Fast Kurtogram Research Articles

An enhanced cyclostationary method and its application on the incipient fault diagnosis of induction motors

The cyclostationary analysis techniques have been extensively explored for the purpose of fault detection in rotating machinery. However, there are still huge challenges because of both limited detection frequency range and low fault identification accuracy. This paper proposes an improved cyclostationary method to enhance incipient fault features. Firstly, the continuous wavelet transform is used to accurately locate important frequency bands, and the fault modulation mechanism or fast kurtogram can be adopted to design the optimal wavelet transform scale factor. Secondly, the Teager-Kaiser energy operator is improved to be used in the frequency domain for the weak fault feature enhancement. Finally, fault features are presented in the cyclic frequency domain through spectral coherence and enhanced envelope spectrum. The proposed method is verified through both numerical simulation and experiments, including incipient half-broken rotor bar, and rolling bearing outer race faults in induction motors.

Multivariable signal processing algorithm for identification of power quality disturbances

This paper investigated a multi-variable power quality disturbance identification algorithm (MPQDIA) applying the Stockwell transform (ST), Hilbert transform (HT) and rule based decision tree (RBDT). Voltage waveform with associated power quality disturbances (PQDs) are realized by the mathematical formulation in compliance with standard IEEE-1159. These voltage signals with PQDs are processed applying the ST and HT for computing the index for power quality identification (IPI) and index for power quality location (IPL). IPI and IPL plots effectively identify and locate the PQDs of simple nature and multiple nature. Four features are extracted from data sets of IPI and IPL. These features are considered as input for the RBDT to classify the PQDs. MPQDIA is effectively tested for identification, to locate and to classify the total 21 PQDs of simple as well as multiple natures. Performance of MPQDIA is analysed in terms of rightly and wrongly categorized PQDs in noise free environment and considering noise of 20 dB SNR (signal to noise ratio) level. Efficiency of MPQDIA is compared with the ST and RBDT based algorithm, WT based fast Kurtogram and decision tree powered algorithm, and ST and RBDT powered method in terms of classification accuracy, noise level for which performance is not affected, effectiveness to detect the simple nature and multiple nature PQDs. It is established that MPQDIA effectively recognizes the PQDs on a real time power system network. Study is performed with the help of MATLAB software.

Advanced Detection of REB Defects through Sound Emission using Envelope Analysis and Spectral Kurtosis

Rolling elements bearings (REBs) are considered between the critical components in rotating machinery and their failures can provoke severe damage to the machine. Monitoring the condition of these components is essential to ensure the availability of the machine and improve its reliability. This article presents a low-cost acoustic approach based on the smartphone to monitor the bearing components. This approach stands on the use of a stethoscope connected to the smartphone via input Jack, to acquire the acoustic emission of the bearing at specific points. Firstly, the Hilbert transform (HT) was performed on acoustic signals to derive the envelope signal. Then, the Fast Fourier Transform (FFT) was applied to calculate the spectrum of the envelope signal. In the case of a noisy envelope spectrum where the fault signature is not noticeable, the Spectral kurtosis (SK) will be implemented to design an optimal filter to filter the acoustic signal using the Fast Kurtogram. After the filtering step, the process will be repeated to calculate the envelope spectrum. This study evaluates a defective bearing with a small inner race fault under different operating speeds (648, 1240, and 1816 rpm). Finally, the experimental results indicate that the proposed approach shows good results compared to the theoretical results for the early detection and identification of bearing failures. Furthermore, this technique is highly cost-effective and practical for rolling bearing condition monitoring.

Identification of Multiple Defects from Rail Vibration Signals Based on Fast Kurtogram

Identification of Multiple Defects from Rail Vibration Signals Based on Fast Kurtogram

A new fault diagnosis method for wheelset-bearing system based on VME convergence tendency diagram

Aiming at the difficulty of accurate diagnosis of wheelset-bearing system composite faults, a multi-fault feature extraction method based on self-adaptive variational mode extraction (SAVME) was proposed. Variational mode extraction (VME) can extract a specific sub-signal from a multi-component signal. The key to the success of this algorithm is to determine appropriate initial parameters in advance, including initial center frequency (ICF) and penalty factor. To determine the key parameters of VME adaptively, the convergence characteristics of VME are analyzed deeply, and the VME convergence tendency diagram is proposed creatively according to the trend of the iterative curve of the center frequency of the desired mode. By analyzing the test signal with the VME convergence tendency diagram, the number of main latent sub-signals in the test signal and the ICF of each sub-signal corresponding to the VME can be determined efficiently. Then, according to the position of the ICF of each sub-signal in the frequency domain, the empirical formula of the penalty factor is used to quickly obtain the appropriate penalty factor. The proposed SAVME method not only improves the parameter selection adaptability of the traditional VME algorithm but also extends the VME algorithm to the field of multi-fault diagnosis. By analyzing the simulated signal and two experimental signals, the effectiveness of the SAVME algorithm is verified. Compared with the fast kurtogram method and the adaptive variational mode decomposition method, the proposed method is more accurate and superior in the multi-fault feature extraction of the wheelset-bearing system.

Optimal periodicity-enhanced group sparse for bearing incipient fault feature extraction

Efficient and automatic fault feature extraction of rotating machinery, especially for incipient faults is a challenging task of great significance. In this article, an optimal periodicity-enhanced group sparse method is proposed. Firstly, a period sequence determination method without any prior information is proposed, and the amplitude is calculated by the numerical characteristics of the vibration signal to obtain period square waves. Secondly, the periodic square waves are embedded into the group sparse algorithm, to eliminate the influence of random impulses, and intensify the periodicity of the acquisition signal. Thirdly, a fault feature indicator reflecting both signal periodicity and sparsity within and across groups is proposed as the fitness of the marine predator algorithm for parameter automatic selection. In addition, the method proposed is evaluated and compared by simulation and experiment. The results show that it can effectively extract incipient fault features and outperforms traditional overlapping group shrinkage and Fast Kurtogram.

A signal-filtering and feature-enhancement method based on ensemble local mean decomposition and adaptive morphological filtering

The bearing fault signals from the spindle motors of computer numerical control machines are complex and non-linear due to being coupled to multiple subsystems. The complexity of industrial signals, with increased industrial noise, and the difference in fault features in different life cycles and different individual signals bring great challenges for fault feature extraction. In this paper, a signal-filtering and feature-enhancement method based on an ensemble local mean decomposition and adaptive morphological filtering (ELMD-AMF) method is proposed. First, the original vibration signal of the bearing is reconstructed by ELMD to reducing interference from background noise. Next, an improved feature-enhancement process based on AMF is constructed, a particle swarm optimization with maximum-weighted spectral kurtosis as an optimization objective is used to adaptively construct the size of the structural element, and a morphology hat product operator one is adapted to extract the periodic impulse features. Finally, the effectiveness of the method is proved by using an actual three-phase induction motor matched with an NTN ceramic bearing and a FAG metal bearing, respectively. Further, compared with minimum entropy deconvolution and fast kurtogram methods, the result proves that the proposed method has better performance for both early-failure and late-failure scenarios under real-world engineering conditions.

Stochastic Resonance with Parameter Estimation for Enhancing Unknown Compound Fault Detection of Bearings.

Although stochastic resonance (SR) has been widely used to enhance weak fault signatures in machinery and has obtained remarkable achievements in engineering application, the parameter optimization of the existing SR-based methods requires the quantification indicators dependent on prior knowledge of the defects to be detected; for example, the widely used signal-to-noise ratio easily results in a false SR and decreases the detection performance of SR further. These indicators dependent on prior knowledge would not be suitable for real-world fault diagnosis of machinery where their structure parameters are unknown or are not able to be obtained. Therefore, it is necessary for us to design a type of SR method with parameter estimation, and such a method can estimate these parameters of SR adaptively by virtue of the signals to be processed or detected in place of the prior knowledge of the machinery. In this method, the triggered SR condition in second-order nonlinear systems and the synergic relationship among weak periodic signals, background noise and nonlinear systems can be considered to decide parameter estimation for enhancing unknown weak fault characteristics of machinery. Bearing fault experiments were performed to demonstrate the feasibility of the proposed method. The experimental results indicate that the proposed method is able to enhance weak fault characteristics and diagnose weak compound faults of bearings at an early stage without prior knowledge and any quantification indicators, and it presents the same detection performance as the SR methods based on prior knowledge. Furthermore, the proposed method is more simple and less time-consuming than other SR methods based on prior knowledge where a large number of parameters need to be optimized. Moreover, the proposed method is superior to the fast kurtogram method for early fault detection of bearings.

Iterative HOEO fusion strategy: a promising tool for enhancing bearing fault feature

As parameter independent yet simple techniques, the energy operator (EO) and its variants have received considerable attention in the field of bearing fault feature detection. However, the performances of these improved EO techniques are subjected to the limited number of EOs, and they cannot reflect the non-linearity of the machinery dynamic systems and affect the noise reduction. As a result, the fault-related transients strengthened by these improved EO techniques are still subject to contamination of strong noises. To address these issues, this paper presents a novel EO fusion strategy for enhancing the bearing fault feature nonlinearly and effectively. Specifically, the proposed strategy is conducted through the following three steps. First, a multi-dimensional information matrix (MDIM) is constructed by performing the higher order energy operator (HOEO) on the analysis signal iteratively. MDIM is regarded as the fusion source of the proposed strategy with the properties of improving the signal-to-interference ratio and suppressing the noise in the low-frequency region. Second, an enhanced manifold learning algorithm is performed on the normalized MDIM to extract the intrinsic manifolds correlated with the fault-related impulses. Third, the intrinsic manifolds are weighted to recover the fault-related transients. Simulation studies and experimental verifications confirm that the proposed strategy is more effective for enhancing the bearing fault feature than the existing methods, including HOEOs, the weighting HOEO fusion, the fast Kurtogram, and the empirical mode decomposition.

Enhanced generalized nonlinear sparse spectrum based on dual-tree complex wavelet packet transform for bearing fault diagnosis

The generalized nonlinear sparse spectrum (GNSS), as an improved fast kurtogram (FK) method, effectively suppresses the interference of abnormal signals through nonlinear preprocessing and sparse enhancement. However, the GNSS method inherits the shortcoming of the traditional FK method, using finite impulse response filters to process nonstationary signals, which limits the accuracy of fault extraction. Therefore, more precise filters should be developed to further improve the performance of fault features. Inspired by this, this paper introduces the dual-tree complex wavelet packet transform (DTCWPT) into the sparse spectrum, and proposes an enhanced generalized nonlinear sparse spectrum (EGNSS) for bearing fault diagnosis. Firstly, nonlinear preprocessing is performed on the input signal to weaken the interference of abnormal impacts. Secondly, the generalized pq-mean value of each subband obtained by DTCWPT is calculated. Finally, the sparse spectrum is constructed and the signal reconstruction is performed on the frequency band where the maximum generalized pq-mean value is located for the envelope analysis. Simulation signals and experimental bearing fault signals have been applied to demonstrate the superiority of the proposed EGNSS in improving fault performance and accuracy.

Optimized weights spectrum autocorrelation: A new and promising method for fault characteristic frequency identification for rotating Machine fault diagnosis

Since fault characteristic frequencies (FCFs) and their harmonics are closely connected with specific fault types of rotating machines, identification of FCFs and their harmonics is a very crucial step for signal processing-based rotating machine fault diagnosis. Nowadays, Hilbert transform (HT) based square envelope spectrum (SES) and spectral coherence (SC) based SES are two main tools for FCF identification. Since the HT demodulates signals by calculating envelope signals in the time domain and the SC is based on the temporal instantaneous autocorrelation function of demodulated signals, the temporal waveform of a demodulated signal must be purified by using fault signature extraction methods, e.g., fast kurtogram, blind deconvolution, and their variants, etc. However, it has been extensively reported that these fault signature extraction methods are prone to be affected by interference components such as impulsive noise. Unlike the HT and SC which demodulate from the time domain, this paper aims to demodulate signals from the frequency domain to identify FCFs and their harmonics for rotating machine fault diagnosis. Firstly, it is demonstrated that Fourier spectrum autocorrelation is possible to indicate FCFs and their harmonics. Nevertheless, a troublesome problem is that interference spectral lines and noise spectral lines of real-world signals in the frequency domain will severely affect the performance of the Fourier spectrum autocorrelation. To solve such problem, this paper introduces a recently developed optimized weights spectrum (OWS) and innovatively designs an adaptive threshold method to respectively eliminate an influence of interference spectral lines and noise spectral lines. Thus, a new FCF identification method named optimized weights spectrum autocorrelation (OWSAC) is accordingly proposed. One main merit of the proposed OWSAC is that it does not need any fault signature extraction methods to do signal preprocessing. Two experimental case studies respectively on incipient bearing and gearbox diagnosis validate the effectiveness of the proposed OWSAC. The proposed OWSAC can achieve satisfactory performance respectively in two case studies and it is superior to five methods including HT-based SES, SC-based SES, optimized SES, fast kurtogram guided SES, and Fourier spectrum autocorrelation.

Harmonic-Gaussian double-well potential stochastic resonance with its application to enhance weak fault characteristics of machinery

Noise would give rise to incorrect filtering frequency-band selection in signal filtering-based methods including fast kurtogram, teager energy operators and wavelet packet transform filters and meanwhile would result in incorrect selection of useful components and even mode mixing, end effects, etc., in signal decomposition-based methods including empirical mode decomposition, singular value decomposition and local mean decomposition. On the contrary, noise in stochastic resonance (SR) is beneficial to enhance weak signals of interest embedded in signals with strong background noise. Taking into account that nonlinear systems are crucial ingredients to activate the SR, here we investigate the SR in the cases of overdamped and underdamped harmonic-Gaussian double-well potential systems subjected to noise and a periodic signal. We derive and measure the analytic expression of the output signal-to-noise ratio (SNR) and the steady-state probability density (SPD) function under approximate adiabatic conditions. When the harmonic-Gaussian double-well potential loses its stability, we can observe the antiresonance phenomenon, whereas adding the damped factor into the overdamped system can change the stability of the harmonic-Gaussian double-well potential, resulting that the antiresonance behavior disappears in the underdamped system. Then, we use the overdamped and underdamped harmonic-Gaussian double-well potential SR to enhance weak useful characteristics for diagnosing incipient rotating machinery failures. Theoretical and experimental results show that adjusting both noise intensity and system parameters can activate overdamped and underdamped harmonic-Gaussian double-well potential SR in which there is a bell-shaped peak for the SNR. Additionally, the underdamped harmonic-Gaussian double-well potential SR is independent of frequency-shifted and rescaling transform to process large machine parameter signals and outperforms the overdamped one. Finally, comparing the advanced robust local mean decomposition (RLMD) method based on signal decomposition and the wavelet transform method based on noise cancellation or infogram method based on signal filtering, the overdamped or underdamped harmonic-Gaussian double-well potential SR methods characterize a better performance to detect a weak signal. Fault characteristics in the early stage of failures are successful in improving the incipient fault characteristic identification of rolling element bearings.

Weighted envelope spectrum based on reselection mechanism and its application in bearing fault diagnosis

As a powerful algorithm, fast spectral correlation (Fast-SC) is widely used in bearing fault diagnosis. However, the interference of strong background noise and the existence of multiple fault-related frequency bands make it difficult to diagnose bearing faults using enhanced envelope spectrum and improved envelope spectrum on the basis of Fast-SC. To alleviate the problem, fast kurtogram is imitated to divide the spectral frequency bands; then, the threshold-based diagnostic feature (TDF) of each integration band is calculated to guide the weighting function of the corresponding level; finally, weighted envelope spectrum with the largest TDF is determined as the output; this process is called the reselection mechanism. Simulation and experimental results indicate that the design of weighting function highlights the contribution of the fault-related frequency bands, and the reselection mechanism further improves its performance.

Optimal Demodulation Band Extraction Method for Bearing Faults Diagnosis Based on Weighted Geometric Cyclic Relative Entropy

Optimal demodulation band extraction is a significant step in rolling bearing fault analysis. However, existing methods, primarily based on global indexes and neglecting negative local outliers, cannot identify compound faults in intense noise environments. To address this problem, a novel demodulation band extraction method based on weighted geometric cyclic relative entropy (WGCRE) is proposed. WGCRE is defined on the cyclic sub-bands model of the logarithmic envelope spectrum (LES) to fully consider the bearing characteristic frequency of pseudo-cyclostationarity. In detail, local and global thresholds are separately set by the white noise parameter and harmonic-to-noise ratio to exclude the exogenous noise outliers. On this basis, the WGCRE is defined as a geometrically weighted index of several different fault types to avoid harmonic interference and improve the identification of composite faults. WGCRE–gram, similar to fast kurtogram (FK), is then constructed by replacing kurtosis with WGCRE to extract the optimal demodulation band. Compared with FK and another LES-based method, logarithmic-cycligram, the proposed method is more robust for accurately identifying single and compound faults under external noise. The effectiveness of this method is verified through simulations and actual tests. Simulation experiments of different kinds and intensities of exogenous noise interference preliminarily determine the superior robustness of WGCRE in the face of solid noise. The inner ring, outer ring, and composite fault experiments further confirmed the robust adaptability of WGCRE in the face of complex working conditions.

The Msegram: A useful multichannel feature synchronous extraction tool for detecting rolling bearing faults

Multichannel signals collected by multiple sensors contain richer condition information of equipment than single-channel signals. However, such issues as simultaneous denoising, adaptive decomposition and synchronous extraction are still challenging for multichannel signals, which are beneficial to accurate fault diagnosis. Thus, a useful multichannel feature synchronous extraction tool is proposed for detecting rolling bearing faults, named as Msegram. First, a tensor synchronization denoising method based on high order singular value decomposition (HOSVD) is proposed for multichannel signal preprocessing. Original multichannel signals of testing bearings are constructed to be a third-order tensor by phase space reconstruction. Hereinto, a singular entropy increment is adopted to determine a reasonable singular order for each unfolding, and an optimal core tensor is obtained for local reconstruction analysis. Second, multi-layer K-value multivariate variational mode decomposition (MVMD) is designed after the multichannel noise reduction to realize synchronous adaptive filtering and decomposition for the multichannel signals. Third, inspired by the idea of the spectral kurtosis, a tower-shaped crest factor of envelope spectrum (EC) diagram similar to Fast Kurtogram (FK) is proposed to visualize the output of multichannel bearing fault feature results. According to the tower-shaped EC diagram with the maximum fault crest factor, the optimal analytic results of multichannel signals are selected and output to synchronously extract bearing fault features. Finally, repeatable simulations and two experimental fault cases of rolling bearings are implemented to demonstrate the practicability and effectiveness of the proposed method. The results show that the proposed method can successfully reveal the compound faults from experimental bearing and effectively identify the compound faults from locomotive wheelset bearing.

An adaptive variational mode extraction method based on multi-domain and multi-objective optimization for bearing fault diagnosis

When a local fault in the rolling element bearing appears during operational running, the induced bearing vibration signal is essentially equivalent to a mixed multi-component signal, which usually includes multiple frequency components (e.g., periodic impulses, random impulses, discrete harmonics, and heavy environmental noise). This indicates that it is difficult to detect the weak periodic impulses related to bearing faults by traditional signal processing methods. Variational mode extraction (VME) as a new signal processing method with band-pass filtering properties can separate the desired periodic impulse component from the mixed multi-component signal due to its similar basis as the popular variational mode decomposition (VMD). However, the filtering performance of VME is significantly influenced by two parameters (i.e., penalty factor and center-frequency). To address this issue, all the previous work focused on single-domain and single-objective parameter optimization from the filtering signal or its envelope, whereas the objective function with a single-criterion cannot depict bearing fault signatures from the impulsiveness and cyclostationarity simultaneously in general cases. Therefore, to improve the bearing fault feature extraction ability and avoid the problem of artificial parameter selection of VME, this paper proposes an adaptive variational mode extraction method based on multi-domain and multi-objective optimization (AVME-MDMO), in which two key parameters of VME are automatically determined by multi-objective gray wolf optimizer (MOGWO) with a novel multi-objective function named integrated measure of sparsity-impact (IMSI) of square envelope (SE) and square envelope spectrum (SES). As a result, the optimal VME is employed to obtain the specific mode component and its corresponding SES for achieving bearing fault diagnosis. The effectiveness of the proposed method has been validated on simulation signal and experiment data of rolling element bearing. Besides, the comparison results demonstrate its superiority and robustness in excavating fault signatures over the VME or VMD with single-objective function, and the fast kurtogram.

Nonlinear fast kurtogram for the extraction of gear fault features with shock interference

The extraction of gearbox fault features under shock interference is an exceedingly difficult and valuable subject. The effective usage of the resonance frequency band is one of the solutions for this subject. However, the existing fast kurtogram (FK) method is prone to misdiagnosis due to the sensitivity of this method to aperiodic shocks. To overcome the sensitivity of the FK method to irrelevant shock, this paper proposes a nonlinear fast kurtogram (NFK) method. First, Z-score normalization is performed on the signal. Then, Sigmoid is used to improve the fault representation under shock interference. Third, the signal is divided into different frequency bands, and the band with the largest kurtosis is selected for filtering. Finally, the gear fault is analyzed by the square envelope spectrum. Simulation and experimental verification are used to demonstrate the effectiveness of the proposed method. The results show that gear fault features can be extracted under shock interference by the NFK method.

Impulse feature extraction via combining a novel voting index and a variational model penalized by center frequency constraint

A key step in rotating machinery fault diagnosis is extracting the subcomponent that best characterizes the fault features. To this end, a fault feature extraction methodology based on an adaptive spectrum segmentation method, a new voting index, and a new variational model is constructed in this paper. More specifically, the spectrum is divided into a series of sub-bands through a fast iteration filter by changing the width of the window. Then, by considering the amplitudes and locations of the fault feature spectral lines in squared envelope spectrum, a novel index based on voting mechanism is constructed to evaluate the periodic impulses in each sub-band. Finally, a new variational model penalized by a center frequency penalty item is proposed to extract the fault characteristics from the raw vibration signal by maximining the proposed index iteratively. The proposed methodology is applied to extract the fault characteristics from rolling bearing and planetary gearbox signals. The comparative results indicate the proposed method is superior to fast kurtogram, fast entrogram, and the proposed fault feature extraction methods based on other classical indices.

A novel entropy-based sparsity measure for prognosis of bearing defects and development of a sparsogram to select sensitive filtering band of an axial piston pump

This study aims to establish a novel entropy-based sparsity measure for two main purposes: first is for the prognosis of bearing defects, secondly it is employed to construct sparsogram for identifying sensitive filtering band to carry out envelope analysis for identifying defects in the complex hydraulic machinery (axial piston pump). The newly developed symmetrized directed divergence measure is first authenticated after satisfying the necessary conditions such as convexity, non-negativity and symmetric properties and then reformulated to generate another novel probabilistic entropy measure. The entropy measure so obtained has been mathematically proven to satisfy all essential conditions as laid down by Shannon such as permutationally symmetric, degeneracy, separability, continuity, concavity, maximum value, and non-negativity. Furthermore, the proclaimed probabilistic entropy measure is modified to become a novel sparsity measure that can satisfy all of the six intuitive sparse attributes. The sparsity measure so obtained is applied in two ways. First application is of defect degradation monitoring of the rolling element bearing. Here, LSTM network is used for the carrying out defect prognosis. The degradation monitoring has been carried out on the life time accelerating data of IMS and PRONOSTIA. Second application of the proposed sparsity measure is for the development of a sparsogram for selecting the suitable filtering band to carry out envelop analysis, needed to identify bearing defects in the axial piston pump. To authenticate the validity of the proposed sparsogram, a comparative study has also been done with the existing tool such as fast Kurtogram, spectral kurtosis and Protugram.

Adaptive single-mode variational mode decomposition and its applications in wheelset bearing fault diagnosis

In recent years, many studies on variational mode decomposition (VMD) have mainly focused on choosing the number of modes and balancing parameter, while less research focuses on the internal properties of VMD. This paper proposes an adaptive single-mode VMD (ASMVMD) method based on the convergence characteristics of VMD and the adaptivity of particle swarm optimization (PSO). Firstly, we study the convergence characteristics of single-mode VMD and find that the U-shaped convergence region related to fault impact is very wide in the whole frequency domain. Secondly, based on the characteristics of the U-shaped convergence region, a new population position initialization strategy is proposed. Finally, the improved PSO is used to optimize the initial center frequency and balancing parameter of single-mode VMD. The effectiveness of the proposed method is verified by analyzing the simulated signal and wheelset bearing fault signals. Compared with the fast kurtogram and Autogram, it is shown that ASMVMD has a stronger capability of fault feature extraction.