Envelope Spectrum Analysis Research Articles

Rolling bearing fault diagnosis method based on SSA-IWT-EMD

Aiming at the problem of insufficient wavelet threshold noise reduction and unclear extraction of characteristic frequency of EMD decomposition, a rolling bearing fault diagnosis method based on SSA-IWT-EMD is proposed. Two adjustment factors are introduced to propose an improved threshold function (IWT), which overcomes the shortcomings of traditional soft and hard thresholds, and the sparrow search optimization algorithm (SSA) is used to globally optimize its parameters to achieve rolling bearing signal noise reduction. A comprehensive index P is proposed to select and reconstruct the components generated by empirical mode decomposition (EMD) to highlight the fault characteristic information of the signal. Envelope spectrum analysis is used to realize bearing fault diagnosis. Simulation and measurement results verify the effectiveness of the proposed method; at the same time, compared with the method of selecting components with a single index and the literature method, it is shown that the comprehensive index P and the proposed method have stronger noise reduction and feature extraction capabilities, and the envelope spectrum amplitude and frequency doubling components are more obvious, which can better realize the fault diagnosis of rolling bearings.

Rotating machinery early fault detection integrating variational mode decomposition and multiscale singular value decomposition

Abstract Security and reliability are important issues that must be paid attention to during the operation of rotating machinery. If defects can be found in the early stage, there will be enough time to take maintenance measures and realize the stable operation of equipment. However, the presence of noise, shaft rotation signals, gear meshing signals, and other interfering factors often obfuscate fault signals, rendering the early detection of defects an arduous undertaking. Against this backdrop, this study presents an advanced approach for early defect detection, integrating the virtues of variational mode decomposition (VMD) and multiscale singular value decomposition (MSVD). Initially, a novel evaluation index is constructed by combining envelope entropy and envelope spectrum sparsity. Based on this a method is proposed to adaptively determine the critical parameters of VMD, enabling the adaptive decomposition of vibration signals into a series of modal components. The optimal sensitive components are then discerned utilizing the characteristic frequency intensity coefficient index. Subsequently, to address the limitations of single VMD methods in effectively suppressing low-frequency noise, the MSVD method is proposed for effective noise reduction, which reconstructs the signal after SVD of the signal within each segment through the operation of successive signal segmentation. Ultimately, envelope spectrum analysis is conducted on the reconstructed signal, facilitating the precise extraction of fault characteristic frequency information and enabling early fault identification. The efficacy of this novel methodology is evaluated through simulations and actual vibration signals, successfully discerning early faults afflicting rotating machinery.

Research on ACMD-ICYCBD method for rolling bearing fault feature extraction

Aiming at the difficulty in obtaining the eigenfrequency of the vibration component of rolling bearing faults in a strong background noise environment and the problem of extraction efficiency, the adaptive chirp mode decomposition (ACMD) combined with Improved maximum second-order cyclostationary blind deconvolution (ICYCBD) fault feature extraction algorithm is proposed. Firstly, to improve the signal-to-noise ratio, the original signal is adaptively decomposed using the ACMD method, and the optimal components are selected based on the principle of maximizing the correlation gini coefficient index. Secondly, to improve the accuracy of parameter setting and extraction efficiency, an improved CYCBD method is proposed to estimate the cyclic frequency set of CYCBD using the proposed enhanced energy harmonic product spectrum (EEHPS) method for the optimal components, the envelope spectrum peak factor index is improved by proposing the envelope spectral period pulse factor (EPPF) index, and the filtering length of the CYCBD is selected adaptively using the step search to obtain the optimized filtered signal. Finally, the envelope spectrum analysis is carried out to extract the fault information accurately. The simulation signals and experimental data show that the method can quickly and accurately extract the fault characteristics of rolling bearings under strong background noise, and the comparison with other methods shows the effectiveness and superiority of the proposed method.

Concept and Application of Envelope Spectrum Analysis in the Field of Vibration Signal Processing

Concept and Application of Envelope Spectrum Analysis in the Field of Vibration Signal Processing

Separation and Extraction of Compound-Fault Signal Based on Multi-Constraint Non-Negative Matrix Factorization.

To solve the separation of multi-source signals and detect their features from a single channel, a signal separation method using multi-constraint non-negative matrix factorization (NMF) is proposed. In view of the existing NMF algorithm not performing well in the underdetermined blind source separation, the β-divergence constraints and determinant constraints are introduced in the NMF algorithm, which can enhance local feature information and reduce redundant components by constraining the objective function. In addition, the Sine-bell window function is selected as the processing method for short-time Fourier transform (STFT), and it can preserve the overall feature distribution of the original signal. The original vibration signal is first transformed into time-frequency domain with the STFT, which describes the local characteristic of the signal from the time-frequency distribution. Then, the multi-constraint NMF is applied to reduce the dimensionality of the data and separate feature components in the low dimensional space. Meanwhile, the parameter WK is constructed to filter the reconstructed signal that recombined with the feature component in the time domain. Ultimately, the separated signals will be subjected to envelope spectrum analysis to detect fault features. The simulated and experimental results indicate the effectiveness of the proposed approach, which can realize the separation of multi-source signals and their fault diagnosis of bearings. In addition, it is also confirmed that the proposed method, juxtaposed with the NMF algorithm of the traditional objective function, is more applicable for compound fault diagnosis of the rotating machinery.

Iterative feature mode decomposition: a novel adaptive denoising method for mechanical fault diagnosis

Remaining useful life prediction of rolling bearings highly relies on feature extraction of signals. The use of denoising algorithms helps to better eliminate noise and extract features, thereby constructing health indicators to predict remaining useful life. This paper proposes a novel adaptive denoising method based on iterative feature mode decomposition (IFMD) to accurately and efficiently extract fault features. The feature mode decomposition (FMD) employs correlation kurtosis (CK) as the objective function for iterative filter bank updates, enabling rapid identification of fault features. To achieve IFMD, the sparrow search algorithm combines sine-cosine algorithm and cauchy variation (SCSSA) to optimize two key parameters in FMD. During the continuous iteration process of the SCSSA algorithm, filter length and number of modes were determined. IFMD does not require empirical setting of initial parameters. During iterative process, the signal is accurately decomposed and the noise is eliminated. Compared with other optimization algorithms, SCSSA has obvious advantages in iterative rate and global optimization. The envelope spectrum feature energy ratio (ES-FER) is used to select decomposed modes, and the mode with the largest ES-FER is chosen as the optimal mode. Bearing fault diagnosis is realized by envelope spectrum analysis of the optimal mode. The numerical simulations and experimental verifications both validate the effectiveness and superiority of the proposed IFMD in mechanical fault diagnosis.

Fault feature extraction method based on maximum envelope spectrum PFGI2 and empirical wavelet transform

Fast kurtogram (FK) is an efficient method for processing non-stationary signals, widely recognized by scholars as a rapid and effective approach for fault diagnosis. However, it has limitations in distinguishing between periodic pulse and random interference pulses due to the drawbacks in its frequency band segmentation methods and the inherent shortcomings of the kurtosis index itself. To address this, this paper proposes a fault feature extraction method based on the maximum envelope spectrum power function-based Gini indices (PFGI2) and empirical wavelet transform. This method, inspired by the concept of FK, constructs a series of band-pass filters following the principles of empirical wavelet decomposition. It applies envelope spectrum analysis to a series of sub-bands and calculates the PFGI2 value for each, to identify the optimal sub-band. The effectiveness of the proposed method is validated through simulations of vibration signals and experimental data.

Rolling Bearing Fault Feature Extraction Method based on SSA-VMD and MOMEDA

To address the challenge of extracting bearing fault features, this study proposes a new rolling bearing fault feature extraction method based on the Sparrow Search Algorithm (SSA) to optimize Variational Mode Decomposition (VMD) and Multipoint Optimal Minimum Entropy Deconvolution with Convolution Adjustment (MOMEDA). Firstly, SSA is employed to identify optimal parameters in VMD, followed by the utilization of correlation coefficients and kurtosis to filter relevant Intrinsic Mode Function (IMF) components. Subsequently, MOMEDA is applied to denoise the reconstructed signal, mitigating the interference caused by pulse fault signals. Finally, the envelope spectrum analysis is conducted on the denoised signal. Experimental results demonstrate the efficacy of the proposed method in extracting fault features and mitigating noise interference.

Smart Sensor-Based Monitoring Technology for Machinery Fault Detection.

Rotary machines commonly use rolling element bearings to support rotation of the shafts. Most machine performance imperfections are related to bearing defects. Thus, reliable bearing condition monitoring systems are critically needed in industries to provide early warning of bearing fault so as to prevent machine performance degradation and reduce maintenance costs. The objective of this paper is to develop a smart monitoring system for real-time bearing fault detection and diagnostics. Firstly, a smart sensor-based data acquisition (DAQ) system is developed for wireless vibration signal collection. Secondly, a modified variational mode decomposition (MVMD) technique is proposed for nonstationary signal analysis and bearing fault detection. The proposed MVMD technique has several processing steps: (1) the signal is decomposed into a series of intrinsic mode functions (IMFs); (2) a correlation kurtosis method is suggested to choose the most representative IMFs and construct the analytical signal; (3) envelope spectrum analysis is performed to identify the representative features and to predict bearing fault. The effectiveness of the developed smart sensor DAQ system and the proposed MVMD technique is examined by systematic experimental tests.

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.

Adaptive minimum noise amplitude deconvolution and its application for early fault diagnosis of rolling bearings

To address the challenge of detecting early faults in rolling bearings, where weak fault features are occasionally obscured by background noise, an innovative early fault diagnosis method based on adaptive minimum noise amplitude deconvolution (MNAD) is introduced. Initially, a correlation Gini index function is defined to estimate the fault period, while leveraging the iterative advantages of MNAD to progressively approach the true fault period. This resolution effectively overcomes the requirement of prior knowledge regarding the fault period, thus reducing the number of input parameters. Subsequently, a composite index, combining square envelope Gini index and square envelope entropy, is constructed as the fitness function. The sand cat swarm optimization algorithm is employed to adaptively determine the optimal noise ratio and filter length for deconvolution, ensuring the acquisition of the finest filtered signal. Ultimately, envelope spectrum analysis is conducted on the filtered signal to extract fault features and facilitate early fault diagnosis. The effectiveness of the proposed method is validated through simulated and experimental data, highlighting its superior feature extraction capabilities and robustness compared to original MNAD and other sophisticated blind deconvolution methods.

A novel performance degradation assessment method for rotating machinery based on the fault information and the dynamic simulation

The performance degradation assessment (PDA) of key components such as gears and rolling bearings is the core technology of prognostics and health management for rotating machinery. Most existing PDA methods may have two deficiencies: (1) the assessment indicator constructed does not consider capturing fault characteristics directly; (2) feature selection is generally based on the measured data of different fault levels, which is difficult to obtain in actual processes; moreover, the selection results lack universality and are difficult to extend to other equipment. To address these issues, this paper proposes a novel PDA method based on fault information and dynamic simulation. First, anomaly detection is performed using four well-known indicators in combination with Mahalanobis distance. Secondly, fault identification is performed using envelope spectrum analysis on anomaly signals to determine the fault type, e.g. gear fault or outer race fault. Thirdly, based on the fault type information, the candidate feature set including fault-domain indicators is selected based on the established dynamic simulation signals to obtain a preliminary assessment vector for the first stage. The stability of the fault domain indicators which capture fault characteristics directly is tested through actual measured normal data. It is used as the second stage of selecting to obtain the assessment vector. Finally, the PDA indicator is calculated based on the assessment vector and Mahalanobis distance. Four experiment case studies demonstrate the proposed PDA method can effectively isolate faults with different defect sizes as well as track the whole performance degradation. The above analysis indicates that the proposed PDA method is expected to be used for the actual rotating machinery.

Early pitting fault detection for polymer gears using kurtosis-VMD based condition indicators

The vibration signals of a polymer gear are considerably weak and susceptible to ambient noise at the early stage of the fault, which makes the fault difficult to detect. Efficient detection of an early fault in a polymer gear may improve the operation safety of the machinery system that utilizes it for power transmission. This study introduces an innovative approach for the early detection of pitting faults in polymer gears, utilizing condition indicators (CIs) derived from kurtosis-variational mode decomposition (VMD). First, the vibration signal of the polymer gear is decomposed using VMD into several components. Second, the sensitive components are selected to construct a new signal from the first two largest kurtosis values. Third, the CIs are extracted from newly constructed signals, and envelope spectrum analysis is performed. It is observed from the results that the kurtosis-VMD based CIs are effective in the early pitting fault detection of polymer gears. Finally, it is found that the proposed method performs better in all operating conditions considered in the experiment, compared with raw signal and kurtosis-empirical mode decomposition (EMD) based analysis. The proposed method’s response to noise is also explored. Furthermore, the proposed method is compared with the existing time synchronous averaging (TSA), difference, and residual methods.

A novel joint denoising method for gear fault diagnosis with improved quaternion singular value decomposition

Singular value decomposition (SVD) has drawn increasing attention in recent years as an effective signal noise reduction method. However, it is inapplicable to multivariate signals with abundant fault information. Existing quaternion singular value decomposition (QSVD) can decompose multivariate signals simultaneously, but the methods based on QSVD dependent on the embedding dimension and reconstructed components order seriously, and they are not suitable to noisy signals. To solve the problem, a novel joint denoising method improved quaternion singular value decomposition (IQSVD) is proposed, which can determine two parameters adaptively. Firstly, to select the embedding dimension, the improved power spectral density (IPSD) is proposed with considering frequency features and time-domine traits together. And then the periodic intensity (PI) is used to determine the reconstructed components by searching the component composing the most abundant periodic part. Finally, combined with envelope spectrum analysis, the gear fault is diagnosed. The results of the gear simulated and experimental multivariate signals verify the effectiveness of proposed method.

Legendre Multiwavelet Transform and Its Application in Bearing Fault Detection

Bearing failures often result from compound faults, where the characteristics of these compound faults span across multiple domains. To tackle the challenge of extracting features from compound faults, this paper proposes a novel fault detection method based on the Legendre multiwavelet transform (LMWT) combined with envelope spectrum analysis. Additionally, to address the issue of identifying suitable wavelet decomposition coefficients, this paper introduces the concept of relative energy ratio. This ratio assists in identifying the most sensitive wavelet coefficients associated with fault frequency bands. To assess the performance of the proposed method, the results obtained from the LMWT method are compared with those derived from the empirical wavelet transform (EWT) method using different datasets. Experimental findings demonstrate that the proposed method exhibits more effective frequency spectrum segmentation and superior detection performance across various experimental conditions.

A Bearing Fault Diagnosis Strategy Based on Complete Ensemble Empirical Mode Decomposition with Adaptive Noise and Correlation Coefficient Method

In response to the difficulties in extracting fault features from bearing vibration signals and the serious mode mixing and endpoint effects in traditional empirical mode decomposition (EMD) methods, a bearing fault diagnosis strategy combining complete ensemble empirical mode decomposition with adaptive noise(CEEMDANAN) and correlation coefficient method is proposed. This method fully combines the advantages of CEEMDANAN algorithm and correlation coefficient method in signal random detection. Firstly, CEEMDANAN decomposition is performed on the bearing vibration signals to obtain a series of intrinsic mode function (IMF) components. Select IMF components with high correlation coefficients for Hilbert envelope spectrum analysis to achieve bearing fault diagnosis. The experimental results show that the proposed method can effectively achieve fault diagnosis of bearings.

A novel spectral coherence-based weighted envelope spectrum analysis method for bearing fault diagnosis

Spectral coherence (SCoh) consists of spectral and cyclic frequencies and exhibits unique merits in simultaneously revealing the resonance frequency band and the fault characteristic frequency (FCF) of bearing signals. Most SCoh-based methods only consider the spectral frequency information, while the cyclic frequency information is ignored. However, the fault information and interference components are difficult to distinguish when only the spectral frequency is considered. To address this challenge, a novel bidirectional weighted enhanced envelope spectrum (BWEES) analysis method is proposed in this paper. First, an improved spectral weighting method is developed, which is conducted in the spectral frequency direction to enhance the resonance frequency band that carries the fault information. An autocorrelation function is exploited to reveal the cyclic information hidden in noises and appropriate weights are assigned to the spectral frequencies according to the magnitudes of autocorrelation values. Second, a cyclic weighting function is designed, which is operated in the cyclic frequency direction to enhance the FCF and suppress noise interference. The cyclic frequency components with the highest magnitudes are selected as a basis to reconstruct the one-dimensional cyclic frequency map for assigning different weights. Finally, the two-dimensional weighted bivariable map is constructed and then converted into spectral coherence to reveal the fault features. The BWEES is tested by simulation signals and experimental data, and compared with four state-of-art methods. In particular, the kurtosis values of BWEES in four different cases are 7.637, 12.831, 15.269, and 80.269, which are higher than other methods. The Gini index values of BWEES in four different cases are 0.866, 0.812, 0.424, and 0.306, which are also the largest. The above numerical results show that BWEES can achieve better performance.

A Condition-Monitoring Method for Rolling Bearings Based on Dynamic Asynchronous Peak-Factor Ratios

In response to issues such as the lack of capability for timely early warning and the difficulty in monitoring the status of rolling bearings, a condition-monitoring method for rolling bearings based on the Honey Badger Algorithm (HBA) for optimizing dynamic asynchronous periods is proposed. This method is founded on the peak factor and involves comparing peak factors at different periods to construct a dynamic asynchronous peak-factor-ratio-monitoring index, which is then optimized using the HBA. Simulated experiments were carried out using the XJTU-SY dataset. The results indicate that, compared to the early warning times defined by international standards, the warning times provided using this method are consistently over 33 min in advance within the test dataset. Additionally, an envelope spectrum analysis of the warning data confirms the existence of early faults. This demonstrates that the monitoring indicator developed in this paper is capable of delivering earlier and more accurate early fault warnings and condition monitoring for rolling bearings.

Early Fault Detection of Rolling Bearings Based on Time-Varying Filtering Empirical Mode Decomposition and Adaptive Multipoint Optimal Minimum Entropy Deconvolution Adjusted.

Due to the early formation of rolling bearing fault characteristics in an environment with strong background noise, the single use of the time-varying filtering empirical mode decomposition (TVFEMD) method is not effective for the extraction of fault characteristics. To solve this problem, a new method for early fault detection of rolling bearings is proposed, which combines multipoint optimal minimum entropy deconvolution adjusted (MOMEDA) with parameter optimization and TVFEMD. Firstly, a new weighted envelope spectrum kurtosis index is constructed using the correlation coefficient and envelope spectrum kurtosis, which is used to identify the effective component and noise component of the bearing fault signal decomposed by TVFEMD, and the intrinsic mode function (IMF) containing rich fault information is selected for reconstruction. Then, a new synthetic impact index (SII) is constructed by combining the maximum value of the autocorrelation function and the kurtosis of the envelope spectrum. The SII index is used as the fitness function of the gray wolf optimization algorithm to optimize the fault period, T, and the filter length, L, of MOMDEA. The signal reconstructed by TVF-EMD undergoes adaptive filtering using the MOMEDA method after parameter optimization. Finally, an envelope spectrum analysis is performed on the signal filtered by the adaptive MOMEDA method to extract fault feature information. The experimental results of the simulated and measured signals indicate that this method can effectively extract early fault features of rolling bearings and has good reliability. Compared to the classical FSK, MCKD, and TVFEMD-MOMEDA methods, the first-order correlated kurtosis (FCK) and fault feature coefficient (FFC) of the filtered signal obtained using the proposed method are the largest, while the sample entropy (SE) and envelope spectrum entropy (ESE) are the smallest.

Unsupervised transfer learning for intelligent health status identification of bearing in adaptive input length selection

Input length (IL) is an important element in transfer learning (TL) network for intelligent health status identification of bearing (IHSIB). However, fixed IL are used in most studies. In this paper, a TL network via adaptive IL selection module for IHSIB (AILTLN) is proposed, which includes adaptive IL module, feature extractor module, health status identification module, and domain discriminator module. Firstly, an adaptive IL selection module based on envelope spectrum analysis is proposed. The module varies with bearing structure, motor speed, and sampling frequency. Secondly, group convolution, transposed convolution, and instant normalization are constructed in feature extractor. Thirdly, softmax cross-entropy loss function and maximum mean discrepancy are used for health status identification and domain alignment. The TL results of open bearing dataset and high-speed train bearing experiment show that AILTLN is better than the other existing methods in the TL of IHSIB. The ablation study shows the reuse of low-dimensional features and the adaptive IL help to improve to the accuracy of the proposed method.