Bearing Fault Characteristic Frequency Research Articles

Toward accurate extraction of bearing fault modulation characteristics with novel time–frequency modulation bispectrum and modulation Gini index analysis

Rolling bearings are extremely critical rotating mechanical components, and when they fail, they can damage the equipment, causing safety threats or economic losses. Collecting and analyzing vibration signals of faulty bearings is a common fault diagnosis method. Modulation signal bispectrum (MSB) can utilize the inherent modulation characteristics of the signal to achieve fault feature recognition, but it is easily affected by strong background noise and other modulation signals, making it difficult to detect the fault feature frequency in the end. Based on this, a time–frequency modulation bispectrum (TFMB) method is proposed in this paper. The signal is first transformed into the time–frequency domain through short-time Fourier transform, retaining both time and frequency information. It reduces the amplitude of bispectral noise, highlights spectral lines related to fault information, and displays modulation information more clearly, making the demodulation results more accurate. Based on the characteristics of bispectrum, a two-dimensional singular value decomposition (2D SVD) strategy is designed to reduce the amplitude of the noise components in the bispectrum, and the relative change rate is proposed to automatically determine the number of effective singular values. At the same time, considering that the Gini index has good sparse property, the modulation Gini index (MGI) is proposed based on the Gini index, which can identify the repetitive pulses in the signal, suppress the random pulses and noise interference, and extract the modulation component. MGI can be used to evaluate the proportion of fault information contained in TFMB slices and select the optimal frequency slice. The simulation signal verifies the effectiveness of the method in fault diagnosis of rolling bearing, and the proposed method is applied to the diagnosis of rolling bearing outer ring fault, inner ring fault, and compound fault respectively. The experimental results show that the method can effectively reduce noise amplitude, enhance fault information in the bispectrum, and extract the optimal frequency slice to accurately detect bearing fault characteristic frequencies. The proposed method is compared with MSB detector, Fast Kurtogram and Autogram, which proves the superiority of TFMB method in extraction of rolling bearing fault characteristics.

Fault diagnosis of rolling bearing based on the three-dimensional coupled periodic potential-induced stochastic resonance

Abstract Conventional bistable and monostable stochastic resonance (SR) methods exhibit certain limitations in their capacity to enhance and extract incipient characteristics. Firstly, the inherent potential function structure, characterized by a singular stable-state paradigm, proves inadequate in accommodating the heterogeneous and multifaceted condition monitoring signals. Secondly, the interconnected dynamic characteristics of the mechanical signals remain unaccounted for. Furthermore, conventional SR methods persist in utilizing a fixed constant as the critical system parameter, thereby neglecting the synergistic interaction among monitoring signals, potential function structures, and scale factors. Owing to the rich dynamic characteristics of the three-dimensional multi-stable coupled periodic potential SR system, it demonstrates superior noise utilization compared to monostable and bistable systems. In view of this, the present formulates a three-dimensional spatial model employing a coupled periodic potential model with nonlinear coupling. Subsequently, a pioneering method for diagnosing rolling bearing faults is introduced, utilizing the framework of three-dimensional multi-stable coupled periodic potential-induced SR. Simulation and experimental results illustrate that this approach effectively enhances and extracts the subtle fault characteristics of rolling bearings, ensuring a clear distinction between the spectral peak at the bearing fault characteristic frequency and the spectral peak originating from the interference noise.

Early Prediction of Remaining Useful Life for Rolling Bearings Based on Envelope Spectral Indicator and Bayesian Filter

On top of the condition-based maintenance (CBM) practice for rotating machinery, the robust estimation of remaining useful life (RUL) for rolling-element bearings (REB) is of particular interest. The failure of a single bearing often results in secondary defects in the connected structure and catastrophic system failures. The prediction of RUL facilitates proactive maintenance planning to ensure system reliability and minimize financial loss due to unscheduled downtime. In this paper, to acquire early and reliable estimations of useful life, the RUL prediction of REBs is formulated into nonlinear degradation state estimation tackled by the combination of the envelope spectral indicator (ESI) and extended Kalman filter (EKF). By fusing the spectral energy of the bearing fault characteristic frequencies (FCFs) in the averaged envelope spectrum, the ESI is crafted to remove the interference from rotor-dynamics and reveal the bearing deterioration process. Once the fault is identified, the recursive Bayesian method based on EKF is utilized for estimating the bearing end-of-life time via the exponential state-space model. The distinctive advantage of the proposed approach lies in its ability to make an early prediction of RUL using a small number of ESI observations, offering an efficient practice for predictive health management at the early stage of bearing fault. The performance of the proposed method is validated using publicly available experimental bearing vibration data across three different operating conditions.

A Current Noise Cancellation Method Based on Integration of Stator Synchronized Currents for Bearing Fault Diagnosis

In bearing fault diagnosis using motor stator currents, anything unrelated to the fault characteristic frequencies is considered "noise". Noise cancellation provides a better estimation of the bearing fault signal. This paper aims to develop a noise cancellation method for a better estimation of the bearing fault signal in induction motors using three current signals, rather than just one. The paper proposes a method of time shifting in two phases of the three-phase current and integrating them with the third phase current as a noise cancellation method. The proposed method efficiently diagnoses bearing fault characteristic frequencies in spectral analysis. Simulation and experimental results confirm the effectiveness of the proposed method in detecting outer/inner raceway and ball bearing faults.

Bearing fault diagnosis under non-stationary conditions based on a speed signal resonance component demodulation algorithm

This paper proposes a novel bearing fault diagnosis indicator, the resonance component, for motor speed signals. The speed signal was modulated into a higher-frequency band using a double-inertia system, and the bearing fault information was carried and reserved in this high-frequency resonance component. Variational mode decomposition was then used to separate the components unrelated to the resonance based on the parameters optimized using the artificial bee colony algorithm. After envelope demodulation and angular resampling, the multipoint optimal minimum entropy deconvolution adjusted algorithm was utilized to enhance the amplitude of the order spectrum at the corresponding faulty order. Additionally, experiments were successfully conducted on both the outer and inner raceway bearing faults under time-varying conditions using the proposed method. The results indicate that the ordinary diagnosis method using the basic bearing fault characteristic frequency as an indicator is less effective.

Bearing fault feature extraction method: improved weighted envelope spectrum

Many existing cyclic spectrum analysis methods are ineffective in solving bearing fault diagnosis in multi-information frequency bands. Based on this, an improved weighted envelope spectrum (IWES) method is proposed. Firstly, IWES uses the fault information intensity index to quantify bearing fault information and evaluate bearing fault information of spectral frequency bands in spectral coherence. Secondly, the threshold function is constructed to determine the threshold adaptively, so as to identify the spectrum frequency components with rich fault information in the spectral coherence. Meanwhile, a weight function is designed based on threshold function to eliminate the interference noise components and keep the fault information. Finally, the spectral coherence and weight function are used to generate IWES with multi-band information. The bearing experiments show that the IWES has excellent noise robustness and can accurately extract the bearing fault characteristic frequency.

A physics-informed feature weighting method for bearing fault diagnostics

Intelligent bearing diagnostics has gained popularity over the last few years. However, most of the diagnostic methods are developed under the assumption that training and test data sets are collected under the same working conditions. This assumption is rare in practical scenarios because rotating machinery usually works under wide ranges of rotational speeds and loads. As bearings work under complex and time-varying operating conditions, the test data might come from a data distribution outside the training distribution. Purely data-driven diagnostic models often cannot provide reliable classifications for out-of-distribution test data. To tackle this challenge, this paper proposes a physics-informed feature weighting method for bearing diagnostics. First, a signal processing step is proposed that leverages physical knowledge of bearing faults to extract discriminative features that are robust to bearing speed variation. Then, a novel physics-informed feature weighting layer is developed to assign higher weights for features located closer to bearing fault characteristic frequencies. The feature weighting layer enhances the model’s sensitivity towards the fault-related features among the speed invariant features. Through experiments on three bearing datasets, the effectiveness of the proposed method is validated and shown to have promise for bearing fault diagnostics under different operating conditions. This study also details the deployment of a physics-informed convolutional neural network model on an Industrial Internet of Things (IIoT) device, where edge computing gives users a real-time evaluation of bearing health.

Fault Diagnosis and Verification of Rolling Bearings Based on Optimal Resonance Demodulation with Deconvolution MRSVD

As one of the important aviation equipment components, rolling bearings will bring hidden dangers to the safety of aviation equipment once they fail. In aviation equipment, the sensor is far away from the bearing, and the collected signal of the rolling bearing is relatively weak. In this paper, the deconvolution algorithm is used to compensate the transfer function, and the optimal resonance demodulation algorithm based on the improved multi-resolution singular value decomposition (MRSVD) is constructed to determine the resonance frequency band, and then the bearing fault state is determined by the normalized squared envelope spectrum. The analysis results of the rolling bearing seed fault experiment show that this algorithm can adaptively extract the periodic fault pulse components under strong noise; compared with the normal spectral analysis and fast spectral kurtosis methods, this algorithm can completely extract the bearing fault characteristic frequency components, and effectively improve the bearing fault diagnosis accuracy.

A three-stage method for efficiently extracting the higher-order harmonics of bearing fault characteristic frequencies

Weak bearing fault feature extraction (FFE) research has previously focused on bearing fault signal of transient impulse extraction whereas higher harmonic feature extraction of fault feature frequency aspects are relatively less. While traditional envelope demodulation method has certain limitations to capture the rolling bearing fault characteristic frequency of higher harmonic. To this end, combining adaptive chirp mode decomposition (ACMD), improved maximum correlation kurtosis deconvolution (IMCKD), and 1.5-dimensional Teager energy cyclo-stationary spectrum (1.5-DTECS), in the current work we propose a three-stage defect detection system. The performance of the proposed method is evaluated by analyzing the three-stage FFE (STFFE) of multiple kinds of rolling bearing fault data. The findings reveal that the three-stage fault detection approach successfully suppresses noise, highlights the fault impact, and extracts the higher order harmonics of the bearing defect characteristic frequency more effectively. The research contributes to the field of bearing fault high harmonic component extraction and provides guidance on techniques related to the extraction of bearing impulse characteristic.

Research on Fault Feature Extraction Method of Rolling Bearing Based on SSA–VMD–MCKD

In response to the problem that nonlinear and non-stationary rolling bearing fault signals are easily disturbed by noise, which leads to the difficulty of fault feature extraction, to take full advantage of the superiority of variational mode decomposition (VMD) in noise reduction, and of maximum correlation kurtosis deconvolution (MCKD) in highlighting continuous pulses masked by noise, a method based on sparrow search algorithm (SSA), VMD, and MCKD is proposed, namely, SSA–VM–MCKD, for rolling bearing faint fault extraction. To improve the feature extraction effect, the method uses the inverse of the peak factor squared of the envelope spectrum as the fitness function, and the parameters to be determined in both algorithms are searched adaptively by SSA. Firstly, the parameter-optimized VMD is used to decompose the fault signal to obtain the intrinsic mode function (IMF) components, from which the optimal mode component is selected, and then the optimal component signal is deconvoluted by the parameter-optimized MCKD to enhance the periodic fault pulses in the optimal component signal, and finally extracts the rolling bearing fault characteristic frequency by envelope demodulation. Experiments on simulated signals and measured data show that the method can adaptively determine the parameters in VMD and MCKD, enhance the fault impact components in the signals, and effectively extract the fault characteristic frequencies of rolling bearings, with a success rate up to 100%, providing a new idea for rolling bearing fault feature extraction.

Bearing inner race fault detection and size estimation using the variable reluctance sensor

The variable reluctance sensor (VRS) has been widely used in the speed measurement system in the fields of automobile, helicopter, and ship, because of its high robustness. In recent years, most studies have verified the effectiveness of the application in rotor torsional vibration measurement and blade monitoring by the VRS. However, there is less research devoted to the VRS in bearing fault diagnosis, and its influencing mechanism between bearing faults and signal characteristics is not clear. In this paper, the raw signal of the VRS is used for bearing diagnosis. The mechanism of bearing partial fault signal response is analyzed by establishing the bearing inner ring fault model and the sensor signal response model. The characteristics of the VRS signal are given and verified by experiments. The results show that the gearwheel tooth-pass frequency is modulated by the bearing fault characteristic frequency, and there is an obvious double peak phenomenon in the high-frequency part. Moreover, the fault data with widths of 1 mm and 2 mm are analyzed by using the interval time of double peak. It is found that the fault sizes estimated are close to the actual defect size, and have small standard deviations. The original signal of the VRS has great potential in bearing diagnosis.

Research on Fault Feature Extraction of Rolling Bearing Based on dFIF

Aiming at the problems that the traditional adaptive mode decomposition method has low decomposition efficiency, poor ability of anti-mode mixing and decomposition accuracy, a rolling bearing fault feature recognition method based on direct fast iterative filtering (dFIF) and the crest factor of envelope spectrum is proposed. dFIF first decomposes the raw rolling bearing vibration signal into a set of intrinsic mode function (IMFs), then the optimal component is chosen based on the maximal crest factor of envelope spectrum, and finally the bearing fault characteristic frequency and its frequency multiplication are extracted using envelope demodulation analysis. It is demonstrated by relevant experimental data that the proposed method has efficient decomposition speed, accurate decomposition accuracy, and the accurate selection of effective components, and can effectively realize rolling bearing fault detection.

Extraction and enhancement of unknown bearing fault feature in the strong noise under variable speed condition

Rolling bearings often run under variable speed condition, in addition to constant speed condition. How to achieve the bearing fault diagnosis under variable speed condition has been an important and hot issue. Nevertheless, there are few works on bearing fault diagnosis under variable speed condition especially for the feature extraction of unknown fault. Thus, this paper proposes a method based on fractional Fourier transform (FRFT) and stochastic resonance (SR) to extract bearing fault features. First, we use FRFT filtering algorithm to extract fault formation from the original signal. Next, we apply zero centering and high pass filtering to the signal which contains the fault information. Since the separated fault information is usually relatively weak and is not easy to identify, SR is used to enhance the weak fault feature information. Finally, bearing fault is diagnosed by observing the fault characteristic frequency in the time-frequency distribution plane. The method can achieve the extraction of the bearing fault characteristic frequency in the unknown situation and meanwhile remove a lot of noise interference. The method has been validated by numerical simulations and experimental analyses, where the scratches on both outer race and rolling element can be diagnosed successfully. By comparison with previous methods, fast kurtogram and variable mode decomposition, fault features extracted by the proposed method are much clearer and more accurate. The method may provide reference for the application of fault diagnosis in engineering occasions.

A fault pulse extraction and feature enhancement method for bearing fault diagnosis

Generally, the transient characteristics of early bearing failure are not obvious. How to extract weak transient features is a big challenge. Dictionary learning has been successfully used to extract bearing fault features. However, the traditional dictionary learning is easy to fall into local optimum and cannot extract fault features from complex signals. And it often consumes huge computational costs. In order to solve the above problems, this paper proposes a fault pulse extraction and feature enhancement method for bearing fault diagnosis. Firstly, the bearing vibration signal is segmented in the time domain. Then this paper proposes a multi-scale alternating direction multiplier method for dictionary learning (MADMMDL) to extract fault impact signal from the segment signal. Finally, frequency spectrum averaging is used to enhance the bearing fault characteristic frequency. Through numerical simulation and rail transit transmission failure simulation experimental analysis, the feasibility of this method in bearing fault diagnosis is verified.

Weighted envelope spectrum based on the spectral coherence for bearing diagnosis

The key idea behind demodulation analysis for bearing diagnosis is to determine the fault-induced frequency band and directly detect the potential bearing fault characteristic frequency (FCF) in the demodulated spectrum. Till now, most demodulation methods are based on the optimal selection of only one informative frequency band. However, the unwanted in-band noise will be retained or some fault information may be ignored in the case of the discrete resonant frequency band or multiple informative frequency bands. To address the issue, a FCF-oriented criterion is proposed to determine all the informative frequency bands rather than only one specified frequency band. A new weighting vector is obtained to control the contribution of each spectral frequency in the demodulated spectrum. Subsequently, a weighted envelope spectrum (WES) is introduced by integrating the spectral correlation over the full spectral frequency band and assigning the new weighting vector on each spectral frequency. In this way, all frequency components with fault information are enhanced while other components are inhibited. Furthermore, expanded to the diagnosis of compound-fault, the FCF-oriented criterion can provide the different weighting vectors relevant to the different potential faults, and the separated fault features can be identified directly in the generated WESs. Finally, the advantages of WES over the traditional methods are testified by the simulated signal and experimental data.

Bearing Fault Feature Enhancement and Diagnosis Based on Statistical Filtering and 1.5-Dimensional Symmetric Difference Analytic Energy Spectrum

Bearing fault impulses are easily submerged by background noise, resulting in the inconspicuous fault feature and affecting the accuracy of the fault diagnosis. This paper presents a novel method for bearing the fault feature enhancement and diagnosis based on the statistical filtering and the 1.5-dimensional symmetric difference analytic energy operator (1.5D-SDAEO) to solve the problem. 1). The statistical filtering is used to filter the background noise under the standard distinction index. 2). The 1.5D-SDAEO is used to enhance the signal impulse, suppress the residual noise, and improve the SNR. 3). The dominant frequency in the energy spectrum is compared with the rolling bearing fault characteristic frequency to the fault diagnosis. The feasibility and the superiority of the presented method are verified by the simulation, engineering, and comparison experiments. All results show that the presented method can effectively enhance the fault feature and accurately diagnose the rolling bearing fault.

A Bearing Fault Diagnosis Method Based on Enhanced Singular Value Decomposition

For the two shortcomings of singular value decomposition (SVD), the determination of the reconstruction order and the poor noise reduction ability, an enhanced SVD is introduced in this article. The core ideas include: first, an efficient method to determine the reconstructed order of SVD and the relative-change rate of the singular envelope kurtosis is presented, composed of improved SVD (ISVD). Then, the method to select the optimal node of wavelet packet transform (WPT) by the criterion of envelope kurtosis maximum is presented, composed of improved WPT (IWPT). The flexible filter design and superior noise reduction abilities of the IWPT and the passband denoise ability of the ISVD are organicly combined to form enhanced singular value decomposition (E-SVD) method. In addition, an indicator is introduced to evaluate the performance of the results. First, the reconstructed signal is obtained by performing ISVD on the original signal. Second, IWPT is executed on the reconstructed signal to achieve the optimal node. Finally, the filtered signal is combined with the envelope power spectrum to extract the bearing fault characteristic frequency. The method's validity and superiority are verified by the analysis of simulated data and actual cases of rolling bearing.

An improved empirical wavelet transform method for rolling bearing fault diagnosis

Empirical wavelet transform (EWT) based on the scale space method has been widely used in rolling bearing fault diagnosis. However, using the scale space method to divide the frequency band, the redundant components can easily be separated, causing the band to rupture and making it difficult to extract rolling bearing fault characteristic frequency effectively. This paper develops a method for optimizing the frequency band region based on the frequency domain feature parameter set. The frequency domain feature parameter set includes two characteristic parameters: mean and variance. After adaptively dividing the frequency band by the scale space method, the mean and variance of each band are calculated. Sub-bands with mean and variance less than the main frequency band are combined with surrounding bands for subsequent analysis. An adaptive empirical wavelet filter on each frequency band is established to obtain the corresponding empirical mode. The margin factor sensitive to the shock pulse signal is introduced into the screening of empirical modes. The empirical mode with the largest margin factor is selected to envelope spectrum analysis. Simulation and experiment data show this method avoids over-segmentation and redundancy and can extract the fault characteristic frequency easier compared with only scale space methods.

Adaptive Asymmetric Real Laplace Wavelet Filtering and Its Application on Rolling Bearing Early Fault Diagnosis

The early fault of rolling bearing is weak and may not be readily detected. To overcome this issue, the present paper comes up with a rolling bearing fault‐diagnosing approach based on adaptive asymmetric real Laplace wavelet (ARLW) filtering, which is on the strength of water cycle optimization algorithm (WCA). Firstly, ARLW is introduced to filter the initial vibration signal since its waveform has the same asymmetric structure as the fault impact. Secondly, the optimum center frequency and bandwidth of ARLW is found out adaptively by applying the WCA through the proposed square envelope fault energy ratio (SEFER). Finally, envelope analysis is conducted to the narrowband signal obtained by the optimum ARLW filtering, and its envelope spectrum presents the rolling bearing fault characteristic frequency apparently. The proposed approach and two existing approaches are all tested in four signal analysis cases. The results are analyzed, and the conclusion is that the approach proposed by the present paper can detect the early fault of rolling bearing more accurately. The present research is valuable for diagnosing the early fault of rolling bearing.

Application of Human Cognitive Self Regulating Particle Swarm Optimization and Stochastic Resonance in Bearing Fault Diagnosis

This paper presents a bearing fault diagnosis algorithm based on human self regulating particle swarm optimization and stochastic resonance. The algorithm first sets up the objective function according to the stochastic resonance structural parameters a and b. Then the self regulating particle swarm optimization algorithm is used to optimize the objective function, and the optimized optimal values a and b are substituted into the system of variable scale stochastic resonance. Finally, the measured bearing vibration signal to noise reduction and spectrum analysis to find the bearing fault characteristic frequency. Experimental results show that this method is effective in bearing fault diagnosis.