressure levels demonstrated that the new method outperformed existing deep learning and entropy-based methods in generalization capability, with classification accuracies of more than 99% 24 . Umar et al. 25 developed a burst-informed framework for milling machines that aimed to solve problems related to interpretation of non-stationary acoustic emission (AE) signals as well as a lack of explainability in current fault diagnosis models. Burst-Informed Wavelet Denoising (BIWD) together with adaptive segmentation was employed by the researchers to extract high-energy transients, from which multi-domain features were obtained and eventually combined through an attention-guided fusion mechanism. The combination of a Performance-Weighted Stacked Ensemble (PWSE) classifier with SHAP and LIME interpretability tools enabled the authors to build a fault diagnosis system that is not only physically consistent but also interpretable at the burst level. Experiments on datasets at various operating speeds demonstrated superior generalization performance of the proposed method over state-of-the-art deep learning models as evidenced by the diagnostic accuracy of 99.21% 25 . Fallahy and Rezazadeh 26 demonstrated that one can avoid deep learning’s high resource and time overhead for retraining when one freezes the backbone of the model and only allows a few parameters like batch normalization statistics to be updated during Test-time Entropy Minimisation. They argued that a process like Exponential Moving Average that essentially looks at recent history can help prevent the model from getting confused and changing drastically as it gets data from new domains. Also, a set of methods could be made more trustworthy by applying Test-time Augmentation which is essentially a technique that removes noise and makes it easier to identify particular anomalies. Creating different versions of an image and forcing the model to be consistent across them, the approach effectively reduces the model’s hesitation that is unavoidable in distinguishing heterogeneous masonry textures. To sum up, the technologies mentioned above can be combined to conduct high-level structural health monitoring without any specialized high-performance computing equipment 26 . Literature gap A review of existing work shows that deep learning models have been used for bearing fault diagnosis. However, many studies focus on developing a single model and testing it on one dataset. This leads to important gaps in the literature. There is limited work that provides a clear comparison between modern and high-performing architectures such as EfficientNetB0, InceptionV3, and MobileNetV2 within the same hybrid framework. Most studies mainly report classification accuracy. Often, practical factors such as training time and computational cost measured in GFLOPS are neglected. However, these factors play an important role in real industrial usage. Problem statement The gaps in the existing literature are hindering the adoption of deep learning in the industry are a suitable deep learning architecture that would give the best trade-off between diagnostic accuracy and computational cost is still unknown. Model performance generally decreases when different loads and speeds are experienced. Such situations are typical of real-world machinery. Without a benchmark that considers both accuracy and computational cost, selecting a reliable method for real-time condition monitoring remains difficult. Objectives To address the identified problems, this study focuses on the following objectives. To implement a hybrid deep learning framework using pre-trained models such as EfficientNetB0, InceptionV3, and MobileNetV2 along with custom residual blocks. To apply the Constant-Q Non-stationary Gabor Transform (CQ-NSGT) to convert one-dimensional vibration signals into two-dimensional spectrograms for feature extraction. To evaluate performance of models under different loads and speeds. The research compares computational efficiency using training time and GFLOPS as well. Novelty of research Architectural Novelty This work uses a hybrid transfer learning model. A pre-trained network is kept frozen and used only for feature extraction. After which custom residual blocks are added and trained. This helps the model learn bearing fault patterns from spectrograms. Methodological Novelty The study follows a fixed evaluation procedure for all models. Accuracy is not treated as the only factor. Also, the training time and computational cost have been taken into account when comparing different architectures. Therefore, the comparison becomes more realistic. Transform Application CQ-NSGT is the method applied to change the 1D vibration signals into 2D time-frequency images. These images represent the input to the deep learning models. Experimental work Experimental setup A bearing fault simulator test rig was utilized to simulate various speed conditions. The vibration signals generated were captured through a data acquisition system. In addition to DEWESoft software for vibration data collection, an IEPE accelerometer was used. Figure 1 depicts the experimental setup for the measurement of both single and multiple bearing defects. The test rig includes a double bearing box that supports the drive shaft. The shaft is driven by a 220 V DC motor with a power rating between 1/3 and 1/4 horsepower. Vibration monitoring was carried out using a deep-groove ball bearing set (MB ER-10 K). The bearing has a bore diameter of 0.98 inches and an outer diameter of 2.05 inches. The pitch diameter is 1.49 inches. Each bearing contains eight spherical balls with a diameter of 0.34 inches. Table 1 lists the different bearing defect types considered in this work. Figure 2 shows the actual test bearings used in the experiments. Fig. 1. Open in a new tab Experimental set-up: (1) Frequency variable unit, (2) Electric motor with Tachometer, (3) Balance rotor, (4) Test bearing and housing, (5) Accelerometer, (6) DAQ System, and (7) Display and Storage device. Table 1. Details of bearing fault size. Condition of the bearing Fault size/description Healthy bearing NA Inner race fault 1.5 mm span, 1.2 mm wide, 0.5 mm deep Outer race fault 1.5 mm span, 1.2 mm wide, 0.5 mm deep Ball fault Two 1.2 mm dia. dimples at 90° on one ball Combined fault Above faults are induced Open in a new tab Fig. 2. Open in a new tab From left to right: Bearings with—Ball fault, Combined fault, Inner race fault, Outer race fault. Defects were introduced in the ball, outer race, inner race, and combined faults. The defects were created with a diamond-tipped cutter (such as the Dremel 7134), and their size was validated through microscopic examination. A triaxial piezoelectric accelerometer (Kistler 8763A50) was mounted to the bearing housing using wax as shown in Fig. 3 . This system enabled exact measurement of vibration signals. Atlan DAQ system was used to improve the quality of the recorded vibration signals quality for each fault scenario. The entire process followed is summarized in Fig. 4 . Fig. 3. Open in a new tab Kistler 8763A50 Triaxial IEPE accelerometer. Fig. 4. Open in a new tab Process flow diagram. Optimizer : Adam Optimizer was used for its adaptive learning rate capabilities which are well-suited for complex loss related to deep neural networks. Loss Function: sparse_categorical_crossentropy : was employed as the loss function. Performance Metric : The primary metric used for model performance was accuracy. Epochs : Maximum of 100. To prevent overfitting and manage the training process, the following callbacks were implemented: Early Stopping : Training was configured to stop early if the validation loss (val_loss) did not improve for 3 consecutive epochs, preventing unnecessary training and selecting the best-performing model. Reduce LR On Plateau : The learning rate was dynamically reduced by a factor of 0.5 if the validation loss did not improve for 5 consecutive epochs, with a minimum learning rate (min_LR) of 1e−5. This lets the model make finer adjustments to the weights as it approaches a minimum. CSV Logger : Training history for each model along with other metrics like loss and accuracy for each epoch, were saved to a model_data.csv file for detailed post-training analysis. Dataset description The sampling rate of the sensor used is crucial for diagnosing faults. It sets the limit on the frequency range content that we can analyze from the signal and it also impacts the time resolution we can get. We picked a sampling rate of 12,800 Hz after a series of preliminary experiments. The rates below this did not really succeed in capturing the high-frequency components indicative of bearing defects in a reliable manner. Meanwhile, 12, 800 Hz is strikes a balance where it is adequate enough to pick up the components we need, while also being feasible for a real-time implementation. Since real machines run in changing environments, we conducted tests at three rotational speeds: 1000 RPM correlates with a low-speed operation, 1500 RPM refers to a medium-speed, and 2000 RPM depicts a high-speed scenario. Besides that, three different loading conditions were considered, no load at 0 g, a light load at 6 g, and a heavy load at 12 g. Such testing in different speed and load scenarios allows us to observe how the characteristics of the fault features change with varying operating conditions. Our data records a total of five different health states of a bearing: Healthy Baseline (HB), Ball Fault (BF), Inner Race Fault (IRF), Outer Race Fault (ORF), and Combined Fault (CF). A data snapshot for every single combination of fault type, rotational speed, and load level was obtained and that resulted in 45 distinct operating conditions altogether. Each of them is accompanied by a separate time-series file with roughly 420, 000 samples to it. In total, the data files hold 18.9 million plus data points. This allowed for the extraction of necessary diversity from this volume of data when training models capable of handling the variability between different conditions. It is also very beneficial for us in terms of the trustworthiness of the performance tests, especially when we evaluate the generalization ability of the model to unseen speed and load conditions. In order to scale the dataset and enhance the model’s robustness we used window splitting to cut the vibration signal into segments of a fixed length. We tried both overlapping and non-overlapping windows, so that each segment could represent a short part of the signal with potentially fault-related patterns. In this way, by training on a large number of segments, the model is enabled to recognize faults as they gradually develop over time instead of depending on isolated snapshots only. Along with window splitting, we used a number of augmentation techniques aimed at improving model robustness against real-world variations. For instance, horizontal flipping was used to produce signal versions that are mirror images of the original ones, while time-domain rotation was intended to simulate the phase change, which could easily take place in real operating conditions. Additionally, we applied the injection of a very small amount of noise to the data so that the model can still perform well even when the quality of the sensor data is not ideal. For model evaluation, we chose scikit-learn’s train-test split function to separate the augmented dataset into training (80%) and validation (20%) sets. The random split of the data ensured that all fault types and operating conditions were naturally distributed in both sets, so we are quite sure that the validation performance will indicate how good the model is at generalizing to unseen data. The dataset offers some significant benefits. Data was recorded at three different rotation speeds. This enables the model to deal with the variation in speed. The sampling frequency is 12, 800 Hz. Such a high sampling rate allows for detecting minute fault-related changes that would otherwise have been overlooked at lower frequencies. Figure 5 depicts the exact process that was followed in our study (Table 2 ). Fig. 5. Open in a new tab Flow diagram for bearing fault diagnosis. Table 2. Specifications for experimental setup. Parameter Details Parameter Details Test Rig Model Spectra Quest MFS-PKG5 Drive Motor Marathon Bearing Type MB ER-10 K Deep Groove Ball Bearing Motor Rating 1/3 hp, 4000 rpm (Max Speed) Rolling Elements Count 8 Shaft Material/Spec 5/8’’ Turned, Ground, Polished (TGP) Steel Rolling Element Diameter 7.939 mm Vibration Sensor Kistler 8763A50 (Tri-Axial IEPE) Pitch Diameter 33.503 mm Sensor Range/Sensitivity 100 mV/g, ± 50 g Contact Angle 0 degree Data Acquisition Unit ATALON: ATA-DAQ 042.451 Inner Race Diameter 19.05 mm DAQ Specifications 4 channels, 24-bit resolution, ± 10 V range Outer Race Diameter 47.96 mm Analysis Software DEWEsoft 7.1 Open in a new tab Physics based validation of fault signatures Roller bearings have different parts. Defects in any of these parts produce vibrations at certain frequencies. The main frequencies are BPFO, BPFI and BSF. BPFO is the frequency at which the rolling elements pass over a defect on the outer race. As the outer race is fixed, thus, the frequency is directly proportional to the shaft speed and produces relatively stable spectral peaks under steady operating conditions. BPFI signifies the frequency at which the rolling elements hit the inner race defect. Since the inner race turns with the shaft, this part usually shows amplitude modulation and sidebands at the shaft rotational frequency. BSF is related to the defects on the rolling elements. It depicts the rate at which a ball spins on its axis and usually comes with harmonics because of periodic slip and changing contacts. Using the formulae in Table 3 (a) and (b) we can calculate the fault frequencies and frequency factors to obtain the theoretical calculated values.When we perform a Fast Fourier Transform on the vibration data to obtain an envelope spectrum of the frequencies in Fig. 6 a–c, we observe peaks at values close to our calculated values as shown in Table 3 (a). This provides physics based evidence confirming that learned features correspond to the expected bearing fault frequencies. Table 3. (a) Formulae for fault frequencies. (b) Frequency factor table. Type of defect Formula (a) Inner race fault Outer race fault Rolling element fault (b) Inner race fault Outer race fault Rolling element fault Open in a new tab Fig. 6. Open in a new tab a – c BPFO, BPFI and BSF on available vibration data. Methodology Signal-to-image transformation The first stage converts one-dimensional vibration signals into two-dimensional images. These images are used as input for deep learning models. This step is required because such models work better with image data. Vibration signals from rotating machines are non-stationary. Their characteristics change over time. Because of this, analysis only in the time domain or only in the frequency domain is not sufficient. A time–frequency analysis method is needed to capture how frequency content changes over time. Several signal-to-image methods were examined for this purpose. However, some limitations were observed. The Short-Time Fourier Transform (STFT) uses a fixed window size. This trade-off between time and frequency resolution mainly arises. The Continuous Wavelet Transform (CWT) allows for multi-resolution analysis. On the other hand, it is computationally very expensive and does not ensure perfect signal reconstruction. As a result, the accuracy of the signal representation can be lower 10 1 2 3 The equations mentioned here refer to the windowed signal defined in Eq. ( 1 ), and the term hx(n) stands for the center window function, whereas fx is the center frequency, and fm the sampling frequency of the signal. We used the raw, unfiltered one-dimensional vibration signals and applied Constant-Q Non-stationary Gabor Transform (CQ-NSGT) as per Eq. ( 3 ) to get two-dimensional time-frequency representations of the signals, i.e. spectrograms. These spectrograms serve as visualizations that illustrate where vibration energy is located in frequency and how it changes over time simultaneously. This conversion is especially useful in detecting faults in bearings as each fault will leave a unique signature in frequency pattern that change over time, thus, those signals from the raw source will be almost impossible to detect. To avoid the model becoming too fitted to the training set, we carried out data augmentation on the spectrograms to increase the diversity of patterns which the network would see during the training. Next, we resized the images to 224 × 224 pixels so our models could process them properly 10 . Transfer learning A transfer learning approach is used in this study. Rather than building a model from the ground up, pre-trained models are fine-tuned for the task of bearing fault classification. This shortens the training period and eliminates the requirement for extremely large labeled datasets. A custom hybrid framework was made instead of just using pre-trained models. The purpose of this framework is to convert general features into vibration fault patterns. Here, a pre-trained model is used as a feature extraction backbone (Refer Fig. 7 ). On top of that, custom residual blocks are added. These blocks assist in the refinement of the features extracted for the task of bearing fault classification. Fig. 7. Open in a new tab Transfer learning architecture. Proposed model architecture This work investigates three deep learning models to classify roller bearing faults. The models utilize vibrational signals transformed into spectrogram images. All the models rely on transfer learning. Custom hybrid architectures incorporate pre-trained networks to function as feature extractors. Furthermore, to make the features suitable for fault classification, custom residual blocks are added. MobileNetV2, InceptionV3, and EfficientNetB0 are the three fundamental models used in this study. The reason behind the selection of these models was their frequent use in image classification as well as their being different in architectural characteristics. In the proposed method, each model is used as a backbone for feature extraction. After that, the extracted features are processed with the help of custom residual blocks for bearing fault classification. Three different backbones were experimented with in this work. Each backbone was assessed separately to compare the results under the same testing conditions. MobileNetV2: lightweight efficiency for resource-constrained applications Lightweight and efficient network. It is can be run on low power devices without any problems. It’s architecture (Fig. 8 ) is based on inverted residual blocks and linear bottlenecks which help to keep it small and fast. Fig. 8. Open in a new tab MobileNetV2 architecture. InceptionV3: multi-scale feature extraction through parallel processing The Inception architecture (Fig. 9 ) addresses the issue of feature extraction at various scales by performing 1 × 1, 3 × 3, and 5 × 5 convolutional filtering simultaneously within each module. Hence, the model can respond to tiny details and large spatial patterns at the same time. To limit the computational cost, the architecture uses factorized convolutions, i.e., splitting a large filter into a series of small ones, which gives the structural power that is maintained while the number of parameters and operations is hugely decreased. Fig. 9. Open in a new tab InceptionV3 architecture. EfficientNetB0: compound scaling for optimal resource utilization EfficientNet (Fig. 10 ) uses compound scaling that gradually and systematically scales depth, width, and resolution of the network by using a fixed set of coefficients; thus, it ensures these dimensions are balanced and not independently tuned. The architecture is comprised of Mobile Inverted Bottleneck Convolution (MBConv) blocks which add Squeeze-and-Excitation (SE) modules to recalibrate channel-wise feature responses—basically the network is enabled to highlight the features it finds most useful and at the same time, it suppresses those less relevant, based on the global context. Fig. 10. Open in a new tab EfficientNetB0 architecture. Unique contribution: the hybrid residual architecture The‍ core idea of this research is to utilize a hybrid deep learning framework. Preliminary trials revealed that the direct application of a pre-trained model for bearing fault classification did not yield satisfactory results. Such models have been trained on huge image datasets and are very good at extracting general features. Nevertheless, they are not geared towards the identification of specific patterns in bearing fault spectrograms. In order to fix this, the pre-trained base model is frozen and retained only for feature extraction. In addition, custom residual blocks are appended to the base model. These blocks allow the model to fine-tune the features extracted for the bearing fault classification task. Thus, the model can retain general feature information and at the same time obtain task-specific patterns from the vibration data. Residual blocks (Refer Fig. 11 ) are implemented primarily for training stability. When deep networks are built, they can easily have the problem of the gradient becoming smaller and smaller. Shortcuts, or skip connections, in residual blocks give the network this ability of reducing the gradient problem. This allows for a deeper network while making the training process more reliable. The deeper network is capable of extracting more complex features from spectrogram data since shallow models have limited capacity. Fig. 11. Open in a new tab Block diagram for residual block. Figuratively, the hybrid model that comprises frozen pre-trained backbone and trainable custom layers generalizes better than the conventional model. In this way, the benefits of transfer learning are preserved and at the same time the model is adapted to bearing fault ​‍data. Common classification head architecture For a fair comparison between the three base models, a standard classification head was used. The models that were evaluated are MobileNetV2, InceptionV3, and EfficientNetB0. To maintain consistency in evaluation, after feature extraction and processing via the hybrid residual blocks, the output of each model is passed to the same classification head, as illustrated in Fig. 12 . Fig. 12. Open in a new tab Block diagram for common architecture. Adaptive optimization strategy for bearing fault detection Model training was done with the Adam optimizer. Adam was chosen since it adjusts the learning rate during training. This is quite handy for spectrogram data, which has variations over time and frequency. Additionally, bearing fault signals can be noisy and may give sparse gradients. Thus, Adam allowed stable training when fine-tuning the custom residual blocks. The pre-trained base model was not altered during this phase. Robustness testing using noise injection Robustness testing was conducted to ensure that the model’s performance is not degraded in noisy situations. Additive White Gaussian Noise (AWGN) was created with the help of the Numpy library. This noise was superimposed on the original vibration signals to imitate industrial interference. Three different signal-to-noise ratios were examined. Namely, these were 5 dB, 3 dB, and 1 dB. The performance of the model was measured independently at each noise ​‍​level. Cross-validation strategy We employed a stratified fivefold cross-validation method. The data set was split into five equal parts. Each part had a balanced distribution of all fault classes. Among these were Ball Fault, Inner Race Fault, Outer Race Fault, Combined Fault, and Healthy conditions. The models were each trained five times, with the validation fold being changed each time. The average and standard deviation of the results across all folds are provided as the final performance results. Samples of different operating conditions (loads and speeds) in whole were combined into a single dataset so that samples were classified based on the type of fault rather than the condition of acquisition. The aim of the current research is to test how well deep learning models can classify faults at the window-level when the operating regimes are mixed, instead of looking at generalization across conditions (e.g., training on one load and testing on another). Therefore, a stratified k-fold cross-validation method was used to maintain class balance in each fold of the dataset while also ensuring that each fold contains samples that are representative of the entire range of operating conditions. In addition, window segmentation was conducted without overlap, thus each sample is a separate time segment of the vibration signal and duplicated or almost identical signal fragments are not allowed to occur across the folds. This lowers the extent to which redundancy-driven performance has been artificially increased and, at the same time, allows one to comfortably estimate the performance of the window-level classifier under different loading and speed conditions. Results and discussion Prior to analyzing model results, the study first examines the effectiveness of different time–frequency conversion methods. These methods are utilized to capture vibration features associated with bearing faults. Table 4 shows a comparison between spectrograms generated by the four different methods. These are the Constant-Q Non-Stationary Gabor Transform (CQ-NSGT), Short-Time Fourier Transform (STFT), Continuous Wavelet Transform (CWT), and Wavelet Packet Transform (WPT). The comparison is performed for various bearing fault conditions. Table 4. Qualitative analysis of spectrograms obtained using various transformation methods. Open in a new tab Qualitative spectrogram analysis and feature visualization Different time–frequency conversion methods were studied prior to delving into the model results. The purpose was to figure out which method most accurately represents vibration features related to bearing faults. Table 4 includes the examples of these methods’ results in the form of spectrograms. Four of such techniques are Constant-Q Non-Stationary Gabor Transform (CQ-NSGT), Short-Time Fourier Transform (STFT), Continuous Wavelet Transform (CWT), and Wavelet Packet Transform (WPT). Checking these methods includes almost all fault states. The vibration signals for these spectrograms were recorded while the instrument was operating at 1500 RPM and a load of 6 g. It is noted that using the same conditions of the experiment allows direct comparability of methods as differences in the spectrograms can be attributed to changes of the transformation technique, not confounded by experimental variation. Each method displays some variations in what features of the fault pattern are more visible. Compared with other methods, CQ-NSGT excels in time–frequency resolution. Consequently, harmonic components related to faults can be more easily detected, especially to the inner and outer race of the fault. Moreover, the constant-Q aspect aids in keeping the frequency resolution at both low and high frequency ranges. STFT generates an even time–frequency distribution. Thus it provides reliable results and can be considered as a standard method for observing general fault patterns. Despite this, the limitation of the fixed window size is to not be able to represent at the same time short transient events and long-duration signal components. CWT quite accurately records the transient events due to its variable resolution. This results in impact-related features being more visible. Such features are typically related to ball faults and combined fault cases. WPT lets the vibration signal be broken down into several frequency bands. From this, one can get a closer look as to how the energy of the signal is spread across frequencies. The differences between healthy and faulty bearings are made quite clear in these representations due to changes in spectral content. The level of success is judged qualitatively based on how well the visualization of the separation of fault-related harmonic components under identical operating conditions can be done. Among several cases, CQ-NSGT is more clearly separating fault related components. The spectrograms thus created are what is given as inputs to convolutional neural networks. These inputs allow the feature extraction process to focus on fault-related features under different operating conditions. Quantitative spectrogram analysis Objective quantitative evaluation was used to further examine the feature- discriminating ability and the structural consistency of the different time, frequency representations. A spectral kurtosis based class separability analysis was executed to mathematically validate how each transformation can keep the fault impulse characteristics which are the bearing defect fingerprints. Spectral kurtosis has become very popular in the field of rotating machinery diagnostics because of its capability of identifying non-Gaussian and transient components of vibration signals, thus allowing the fault-induced impulsive behavior buried in the complex mechanical responses to be effectively detected and characterized 27 . Kurtosis feature vectors were extracted from the spectrograms corresponding to each time, frequency representation. Class separability was evaluated by the ratio of the between-class and within-class scatter measures obtained from these feature vectors. The between-class scatter indicates how far different fault categories are scattered in the feature space, while the within-class scatter is how closely samples of the same class are clustered. A good representation should be able to maximize the separation between classes and at the same time minimize the variability within each class, hence leading to a better discriminative structure in the transformed domain. In addition to evaluating the separability based on scatter, we also separately assessed the intra-class variance of the kurtosis features to quantify the consistency and structural stability of the representation of samples under various operating conditions. When the intra-class variance is low, it means that the transformation has preserved the fault signatures in a consistent and reliable manner, thus, giving less uncertainty to the subsequent classification steps and higher robustness. The comparative analysis reveals CQ-NSGT as the most effective method in terms of class separability among all the techniques that were evaluated, exhibiting a score which falls very close to CWT, which demonstrated the highest score. Besides that, it also demonstrates the minimum intra-class variance that is in line with the physically interpretable preservation of fault-induced impulsive structures. The numeric results convincingly demonstrate that CQ-NSGT yields a significantly tighter and more organized distribution of discriminative features mapped in the kurtosis domain, relative to STFT, CWT, and WPT. In general, the findings statistically and empirically justify the decision of CQ-NSGT being the most suitable time, frequency transformation for the present fault diagnosis framework. The quantitative results in Table 5 give a comparative assessment of time-frequency transformation techniques using spectral kurtosis-based class separability and intra-class variance. Out of all the methods tested, CWT obtains the greatest class separability score (0.0630), with CQ-NSGT (0.0585) almost on par, whereas STFT (0.0408) and WPT (0.0170) show a lower level of separability. CWT only exceeds CQ-NSGT slightly in separability, but separability is not the only factor that can represent the stability and robustness of a feature set. Table 5. Quantitative analysis of spectrograms obtained using various transformation methods. Transformation method Spectral Kurtosis–based class separability Intra-class variance CQ-NSGT 0.0585 70.110 STFT 0.0408 260.025 CWT 0.0630 282.6214 WPT 0.0170 205.29475 Open in a new tab The interpretation becomes much clearer if we consider intra-class variance along with separability. Table 5 reveals that CQ-NSGT has a much lower intra-class variance (70.110) than STFT (260.025), CWT (282.6214), and WPT (205.29475). Therefore, CQ-NSGT keeps the samples from each fault class clustered very tightly, thus representing more structural consistency and less spread in the feature space. On the other hand, CWT, whose separability value is just a little higher, has a huge intra-class variance that indicates less stability and more variability within classes. Altogether, the results in Table 5 reflect that CQ-NSGT is an excellent hybrid method in terms of inter-class discrimination and writhing intra-class dispersion. The method demonstrates its high performance through this compromise because it maintains fault impulsiveness features in a stable and physically understandable manner which creates a more trustworthy compact representation for future classification tasks compared to all other transformation techniques. Training configuration The CNN-based models EfficientNet, InceptionNet and MobileNet were trained using the same hyperparameters. This was done to ensure a fair comparison. All three models used the Adam optimizer. Sparse categorical cross-entropy was used as the loss function. Accuracy was used as the evaluation metric. Early stopping was applied to reduce overfitting. A patience value of three epochs was used based on validation loss. A learning rate scheduler was also applied. The learning rate was reduced by a factor of 0.5 after five epochs without improvement. The minimum learning rate was set to 1 × 10 −5 . Training was limited to a maximum of 100 epochs. Training logs were saved using CSV callbacks for future analysis. The Vision Transformer (ViT) model used a different training setup. Input images of size 224 × 224 were divided into patches of size 16 × 16. This resulted in 196 patches per image. The model consisted of six transformer encoder blocks. Each block used six attention heads. The embedding dimension was set to 384. The MLP expansion ratio was set to 2. The AdamW optimizer was used along with a cosine annealing learning rate schedule. Training was performed for 50 epochs. Weight decay was set to 0.01 and dropout was set to 0.1 to improve generalization. Discussion on partial fine-tuning of pre-trained model backbone Partial fine-tuning of the deeper backbone layers was experimentally evaluated during preliminary studies. In particular, the later convolutional blocks of the pre-trained backbone were unfrozen to assess whether additional task-specific adaptation would improve classification performance. This modification substantially increased the number of trainable parameters, which lead to a higher computation cost, longer training time and increased GPU memory usage. It is important to note that while fine-tuning does not alter total parameter count, it increases the number of trainable parameters. In the MobileNet V2 based hybrid model, unfreezing 25% of the model for fine-tuning resulted in a 30–40% increase in training time. Similarly in EfficientNet, the training time increased by 50% and doubled in the case of InceptionV3. Subsequently, if a higher percentage of the backbone layers are unfrozen, the time and computational penalty is compounded. The proposed model architecture employing a frozen backbone achieved a classification accuracy of 99.83% (in the case of EfficientNet), demonstrating that the pretrained feature representations were sufficiently discriminative for the target fault categories. In our testing, when partial fine-tuning with 25% of the layers were unfrozen, it resulted in marginal improvements of the training accuracy with no improvement in the validation accuracy indicating that the model was overfitting. This behaviour can primarily be attributed to the limited size of the available dataset. This constrains the model’s ability to reliably update millions of additional trainable parameters without memorizing training samples. Therefore, opening up more layers to training essentially raised the limit of what the model could do and made finding the optimum more challenging. Thus, the definitive ensemble architecture constitutes a deliberate and well supported empirical decision to choose robustness and efficiency over excessive expansion through parameters. Cross-validation Five-fold cross-validation was used to evaluate model performance. The dataset was divided into five equal parts. Each part contained samples from all fault classes. They comprise Ball Fault, Combined Fault, Healthy Baseline, Inner Race Fault, and Outer Race Fault. In every run, the test set consisted of one fold, and the other four folds were used for training. So, the whole process was repeated five times with each fold being used once as the test set. From Table 6 , we note that EfficientNetB0 came out as the best model with the highest scores among the models tested. The average values for accuracy, precision, recall, and F1-score were almost 0.999. The standard deviation over the folds was 0.002. The coefficient of variation was 0.203. Table 6. Baseline model performance comparison summary—no noise. Model Accuracy Precision Recall F1-Score Standard deviation Coefficient of variation Base CNN 0.928 0.932 0.928 0.926 0.091 4.404 InceptionV3 0.982 0.983 0.982 0.982 0.006 0.573 MobileNetV2 0.99 0.99 0.99 0.99 0.007 0.716 EfficientNetB0 0.999 0.999 0.999 0.999 0.002 0.203 ViT 0.830 0.852 0.830 0.830 0.049 5.93 Open in a new tab InceptionV3 and MobileNetV2 delivered high scores as well. InceptionV3 hit an accuracy of 0.982, whereas MobileNetV2 achieved an accuracy of 0.990. The precision and recall values for both models stayed within 0.98–0.99 over the folds. The baseline CNN recorded lower accuracy compared to the other models. Its accuracy was 0.928. The coefficient of variation was 4.404%, which shows larger variation between folds. EfficientNetB0 fivefold cross-validation results—no noise EfficientNetB0 recorded high values across all evaluation metrics on the No Noise dataset using fivefold cross-validation (Refer Table 7 ). Table 7. EfficientNetB0: fivefold cross-validation results (no noise). Fold Accuracy Precision Recall F1-Score 1 0.998 0.998 0.998 0.998 2 0.995 0.995 0.995 0.995 3 1 1 1 1 4 1 1 1 1 5 1 1 1 1 Mean 0.999 0.999 0.999 0.999 Standard deviation 0.002 0.002 0.002 0.002 Coefficient of variation 0.219 0.219 0.219 0.219 Open in a new tab The ROC analysis for EfficientNet shows an AUC of 1.00 for all classes. In Fig. 13 d, the ROC curves rise steeply along the y-axis and then move toward the upper-left region of the plot. This indicates high true positive rates with low false positive rates across the classes. The micro-average AUC was also 1.00, which reflects the combined performance when all classes are considered together. Taken together with the ideal confusion matrix, this places EfficientNet as the reference point for this bearing-fault study. Figures 13 b and c also show the stable training behaviour exhibited by EfficientNet. Fig. 13. Open in a new tab a EfficientNetB0 confusion matrix—no noise. b and c EfficientNetB0 training & validation curves—no noise. d AUC–ROC curves for EfficientNetB0. The five confusion matrices in Fig. 13 a show only a handful of mistakes. Per-fold accuracy ranged from 0.9955 to 1.0000, and Folds 3, 4, and 5 achieved 100% classification accuracy. Folds 1 and 2 resulted in similar patterns. All four fault types BF, CF, IRF, and ORF had 90 correct predictions each, while the HB class had 82. The rest of the errors only concerned single samples. Fold 1 mislabeled an IRF case as an ORF. Fold 2 mislabeled an IRF case as a BF, and an ORF as IRF. Very minor mistakes, but isolated ones. The models in the first two folds only showed minor deviations when separating these five categories, BF, CF, HB, IRF, and ORF. Accuracy, Precision, Recall, and F1-Score had a mean value of 0.999 across all folds. The standard deviation was 0.002, and the coefficient of variation was 0.219%. This suggests that the model behaved consistently with different dataset partitions. InceptionV3 fivefold cross-validation results—no noise InceptionNet demonstrated strong classification performance through its innovative residual connections that enable effective training of deep networks. InceptionV3 was consistent in its performance throughout all the folds with the baseline, no-noise scenario. The fivefold cross-validation result in Table 8 shows that the model accuracy ranged between 0.977 and going as high as 0.991 in fold 5. The average accuracy was 0.982, and the standard deviation was 0.006, so the performance scarcely varied across the different partitions. Precision, recall and F1-scores also behaved in a similar manner, their mean values being around 0.982 and 0.983. The coefficient of variation, 0.591 indicates consistent behaviour across folds. Table 8. InceptionV3 fivefold cross-validation results—no noise. Fold Accuracy Precision Recall F1-Score 1 0.977 0.978 0.977 0.977 2 0.984 0.984 0.984 0.984 3 0.982 0.982 0.982 0.982 4 0.977 0.978 0.977 0.977 5 0.991 0.991 0.991 0.991 Mean 0.982 0.983 0.982 0.982 Standard deviation 0.006 0.005 0.006 0.006 Coefficient of variation 0.591 0.546 0.591 0.591 Open in a new tab The ROC analysis shown in Fig. 14 d presents the classification performance for individual fault classes. The AUC values range from 0.86 to 0.99 across classes. Ball Fault (BF) recorded an AUC of 0.99, while Outer Race Fault (ORF) recorded an AUC of 0.97. Combined Fault (CF) achieved an AUC of 0.95. Inner Race Fault (IRF) and Healthy Baseline (HB) showed lower AUC values of 0.89 and 0.86, respectively. The micro-average AUC across all classes was 0.82. This value reflects the combined performance across classes with different discrimination levels. The ROC curves vary in slope across classes, indicating differences in class separability. Fig. 14. Open in a new tab a InceptionV3 confusion matrix—no noise. b and c InceptionV3 training & validation curves—no noise. d AUC-ROC curve for InceptionV3. The confusion matrices shown in Fig. 14 a provide further detail. Folds 3, 4, and 5 show no misclassifications. All samples in these folds were assigned to the correct class. Folds 1 and 2 show a small number of misclassifications.Both had 90 correct predictions in each of the BF, CF, IRF, and ORF categories, and 82 correct for HB. The remaining errors were scattered and small in number. In Fold 1, one IRF instance was labelled as BF, one ORF instance as BF, and one HB instance as IRF. Fold 2 had a few more slips: one BF labelled as ORF, three CF samples labelled as IRF, and one HB labelled as BF. These errors cluster around classes with overlapping features, but the scale is small. The learning curves in Fig. 14 b and c show stable training behaviour. Loss values dropped quickly from about 3.0 to around 1.0 within the first ten epochs, then leveled off for the remainder of training. All five folds produced almost identical trajectories, with training and validation curves staying close to one another. Accuracy rose sharply from roughly 0.3 to above 0.9 in the same early window. By the 20th epoch, all folds showed accuracy values near 1.0 with small fluctuations. The tight alignment between training and validation metrics suggests the model generalized well under the no-noise condition, with no signs of overfitting. MobileNetV2 fivefold cross-validation results—no noise MobileNetV2 was evaluated under the no-noise baseline condition using fivefold cross-validation. As shown in Table 9 , the accuracy values across the folds varied between 0.977 and 0.995. Fold 5 had the highest accuracy of 0.995, whereas Fold 1 had the lowest accuracy of 0.977. The average accuracy over the folds was 0.990 with a standard deviation of 0.007. Similarly, precision, recall, and F1-score averaged 0.990. The coefficient of variation was 0.720, which is a bit of a higher value than InceptionV3. Table 9. InceptionV3 fivefold cross-validation results—no noise. Fold Accuracy Precision Recall F1-Score 1 0.977 0.978 0.977 0.977 2 0.991 0.991 0.991 0.991 3 0.993 0.993 0.993 0.993 4 0.991 0.991 0.991 0.991 5 0.995 0.996 0.995 0.995 Mean 0.99 0.99 0.99 0.99 Standard deviation 0.007 0.007 0.007 0.007 Coefficient of variation 0.72 0.698 0.72 0.72 Open in a new tab The confusion matrices in Fig. 15 a make the behaviour clearer. Fold 5 again showed the strongest performance, reaching 0.995 accuracy with only minor slips. Folds 2, 3, and 4 kept close behind, posting 0.991, 0.993, and 0.991. Fold 1 had more scattered errors but still achieved 0.977 accuracy. BF, CF, and IRF were consistently identified across the folds, with 89, 90 correct predictions out of 90. ORF showed occasional confusion, Fold 1 mislabelled two ORF samples as HB. HB was the class with the most variability. Fold 1 misclassified one HB instance as CF and three as IRF. Folds 4 and 5, however, handled this class nearly perfectly. These mistakes are few and concentrated in specific class boundaries, suggesting the model handles most fault types with ease. Fig. 15. Open in a new tab a MobileNetV2 confusion matrix—no noise. b and c MobileNetV2 training & validation curves—no noise. d AUC-ROC curve for Mobilenetv2. The ROC curves shown in Fig. 15 d present the class-wise performance of MobileNetV2. Four classes, Outer Race Fault (ORF), Combined Fault (CF), Ball Fault (BF), and Inner Race Fault (IRF), recorded AUC values of 1.00. The Healthy Baseline (HB) class recorded an AUC of 0.99. The micro-average AUC across all classes was 1.00. The learning curves shown in Fig. 15 b and c summarize the training behavior. Loss values started in the range of 2.5 to 3.0. A rapid decrease was observed within the first ten epochs. By epoch 15, loss values stabilized between 0.8 and 1.2. Training and validation loss curves remained close across all folds. Accuracy increased from approximately 0.4 to above 0.9 within the first ten epochs. By epoch 20, accuracy values across folds were near 1.0. Minor variations were observed in later epochs. ViT fivefold cross-validation results—no noise The Vision Transformer (ViT) was evaluated under no-noise conditions using fivefold cross-validation. Accuracy values varied across folds. Fold 1 recorded an accuracy of 0.753, while Fold 5 recorded an accuracy of 0.9022. The mean accuracy across folds was 0.829. The standard deviation was 0.0492. The coefficient of variation was 5.93%. Compared to the CNN-based models, ViT showed higher variation across folds. Performance differences were observed between individual validation splits (Table 10 ). Table 10. ViT fivefold cross-validation results—no noise. Fold Accuracy Precision Recall F1 1 0.75337 0.8162 0.7533 0.75966 2 0.8511 0.8563 0.85111 0.8495 3 0.8289 0.8325 0.82894 0.81939 4 0.81337 0.8493 0.8133 0.8125 5 0.9022 0.9061 0.90221 0.9020 Mean 0.8298 0.8521 0.8298 0.8286 Standard deviation 0.0492 0.0324 0.0492 0.0480 Coefficient of variation 5.93 3.80 5.93 5.79 Open in a new tab Confusion matrices drawn for the Vision Transformer indicate variations among the results of different folds 1 to 5. The prediction accuracy of fold 5 was 90.22% whereas fold 1 was as low as 75.33%, the accuracy results reflect the diverse degrees of correctness in different validation data splits. However, certain fault categories were easily misidentified. Predominantly, the cases of mislabelling were between Ball Fault (BF) and Inner Race Fault (IRF). The occurrence of BF-IRF errors in the Vision Transformer model was more frequent than in the CNN-based models. The range of Performance differences across folds was greater for the Vision Transformer than for the convolution-based models (Refer Fig. 16 a–c). Fig. 16. Open in a new tab a ViT confusion matrix—no noise. b , c ViT; training loss, training accuracy, validation loss, validation accuracy for no noise. d AUC-ROC curve for ViT. The ROC analysis for the Vision Transformer presents AUC scores from 0.98 to 1.00 for different fault classes, which is also visually shown in Fig. 16 d. CF, HB, and ORF got the perfect score of AUC = 1.00, indicating their excellent class separation capability from the other classes despite the confusion matrix issues. BF and IRF got AUC scores of 0.99 and 0.98 respectively, thus they both have the ability to strongly separate classes at the feature level. The ROC curves (Fig. 16 d) showed that the steep rises towards the top-left corner of the graph, which is good signal-to-noise ratio become levels several classes as you observe that all curves, obtain the true positive rates high while on the false positive rates low level. The Vision Transformer’s ability to analyze the feature space to distinguish very well different fault signatures is reflected in this performance. Nevertheless, the ultimate classification outcomes may be regarded as borderline because of either threshold selection problems or the model mistaking similar faults for one another. CNN fivefold cross-validation results—no noise The baseline CNN yielded acceptable results but its performance varied to a greater extent than that of the deeper models. As can be seen from Table 11 , the accuracy over the five folds varied between 0.860 in Fold 3 and 0.970 in Fold 1. The average accuracy was 0.928, and the average Precision, Recall, and F1-Score metrics were between 0.926 and 0.932. The accuracy coefficient of variation was 4.404%, which is a significantly higher value than that of the advanced architectures. A more considerable variation in performance was seen across the folds. Table 11. CNN fivefold cross-validation results—no noise. Fold Accuracy Precision Recall F1-Score 1 0.970 0.972 0.970 0.970 2 0.930 0.933 0.930 0.930 3 0.860 0.865 0.860 0.854 4 0.940 0.943 0.940 0.940 5 0.940 0.948 0.940 0.938 Mean 0.928 0.932 0.928 0.926 Standard deviation 0.041 0.040 0.041 0.043 Coefficient of variation 4.404 4.318 4.404 4.678 Open in a new tab The confusion matrices for different folds shown in Fig. 17 a visually represent how each fold performed differently. Fold 1 achieved an accuracy of 0.970, and the number of errors was very low. On the other hand, Fold 3 achieved an accuracy of 0.860. Errors in this fold were very limited and mostly between only a few class pairs. These were Combined Fault (CF) with Healthy Baseline (HB) and Inner Race Fault (IRF) with Outer Race Fault (ORF). Thus, four CF samples in Fold 3 were wrongly classified as HB. These findings show how class-wise performance varies across folds. Some fault categories are more confused in certain validation splits than in others. Fig. 17. Open in a new tab a CNN confusion matrix—no noise. b and c CNN training & validation curves—no noise. d AUC-ROC curve for base CNN model. The ROC analysis for the baseline CNN is displayed in Fig. 17 d. Extremely high AUC values were obtained for all fault classes. Combined Fault (CF), Ball Fault (BF), and Healthy Baseline (HB) each achieved an AUC of 1.00. Outer Race Fault (ORF) had an AUC of 0.99 while Inner Race Fault (IRF) had an AUC of 0.98. The ROC curves are steep and going toward the upper-left corner. The overall classification accuracy was, however, lower despite the high AUC values. This shows that there is a difference between class separability and the final class assignment. Though class separation can be seen in the ROC analysis, there still exist misclassifications when label prediction is done. The learning curves in Fig. 17 b and c depict differences in training behavior. In the initial five epochs, loss values dropped significantly. However, there was an abrupt climb of loss between epochs 8 and 12, with the loss reaching 20 to 25. At that moment, the accuracy was only about 0.2–0.3. The biggest changes were seen in Folds 2 and 5. Training became more stable after completing this cycle. Accuracy increased and surpassed the 0.9 mark at epoch 20. This behavior was seen in several different folds. Robustness analysis under noise conditions Additive white Gaussian noise was added to the vibration signals at three signal-to-noise ratio levels. These levels were 1 dB, 3 dB, and 5 dB. Model performance was evaluated separately at each noise level. Table 10 presents the performance results for all models across the different SNR conditions. The table allows comparison of performance changes as noise levels increase. Table 12 presents classification accuracy for five model architectures under different Signal-to-Noise Ratio (SNR) conditions. Results are reported for the no-noise case and for noise levels of 5 dB, 3 dB, and 1 dB. Table 12. Comprehensive performance across All SNR Levels Model Noise level Accuracy Precision Recall F1-Score Drop in accuracy (%) EfficientNet No Noise 0.999 0.999 0.999 0.999 0 1 dB 0.988 0.988 0.988 0.988 1.1 3 dB 0.992 0.992 0.992 0.992 0.7 5 dB 0.996 0.996 0.996 0.996 0.3 MobileNet No Noise 0.99 0.99 0.99 0.99 0 1 dB 0.952 0.953 0.952 0.952 3.8 3 dB 0.974 0.975 0.974 0.974 1.6 5 dB 0.984 0.984 0.984 0.984 0.6 Inception No Noise 0.982 0.983 0.982 0.982 0 1 dB 0.9 0.902 0.9 0.9 8.2 3 dB 0.922 0.924 0.922 0.923 6.0 5 dB 0.952 0.952 0.952 0.952 3.0 CNN No Noise 0.928 0.932 0.928 0.926 0 1 dB 0.838 0.851 0.838 0.836 9.0 3 dB 0.816 0.836 0.816 0.809 11.2 5 dB 0.836 0.844 0.836 0.831 9.2 ViT No Noise 0.830 0.852 0.830 0.830 0 1 dB 0.733 0.745 0.733 0.732 9.7 3 dB 0.744 0.751 0.744 0.738 8.6 5 dB 0.69 0.735 0.69 0.682 14.0 Open in a new tab EfficientNetB0 recorded a baseline accuracy of 0.999. With added noise, accuracy decreased to 0.996 at 5 dB SNR, 0.992 at 3 dB SNR, and 0.988 at 1 dB SNR. MobileNetV2 recorded a baseline accuracy of 0.990. Accuracy values under noisy conditions were 0.984 at 5 dB SNR, 0.974 at 3 dB SNR, and 0.952 at 1 dB SNR. InceptionV3 recorded a baseline accuracy of 0.982. Accuracy decreased to 0.952 at 5 dB SNR, 0.922 at 3 dB SNR, and 0.900 at 1 dB SNR. The baseline CNN recorded an accuracy of 0.928 under no-noise conditions. Accuracy dropped to 0.836 at 5 dB SNR, 0.816 at 3 dB SNR, and 0.838 at 1 dB SNR. The Vision Transformer (ViT) had the lowest baseline accuracy of 0.830. Its accuracy under noisy conditions was 0.690 at 5 dB SNR, 0.744 at 3 dB SNR, and 0.733 at 1 dB SNR. Performance fluctuated at the different noise levels. The CNN-based models (EfficientNet, MobileNet, Inception, and baseline CNN) show an almost linear decreasing trend in classification accuracy going from no noise to the strongest noise levels in the test data. There are some small non-monotonic changes of the accuracy values at intermediate SNRs which indicate the models are a bit more unpredictable there. When the SNR is reduced to 1 dB, accuracy values drop continuously which can be seen in Fig. 18 . Figure 19 also reveals a similar trend on the heat-map where the performance gradually changes with noise levels. Fig. 18. Open in a new tab Performance degradation line plot. Fig. 19. Open in a new tab Performance Heatmap—Models × SNR Levels. Among these, EfficientNet demonstrates changes in accuracies that are smaller than that of any other CNN model. Its accuracy hardly deviates despite the degradation of signal quality; with the 5 dB SNR accuracy is still as high as 0.996. The Vision Transformer (ViT) behaves quite differently. It initially drops from its baseline value to 0.690 at 5 dB SNR. At low noise levels, the accuracy fluctuates significantly, hitting a high of 0.744 at 3 dB SNR, and follows that with 0.733 at 1 dB SNR. Essentially, there is no steady increasing or decreasing trend but a lot of varied nuances in the performance across noise conditions. Brief analysis of model performance under speed fluctuations Purely additive stochastic noise cannot be regarded as an accurate representation of the full range of mechanically induced disturbances in industrial bearing systems, such as load torque ripple, rotational speed fluctuation, structural resonance, or shaft misalignment. These phenomena can introduce non-stationary modulation, frequency drift, harmonic amplification, and impulsive components that deviate substantially from the assumption of idealized additive noise. However, the robustness analysis in this study was aiming at evaluating the stability of the feature vectors derived by deep neural networks under controlled and standardized degradation of input signals, rather than replicating a mechanical failure mechanism from the surface. Here, additive stochastic disturbance is used as a generic signal stress-testing tool that disrupts the signal in all frequency bands, thus preventing the model from depending on very localized or fragile signal artifacts. A deep neural network that keeps a high classification performance even when the signal is corrupted broadband is indicative of the learned features representing the real fault-related structural characteristics rather than the incidental or narrowband ones. In mathematical terms, a lot of the disturbances caused by the machine can be broken down into additive components that are combined with modulation effects. Hence, being robust against additive perturbations is basically a minimum requirement of diagnostic model resilience that a model should meet before being tested under complicated, scenario-specific noise conditions. In this way, additive noise testing offers a lower-bound robustness guideline that is the foundation for more specialized disturbance models to be developed later on. Apart from noise intensity variation, robustness behavior under mechanically motivated disturbance is also revealed by the results of speed fluctuation simulation. According to Table 13 , EfficientNet essentially keeps the performance level, a very slight drop in performance from 99.90% to 99.83% is hardly detectable, thus it can be said that its stability under temporal variability is quite remarkable. MobileNet shows a moderate decrease in performance from 99.00% to 98.23%, whereas Inception suffers a more significant loss of performance from 98.20% to 95.07%. The comparative results of Table 13 thus indicate that scale-adaptive feature extractors have the ability to preserve at a much higher level the output of the model even in the condition of speed-induced non-stationarity. The few differences in the performance of EfficientNet can therefore be seen as additional evidence that the model is representing the fault signatures in a physically meaningful way rather than fixed temporal patterns. Table 13. Accuracy of model in speed varying conditions. Model Without speed fluctuation With speed fluctuation EfficientNet 99.90% 99.83% MobileNet 99.00% 98.23% Inception 98.20% 95.07 Open in a new tab Realism in this study could be improved by using more physics based disturbance models, for example, amplitude modulation as a way of simulating torque ripple, time-warping for speed variation, or the amplification of a narrowband resonance. However, these methods would necessitate more parameters and assumptions about the specific conditions of the machine operation, which can differ quite a bit from one installation to another. In this paper we propose a fixed, reproducible robustness benchmark and we recognize that the future publication of the work may involve the combination of condition-specific disturbance modeling to not only introduce a higher degree of ecological validity but also an increased level of application relevance. Analysis of time and computational complexities The training time was used as a metric to depict the computational power requirement of each type of model. Table 14 contains the training time for each architecture. These numbers reflect the computational work needed to train the models. Table 14. Comparison of model training times. Model Training time (s) MobileNetV2 121.4 EfficientNetB0 177 Vision Transformer (ViT) 213.6 InceptionV3 230.5 BaseCNN 195.5 Open in a new tab Time complexity analysis MobileNetV2 was the fastest at training, only taking 121s (refer Table 14 ). It is shows the minimal computational power necessitated per epoch when compared to the other models. In addition to the model’s lightweight design and fewer parameters, the shorter training time is consistent with these factors. EfficientNetB0 took 177 s to train. Even though it was slower than MobileNetV2, the training time is still reasonable compared to larger architectures. Vision Transformer (ViT) took 213.6 s to complete training. Training time was longer than the CNN-based models with small architectures. This is an indication of increased computation per epoch when obtaining image patches. InceptionV3 has the longest training time with 230.5 s. The longer training time is a reflection of the higher computational cost per epoch of the model compared to the other models. Computational complexity analysis in GFLOPS Computational complexity is evaluated by the number of floating-point operations (FLOPs). This measurement reflects the count of arithmetic operations that need to be performed to process one input. Hence, the models with a greater number of FLOPs usually entail higher computational resource requirements. Herein, GFLOPs refer to the comparison of the efficiency of the chosen architectures. Table 15 depicts the GFLOPs for the various models that were benchmarked. The computational power required by MobileNetV2 and EfficientNetB0 is the lowest, which correspond to 0.50 GFLOPs and 0.59 GFLOPs, respectively. These values are on the lower end of the spectrum compared to the rest of the models under evaluation. With MobileNetV2 needing a considerably lower number of operations than the baseline CNN, which has 4.05 GFLOPs. Table 15. Comparison of model computational cost. Model Computational cost (GFLOPS) MobileNetV2 0.50 EfficientNetB0 0.59 InceptionV3 3.47 Vision Transformer (ViT) 3.26 BaseCNN 4.05 Open in a new tab Both InceptionV3 and the Vision Transformer (ViT) have onerous computational requirements. Their GFLOPs figures are between the ranges of 3.2 to 3.5 approximately. This implies a higher cost per inference in contrast to the light CNN models. Among the various architectures scrutinized, the baseline CNN has registered the highest GFLOPs value. Even though its design is less complex, the computational cost is quite high when compared to the models which utilize optimized convolutional operations. Such results emphasize the considerable differences in computational efficiency between various architectures. Hence, it becomes a crucial point when choosing models for deployment under limited resources. Computational complexity analysis with latency and memory footprint The study establishes that there are marked differences in computational performance between different architectural configurations and this factor plays a major role when one is deciding to deploy AI models on limited-resource devices. The computational experiments extended beyond mere training time and GFLOPs and thus explicitly identified inference latency and memory usage. Steady-state inference latency was measured for each of the proposed models, with 600 single image forward passes of the resolution 224 × 224, excluding warm-up iterations so that the latency measure was untainted by the compilation overhead and the measured steady-state result was accurate. A comprehensive suite of statistical tools for descriptive statistics, such as the floor latency, measure of dispersion, quartiles, interquartile range, and 95% confidence intervals for latency, were computed to ensure that the measure is statistically reliable. Also, the consistency of latency in real-time during lengthy executions was investigated to ensure stability. Memory usage was monitored by tracking model size and recording the peak memory usage of RAM during inference. After every model, to ensure that tests stayed independent of each other and memory was not retained for the previous model, the TensorFlow sessions were cleared. The testing was done on a MacBook Air with an M4 chip and 16GB RAM using the CPU only to provide a realistic scenario for the deployment. The inference latency and memory footprint figures in Table 16 give a detailed comparison of computational efficiency among the proposed models. Out of these, MobileNet has the lowest average latency of 8.167 ms (refer Fig. 20 ) with the 95% confidence interval being very narrow (0.0085 ms). The interquartile range is also small (0.128 ms), all of which point to very stable performance in real time. EfficientNet is next with an average latency of 12.214 ms and also a low variation (IQR = 0.129 ms). This translates to inference performance stability even though the computational complexity is a higher. Inception, on the other hand, has the highest average latency of 20.735 ms and the interquartile range is also larger (0.581 ms), making the variation in execution time more noticeable. Table 16. Computational characteristics of proposed models in terms of latency and memory footprint. Model Mean latency (ms) 95% CI (ms) Q1 (ms) Median (ms) Q3 (ms) IQR (ms) Parameter Memory (MB) EfficientNet 12.214 0.0124 12.158 12.227 12.286 0.129 24.623 MobileNet 8.167 0.0085 8.105 8.169 8.234 0.128 17.788 Inception 20.735 0.0347 20.435 20.701 21.016 0.581 96.096 Open in a new tab Fig. 20. Open in a new tab Chart depicting latency per image. In terms of memory, Inception uses much more parameter storage (96.096 MB) compared to EfficientNet (24.623 MB) and MobileNet (17.788 MB), thus suggesting a more complex architectural design. MobileNet has the smallest memory footprint and at the same time performs with low-latency, which makes it very suitable for deployment at the edge or in resource-limited environments. As we have already seen with the discussion on accuracy, EfficientNet strikes a balance between accuracy and computational efficiency while Inception, despite its higher competitive classification capability, results in significantly higher latency and memory usage. Overall, the findings in Table 16 clearly indicate that it is equally important to take into account the performance of the models in terms of prediction and metrics oriented to the deployment when choosing models for real-time industrial condition monitoring applications. Statistical evaluation of model performance across architectures All five baseline models (Inception, EfficientNetB0, MobileNet, BaseCNN, and ViT) were tested with grouped fivefold cross-validation. Given that the fold-wise results constitute paired data and the sample size (number of folds) is small ( n = 5), parametric normality testing and one-sample t-tests were not considered. Rather, descriptive statistics with confidence intervals based on t-distribution were calculated, and model comparisons were carried out using the non-parametric Friedman test (Table 17 ). Table 17. (a) The statistical summary for trained models. (b) Friedmann Table. (c) Friedmann Table. Model Mean Std Dev Coefficient of variation (%) 95% CI (t, df = 4) (a) EfficientNetB0 0.9983 0.0015 0.15% [0.9965, 1.0000] MobileNet 0.9823 0.0083 0.85% [0.9720, 0.9926] Inception 0.9507 0.0147 1.55% [0.9323, 0.9691] BaseCNN 0.7740 0.0804 10.38% [0.6739, 0.8741] ViT 0.6898 0.1148 16.64% [0.5474, 0.8322] Statistic Value (b) Number of models (k) 5 Number of folds (N) 5 Friedman χ² 20.00 Degrees of freedom 4 p -value 0.0005 Effect size (η²_F) 1.00 Model Average Rank (c) EfficientNet 1.0 MobileNet 2.0 Inception 3.0 BaseCNN 4.0 ViT 5.0 Open in a new tab The Friedman test indicated significant differences between model architectures (χ²(4) = 20.00, p = 0.0005). The large effect size (η² = 1.00) reflects tremendously strong agreement that the order of performance rankings is the same across folds. EfficientNetB0 delivered the best average accuracy (99.83%) with the smallest variation (CV = 0.15%), thus illustrating not only better performance but also stability. MobileNet and Inception were the next models with gradually declining average accuracies whereas BaseCNN and ViT showed significantly deteriorated performances along with increased variability from one fold to another. The reliability of fold-wise rankings implies that the presence of differences has been on a systematic basis and thus not caused by random noise. Discussion Out of the tested models, EfficientNetB0 was the most accurate across the validation and noise conditions. The accuracy scores showed negligible deviation when 5 dB, 3 dB, and 1 dB noise levels were applied. These findings point to the robustness of the model’s performance across different signal conditions and only moderate computational requirements of the model. InceptionV3 performed well under the baseline condition. With the accuracy scores staying consistent across the different folds. However, this model was more computationally expensive than the lightweight architectures. MobileNetV2 was able to achieve a high level of accuracy under normal conditions while also keeping the computational cost low. Such a combination of factors can be beneficial in scenarios with limited computational resources. The Vision Transformer (ViT) had a low baseline accuracy and a high variability across the folds. Its performance was inconsistent under the various conditions indicating that it was sensitive to data splits and noise levels. Overall, ViT’s performance might be reliant on the nature of the dataset and the training configuration. Interpretation of results and implications EfficientNetB0 achieved the highest accuracy of all models tested for various noise conditions. Accuracy was more than 98.8% at 1 dB SNR and the accuracy performance didn’t drop significantly as the noise levels increased. The model was less affected by the noise and signal degradation than other models (Refer Fig. 21 ). Fig. 21. Open in a new tab Comprehensive visual comparison of all five models under noise-free conditions. The variation of the performance between the models reflects the impact of the different architectural design choices. MobileNetV2 reached a baseline accuracy of 99.0% while still having a relatively low computational load. InceptionV3 scored a baseline accuracy of 98.2% and demonstrated consistency across the different folds. These findings suggest that convolutional design choices impact the trade-off between accuracy and computational cost differently. Vision Transformer (ViT) achieved an average accuracy of only 82.98% and showed larger variability across the different folds with a coefficient of variation of 5.93. The detailed class-wise evaluation indicated that the model was more prone to confuse some fault classes with one another than others. For example, from a total of 450 samples, 380 Inner Race Fault cases were correctly identified, which is a very large number. However, along with that, there was also a mix-up between Ball Fault and Inner Race Fault, as a misclassification was noticed in the results. Among the models, the accuracy of EfficientNetB0 displayed the smallest variation under noise corrupted conditions. The decrease in accuracy caused by noise, going from the baseline to 1 dB SNR, was about 1% point. The model’s performance was not significantly affected by changes in signal quality. To rule out prejudiced comparisons, the models’ performances were evaluated in a comprehensive manner using the same architectural setup. Each model’s architecture consisted of a pre-trained backbone, hybrid residual blocks, and a common classification head. The rationale behind such an arrangement is that the differences in performance metrics are mainly due to the feature extractors rather than the classification layers. Conclusion This research work investigated a hybrid deep-learning framework for bearing fault diagnosis mainly focused on the aspects of accuracy, robustness, and computational efficiency. Five different model architectures, among them EfficientNetB0, MobileNetV2, and Vision Transformer (ViT), were compared by utilizing time-frequency analysis-generated spectrograms. Out of the signal-processing techniques under consideration, the Constant-Q Non-Stationary Gabor Transform (CQ-NSGT) was found to be capable of producing clear representations of fault-related frequency components under various operating conditions. The hybrid model approach fused frozen pre-trained backbones and custom residual blocks. Using this combination the model performances were notably better than when simply pre-trained models were used. EfficientNetB0 was the best in terms of baseline accuracy reaching 99.86% and was able to keep the performance above 98.8% at 1 dB SNR. MobileNetV2 gave a baseline accuracy of 99.0% at the same time it required much less computational resources, with 0.50 GFLOPs and a training time of roughly 121 s. The Vision Transformer (ViT) recorded a lower accuracy mean and a higher variation in the set of validation folds. The decrease in the performance was found in the noisy condition leading to the conclusion that it is affected by the kind of data and the noise levels. In comparison with CNN-based models, ViT in the same application showed less consistent behavior. The comparatively lower performance of the Vision Transformer (ViT) model in our experiments can be attributed to the known sensitivity of transformer-based architectures to model scale and data volume. As demonstrated in An Image is Worth 16 × 16 Words: Transformers for Image Recognition at Scale 28 , Vision Transformers achieve competitive or superior performance only when trained on very large datasets and with sufficiently large model configurations. When trained on smaller datasets without large-scale pretraining, ViTs underperform well-established CNN architectures such as ResNet 28 . The authors explicitly demonstrate that the performance of transformers is very dependent on the size of the model and the amount of training data, and that small ViT variants trained on limited datasets do not perform at the level of CNN baselines. This is mainly explained by the absence of strong spatial inductive biases (e.g., locality and translation equivariance) that CNNs naturally encode. On the other hand, small ViT models have to get such structural priors from data through learning, hence they become more and more dependent on scale for effective representation learning. In this research, a somewhat small ViT model was deliberately chosen so that the computational resources would be equivalent and the results comparable to the CNN baselines. Nevertheless, in line with the scaling trend reported by Dosovitskiy et al., it is very probable that the combination of the model with limited capacity and the moderate dataset size has prevented the transformer from acquiring sufficiently strong global dependencies thereby causing the model to achieve lower accuracy and higher variance. This observed performance gap is in line with previous empirical findings reported in the literature and simply mirrors known scaling characteristics of Vision Transformers rather than representing a fundamental architectural limitation. Therefore, based on the findings of this research, EfficientNetB0 can be considered a suitable solution when extremely high accuracy and stability are paramount, whereas MobileNetV2 may serve as a performance and computational efficiency trade-off option in cases of limited computational resources. To ensure that the variations revealed were mainly attributable to the feature extraction backbones, a standardized evaluation framework was used. The dataset was collected from a controlled laboratory test rig that researchers used to conduct the experiment. In order to maintain the repeatability and experimental consistency, the researchers carefully controlled the operating conditions, fault types, and acquisition parameters. However, real industrial environments present additional challenges, gradually evolving fault severity, changes in lubrication, contamination from the environment, differences in sensor mounting stiffness and placement, etc. These are all factors that can greatly affect the vibration signatures and can change the statistical characteristics of the measured signals in such a way that is not fully demonstrated by the laboratory conditions. Hence, thorough validation under various industrial operating scenarios is still an important task for future research. Therefore, future research may broaden this work by gathering long-term field data from various installations and different operating regimes to assess cross-domain generalization. Adding multi-sensor data, like temperature, acoustic emission, or current signals, can give additional diagnostic information and thus improve the system’s tolerance to environmental variations. Moreover, addressing real-time deployment issues and model interpretability, chiefly through the use of explainable AI methods, would greatly facilitate their application in practice for industrial monitoring systems by offering an increase in transparency, trust, and operational reliability. Acknowledgements The authors would like to thank Vellore Institute of Technology, Vellore for providing support and encouragements to complete this research work. Author contributions Pratyush Vishal—Simulation, Rohith Nair—Investigation, Jonathan Jacob—literature, Narendiranath Babu T—conceptualization and analysis, Pandiyan M—Methodology. Funding Open access funding provided by Vellore Institute of Technology. This work was supported and funded by the Vellore Institute of Technology, Vellore. Data availability The dataset created and handled during the current research is not available publicly due to the limitations set by the institution. Aimed to be shared by the corresponding author only when a reasonable request is made and subject to institutional approval. Declarations Competing interests The authors declare no competing interests. Footnotes Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. References 1. Xu, F. et al. A Review of bearing failure modes, mechanisms and causes. Eng. Fail. 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