Life Prediction of Rolling Bearing Based on Optimal Time-Frequency Spectrum and DenseNet-ALSTM

To address the challenges faced in the prediction of rolling bearing life, where temporal signals are affected by noise, making fault feature extraction difficult and resulting in low prediction accuracy, a method based on optimal time-frequency spectra and the DenseNet-ALSTM network is proposed. Firstly, a signal reconstruction method is introduced to enhance vibration signals. This involves using the CEEMDAN deconvolution method combined with the Teager energy operator for signal reconstruction, aiming to denoise the signals and highlight fault impacts. Subsequently, a method based on the snake optimizer (SO) is proposed to optimize the generalized S-transform (GST) time-frequency spectra of the enhanced signals, obtaining the optimal time-frequency spectra. Finally, all sample data are transformed into the optimal time-frequency spectrum set and input into the DenseNet-ALSTM network for life prediction. The comparison experiment and ablation experiment show that the proposed method has high prediction accuracy and ideal prediction performance. The optimization terms used in different contexts in this paper are due to different optimization methods, specifically the CEEMDAN method.

Fault Diagnosis of the Rolling Bearing by a Multi-Task Deep Learning Method Based on a Classifier Generative Adversarial Network

Accurate fault diagnosis is essential for the safe operation of rotating machinery. Recently, traditional deep learning-based fault diagnosis have achieved promising results. However, most of these methods focus only on supervised learning and tend to use small convolution kernels non-effectively to extract features that are not controllable and have poor interpretability. To this end, this study proposes an innovative semi-supervised learning method for bearing fault diagnosis. Firstly, multi-scale dilated convolution squeeze-and-excitation residual blocks are designed to exact local and global features. Secondly, a classifier generative adversarial network is employed to achieve multi-task learning. Both unsupervised and supervised learning are performed simultaneously to improve the generalization ability. Finally, supervised learning is applied to fine-tune the final model, which can extract multi-scale features and be further improved by implicit data augmentation. Experiments on two datasets were carried out, and the results verified the superiority of the proposed method.

A New Approach to the Degradation Stage Prediction of Rolling Bearings Using Hierarchical Grey Entropy and a Grey Bootstrap Markov Chain

Degradation stage prediction, which is crucial to monitoring the health condition of rolling bearings, can improve safety and reduce maintenance costs. In this paper, a novel degradation stage prediction method based on hierarchical grey entropy (HGE) and a grey bootstrap Markov chain (GBMC) is presented. Firstly, HGE is proposed as a new entropy that measures complexity, considers the degradation information embedded in both lower- and higher-frequency components and extracts the degradation features of rolling bearings. Then, the HGE values containing degradation information are fed to the prediction model, based on the GBMC, to obtain degradation stage prediction results more accurately. Meanwhile, three parameter indicators, namely the dynamic estimated interval, the reliability of the prediction result and dynamic uncertainty, are employed to evaluate the prediction results from different perspectives. The estimated interval reflects the upper and lower boundaries of the prediction results, the reliability reflects the credibility of the prediction results and the uncertainty reflects the dynamic fluctuation range of the prediction results. Finally, three rolling bearing run-to-failure experiments were conducted consecutively to validate the effectiveness of the proposed method, whose results indicate that HGE is superior to other entropies and the GBMC surpasses other existing rolling bearing degradation prediction methods; the prediction reliabilities are 90.91%, 90% and 83.87%, respectively.

Adaptive VMD-K-SVD-Based Rolling Bearing Fault Signal Enhancement Study

To address the challenges associated with nonlinearity, non-stationarity, susceptibility to redundant noise interference, and the difficulty in extracting fault feature signals from rolling bearing signals, this study introduces a novel combined approach. The proposed method utilizes the variational mode decomposition (VMD) and K-singular value decomposition (K-SVD) algorithms to effectively denoise and enhance the collected rolling bearing signals. Initially, the VMD method is employed to separate the overall noise into intrinsic mode functions (IMFs), reducing the noise content within each IMF. To optimize the mode component, K, and the penalty factor, α, in VMD, an improved arithmetic optimization algorithm (IAOA) is employed. This ensures the selection of optimal parameters and the decomposition of the signal into a set of IMFs, forming the original dictionary. Subsequently, the signals are decomposed into multiple IMFs using VMD, and an original dictionary is constructed based on these IMFs. K-SVD is then applied to the original dictionary to further reduce the noise in each IMF, resulting in a denoised and enhanced signal. To validate the efficacy of the proposed method, rolling bearing signals collected from Case Western Reserve University (CWRU) and thrust bearing test rigs were utilized. The experimental results demonstrate the feasibility and effectiveness of the proposed approach in denoising and enhancing the rolling bearing signals.

A Symmetrized Dot Pattern Extraction Method Based on Frobenius and Nuclear Hybrid Norm Penalized Robust Principal Component Analysis and Decomposition and Reconstruction

Due to their symmetrized dot pattern, rolling bearings are more susceptible to noise than time-frequency characteristics. Therefore, this article proposes a symmetrized dot pattern extraction method based on the Frobenius and nuclear hybrid norm penalized robust principal component analysis (FNHN-RPCA) as well as decomposition and reconstruction. This method focuses on denoising the vibration signal before calculating the symmetric dot pattern. Firstly, the FNHN-RPCA is used to remove the non-correlation between variables to realize the separation of feature information and interference noise. After, the residual interference noise, irrelevant information, and fault features in the separated signal are clearly located in different frequency bands. Then, the ensemble empirical mode decomposition is applied to decompose this information into different intrinsic mode function components, and the improved DPR/KLdiv criterion is used to select components containing fault features for reconstruction. In addition, the symmetrized dot pattern is used to visualize the reconstructed signal. Finally, method validation and comparative analysis are conducted on the CWRU datasets and experimental bench data, respectively. The results show that the improved criteria can accurately complete the screening task, and the proposed method can effectively reduce the impact of strong noise interference on SDPs.

A New Dual-Input Deep Anomaly Detection Method for Early Faults Warning of Rolling Bearings

To address the problem of low fault diagnosis accuracy caused by insufficient fault samples of rolling bearings, a dual-input deep anomaly detection method with zero fault samples is proposed for early fault warning of rolling bearings. First, the main framework of dual-input feature extraction based on a convolutional neural network (CNN) is established, and the two outputs of the main frame are subjected to the autoencoder structure. Then, the secondary feature extraction is performed. At the same time, the experience pool structure is introduced to improve the feature learning ability of the network. A new objective loss function is also proposed to learn the network parameters. Then, the vibration acceleration signal is preprocessed by wavelet to obtain multiple signals in different frequency bands, and the two signals in the high-frequency band are two-dimensionally encoded and used as the network input. Finally, the unsupervised learning of the model is completed on five sets of actual full-life rolling bearing fault data sets relying only on some samples in a normal state. The verification results show that the proposed method can realize earlier than the RMS, Kurtosis, and other features. The early fault warning and the accuracy rate of more than 98% show that the method is highly capable of early fault warning and anomaly detection.

Fault Diagnosis of Rolling Bearings in Primary Mine Fans under Sample Imbalance Conditions

Rolling bearings are crucial parts of primary mine fans. In order to guarantee the safety of coal mine production, primary mine fans commonly work during regular operation and are immediately shut down for repair in case of failure. This causes the sample imbalance phenomenon in fault diagnosis (FD), i.e., there are many more normal state samples than faulty ones, seriously affecting the precision of FD. Therefore, the current study presents an FD approach for the rolling bearings of primary mine fans under sample imbalance conditions via symmetrized dot pattern (SDP) images, denoising diffusion probabilistic models (DDPMs), the image generation method, and a convolutional neural network (CNN). First, the 1D bearing vibration signal was transformed into an SDP image with significant characteristics, and the DDPM was employed to create a generated image with similar feature distributions to the real fault image of the minority class. Then, the generated images were supplemented into the imbalanced dataset for data augmentation to balance the minority class samples with the majority ones. Finally, a CNN was utilized as a fault diagnosis model to identify and detect the rolling bearings' operating conditions. In order to assess the efficiency of the presented method, experiments were performed using the regular rolling bearing dataset and primary mine fan rolling bearing data under actual operating situations. The experimental results indicate that the presented method can more efficiently fit the real image samples' feature distribution and generate image samples with higher similarity than other commonly used methods. Moreover, the diagnostic precision of the FD model can be effectively enhanced by gradually expanding and enhancing the unbalanced dataset.

Fault Diagnosis for Rolling Bearing of Combine Harvester Based on Composite-Scale-Variable Dispersion Entropy and Self-Optimization Variational Mode Decomposition Algorithm

Because of the influence of harsh and variable working environments, the vibration signals of rolling bearings for combine harvesters usually show obvious characteristics of strong non-stationarity and nonlinearity. Accomplishing accurate fault diagnosis using these signals for rolling bearings is a challenging subject. In this paper, a novel fault diagnosis method based on composite-scale-variable dispersion entropy (CSvDE) and self-optimization variational mode decomposition (SoVMD) is proposed, systematically combining the nonstationary signal analysis approach and machine learning technology. Firstly, an improved SoVMD algorithm is developed to realize adaptive parameter optimization and to further extract multiscale frequency components from original signals. Subsequently, a CSvDE-based feature learning model is established to generate the multiscale fault feature space (MsFFS) of frequency components for the improvement of fault feature learning ability. Finally, the generated MsFFS can serve as the inputs of the Softmax classifier for fault category identification. Extensive experiments on the vibration datasets collected from rolling bearings of combine harvesters are conducted, and the experimental results demonstrate the more superior and robust fault diagnosis performance of the proposed method compared to other existing approaches.

Rolling Bearing Fault Diagnosis Based on Support Vector Machine Optimized by Improved Grey Wolf Algorithm

This study targets the low accuracy and efficiency of the support vector machine (SVM) algorithm in rolling bearing fault diagnosis. An improved grey wolf optimizer (IGWO) algorithm was proposed based on deep learning and a swarm intelligence optimization algorithm to optimize the structural parameters of SVM and improve the rolling bearing fault diagnosis. A nonlinear contraction factor update strategy was also proposed. The variable coefficient changes with the shrinkage factor α. Thus, the search ability was balanced at different early and late stages by controlling the dynamic changes of the variable coefficient. In the early stages of optimization, its speed is low to avoid falling into local optimization. In the later stages of optimization, the speed is higher, and finding the optimal solution is easier, balancing the two different global and local optimization capabilities to complete efficient convergence. The dynamic weight update strategy was adopted to perform position updates based on adaptive dynamic weights. First, the dataset of Case Western Reserve University was used for simulation, and the results showed that the diagnosis accuracy of IGWO-SVM was 98.75%. Then, the IGWO-SVM model was trained and tested using data obtained from the full-life-cycle test platform of mechanical transmission bearings independently researched and developed by Nanjing Agricultural University. The fault diagnosis accuracy and convergence value of the adaptation curve were compared with those of PSO-SVM (particle swarm optimization) and GWO-SVM diagnosis models. Results showed that the IGWO-SVM model had the highest rolling bearing fault diagnosis accuracy and the best diagnosis convergence.

WPD-Enhanced Deep Graph Contrastive Learning Data Fusion for Fault Diagnosis of Rolling Bearing

Rolling bearings are crucial mechanical components in the mechanical industry. Timely intervention and diagnosis of system faults are essential for reducing economic losses and ensuring product productivity. To further enhance the exploration of unlabeled time-series data and conduct a more comprehensive analysis of rolling bearing fault information, this paper proposes a fault diagnosis technique for rolling bearings based on graph node-level fault information extracted from 1D vibration signals. In this technique, 10 categories of 1D vibration signals from rolling bearings are sampled using a sliding window approach. The sampled data is then subjected to wavelet packet decomposition (WPD), and the wavelet energy from the final layer of the four-level WPD decomposition in each frequency band is used as the node feature. The weights of edges between nodes are calculated using the Pearson correlation coefficient (PCC) to construct a node graph that describes the feature information of rolling bearings under different health conditions. Data augmentation of the node graph in the dataset is performed by randomly adding nodes and edges. The graph convolutional neural network (GCN) is employed to encode the augmented node graph representation, and deep graph contrastive learning (DGCL) is utilized for the pre-training and classification of the node graph. Experimental results demonstrate that this method outperforms contrastive learning-based fault diagnosis methods for rolling bearings and enables rapid fault diagnosis, thus ensuring the normal operation of mechanical systems. The proposed WPDPCC-DGCL method offers two advantages: (1) the flexibility of wavelet packet decomposition in handling non-smooth vibration signals and combining it with the powerful multi-scale feature encoding capability of GCN for richer characterization of fault information, and (2) the construction of graph node-level fault samples to effectively capture underlying fault information. The experimental results demonstrate the superiority of this method in rolling bearing fault diagnosis over contrastive learning-based approaches, enabling fast and accurate fault diagnoses for rolling bearings and ensuring the normal operation of mechanical systems.

Fault Diagnosis of Rolling Bearing Based on HPSO Algorithm Optimized CNN-LSTM Neural Network

The quality of rolling bearings is vital for the working state and rotation accuracy of the shaft. Timely and accurately acquiring bearing status and early fault diagnosis can effectively prevent losses, making it highly practical. To improve the accuracy of bearing fault diagnosis, this paper proposes a CNN-LSTM bearing fault diagnosis model optimized by hybrid particle swarm optimization (HPSO). The HPSO algorithm has a strong global optimization ability and can effectively solve nonlinear and multivariate optimization problems. It is used to optimize and match the parameters of the CNN-LSTM model and dynamically find the optimal value of the parameters. This model overcomes the problem that the parameters of the CNN-LSTM model depend on empirical settings and cannot be adjusted dynamically. This model is used for bearing fault diagnosis, and the accuracy rate of fault diagnosis classification reaches 99.2%. Compared with the traditional CNN, LSTM, and CNN-LSTM models, the accuracy rates are increased by 6.6%, 9.2%, and 5%, respectively. At the same time, comparing the models with different optimization parameters shows that the model proposed in this paper has the highest accuracy. The experimental results verified the superiority of the HPSO algorithm to optimize model parameters and the feasibility and accuracy of the HPSO-CNN-LSTM model for bearing fault diagnosis.

Use of Composite Multivariate Multiscale Permutation Fuzzy Entropy to Diagnose the Faults of Rolling Bearing

The study focuses on the fault signals of rolling bearings, which are characterized by nonlinearity, periodic impact, and low signal-to-noise ratio. The advantages of entropy calculation in analyzing time series data were combined with the high calculation accuracy of Multiscale Fuzzy Entropy (MFE) and the strong noise resistance of Multiscale Permutation Entropy (MPE), a multivariate coarse-grained form was introduced, and the coarse-grained process was improved. The Composite Multivariate Multiscale Permutation Fuzzy Entropy (CMvMPFE) method was proposed to solve the problems of low accuracy, large entropy perturbation, and information loss in the calculation process of fault feature parameters. This method extracts the fault characteristics of rolling bearings more comprehensively and accurately. The CMvMPFE method was used to calculate the entropy value of the rolling bearing experimental fault data, and Support Vector Machine (SVM) was used for fault diagnosis analysis. By comparing with MPFE, the Composite Multiscale Permutation Fuzzy Entropy (CMPFE) and the Multivariate Multiscale Permutation Fuzzy Entropy (MvMPFE) methods, the results of the calculations show that the CMvMPFE method can extract rolling bearing fault characteristics more comprehensively and accurately, and it also has good robustness.

Modelling and Experimental Study of Power Losses in Toothed Wheels

In recent decades, the request for more efficient performances in the aeronautical sector moved researchers to pay particular attention to all the related mechanisms and systems, especially with respect to the saving of power. In this context, the bearing modeling and design, as well as gear coupling, play a fundamental role. Moreover, the need for low power losses also concerns the study and the implementation of advanced lubrication systems, especially for high peripheral speed. With the previous aims, this paper presents a new validated model for toothed gears, added to a bearing model; with the link of these different submodels, the whole model describes the system's dynamic behavior, taking into account the different kinds of power losses (windage losses, fluid dynamic losses, etc.) generated by the mechanical system parts (especially rolling bearings and gears). As the bearing model, the proposed model is characterized by high numerical efficiency and allows the investigation of different rolling bearings and gears with different lubrication conditions and frictions. A comparison between the experimental and simulated results is also presented in this paper. The analysis of the results is encouraging and shows a good agreement between experiments and model simulations, with particular attention to the power losses in the bearing and gears.

Research on Rolling Bearing Fault Diagnosis Based on Digital Twin Data and Improved ConvNext

This article introduces a novel framework for diagnosing faults in rolling bearings. The framework combines digital twin data, transfer learning theory, and an enhanced ConvNext deep learning network model. Its purpose is to address the challenges posed by the limited actual fault data density and inadequate result accuracy in existing research on the detection of rolling bearing faults in rotating mechanical equipment. To begin with, the operational rolling bearing is represented in the digital realm through the utilization of a digital twin model. The simulation data produced by this twin model replace traditional experimental data, effectively creating a substantial volume of well-balanced simulated datasets. Next, improvements are made to the ConvNext network by incorporating an unparameterized attention module called the Similarity Attention Module (SimAM) and an efficient channel attention feature referred to as the Efficient Channel Attention Network (ECA). These enhancements serve to augment the network's capability for extracting features. Subsequently, the enhanced network model is trained using the source domain dataset. Simultaneously, the trained model is transferred to the target domain bearing using transfer learning techniques. This transfer learning process enables the accurate fault diagnosis of the main bearing to be achieved. Finally, the proposed method's feasibility is validated, and a comparative analysis is conducted in comparison with similar approaches. The comparative study demonstrates that the proposed method effectively addresses the issue of low mechanical equipment fault data density, leading to improved accuracy in fault detection and classification, along with a certain level of robustness.

A Rolling Bearing Fault Diagnosis Method Based on the WOA-VMD and the GAT

In complex industrial environments, the vibration signal of the rolling bearing is covered by noise, which makes fault diagnosis inaccurate. In order to overcome the effect of noise on the signal, a rolling bearing fault diagnosis method based on the WOA-VMD (Whale Optimization Algorithm-Variational Mode Decomposition) and the GAT (Graph Attention network) is proposed to deal with end effect and mode mixing issues in signal decomposition. Firstly, the WOA is used to adaptively determine the penalty factor and decomposition layers in the VMD algorithm. Meanwhile, the optimal combination is determined and input into the VMD, which is used to decompose the original signal. Then, the Pearson correlation coefficient method is used to select IMF (Intrinsic Mode Function) components that have a high correlation with the original signal, and selected IMF components are reconstructed to remove the noise in the original signal. Finally, the KNN (K-Nearest Neighbor) method is used to construct the graph structure data. The multi-headed attention mechanism is used to construct the fault diagnosis model of the GAT rolling bearing in order to classify the signal. The results show an obvious noise reduction effect in the high-frequency part of the signal after the application of the proposed method, where a large amount of noise was removed. In the diagnosis of rolling bearing faults, the accuracy of the test set diagnosis in this study was 100%, which is higher than that of the four other compared methods, and the diagnosis accuracy rate of various faults reached 100%.

Bayesian-Optimized Hybrid Kernel SVM for Rolling Bearing Fault Diagnosis

We propose a new fault diagnosis model for rolling bearings based on a hybrid kernel support vector machine (SVM) and Bayesian optimization (BO). The model uses discrete Fourier transform (DFT) to extract fifteen features from vibration signals in the time and frequency domains of four bearing failure forms, which addresses the issue of ambiguous fault identification caused by their nonlinearity and nonstationarity. The extracted feature vectors are then divided into training and test sets as SVM inputs for fault diagnosis. To optimize the SVM, we construct a hybrid kernel SVM using a polynomial kernel function and radial basis kernel function. BO is used to optimize the extreme values of the objective function and determine their weight coefficients. We create an objective function for the Gaussian regression process of BO using training and test data as inputs, respectively. The optimized parameters are used to rebuild the SVM, which is then trained for network classification prediction. We tested the proposed diagnostic model using the bearing dataset of the Case Western Reserve University. The verification results show that the fault diagnosis accuracy is improved from 85% to 100% compared with the direct input of vibration signal into the SVM, and the effect is significant. Compared with other diagnostic models, our Bayesian-optimized hybrid kernel SVM model has the highest accuracy. In laboratory verification, we took sixty sets of sample values for each of the four failure forms measured in the experiment, and the verification process was repeated. The experimental results showed that the accuracy of the Bayesian-optimized hybrid kernel SVM reached 100%, and the accuracy of five replicates reached 96.7%. These results demonstrate the feasibility and superiority of our proposed method for fault diagnosis in rolling bearings.

Rolling Bearing Composite Fault Diagnosis Method Based on Enhanced Harmonic Vector Analysis

Composite fault diagnosis of rolling bearings is very challenging work, especially when the characteristic frequency ranges of different fault types overlap. To solve this problem, an enhanced harmonic vector analysis (EHVA) method was proposed. Firstly, the wavelet threshold (WT) denoising method is used to denoise the collected vibration signals to reduce the influence of noise. Next, harmonic vector analysis (HVA) is used to remove the convolution effect of the signal transmission path, and blind separation of fault signals is carried out. The cepstrum threshold is used in HVA to enhance the harmonic structure of the signal, and a Wiener-like mask will be constructed to make the separated signals more independent in each iteration. Then, the backward projection technique is used to align the frequency scale of the separated signals, and each fault signal can be obtained from composite fault diagnosis signals. Finally, to make the fault characteristics more prominent, a kurtogram was used to find the resonant frequency band of the separated signals by calculating its spectral kurtosis. Semi-physical simulation experiments are conducted using the rolling bearing fault experiment data to verify the effectiveness of the proposed method. The results show that the proposed method, EHVA, can effectively extract the composite faults of rolling bearings. Compared to fast independent component analysis (FICA) and traditional HVA, EHVA improves separation accuracy, enhances fault characteristics, and has higher accuracy and efficiency compared to fast multichannel blind deconvolution (FMBD).

Multi-Fault Classification and Diagnosis of Rolling Bearing Based on Improved Convolution Neural Network

At present, the fault diagnosis methods for rolling bearings are all based on research with fewer fault categories, without considering the problem of multiple faults. In practical applications, the coexistence of multiple operating conditions and faults can lead to an increase in classification difficulty and a decrease in diagnostic accuracy. To solve this problem, a fault diagnosis method based on an improved convolution neural network is proposed. The convolution neural network adopts a simple structure of three-layer convolution. The average pooling layer is used to replace the common maximum pooling layer, and the global average pooling layer is used to replace the full connection layer. The BN layer is used to optimize the model. The collected multi-class signals are used as the input of the model, and the improved convolution neural network is used for fault identification and classification of the input signals. The experimental data of XJTU-SY and Paderborn University show that the method proposed in this paper has a good effect on the multi-classification of bearing faults.

Approach to the Quantitative Diagnosis of Rolling Bearings Based on Optimized VMD and Lempel-Ziv Complexity under Varying Conditions

The quantitative diagnosis of rolling bearings is essential to automating maintenance decisions. Over recent years, Lempel-Ziv complexity (LZC) has been widely used for the quantitative assessment of mechanical failures as one of the most valuable indicators for detecting dynamic changes in nonlinear signals. However, LZC focuses on the binary conversion of 0-1 code, which can easily lose some effective information about the time series and cannot fully mine the fault characteristics. Additionally, the immunity of LZC to noise cannot be insured, and it is difficult to quantitatively characterize the fault signal under strong background noise. To overcome these limitations, a quantitative bearing fault diagnosis method based on the optimized Variational Modal Decomposition Lempel-Ziv complexity (VMD-LZC) was developed to fully extract the vibration characteristics and to quantitatively characterize the bearing faults under variable operating conditions. First, to compensate for the deficiency that the main parameters of the variational modal decomposition (VMD) have to be selected by human experience, a genetic algorithm (GA) is used to optimize the parameters of the VMD and adaptively determine the optimal parameters [k, α] of the bearing fault signal. Furthermore, the IMF components that contain the maximum fault information are selected for signal reconstruction based on the Kurtosis theory. The Lempel-Ziv index of the reconstructed signal is calculated and then weighted and summed to obtain the Lempel-Ziv composite index. The experimental results show that the proposed method is of high application value for the quantitative assessment and classification of bearing faults in turbine rolling bearings under various operating conditions such as mild and severe crack faults and variable loads.

A Sound and Vibration Fusion Method for Fault Diagnosis of Rolling Bearings under Speed-Varying Conditions

The fault diagnosis of rolling bearings is critical for the reliability assurance of mechanical systems. The operating speeds of the rolling bearings in industrial applications are usually time-varying, and the monitoring data available are difficult to cover all the speeds. Though deep learning techniques have been well developed, the generalization capacity under different working speeds is still challenging. In this paper, a sound and vibration fusion method, named the fusion multiscale convolutional neural network (F-MSCNN), was developed with strong adaptation performance under speed-varying conditions. The F-MSCNN works directly on raw sound and vibration signals. A fusion layer and a multiscale convolutional layer were added at the beginning of the model. With comprehensive information, such as the input, multiscale features are learned for subsequent classification. An experiment on the rolling bearing test bed was carried out, and six datasets under various working speeds were constructed. The results show that the proposed F-MSCNN can achieve high accuracy with stable performance when the speeds of the testing set are the same as or different from the training set. A comparison with other methods on the same datasets also proves the superiority of F-MSCNN in speed generalization. The diagnosis accuracy improves by sound and vibration fusion and multiscale feature learning.

Fault Diagnosis of Rolling Bearing Based on a Priority Elimination Method

Aiming at the fault diagnosis accuracy of rolling bearings is not high enough, and unknown faults cannot be correctly identified. A priority elimination (PE) method is proposed in this paper. First, the priority diagnosis sequence of faults was determined by comparing the ratios of the inter-class distance to the intra-class distance for all faults. Then, the model training and fault diagnosis were carried out in order of the priority sequence, and the samples of the fault that had been identified were eliminated from the data set until all faults were diagnosed. For the diagnosis model, the stacked sparse auto-encoder network (SSAE) was selected to extract the features of the vibration signal. The extreme gradient boosting algorithm (XGBoost) was chosen to identify the fault type. Finally, the method was tested and verified by experimental data and compared with classical algorithms. Research results indicate the following: (1) with the addition of PE based on SSAE-XGBoost, the fault diagnosis accuracy can be improved from 96.3% to 99.27%, which is higher than other methods; (2) for the test set with the samples of unknown faults, the diagnosis accuracy of SSAE-XGBoost with PE can reach 92.34%, which is nearly 6% higher than that without PE and is also obviously higher than other classical fault diagnosis methods with or without PE. The PE method can not only improve the diagnosis accuracy of faults but also identify unknown faults, which provides a new method and way for fault diagnosis.

A Fault Feature Extraction Method Based on Improved VMD Multi-Scale Dispersion Entropy and TVD-CYCBD

In modern industry, due to the poor working environment and the complex working conditions of mechanical equipment, the characteristics of the impact signals caused by faults are often submerged in strong background signals and noises. Therefore, it is difficult to effectivelyextract the fault features. In this paper, a fault feature extraction method based on improved VMD multi-scale dispersion entropy and TVD-CYCBD is proposed. First, the marine predator algorithm (MPA) is used to optimize the modal components and penalty factors in VMD. Second, the optimized VMD is used to model and decompose the fault signal, and then the optimal signal components are filtered according to the combined weight index criteria. Third, TVD is used to denoise the optimal signal components. Finally, CYCBD filters the de-noised signal and then envelope demodulation analysis is carried out. Through the simulation signal experiment and the actual fault signal experiment, the results verified that multiple frequency doubling peaks can be seen from the envelope spectrum, and there is little interference near the peak, which shows the good performance of the method.

Remaining Useful Life Prediction of Rolling Bearings Using GRU-DeepAR with Adaptive Failure Threshold

Aiming at the problem that a single neural network model has difficulty in accurately predicting trends of the remaining useful life of a rolling bearing, a method of predicting the remaining useful life of rolling bearings using a gated recurrent unit-deep autoregressive model (GRU-DeepAR) with an adaptive failure threshold was proposed. First, time domain and frequency domain features were extracted from the rolling bearing vibration signal. Second, its operation process was divided into a smooth operation stage and degradation stage according to the trend of the accumulated root mean square of maximum. Then, the failure threshold for different bearings were determined adaptively by the maximum of the smooth operation data. The degradation dataset of a rolling bearing was subsequently obtained. In the meantime, a GRU-DeepAR model was built to obtain predictions of the failure time and failure probability. Appropriate model parameters were determined after a large number of tests to assure the effectiveness and prediction accuracy. Finally, the trend of time series and failure times were predicted by inputting the degradation dataset into the GRU-DeepAR model. Experiments showed that the proposed method can effectively improve the accuracy of the remaining useful life prediction of a rolling bearing with good stability.

Rolling Bearing Performance Degradation Assessment with Adaptive Sensitive Feature Selection and Multi-Strategy Optimized SVDD

In light of the problems of a single vibration feature containing limited information on the degradation of rolling bearings, the redundant information in high-dimensional feature sets inaccurately reflecting the reliability of rolling bearings in service, and assessments of the degradation performance being disturbed by outliers and false fluctuations in the signal, this study proposes a method of assessing rolling bearings' performance in terms of degradation using adaptive sensitive feature selection and multi-strategy optimized support vector data description (SVDD). First, a high-dimensional feature set of vibration signals from rolling bearings was extracted. Second, a method combining the Technique for Order Preference by Similarity to an Ideal Solution (TOPSIS) and K-medoids was used to comprehensively evaluate the features with multiple evaluation indicators and to adaptively select better degradation features to construct the sensitive feature set. Next, multi-strategy optimization of the SVDD model was carried out by introducing the autocorrelation kernel regression (AAKR) and a multi-kernel function to improve the ability of the evaluation model to overcome outliers and false fluctuations. Through validation, it could be seen that the method in this study uses samples of rolling bearings in the healthy early stage to establish the evaluation model, which can adaptively determine the starting point of the bearing's degradation. The stability and accuracy of the model were effectively improved.

Method for Predicting RUL of Rolling Bearings under Different Operating Conditions Based on Transfer Learning and Few Labeled Data

As industrial development increases, electric machine systems are more widely used in industrial production. Rolling bearings play a key role in machine systems and so the prevention of faults in rolling bearings is more important than ever before. Recently, with the development of artificial intelligence, neural networks have been used to monitor the remaining useful life of rolling bearings. However, there are two problems with this technique. First, a network trained by data for a single operating condition (source domain) cannot predict the remaining useful life of bearings under a different operating condition (target domain), such as a different load or speed. Second, a large number of labeled data are needed for network training, but the acquisition of labeled data for different operating conditions is a challenging task. To address these problems, this paper proposes a domain-adaptive adversarial network, in which a transfer learning strategy and maximum mean discrepancy algorithm are used for network optimization, so that remaining useful life can be predicted without labeled data in target domain training. Our results confirm that a model trained by source domain data alone cannot predict the remaining useful life of bearings under different conditions, but the domain-adaptive adversarial network can accurately predict remaining useful life for varying operating conditions. The method proposed also exhibits good performance even if there are noises in the signals.

Rolling Bearing Fault Monitoring for Sparse Time-Frequency Representation and Feature Detection Strategy

Data-driven fault diagnosis methods for rotating machinery have developed rapidly with the help of deep learning methods. However, traditional intelligent fault diagnosis methods still have some limitations in fault feature extraction and the latest object detection theory has not been applied in fault diagnosis. To this end, a fault diagnosis method based on a sparse short-term Fourier transform (SSTFT) and object detection theory is developed in this paper. First, a sparse constraint is introduced in time-frequency analysis to improve the time-frequency resolution of the model without cross-term interference and proximal gradient descent (PGD) is adopted to quickly and effectively optimize the model to obtain a high-quality time-frequency representation (TFR). Second, a fault diagnosis model based on a region-based convolutional neural network (RCNN) is built; the model can extract multiple regions that can characterize fault features from the TFR. This process avoids the interference of irrelevant vibration components and improves the interpretability of the fault diagnosis model. Finally, multicategory rolling bearing fault identification is realized. The effectiveness of the proposed method is validated by simulation signals and bearing experiments. The results indicate that the proposed method is more effective than existing methods.

Numerical Model Driving Multi-Domain Information Transfer Method for Bearing Fault Diagnosis

Given the complexity of the application scenarios of rolling bearing and the severe scarcity of fault samples, a solution to the issue of fault diagnosis under varying working conditions along with the absence of fault samples is required. A numerical model-driven cross-domain fault diagnosis method targeting variable working conditions is proposed based on the cross-Domain Nuisance Attribute Projection (cDNAP). Firstly, the simulation datasets consisting of multiple fault types under variable working conditions are constructed to solve the problem of incomplete fault samples. Secondly, the simulation datasets are expanded by means of generating adversarial network to ensure sufficient samples for subsequent model training. Finally, cDNAP is used to obtain the cross-domain simulation projection matrix, which eliminates the variance in the distribution of measured and simulated sample features under varying working conditions. The experimental results of cross-domain for variable working conditions show that the diagnostic accuracy reaches up to 99%. Compared with DANN, DSAN, and DAAN domain adversarial neural networks, the proposed method performs better in bearing fault diagnosis.

A Novel Joint Adversarial Domain Adaptation Method for Rotary Machine Fault Diagnosis under Different Working Conditions

In real-world applications of detecting faults, many factors-such as changes in working conditions, equipment wear, and environmental causes-can cause a significant mismatch between the source domain on which classifiers are trained and the target domain to which those classifiers are applied. As such, existing deep network algorithms perform poorly under different working conditions. To solve this problem, we propose a novel fault diagnosis method named Joint Adversarial Domain Adaptation (JADA) for fault detection under different working conditions. Our approach simultaneously aligns marginal distribution and conditional distribution across the source and target through a unified adversarial learning process. JADA aims to construct domain-invariant and category-discriminative feature representation that is effective and robust for substantial distribution difference caused by working conditions. We also introduce a supervision signal, namely center loss, that penalizes the distances between the deep features and their corresponding class centers. This makes the learned features better equipped with more discriminative structures and effectively prevents mode collapse. Twenty-four transfer fault diagnosis tasks based on two experimental platforms were conducted to evaluate the effectiveness of the proposed methods. Extensive experiments verified that the JADA can significantly outperform several popular methods under different transfer diagnosis tasks.

A Review on Rolling Bearing Fault Signal Detection Methods Based on Different Sensors

As a precision mechanical component to reduce friction between components, the rolling bearing is widely used in many fields because of its slight friction loss, strong bearing capacity, high precision, low power consumption, and high mechanical efficiency. This paper reviews several excellent kinds of study and their relevance to the fault detection of rolling bearings. We summarize the fault location, sensor types, bearing fault types, and fault signal analysis of rolling bearings. The fault signal types are divided into one-dimensional and two-dimensional images, which account for 40.14% and 31.69%, respectively, and their classification is clarified and discussed. We counted the proportions of various methods in the references cited in this paper. Among them, the method of one-dimensional signal detection with external sensors accounted for 3.52%, the method of one-dimensional signal detection with internal sensors accounted for 36.62%, and the method of two-dimensional signal detection with external sensors accounted for 19.72%. The method of two-dimensional signal detection with internal sensors accounted for 11.97%. Among these methods, the highest detection rate is 100%, and the lowest detection rate is more than 70%. The similarities between the different methods are compared. The research results summarized in this paper show that with the progress of the times, a variety of new and better research methods have emerged, which have sped up the detection and diagnosis of rolling bearing faults. For example, the technology using artificial intelligence is still developing rapidly, such as artificial neural networks, convolutional neural networks, and machine learning. Although there are still defects, such methods can quickly discover a fault and its cause, enrich the database, and accumulate experience. More and more advanced techniques are applied in this field, and the detection method has better robustness and superiority.

Fault Feature-Extraction Method of Aviation Bearing Based on Maximum Correlation Re’nyi Entropy and Phase-Space Reconstruction Technology

To address the difficulty of extracting the features of composite-fault signals under a low signal-to-noise ratio and complex noise conditions, a feature-extraction method based on phase-space reconstruction and maximum correlation Re’nyi entropy deconvolution is proposed. Using the Re’nyi entropy as the performance index, which allows for a favorable trade-off between sporadic noise stability and fault sensitivity, the noise-suppression and decomposition characteristics of singular-value decomposition are fully utilized and integrated into the feature extraction of composite-fault signals by the maximum correlation Re’nyi entropy deconvolution. Verification based on simulation, experimental data, and a bench test proves that the proposed method is superior to the existing methods regarding the extraction of composite-fault signal features.

A New Method of Wheelset Bearing Fault Diagnosis

During the movement of rail trains, trains are often subjected to harsh operating conditions such as variable speed and heavy loads. It is therefore vital to find a solution for the issue of rolling bearing malfunction diagnostics in such circumstances. This study proposes an adaptive technique for defect identification based on multipoint optimal minimum entropy deconvolution adjusted (MOMEDA) and Ramanujan subspace decomposition. MOMEDA optimally filters the signal and enhances the shock component corresponding to the defect, after which the signal is automatically decomposed into a sequence of signal components using Ramanujan subspace decomposition. The method's benefit stems from the flawless integration of the two methods and the addition of the adaptable module. It addresses the issues that the conventional signal decomposition and subspace decomposition methods have with redundant parts and significant inaccuracies in fault feature extraction for the vibration signals under loud noise. Finally, it is evaluated through simulation and experimentation in comparison to the current widely used signal decomposition techniques. According to the findings of the envelope spectrum analysis, the novel technique can precisely extract the composite flaws that are present in the bearing, even when there is significant noise interference. Additionally, the signal-to-noise ratio (SNR) and fault defect index were introduced to quantitatively demonstrate the novel method's denoising and potent fault extraction capabilities, respectively. The approach works well for identifying bearing faults in train wheelsets.

Application of Teager-Kaiser Energy Operator in the Early Fault Diagnosis of Rolling Bearings

Rolling bearings are key components that support the rotation of motor shafts, operating with a quite high failure rate among all the motor components. Early bearing fault diagnosis has great significance to the operation security of motors. The main contribution of this paper is to illustrate Gaussian white noise in bearing vibration signals seriously masks the weak fault characteristics in the diagnosis based on the Teager-Kaiser energy operator envelope, and to propose improved TKEO taking both accuracy and calculation speed into account. Improved TKEO can attenuate noise in consideration of computational efficiency while preserving information about the possible fault. The proposed method can be characterized as follows: a series of band-pass filters were set up to extract several component signals from the original vibration signals; then a denoised target signal including fault information was reconstructed by weighted summation of these component signals; finally, the Fourier spectrum of TKEO energy of the resulting target signal was used for bearing fault diagnosis. The improved TKEO was applied to a vibration signal dataset of run-to-failure rolling bearings and compared with two advanced diagnosis methods. The experimental results verify the effectiveness and superiority of the proposed method in early bearing fault detection.

An Attention EfficientNet-Based Strategy for Bearing Fault Diagnosis under Strong Noise

With the continuous development of artificial intelligence, data-driven fault diagnosis methods are gradually attracting widespread attention. However, in practical industrial applications, noise in the working environment is inevitable. This leads to the fact that the performance of traditional intelligent diagnosis methods is hardly sufficient to satisfy the requirements. In this paper, a developed intelligent diagnosis framework is proposed to overcome this deficiency. The main contributions of this paper are as follows: Firstly, a fault diagnosis model is established using EfficientNet, which achieves optimal diagnosis performance with limited computing resources. Secondly, an attention mechanism is introduced into the basic model for accurately establishing the relationship between fault features and fault modes, while improving the diagnosis accuracy in complex noise environments. Finally, to explain the proposed method, the weights and features of the model are visualized, and further attempts are made to analyze the reasons for the high performance of the model. The comprehensive experiment results reveal the superiority of the proposed method in terms of accuracy and stability in comparison with other benchmark diagnosis approaches. The diagnostic accuracy under actual working conditions is 86.24%.

End-to-End Continuous/Discontinuous Feature Fusion Method with Attention for Rolling Bearing Fault Diagnosis

Mechanical equipment failure may cause massive economic and even life loss. Therefore, the diagnosis of the failures of machine parts in time is crucial. The rolling bearings are one of the most valuable parts, which have attracted the focus of fault diagnosis. Many successful rolling bearing fault diagnoses have been made based on machine learning and deep learning. However, most diagnosis methods still rely on complex signal processing and artificial features, bringing many costs to the deployment and migration of diagnostic models. This paper proposes an end-to-end continuous/discontinuous feature fusion method for rolling bearing fault diagnosis (C/D-FUSA). This method comprises long short-term memory (LSTM), convolutional neural networks (CNN) and attention mechanism, which automatically extracts the continuous and discontinuous features from vibration signals for fault diagnosis. We also propose a contextual-dependent attention module for the LSTM layers. We compare the method with the other simpler deep learning methods and state-of-the-art methods in rolling bearing fault data sets with different sample rates. The results show that our method is more accurate than the other methods with real-time inference. It is also easy to be deployed and trained in a new environment.

Rolling Bearing Fault Diagnosis Based on WGWOA-VMD-SVM

A rolling bearing fault diagnosis method based on whale gray wolf optimization algorithm-variational mode decomposition-support vector machine (WGWOA-VMD-SVM) was proposed to solve the unclear fault characterization of rolling bearing vibration signal due to its nonlinear and nonstationary characteristics. A whale gray wolf optimization algorithm (WGWOA) was proposed by combining whale optimization algorithm (WOA) and gray wolf optimization (GWO), and the rolling bearing signal was decomposed by using variational mode decomposition (VMD). Each eigenvalue was extracted as eigenvector after VMD, and the training and test sets of the fault diagnosis model were divided accordingly. The support vector machine (SVM) was used as the fault diagnosis model and optimized by using WGWOA. The validity of this method was verified by two cases of Case Western Reserve University bearing data set and laboratory test. The test results show that in the bearing data set of Case Western Reserve University, compared with the existing VMD-SVM method, the fault diagnosis accuracy rate of the WGWOA-VMD-SVM method in five repeated tests reaches 100.00%, which preliminarily verifies the feasibility of this algorithm. In the laboratory test case, the diagnostic effect of the proposed fault diagnosis method is compared with backpropagation neural network, SVM, VMD-SVM, WOA-VMD-SVM, GWO-VMD-SVM, and WGWOA-VMD-SVM. Test results show that the accuracy rate of WGWOA-VMD-SVM fault diagnosis is the highest, the accuracy rate of a single test reaches 100.00%, and the accuracy rate of five repeated tests reaches 99.75%, which is the highest compared with the above six methods. WGWOA plays a good optimization role in optimizing VMD and SVM. The signal decomposed by VMD is optimized by using the WGWOA algorithm without mode overlap. WGWOA has the better convergence performance than WOA and GWO, which further verifies its superiority among the compared methods. The research results can provide an effective improvement method for the existing rolling bearing fault diagnosis technology.

Bearing Fault Feature Extraction Method Based on Enhanced Differential Product Weighted Morphological Filtering

Aimed at the problem of fault characteristic information bearing vibration signals being easily submerged in some background noise and harmonic interference, a new algorithm named enhanced differential product weighted morphological filtering (EDPWMF) is proposed for bearing fault feature extraction. In this method, an enhanced differential product weighted morphological operator (EDPWO) is first constructed by means of infusing the differential product operation and weighted operation into four basic combination morphological operators. Subsequently, aiming at the disadvantage of the parameter selection of the structuring element (SE) of EDPWO depending on artificial experience, an index named fault feature ratio (FFR) is employed to automatically determine the flat SE length of EDPWO and search for the optimal weighting correlation factors. The fault diagnosis results of simulation signals and experimental bearing fault signals show that the proposed method can effectively extract bearing fault feature information from raw bearing vibration signals containing noise interference. Moreover, the filtering result obtained by the proposed method is better than that of traditional morphological filtering methods (e.g., AVG, STH and EMDF) through comparative analysis. This study provides a reference value for the construction of advanced morphological analysis methods.

Failure Mode Detection and Validation of a Shaft-Bearing System with Common Sensors

Failure mode detection is essential for bearing life prediction to protect the shafts on the machinery. This work demonstrates the rolling bearing vibration measurement, signals converting and analysis, feature extraction, and machine learning with neural networks to achieve failure mode detection for a shaft bearing. Two self-designed bearing test platforms with two types of sensors conduct the bearing vibration collection in normal and abnormal states. The time-domain signals convert to the frequency domain for analysis to observe the dominant frequency between these two types of sensors. In feature extraction, principal components analysis (PCA) combines with wavelet packet decomposition (WPD) to form the two feature extraction methods: PCA-WPD and WPD-PCA for optimization. The features extracted by these two methods serve as input to the long short-term memory (LSTM) networks for classification and training to distinguish bearing states in normal, misaligned, unbalanced, and impact loads. The evaluation arguments include sensor types, vibration directions, failure modes, feature extraction methods, and neural networks. In conclusion, the developed methods with the typical lower-cost sensor can achieve 97% accuracy in bearing failure mode detection.

Deep Transfer Network with Multi-Space Dynamic Distribution Adaptation for Bearing Fault Diagnosis

Domain adaptation-based bearing fault diagnosis methods have recently received high attention. However, the extracted features in these methods fail to adequately represent fault information due to the versatility of the work scenario. Moreover, most existing adaptive methods attempt to align the feature space of domains by calculating the sum of marginal distribution distance and conditional distribution distance, without considering variable cross-domain diagnostic scenarios that provide significant cues for fault diagnosis. To address the above problems, we propose a deep convolutional multi-space dynamic distribution adaptation (DCMSDA) model, which consists of two core components: two feature extraction modules and a dynamic distribution adaptation module. Technically, a multi-space structure is proposed in the feature extraction module to fully extract fault features of the marginal distribution and conditional distribution. In addition, the dynamic distribution adaptation module utilizes different metrics to capture distribution discrepancies, as well as an adaptive coefficient to dynamically measure the alignment proportion in complex cross-domain scenarios. This study compares our method with other advanced methods, in detail. The experimental results show that the proposed method has excellent diagnosis performance and generalization performance. Furthermore, the results further demonstrate the effectiveness of each transfer module proposed in our model.

Research on Fault Diagnosis of Rolling Bearings Based on Variational Mode Decomposition Improved by the Niche Genetic Algorithm

Due to the influence of signal-to-noise ratio in the early failure stage of rolling bearings in rotating machinery, it is difficult to effectively extract feature information. Variational Mode Decomposition (VMD) has been widely used to decompose vibration signals which can reflect more fault omens. In order to improve the efficiency and accuracy, a method to optimize VMD by using the Niche Genetic Algorithm (NGA) is proposed in this paper. In this method, the optimal Shannon entropy of modal components in a VMD algorithm is taken as the optimization objective, by using the NGA to constantly update and optimize the combination of influencing parameters composed of α and K so as to minimize the local minimum entropy. According to the obtained optimization results, the optimal input parameters of the VMD algorithm were set. The method mentioned is applied to the fault extraction of a simulated signal and a measured signal of a rolling bearing. The decomposition process of the rolling-bearing fault signal was transferred to the variational frame by the NGA-VMD algorithm, and several eigenmode function components were obtained. The energy feature extracted from the modal component containing the main fault information was used as the input vector of a particle swarm optimized support vector machine (PSO-SVM) and used to identify the fault type of the rolling bearing. The analysis results of the simulation signal and measured signal show that: the NGA-VMD algorithm can decompose the vibration signal of a rolling bearing accurately and has a better robust performance and correct recognition rate than the VMD algorithm. It can highlight the local characteristics of the original sample data and reduce the interference of the parameters selected artificially in the VMD algorithm on the processing results, improving the fault-diagnosis efficiency of rolling bearings.

Rolling Bearing Fault Diagnosis Based on Successive Variational Mode Decomposition and the EP Index

Rolling bearing is an important part guaranteeing the normal operation of rotating machinery, which is also prone to various damages due to severe running conditions. However, it is usually difficult to extract the weak fault characteristic information from rolling bearing vibration signals and to realize a rolling bearing fault diagnosis. Hence, this paper offers a rolling bearing fault diagnosis method based on successive variational mode decomposition (SVMD) and the energy concentration and position accuracy (EP) index. Since SVMD decomposes a vibration signal of a rolling bearing into a number of modes, it is difficult to select the target mode with the ideal fault characteristic information. Comprehensively considering the energy concentration degree and frequency position accuracy of the fault characteristic component, the EP index is proposed to indicate the target mode. As the balancing parameter is crucial to the performance of SVMD and must be set properly, the line search method guided by the EP index is introduced to determine an optimal value for the balancing parameter of SVMD. The simulation and experiment results demonstrate that the proposed SVMD method is effective for rolling bearing fault diagnosis and superior to the variational mode decomposition (VMD) method.

Performance Degradation Prediction Using LSTM with Optimized Parameters

Predicting the degradation of mechanical components, such as rolling bearings is critical to the proper monitoring of the condition of mechanical equipment. A new method, based on a long short-term memory network (LSTM) algorithm, has been developed to improve the accuracy of degradation prediction. The model parameters are optimized via improved particle swarm optimization (IPSO). Regarding how this applies to the rolling bearings, firstly, multi-dimension feature parameters are extracted from the bearing’s vibration signals and fused into responsive features by using the kernel joint approximate diagonalization of eigen-matrices (KJADE) method. Then, the between-class and within-class scatter (SS) are calculated to develop performance degradation indicators. Since network model parameters influence the predictive accuracy of the LSTM model, an IPSO algorithm is used to obtain the optimal prediction model via the LSTM model parameters’ optimization. Finally, the LSTM model, with said optimal parameters, was used to predict the degradation trend of the bearing’s performance. The experiment’s results show that the proposed method can effectively identify the trends of degradation and performance. Moreover, the predictive accuracy of this proposed method is greater than that of the extreme learning machine (ELM) and support vector regression (SVR), which are the algorithms conventionally used in degradation modeling.

A Bearing Fault Diagnosis Method Based on PAVME and MEDE

When rolling bearings have a local fault, the real bearing vibration signal related to the local fault is characterized by the properties of nonlinear and nonstationary. To extract the useful fault features from the collected nonlinear and nonstationary bearing vibration signals and improve diagnostic accuracy, this paper proposes a new bearing fault diagnosis method based on parameter adaptive variational mode extraction (PAVME) and multiscale envelope dispersion entropy (MEDE). Firstly, a new method hailed as parameter adaptive variational mode extraction (PAVME) is presented to process the collected original bearing vibration signal and obtain the frequency components related to bearing faults, where its two important parameters (i.e., the penalty factor and mode center-frequency) are automatically determined by whale optimization algorithm. Subsequently, based on the processed bearing vibration signal, an effective complexity evaluation approach named multiscale envelope dispersion entropy (MEDE) is calculated for conducting bearing fault feature extraction. Finally, the extracted fault features are fed into the k-nearest neighbor (KNN) to automatically identify different health conditions of rolling bearing. Case studies and contrastive analysis are performed to validate the effectiveness and superiority of the proposed method. Experimental results show that the proposed method can not only effectively extract bearing fault features, but also obtain a high identification accuracy for bearing fault patterns under single or variable speed.

Fault Recognition of Rolling Bearings Based on Parameter Optimized Multi-Scale Permutation Entropy and Gath-Geva

To extract fault features of rolling bearing vibration signals precisely, a fault diagnosis method based on parameter optimized multi-scale permutation entropy (MPE) and Gath-Geva (GG) clustering is proposed. The method can select the important parameters of MPE method adaptively, overcome the disadvantages of fixed MPE parameters and greatly improve the accuracy of fault identification. Firstly, aiming at the problem of parameter determination and considering the interaction among parameters comprehensively of MPE, taking skewness of MPE as fitness function, the time series length and embedding dimension were optimized respectively by particle swarm optimization (PSO) algorithm. Then the fault features of rolling bearing were extracted by parameter optimized MPE and the standard clustering centers is obtained with GG clustering. Finally, the samples are clustered with the Euclid nearness degree to obtain recognition rate. The validity of the parameter optimization is proved by calculating the partition coefficient and average fuzzy entropy. Compared with unoptimized MPE, the propose method has a higher fault recognition rate.

Negative Poisson's Ratio-Spacer Design and Its Thermo-Mechanical Coupling Analysis Considering Specific Force Output

Aiming at the problems of a complex structure or poor controllability of the existing bearing preload control devices, a method of self-regulation via a negative Poisson’s ratio (NPR) spacer is proposed. Firstly, the principle of preload automatic adjustment at the bearing operation was introduced and the NPRs with three types of cell structures were analyzed. Furthermore, a thermo-mechanical coupling analysis model of the NPR spacer was established and the deformation and force output characteristics of the NPR spacer were studied and experimentally verified. It is found that the concave hexagonal cell structure has the optimal deformation characteristics for bearing preload adjustment. When the temperature is considered, the absolute value of Poisson’s ratio of the NPR spacer decreases as the speed increases and the elongation of the NPR spacer and the output forces are much larger than those without temperature consideration. With the increase in temperature or rotating speed, the axial elongation and output forces of the NPR spacer increases while the effect of temperature is relatively larger.

Rolling Bearing Fault Diagnosis Based on VMD-MPE and PSO-SVM

The goal of the paper is to present a solution to improve the fault detection accuracy of rolling bearings. The method is based on variational mode decomposition (VMD), multiscale permutation entropy (MPE) and the particle swarm optimization-based support vector machine (PSO-SVM). Firstly, the original bearing vibration signal is decomposed into several intrinsic mode functions (IMF) by using the VMD method, and the feature energy ratio (FER) criterion is introduced to reconstruct the bearing vibration signal. Secondly, the multiscale permutation entropy of the reconstructed signal is calculated to construct multidimensional feature vectors. Finally, the constructed multidimensional feature vector is fed into the PSO-SVM classification model for automatic identification of different fault patterns of the rolling bearing. Two experimental cases are adopted to validate the effectiveness of the proposed method. Experimental results show that the proposed method can achieve a higher identification accuracy compared with some similar available methods (e.g., variational mode decomposition-based multiscale sample entropy (VMD-MSE), variational mode decomposition-based multiscale fuzzy entropy (VMD-MFE), empirical mode decomposition-based multiscale permutation entropy (EMD-MPE) and wavelet transform-based multiscale permutation entropy (WT-MPE)).

Application of Parameter Optimized Variational Mode Decomposition Method in Fault Feature Extraction of Rolling Bearing

The decomposition effect of variational mode decomposition (VMD) mainly depends on the choice of decomposition number K and penalty factor α. For the selection of two parameters, the empirical method and single objective optimization method are usually used, but the aforementioned methods often have limitations and cannot achieve the optimal effects. Therefore, a multi-objective multi-island genetic algorithm (MIGA) is proposed to optimize the parameters of VMD and apply it to feature extraction of bearing fault. First, the envelope entropy (Ee) can reflect the sparsity of the signal, and Renyi entropy (Re) can reflect the energy aggregation degree of the time-frequency distribution of the signal. Therefore, Ee and Re are selected as fitness functions, and the optimal solution of VMD parameters is obtained by the MIGA algorithm. Second, the improved VMD algorithm is used to decompose the bearing fault signal, and then two intrinsic mode functions (IMF) with the most fault information are selected by improved kurtosis and Holder coefficient for reconstruction. Finally, the envelope spectrum of the reconstructed signal is analyzed. The analysis of comparative experiments shows that the feature extraction method can extract bearing fault features more accurately, and the fault diagnosis model based on this method has higher accuracy.

A New Method Based on Time-Varying Filtering Intrinsic Time-Scale Decomposition and General Refined Composite Multiscale Sample Entropy for Rolling-Bearing Feature Extraction

The early fault diagnosis of rolling bearings has always been a difficult problem due to the interference of strong noise. This paper proposes a new method of early fault diagnosis for rolling bearings with entropy participation. First, a new signal decomposition method is proposed in this paper: intrinsic time-scale decomposition based on time-varying filtering. It is introduced into the framework of complete ensemble intrinsic time-scale decomposition with adaptive noise (CEITDAN). Compared with traditional intrinsic time-scale decomposition, intrinsic time-scale decomposition based on time-varying filtering can improve frequency-separation performance. It has strong robustness in the presence of noise interference. However, decomposition parameters (the bandwidth threshold and B-spline order) have significant impacts on the decomposition results of this method, and they need to be artificially set. Aiming to address this problem, this paper proposes rolling-bearing fault diagnosis optimization based on an improved coyote optimization algorithm (COA). First, the minimal generalized refined composite multiscale sample entropy parameter was used as the objective function. Through the improved COA algorithm, optimal intrinsic time-scale decomposition parameters based on time-varying filtering that match the input signal are obtained. By analyzing generalized refined composite multiscale sample entropy (GRCMSE), whether the mode component is dominated by the fault signal is determined. The signal is reconstructed and decomposed again. Finally, the mode component with the highest energy in the central frequency band is selected for envelope spectrum variation for fault diagnosis. Lastly, simulated and experimental signals were used to verify the effectiveness of the proposed method.

Rolling Bearing Fault Diagnosis Based on Refined Composite Multi-Scale Approximate Entropy and Optimized Probabilistic Neural Network

A rolling bearing early fault diagnosis method is proposed in this paper, which is derived from a refined composite multi-scale approximate entropy (RCMAE) and improved coyote optimization algorithm based probabilistic neural network (ICOA-PNN) algorithm. Rolling bearing early fault diagnosis is a time-sensitive task, which is significant to ensure the reliability and safety of mechanical fault system. At the same time, the early fault features are masked by strong background noise, which also brings difficulties to fault diagnosis. So, we firstly utilize the composite ensemble intrinsic time-scale decomposition with adaptive noise method (CEITDAN) to decompose the signal at different scales, and then the refined composite multi-scale approximate entropy of the first signal component is calculated to analyze the complexity of describing the vibration signal. Afterwards, in order to obtain higher recognition accuracy, the improved coyote optimization algorithm based probabilistic neural network classifiers is employed for pattern recognition. Finally, the feasibility and effectiveness of this method are verified by rolling bearing early fault diagnosis experiment.

A Novel Method Based on Multi-Island Genetic Algorithm Improved Variational Mode Decomposition and Multi-Features for Fault Diagnosis of Rolling Bearing

Aiming at the problem that it is difficult to extract fault features from the nonlinear and non-stationary vibration signals of wind turbine rolling bearings, which leads to the low diagnosis and recognition rate, a feature extraction method based on multi-island genetic algorithm (MIGA) improved variational mode decomposition (VMD) and multi-features is proposed. The decomposition effect of the VMD method is limited by the number of decompositions and the selection of penalty factors. This paper uses MIGA to optimize the parameters. The improved VMD method is used to decompose the vibration signal into a number of intrinsic mode functions (IMF), and a group of components containing the most information is selected through the Holder coefficient. For these components, multi-features based on Renyi entropy feature, singular value feature, and Hjorth parameter feature are extracted as the final feature vector, which is input to the classifier to realize the fault diagnosis of rolling bearing. The experimental results prove that the proposed method can more effectively extract the fault characteristics of rolling bearings. The fault diagnosis model based on this method can accurately identify bearing signals of 16 different fault types, severity, and damage points.

A Fault Diagnosis Approach for Rolling Bearing Integrated SGMD, IMSDE and Multiclass Relevance Vector Machine

The vibration signal induced by bearing local fault has strong nonstationary and nonlinear property, which indicates that the conventional methods are difficult to recognize bearing fault patterns effectively. Hence, to obtain an efficient diagnosis result, the paper proposes an intelligent fault diagnosis approach for rolling bearing integrated symplectic geometry mode decomposition (SGMD), improved multiscale symbolic dynamic entropy (IMSDE) and multiclass relevance vector machine (MRVM). Firstly, SGMD is employed to decompose the original bearing vibration signal into several symplectic geometry components (SGC), which is aimed at reconstructing the original bearing vibration signal and achieving the purpose of noise reduction. Secondly, the bat algorithm (BA)-based optimized IMSDE is presented to evaluate the complexity of reconstruction signal and extract bearing fault features, which can solve the problems of missing of partial fault information existing in the original multiscale symbolic dynamic entropy (MSDE). Finally, IMSDE-based bearing fault features are fed to MRVM for achieving the identification of bearing fault categories. The validity of the proposed method is verified by the experimental and contrastive analysis. The results show that our approach can precisely identify different fault patterns of rolling bearings. Moreover, our approach can achieve higher recognition accuracy than several existing methods involved in this paper. This study provides a new research idea for improvement of bearing fault identification.