Bearing Fault Simulation Research Articles

An Enhanced Modeling Framework for Bearing Fault Simulation and Machine Learning-based Identification with Bayesian-optimized Hyperparameter Tuning

Abstract Condition monitoring of rotating machinery offers a salient tool for predictive maintenance on rolling elements, subjected to continuous working loads, wear, fatigue, and degradation. In this study, an enhanced computational tool for bearing fault simulation and feature extraction is proposed. A subsequent identification scheme is realized, through Bayesian optimization of hyperparameters, including support vector classifier (SVC), gradient boosting (GBoost), random forest (RF), extreme gradient boosting (XBoost), light gradient boosting machine (LightGBM), and categorical boosting (CatBoost). The proposed hyperparameter optimization technique stands out from traditional methods by offering a more informed and efficient pathway to optimal performance in predictive maintenance. Utilizing Bayesian optimization for hyperparameter tuning of machine learning models, which has not been extensively explored in this field, our approach demonstrates significant advancements. Typical instances of bearing faults, like inner race, outer race, and ball faults are considered. The analysis relies on extraction of statistical and engineering features form collected response signals, including kurtosis, root mean square, peak, and ridge factor. Highly influential variables are highlighted based on feature selection and importance algorithms, allowing bearing fault classification. We demonstrate that SVC and LightGBM produce over 97% of accuracy at low computational cost. This approach constitutes a scalable and robust framework for similar applications in engineering diagnostics.

Multi-stream domain adversarial prototype network for integrated smart roller TBM main bearing fault diagnosis across various low rotating speeds

The well-being of tunnel boring machines (TBM) heavily relies on the health status of main bearings, significantly impacting both safety and operational efficiency. Investigating the operation monitoring and diagnosis algorithms of TBM main bearings in practical scenarios with limited fault data and real-time variations in low-speed heavy-load operating conditions poses a research challenge. To solve these issues, a novel domain-adversarial prototype network diagnostic algorithm with a multi-stream fusion feature encoder (MDAPN) based on smart roller monitoring data is proposed. In contrast to existing external vibration monitoring schemes for bearings, monitoring data from smart rollers can mitigate complex external interference and greatly shorten the transmission path of fault sources. The algorithm encompasses a multi-stream fusion feature encoder, domain discriminator, and prototype network classifier. Specifically, the multi-stream fusion feature encoder adopts the two-stream convolutional network to deeply extract the axial-radial fused features of rollers, incorporating shallow statistical feature information. Domain-invariant features are generated based on domain adversarial learning strategies, and the prototype network classifier reduces dependence on target domain samples. An integrated smart roller main bearing fault simulation testbed was built, conducting 6 sets of cross-domain experiments. The proposed method reached an average accuracy of 98.41 % under 5-shot, surpassing the baseline method by 6.57 % at least. This validates that the MDAPN based on smart roller state exhibits excellent fault recognition performance for the main bearing under varying operational conditions with scarce available samples.

Research on rolling bearing fault diagnosis method based on simulation and experiment fusion drive.

Aiming at the problem that the rolling bearing fault data are difficult to obtain and that the traditional fault diagnosis method does not consider the signal uncertainty characteristics and the low accuracy of models in the process of rolling bearing fault, a fault diagnosis method based on simulation and experiment fusion drive is proposed. First, the dynamics simulation model of rolling bearings under different fault conditions is established to obtain the bearing fault simulation signals. Second, a sequence generative adversarial network is used to fuse the simulation and experimental data. Bearing vibration signals are often very uncertain, so considering the probability characteristics of fault signals, the probability box model under different fault states is constructed by the direct probability box modeling method, and its characteristic vectors are extracted. Finally, an extreme gradient boosting Tree model for fault diagnosis classification is constructed to compare and evaluate the classification and diagnosis effects of bearing states before and after data fusion. The results show that the proposed method has a good diagnostic effect and is suitable for solving the fault diagnosis problem under the condition of insufficient data.

Fuzzy Entropy-Assisted Deconvolution Method and Its Application for Bearing Fault Diagnosis.

Vibration signal analysis is an important means for bearing fault diagnosis. Affected by the vibration of other machine parts, external noise and the vibration transmission path, the impulses induced by a bearing defect in the measured vibrations are very weak. Blind deconvolution (BD) methods can counteract the effect of the transmission path and enhance the fault impulses. Most BD methods highlight fault features of the filtered signals by impulse-featured objective functions (OFs). However, residual noise in the filtered signals has not been well tackled. To overcome this problem, a fuzzy entropy-assisted deconvolution (FEAD) method is proposed. First, FEAD takes advantage of the high noise sensitivity of fuzzy entropy (FuzzyEn) and constructs a weighted FuzzyEn-kurtosis OF to enhance the fault impulses while suppressing noise interference. Then, the PSO algorithm is used to iteratively solve the optimal inverse deconvolution filter. Finally, envelope spectrum analysis is performed on the filtered signal to realize bearing fault diagnosis. The feasibility of FEAD was first verified by the bearing fault simulation signals at constant and variable speeds. The bearing test signals from Case Western Reserve University (CWRU), the railway wheelset and the test bench validated the good performance of FEAD in fault feature enhancement. A comparison with and quantitative results for the other state-of-the-art BD methods indicated the superiority of the proposed method.

Bearing Fault Diagnosis Method Based on Multi-Domain Feature Selection and the Fuzzy Broad Learning System

In recent years, the Broad Learning System (BLS) has been acknowledged for its potential to revolutionize traditional artificial intelligence methods due to its short training time, strong interpretability, and simple structure. In the evolution of BLS, Prof. C. L. Philip Chen’s team introduced the Fuzzy Broad Learning System (FBLS) by replacing the feature nodes of BLS with fuzzy subsystems, thereby further reducing the training time. However, the traditional FBLS, with its straightforward structure, falls short in achieving higher fault diagnosis accuracy when handling raw vibration signals. This paper presents a bearing fault diagnosis approach employing multi-domain feature selection and the fuzzy broad learning system (MS-FBLS), aiming to enhance the diagnostic accuracy of FBLS through multi-domain feature selection. Primarily, a set of 49 features spanning time domain, frequency domain, time-frequency domain, and entropy values is extracted from the original vibrational signals. This combination builds a 49-dimensional multidomain feature set that exploits the information behind the input data as much as possible, thus compensating for the lack of feature extraction capability in FBLS. Afterward, the Random Forest algorithm assesses the significance of all features, leading to a reordering of the multidomain feature set based on their respective importance levels. Ultimately, the reorganized multidomain feature set is then fed into the FBLS, enabling the identification of various failure states within the bearing. The experimental validation conducted on the rolling bearing fault simulation test bed showcased that, in comparison to the traditional FBLS, the MS-FBLS method not only elevates diagnostic accuracy by 23.46%, but also substantially enhances diagnostic speed. These results serve as comprehensive evidence affirming the effectiveness of the method.

An imbalanced sample intelligent fault diagnosis method using data enhancement and improved broad learning system

Broad learning system (BLS) has been widely applied in the field of fault diagnosis because of its high computational efficiency, simple structure, and strong interpretability. However, traditional BLS cannot extract deep level fault features. Meanwhile, some fault samples are difficult to obtain, which leads to the imbalance of samples and further affects the diagnostic results of BLS. To solve these problems, an improved BLS fault diagnosis method based on data enhancement and multi-domain feature fusion is proposed. First, to solve the problem of sample imbalance, some false samples are generated through deep convolutional generative adversarial networks. Second, to solve the problem of poor feature extraction ability of BLS, the multi-domain feature extraction and feature optimization based on ReliefF algorithm are carried out for the enhanced samples. Compared with traditional BLS, the improved BLS effectively solves the problem of sample imbalance and greatly improves the diagnostic accuracy. The proposed method is then testified on the rolling bearing fault simulation test bench. The results show that, samples generated by the proposed method are highly similar to the real samples. In addition, the diagnostic accuracy of the BLS after multi-domain feature extraction and optimization is improved by about 19.67%, which proves the effectiveness of the method. This method provides a new perspective in fault diagnosis and could further expand the application of BLS in fault diagnosis.

Weak Fault Feature Extraction of Axle Box Bearing Based on Pre-Identification and Singular Value Decomposition

The axle box bearing is one of the core rotating components in high-speed trains, having served in complex working conditions for a long time. With the fault feature extraction of the vibration signal, the noise interference caused by the interaction between the wheels and rails becomes apparent. Especially when there is a shortwave defect in the rail, the interaction between wheels and rails will produce high-amplitude impulse interference. To solve the problem of the collected vibration signals of axle box bearings containing strong noise interference and high amplitude impact interference caused by rail shortwave irregularities, this paper proposes a method based on pre-identification via singular value decomposition technology to select the signals in sections and filter the noise, followed by feature extraction and fault diagnosis. The method is used to analyze the axle box bearing fault simulation signal and the weak fault signal collected by the railway bearing comprehensive experimental platform, and these signals are then compared with the random screening signal and the manual screening signal to verify the effectiveness of the method.

Research on the Sparse Optimization Method of Periodic Weights and its Application in Bearing Fault Diagnosis

The vibration state monitoring signal of rolling bearings usually shows periodic transient impulse characteristics at the time of the fault, but in the fault sprouting stage and actual monitoring, its impulse components are easily disturbed by random pulses, harmonics, background noise, etc., which increases the difficulty of extracting the periodic shock characteristics of the fault. This paper proposed a rolling bearing fault feature extraction method based on sparse coefficient weighting theory and periodic enhancement strategy to effectively extract weak periodic shock features with a low signal-to-noise ratio. In the proposed period weighted sparse wavelet representation (PWSWR) method, firstly, based on the sparse wavelet model, the mean kurtosis (MK) index was introduced as a weight to distinguish the contribution of the wavelet coefficients of each signal component. Secondly, a sparse signal period enhancement strategy was proposed using the improved envelope harmonic product spectrum period estimation method. The strategy is embedded into the sparse representation model to achieve the periodic enhancement of filtered signals. Finally, the envelope detection of the sparse signal was carried out to identify the fault. The results of bearing fault simulation signals and two engineering test signals showed that the proposed method could effectively extract weak fault features of bearings and had certain advantages compared with other sparse methods.

Robust fault diagnosis of rolling bearings via entropy-weighted nuisance attribute projection and neural network under various operating conditions

Rolling bearings are crucial components in the fields of mechanical, civil, and aerospace engineering. They sometimes work under various operating conditions, which makes it harder to distinguish faults from normal signals. Nuisance attribute projection (NAP) is a technique that has been widely used in audio and image recognition to eliminate interference information in the extracted feature space. In constructing the weighted matrix of NAP, the setting of the weighted value represents the degree of interference between the feature vectors. The interference is either taken into consideration in whole, or not considered at all, which will inevitably lead to information loss. In our work, an entropy-weighted NAP (EWNAP) is proposed to deal with such “bipolar problem” in constructing the weighted matrix. The eigenvalues of covariance matrix of collected signals contain dynamical information, and the fuzzy entropy is adopted to evaluate the dispersion degree of these eigenvalues. After normalization, these entropy values are used to express the weight relationship in the weighted matrix of EWNAP. The features processed by EWNAP can be used as samples and combined with neural network to achieve fault diagnosis of rolling bearings. Furthermore, a fault diagnosis approach with insufficient data is demonstrated to validate the effectiveness of the proposed scheme. In the case studies, Case Western Reserve University bearing database and data collected from the bearing fault simulation bench are used. These case studies show that the proposed EWNAP alleviates the interference caused by various operating conditions, and the comparative analysis confirms that the proposed method works better than the conventional methods.

A Minimum Mutual Information Optimized SSD and Application In Bearing Fault Detection

For purpose of efficiently extracting the fault detailed characteristics of rolling bearing vibration signals in the midst of heavy noise interference, the author combines the mutual information theory and proposes a singular spectrum decomposition effective component discrimination method based on the minimum mutual information criterion. First, the SSD algorithm is used to decompose the original vibration signal into a number of SSC; then the mutual information value between the original signal and each singular spectrum component is calculated separately, based on the nature of the bearing fault vibration signal and the mutual information theory for derivation and analysis, and the selection is determined the singular spectrum component with the smallest mutual information value among the original signal and each component is taken as the best component; finally, the best component selected based on the minimum mutual information value criterion is analysed by envelope spectrum to extract the fault characteristics of rolling bearing. Through the analysis of bearing fault simulation signal and the comparison with other indicators, it is shown that this set of experiments significantly extracts the characteristics of the vibration signals emitted by rolling bearings due to faults in noisy environments, thus revealing promising applications and development prospects.

Early bearing fault diagnosis based on the improved singular value decomposition method

The traditional singular value decomposition (SVD) method is unable to diagnose the weak fault feature of bearings effectively, which means, it is difficult to retain the effective singular components (SCs). Therefore, a new singular value decomposition method, SVD based on the FIC (fault information content), is proposed, which takes the amplitude characteristics of fault feature frequency as the selection index FIC of singular components. Firstly, the Hankel matrix of the original signal is constructed, and SVD is applied in the matrix. Secondly, the proposed index FIC is used to evaluate the information of the decomposed SCs. Finally, the SCs with fault information are selected and added to obtain the denoised signal. The results of bearing fault simulation signals and experimental signals show that compared with the traditional differential singular value decomposition (DS-SVD), the proposed method can select the singular components with larger amount of fault information and is able to diagnose the fault under the heavy noise interference. The new method can be used for signal denoising and weak fault feature extraction.

Rolling Bearing Fault Diagnosis by Aperiodic Stochastic Resonance Under Variable Speed Conditions

The fault characteristic of rolling bearings under variable speed condition is a typical non-stationary stochastic signal. It is difficult to extract due to the interference of strong background noise makes the applicability of traditional noise reduction methods less. In this paper, an aperiodic stochastic resonance (ASR) method is proposed to study the fault diagnosis of rolling bearings under variable speed conditions. Based on numerical simulation, the effect of noise intensity and damping coefficient on the ASR of the second-order underdamped system is discussed, and an appropriate damping coefficient is found to reach the optimal ASR. The proposed method enhances the fault characteristic information of bearing fault simulation signal. Corresponding to rising-stationary and the stationary-declining running conditions, the method is verified by both simulated and experimental signals. It provides reference for fault diagnosis under variable speed condition.

A promising new tool for fault diagnosis of railway wheelset bearings: SSO-based Kurtogram

A promising method is proposed systematically to select an accurate resonance frequency band and separate refined resonance response from periodic excitation in this study. This work expanded the short-time Fourier transform (STFT)- and wavelet transform (WT)-based Kurtograms and developed a hybrid signal separation operator (SSO)–spectral kurtosis computational scheme to implement Kurtogram by introducing the SSO method—SSO-based Kurtogram. The ability to accurately extract the refined resonance frequency band of SSO greatly improves its adaptivity for engineering applications. The effectiveness of the SSO-based Kurtogram is studied by using a bearing fault simulation signal, and the influence of window function on the detection effect of the proposed method is explored. Furthermore the validity of the SSO-based Kurtogram for bearing fault detection is verified by a set of railway wheelset-bearing experiments on the wheelset running-in testbed bench. Experimental results show that the SSO-based Kurtogram performs highly in detecting various kinds of single and compound faults of bearings. Compared with the WT- and STFT-based Kurtogram, the proposed method has obvious advantages in terms of effectiveness and visual inspection ability. In engineering practice, a railway wheelset-bearing-fault experiment on an in-service high-speed train in the real world is taken as a case study, which makes the verification of SSO-based Kurtogram more convincing and demonstrates the practical engineering value of the proposed method. The results show that in case of equal effectiveness, SSO-based Kurtogram has an absolute advantage in the visual inspection ability, embodied in eliminating other vibrations unrelated to the target fault and making the fault feature frequency and its harmonics remarkable.

An improved variational mode decomposition method and its application in diesel engine fault diagnosis

The diesel engine is a complex mechanical device, with the characteristics of multi-source, multi moving parts, complex work. For the complex multi-component signal, it is usually necessary to decompose it into a number of single-component AM-FM signals, and each component is analyzed to extract amplitude and frequency information. VMD is essentially composed of a plurality of adaptive Wiener filter and has good noise robustness. Compared with EMD, EEMD, CEEMDAN, LMD and ITD, VMD has strong mathematical theory basis. At the same time, VMD rejects the method of recursive screening stripping. So VMD can effectively alleviate or avoid a series of problems which appear in other methods. However, it is a problem how to determine the number of decomposition layers and the penalty factor, because human factors will affect the decomposition results. In order to solve the problem, an improved adaptive genetic algorithm (IAGA) is proposed to optimize the parameters of VMD. Genetic algorithms mainly include 3 genetic operators: selection, crossover and mutation. The cross probability and mutation probability will directly affect the optimization results. In the traditional genetic algorithm, the probability of cross and mutation are fixed, and the genetic algorithm is easy to fall into the local optimal. According to the regulation of hormone regulation, the cross probability and mutation probability in evolution were improved. The permutation entropy is a new method of mutation detection, which mainly aims at the spatial characteristics of the time series itself. Therefore, the entropy of the components obtained by the VMD decomposition is used as the fitness function of the IAGA. The modal number K and penalty factor α of VMD were iteratively optimized by IAGA, and the optimal combination of parameters was obtained. Based on the proposed method, the vibration signals of the crankshaft bearing fault simulation experiment were decomposed into several components. According to the value of the permutation entropy, the fault components were selected and the energy was extracted. The fault pattern is identified by the support vector machine (SVM) successfully. The simulation analysis and the simulation experiment of the crankshaft bearing fault show that the proposed method is effective. For the diagnosis of other engines, a large number of validation experiments are needed for further research.

Hyper-spherical distance discrimination: A novel data description method for aero-engine rolling bearing fault detection

Abstract A novel method called hyper-spherical distance discrimination (HDD) is proposed in order to meet the requirement of aero-engine rolling bearing on-line monitoring. In proposed method, original multi-dimensional features extracted from vibration acceleration signal are transformed to the same dimensional reconstructed features by de-correlation and normalization while the distribution of feature vectors is transformed from hyper-ellipsoid to hyper-sphere. Then, a simple model built up by distance discriminant analysis is used for rolling bearing fault detection and degradation assessment. HDD is compared with the support vector data description (SVDD) and the self-organizing map (SOM) in rolling bearing fault simulation experiments. The results show that the HDD method is superior to the SVDD and SOM in terms of recognition rate. Besides, HDD is applied to a run-to-failure test of aero-engine rolling bearing. It proves that the evaluating indicator obtained by HDD method is able to reflect the degradation tendency of rolling bearing, and it is also more sensitive to initial fault than the root mean square (RMS) of vibration acceleration signal. With the advantages of low computational complexity and no need to tuning parameters, HDD method can be applied to practical engineering effectively.

Bearing fault diagnosis using a whale optimization algorithm-optimized orthogonal matching pursuit with a combined time–frequency atom dictionary

Condition monitoring and fault diagnosis of rolling element bearings are significant to guarantee the reliability and functionality of a mechanical system, production efficiency, and plant safety. However, this is almost invariably a formidable challenge because the fault features are often buried by strong background noises and other unstable interference components. To satisfactorily extract the bearing fault features, a whale optimization algorithm (WOA)-optimized orthogonal matching pursuit (OMP) with a combined time–frequency atom dictionary is proposed in this paper. Firstly, a combined time–frequency atom dictionary whose atom is a combination of Fourier dictionary atom and impact time–frequency dictionary atom is designed according to the properties of bearing fault vibration signal. Furthermore, to improve the efficiency and accuracy of signal sparse representation, the WOA is introduced into the OMP algorithm to optimize the atom parameters for best approximating the original signal with the dictionary atoms. The proposed method is validated through analyzing the bearing fault simulation signal and the real vibration signals collected from an experimental bearing and a wheelset bearing of high-speed trains. The comparisons with the respect to the state of the art in the field are illustrated in detail, which highlight the advantages of the proposed method.

An improved adaptive stochastic resonance method for improving the efficiency of bearing faults diagnosis

The general scale transformation (GST) method is used in the bistable system to deal with the weak high-frequency signal submerged into the strong noisy background. Then, an adaptive stochastic resonance (ASR) method with the GST is put forward and realized by the quantum particle swarm optimization (QPSO) algorithm. Through the bearing fault simulation signal, the ASR method with the GST is compared with the normalized scale transformation (NST) stochastic resonance (SR). The results show that the efficiency of the GST method is higher than the NST in recognizing bearing fault feature information. In order to simulate the actual engineering environment, both the adaptive GST and the NST methods are implemented to deal with the same experimental signal, respectively. The signal-to-noise ratio (SNR) of the output is obviously improved by the GST method. Specifically, the efficiency is improved greatly to extract the weak high-frequency bearing fault feature information. Moreover, under different noise intensities, although the SNR is decreased versus the increase of the noise intensity, the ASR method with the GST is still better than the traditional NST SR. The proposed GST method and the related results might have referenced value in the problem of weak high-frequency feature extraction in engineering fields.

Vibration model of rolling element bearings in a rotor-bearing system for fault diagnosis

Rolling element bearing faults are among the main causes of breakdown in rotating machines. In this paper, a rolling bearing fault model is proposed based on the dynamic load analysis of a rotor-bearing system. The rotor impact factor is taken into consideration in the rolling bearing fault signal model. The defect load on the surface of the bearing is divided into two parts, the alternate load and the determinate load. The vibration response of the proposed fault signal model is investigated and the fault signal calculating equation is derived through dynamic and kinematic analysis. Outer race and inner race fault simulations are realized in the paper. The simulation process includes consideration of several parameters, such as the gravity of the rotor-bearing system, the imbalance of the rotor, and the location of the defect on the surface. The simulation results show that different amplitude contributions of the alternate load and determinate load will cause different envelope spectrum expressions. The rotating frequency sidebands will occur in the envelope spectrum in addition to the fault characteristic frequency. This appearance of sidebands will increase the difficulty of fault recognition in intelligent fault diagnosis. The experiments given in the paper have successfully verified the proposed signal model simulation results. The test rig design of the rotor bearing system simulated several operating conditions: (1) rotor bearing only; (2) rotor bearing with loader added; (3) rotor bearing with loader and rotor disk; and (4) bearing fault simulation without rotor influence. The results of the experiments have verified that the proposed rolling bearing signal model is important to the rolling bearing fault diagnosis of rotor-bearing systems.

Gearbox bearing fault simulation using a finite element model reduction technique

The dynamics of a mechanical system such as a gearbox assembly comprising shafts, gears and bearings can be simulated using Lumped Parameter Models (LPMs). Finite Element Method (FEM) reduction techniques based on the Craig-Bampton method of Component Mode Synthesis (CMS) are useful in creating more accurate dynamic models. These models, despite having more degrees-of-freedom for the individual components than the LPM, make very much larger FE models computationally tractable. In this paper both these approaches, namely LPM and reduced FEM, are compared to create a dynamic model of a gearbox. Earlier simulation models (both LPM and combined LPM and reduced FEM) are further improved to better match the geometry of the bearing faults used in the experimental measurements, and the experimental results from a gearbox test rig. The dynamic model is used to simulate the vibration signals in the presence of localised inner and outer race faults. The new results show better correspondence with the measured signals, in particular with respect to the detailed response to entry and exit from the fault, which can be used to determine fault size. The paper highlights the plausibility of fault simulation in Machine Condition Monitoring (MCM) where a large amount of data can be gathered without experiencing large numbers of actual failures or carrying out costly and time consuming experiments until failure with seeded faults. The simulation data can be used to train neural networks to automate the diagnostic and prognostic processes.