Fault Diagnostics Based on Pattern Spectrum Entropy and Proximal Support Vector Machine

Fault diagnosis of rotating machinery is vital to identify incipient failures and avoid unexpected downtime in industrial systems. This paper proposes a new rolling bearing fault diagnosis method by integrating the fine-to-coarse multiscale permutation entropy (F2CMPE), Laplacian score (LS) and support vector machine (SVM). A novel entropy measure, named F2CMPE, was proposed by calculating permutation entropy via multiple-scale fine-grained and coarse-grained signals based on the wavelet packet decomposition. The entropy measure estimates the complexity of time series from both low- and high-frequency components. Moreover, the F2CMPE mitigates the drawback of producing time series with sharply reduced data length via the coarse-grained procedure in the conventional composite multiscale permutation entropy (CMPE). The comparative performance of the F2CMPE and CMPE is investigated by analyzing the synthetic and experimental signals for entropy-based feature extraction. In the proposed bearing fault diagnosis method, the F2CMPE is first used to extract the entropy-based features from bearing vibration signals. Then, LS and SVM are used for selection of features and fault classification, respectively. Finally, the effectiveness of the proposed method is verified for rolling bearing fault diagnosis using experimental vibration data sets, and the results have demonstrated the capability of the proposed method to recognize and identify the bearing fault patterns under different fault states and severity levels.

A new rolling bearing fault diagnosis approach based on multiscale permutation entropy (MPE), Laplacian score (LS), and support vector machines (SVMs) is proposed in this paper. Permutation entropy (PE) was recently proposed and defined to measure the randomicity and detect dynamical changes of time series. However, for the complexity of mechanical systems, the randomicity and dynamic changes of the vibration signal will exist in different scales. Thus, the definition of MPE is introduced and employed to extract the nonlinear fault characteristics from the bearing vibration signal in different scales. Besides, the SVM is utilized to accomplish the fault feature classification to fulfill diagnostic procedure automatically. Meanwhile, in order to avoid a high dimension of features, the Laplacian score (LS) is used to refine the feature vector by ranking the features according to their importance and correlations with the main fault information. Finally, the rolling bearing fault diagnosis method based on MPE, LS, and SVM is proposed and applied to the experimental data. The experimental data analysis results indicate that the proposed method could identify the fault categories effectively.

To address the issues of low diagnostic accuracy in traditional rolling bearing fault diagnosis models and the ineffective extraction of spatial and temporal features from vibration signals, this paper proposes a rolling bearing fault diagnosis method based on the improved sparrow search algorithm optimized VMD and multi-scale convolutional neural networks. First, the improved sparrow search algorithm is employed to adaptively optimize the penalty parameter and mode count in variational modal decomposition (VMD). This achieves finer frequency band segmentation and effectively suppresses energy leakage, thereby yielding high quality frequency domain representations. Second, a multi-scale convolutional neural networks (MSCNN) is constructed, with feature level fusion implemented. Subsequently, a bidirectional long short-term memory networks (BiLSTM) is introduced to model the temporal dependencies of the fused features, enabling fault mode learning. A softmax layer is employed to achieve multi-class classification. Finally experimental results and comparisons based on the CWRU bearing dataset demonstrate the effectiveness of the proposed method in the rolling bearing fault classification task, providing significant application value for achieving efficient and reliable bearing fault detection.

Rolling bearings are vital components in rotary machines where even minor faults can lead to the collapse of the entire mechanical system, resulting in significant economic losses. The condition monitoring and fault diagnosis of rolling bearings are crucial for safe operation of complex industrial systems. Traditional fault diagnosis methods mainly depend on expert experience, which leads to obvious deficiencies in diagnostic efficiency, especially in terms of accuracy. To address the issues of traditional bearing fault diagnosis relying on expert experience and low efficiency and accuracy of fault diagnosis, a bearing fault diagnosis model combining synchrosqueezed wavelet transform (SWT) and SE-ResNet is proposed. Firstly, the one-dimensional non-stationary bearing vibration signal is converted into a high-frequency two-dimensional time-frequency image through SWT, which serves as the input for the convolutional neural network; Secondly, an attention mechanism is introduced to construct an SE-ResNet model for extracting two-dimensional image features, which enhances the attention of important features and thus enhances the network's representation ability; Finally, the results of fault diagnosis are output through Softmax layer. To validate the capacity of the proposed model, experiments with the bearing dataset collected from Case Western Reserve University (CWRU) were conducted. The results show that the transfer learning accuracy of the CWRU dataset is 86.25% to 99%. This method has good feasibility, good convergence performance, and has high practical application value.

Support vector machine (SVM) is a supervised machine learning approach that was recognized as a statistical learning apotheosis for the small-sample database. SVM has shown its excellent learning and generalization ability and has been extensively employed in many areas. This paper presents a performance analysis of six types of SVMs for the diagnosis of the classical Wisconsin breast cancer problem from a statistical point of view. The classification performance of standard SVM (St-SVM) is analyzed and compared with those of the other modified classifiers such as proximal support vector machine (PSVM) classifiers, Lagrangian support vector machines (LSVM), finite Newton method for Lagrangian support vector machine (NSVM), Linear programming support vector machines (LPSVM), and smooth support vector machine (SSVM). The experimental results reveal that these SVM classifiers achieve very fast, simple, and efficient breast cancer diagnosis. The training results indicated that LSVM has the lowest accuracy of 95.6107 %, while St-SVM performed better than other methods for all performance indices (accuracy = 97.71 %) and is closely followed by LPSVM (accuracy = 97.3282). However, in the validation phase, the overall accuracies of LPSVM achieved 97.1429 %, which was superior to LSVM (95.4286 %), SSVM (96.5714 %), PSVM (96 %), NSVM (96.5714 %), and St-SVM (94.86 %). Value of ROC and MCC for LPSVM achieved 0.9938 and 0.9369, respectively, which outperformed other classifiers. The results strongly suggest that LPSVM can aid in the diagnosis of breast cancer.

For the situation where the bearing of the lifting mechanism motor of the gantry crane is prone to “inner ring peeling + outer ring cracks” under heavy–load impact and loadswitching conditions (the combined faults cause diagnosis to be difficult due to feature superposition), and the computing power of the industrial edge terminal is limited and complex models are difficult to deploy, a lightweight diagnostic method integrating CWT, Ghost convolution and coordinated attention (CA) is proposed. In the preprocessing stage, CWT is used to convert one–dimensional vibration signals into two–dimensional timefrequency graphs to separate the features of inner ring faults and outer ring faults, while suppressing environmental noise. Then, the model is based on the residual network and adopts the “basic convolution generates core features + linear transformation supplements redundant features” strategy of Ghost convolution to significantly reduce parameters and decrease computational complexity. The CA mechanism is embedded to focus on the fault–related channels from the channel and locate the fault area in the time–frequency graph from the spatial perspective, alleviating the problem of insufficient feature extraction caused by lightweighting. Experiments show that this method has significantly higher diagnostic accuracy than traditional models in both single–fault and multi–fault superposition scenarios, and the number of parameters and computational costs are significantly reduced, verifying its effectiveness and feasibility in practical applications.

The failure of a rolling bearing may cause the shutdown of mechanical equipment and even induce catastrophic accidents, resulting in tremendous economic losses and a severely negative impact on society. Fault diagnosis of rolling bearings becomes an important topic with much attention from researchers and industrial pioneers. There are an increasing number of publications on this topic. However, there is a lack of a comprehensive survey of existing works from the perspectives of fault detection and fault type recognition in rolling bearings using vibration signals. Therefore, this paper reviews recent fault detection and fault type recognition methods using vibration signals. First, it provides an overview of fault diagnosis of rolling bearings and typical fault types. Then, existing fault diagnosis methods are categorized into fault detection methods and fault type recognition methods, which are separately revised and discussed. Finally, a summary of existing datasets, limitations/challenges of existing methods, and future directions are presented to provide more guidance for researchers who are interested in this field. Overall, this survey paper conducts a review and analysis of the methods used to diagnose rolling bearing faults and provide comprehensive guidance for researchers in this field.

Current data-driven fault diagnosis methods are prone to overfitting and a decrease in accuracy when working with only a limited number of labeled samples. Additionally, existing graph neural network-based fault diagnosis methods often fail to comprehensively utilize both global and local features. To address these challenges, we propose a rolling bearing fault diagnosis method based on multi-scale weighted visibility graph and a multi-channel graph convolutional network (MCGCN). Our approach converts vibration signals into multiple weighted graphs from the perspective of geometric meaning and extracts local node feature information and global topology information of graphs using MCGCN. Experimental results demonstrate that our method achieves excellent performance under both sufficient and limited data conditions, providing a promising approach for real-world industrial bearing fault diagnosis.

To realize accurate fault diagnosis of rolling bearing under random noise, a novel fault diagnosis method based on ensemble empirical mode decomposition (EEMD) and optimized Elman_AdaBoost is proposed in this paper. First, the EEMD method is used to decompose the original vibration signal into several intrinsic mode functions (IMFs). Then, the correlation coefficient and kurtosis of IMFs are used to remove any excess ingredients, and the signal is reconstructed by using the rest of IMFs. In addition, based on the analysis of the time–frequency characteristics of the reconstructed signal, the root-mean-square value and the power spectrum center are extracted as a 2-D feature vector from each reconstructed signal and regarded as the input characteristic vector of the Elman neural network. Combined with the AdaBoost classification algorithm, the Elman_AdaBoost algorithm is improved and proposed to establish the strong classifier. Finally, based on the vibration data recorded in the bearing center of the Case Western Reserve University, three kinds of bearings with different faults and normal bearings are selected as the sample data and the training samples and test samples are constructed. Experimental results show that the proposed EEMD method and optimized Elman_AdaBoost model can effectively diagnose the rolling bearing under random noise, and has the advantages of fast speed, small error, and stable performance. Comparing with the traditional Elman_AdaBoost and single Elman neural network algorithm, this paper with fewer characteristics can get better accuracy and real-time processing performance, and presents a simple and practical resolution for the fault diagnosis of rolling bearings.

Based on soft morphological filters and support vector machine (SVM), a roller bearing fault diagnosis method is proposed. It is very difficult to filter the fault vibration signals from the strong noise background because the roller bearing fault diagnosis is a problem of multi-class classification. Soft morphology filter can not only identify the features of fringe and shape of the signals but also give improved performance under certain conditions. Support vector machine has good classification performance especially in the small-sample, nonlinear and high dimensional features and so on. The penalty factors and kernel parameters of SVM are optimized by using particle swarm optimization to avoid dependence on initial parameters and training samples. Firstly, vibration signals are filtered by the soft morphological filters. Secondly, the normalized energy of the different characteristic frequencies is utilized to identify the fault features of input parameters of SVM classifier. The SVM parameters are optimized by using the canonical particle swarm optimization. The experiment results indicate that the modeling method is correct.

Rolling element bearings (REBs) are critical components in rotating machinery, and timely detection of faults in these bearings can prevent catastrophic failure and costly downtime. Vibration signals collected from REBs contain important information regarding the bearing health states. A localized defect in a REB produces periodic impulses in the vibration signals at relevant bearing characteristic frequencies (BCFs) that are commonly used for bearing condition monitoring. Envelope analysis that has been a powerful technique in detecting BCFs in signals, however, poses a significant challenge as it requires the selection of an effective band-pass filtering region due to the variable nature of resonant frequencies in bearing systems. A novel hybrid method for bearing fault diagnosis based on Cepstrum Pre-Whitening (CPW) and high-pass filtering has been developed to overcome this shortcoming in envelope analysis and has shown to be a powerful technique in accurately detecting early bearing faults on a range of machines under different operating conditions. In contrast to the existing signal processing methods, the new hybrid method eliminates the need for manual parameter selection or optimization algorithms, such as filtering bands selection in enveloping analysis. Instead, it requires inputs including bearing geometries and its operating conditions such as shaft rotating speed for bearing fault diagnosis. This enhances the practicality and accuracy of bearing fault diagnosis in real-world scenarios, especially when data is limited. This study evaluates the effectiveness of this hybrid method for bearing fault diagnosis in the highly noisy environments under which machine is often operated in real applications. To achieve this purpose, firstly, numerical simulations of bearing vibration signals have been conducted, wherein Gaussian white noise with varying levels of signal-to-noise ratio (SNR) is DOI: 10.1784/cm2023.3f4 added to the simulated signals. Secondly, the effectiveness of the method is tested on vibration data collected from an experimental run-to-failure bearing dataset, which contains significant amount of background noise in the early stage of the fault progression. The results from this work have shown that the new hybrid method achieves high accuracy in diagnosing fault features in the simulated signals with a SNR of down to ‐ 13 dB for outer ring fault and ‐ 15 dB for inner ring and ball faults, much more effective than other methods in the literature. It has also shown to detect bearing faults at very early stages from a run-to-failure test.

With the automation and complexity of industry, the production planning and scheduling of the smart factory depends on the proper functioning of each part. As a key component of rotating machinery, the faults of rolling bearing is prone to effects under complex and changing working conditions and coupled with other components. Therefore, it is necessary to carry out efficient and accurate fault diagnosis for rolling bearings to ensure the reliability and stability of mechanical equipment operation. This paper introduces a multi-scale rolling bearing fault diagnosis method (MSF-CNN) based on dilated convolution which is able to automatically capture complementary data and feature information of different scales of the original vibration signal through multi-scale convolution to achieve end-to-end fault diagnosis. The experimental results show that the proposed fault diagnosis method achieves an average accuracy of 99.35% under three load conditions. In addition, this method can provide the cross domain data solution to reduce the dependence on missing label data, which achieves the fault diagnosis accuracy of 89+%. It verifies the validity of our proposal.

Deep learning methods are widely used in the field of rolling bearing fault diagnosis and produce good results when faced with datasets with roughly equal numbers of normal and faulty samples. However, real-world data often has a serious imbalance, with the number of fault samples being significantly less than the number of normal samples. This dataset imbalance challenges the performance of traditional deep learning methods. To address this problem, this paper proposes an efficient imbalanced data rolling bearing fault diagnosis method. The method consists of two parts: a deep learning network based on a multi-scale self-attention mechanism and a novel loss function. In terms of the deep learning network, firstly, the one-dimensional vibration signal is converted into a two-dimensional image through the Gramian angular field. This conversion maximises the inherent feature extraction capability of the network. Subsequently, the multi-scale learning capability of the network is enhanced by implementing different expansion rates for the head of the multi-scale self-attention mechanism. This nuanced approach allows the network to capture the underlying information more efficiently. Finally, the inclusion of Ghost bottlenecks and feature pyramid networks (FPNs) helps to optimise network efficiency and improve generalisation performance. A novel loss function is also proposed to make the method more suitable for imbalanced data. During the training process, the classification of samples in each class is analysed using the recall metric of imbalanced classification and the real-time recall is used as a weight to weaken the dominance of the majority class. This weighting ensures the adaptability of the method to imbalanced datasets. The proposed method is evaluated using rolling bearing datasets from Case Western Reserve University, USA, and Southeast University, China. Comparison results with other state-of-the-art deep learning methods show that the proposed method has a robust performance when dealing with imbalanced data.

To achieve the goal of automated rolling bearing fault diagnosis, a variational mode decomposition (VMD) based diagnosis scheme was proposed. VMD was firstly used to decompose the vibration signals into a series of band-limited intrinsic mode functions (BLIMFs). Subsequently, the multiscale fractal dimension (MSFD) and multiscale energy (MSEN) of each BLIMF were calculated and combined together as features of the original vibration signals. In an attempt to accelerate the classification speed, one-way analysis of variance (ANOVA) test was adopted to extract significant features from the redundant features. Finally, those significant features were fed into the optimized support vector machine (SVM), which was optimized by the genetic algorithm (GA), for classification. Experimental results on the international public Case Western Reserve University bearing data indicate the effectiveness of the proposed method with a classification accuracy of 99.75 % for seven classes. Moreover, our approach also shows good anti-noise performance in different signal-to-noise ratios (SNRs).

Fault diagnosis of rolling bearings is significant for the safe operation of engineering equipment. Many intelligent diagnostic methods have been successfully developed. However, it is often susceptible to noisy environments. Therefore, the paper proposes a rolling bearing fault diagnosis method based on multimodal information fusion in time and time–frequency domains by combining an improved 1D-convolutional neural network (CNN) with ResNet50 wavelet improved CNN-ResNet (WCNN-RSN). The algorithm employs the Multi-Head Attention (MHA) mechanism to complementarily fuse fault features in different scales, achieving fault diagnosis by fully extracting fault features. The experimental results show that the diagnostic effect of WCNN-RSN is better than that of the comparison methods under noise interference, which proves that the proposed method possesses good anti-noise and generalization ability.