Correlation Kurtosis Research Articles

Vibration mechanism and improved phenomenological model of the planetary gearbox with broken ring gear fault

Accurate modeling of the vibration signal model of planetary gearboxes is essential for the subsequent fault diagnosis. According to the existing improved phenomenological model based on the meshing vibration, this paper conducts further investigations on the vibration mechanism of the gearbox. The time delay phenomenon of faulty ring gear tooth participating in meshing is theoretically analyzed, and the assisted phases for experimental verification are proposed and deduced. Based on the improved model, the vibration signal under the fault condition is simulated and compared with the results of traditional methods. Subsequently, the paper proposes to divide and reconstruct this signal and use the maximum correlation kurtosis deconvolution (MCKD) to enhance its impact characteristics. The results show that the phase between the fault impact and its adjacent meshing impact is consistent with the proposed assisted phase. Finally, the correctness of the vibration mechanism and the improved phenomenological model are verified experimentally.

Research on gearbox composite fault diagnosis based on improved local mean decomposition

In order to solve the problem of modal aliasing in the processing of complex fault signal with background noise by local mean decomposition(LMD), and the difficulty of extracting and identifying the weak fault feature frequency in the complex fault signal, an improved LMD method is proposed. LMD can adaptively decompose a non-stationary, multi-component signal into a series of instantaneous frequency product functions with physical significance. However, under the influence of noise, the process of LMD will appear modal aliasing, resulting in missed diagnosis and misdiagnosis. In order to solve this problem, the maximum correlation kurtosis deconvolution is proposed to improve the LMD. Firstly, according to the multi-point kurtosis spectrum, the component of fault period contained in fault signal is obtained. According to the fault period, the maximum correlation kurtosis deconvolution is used to denoise the fault signal. Then, the denoised signal is decomposed into a series of components containing fault characteristics by means of LMD. Finally, the component with high correlation is selected for envelope spectrum analysis to extract the component. The characteristic frequencies of different faults and the types of faults are identified. The effectiveness of the proposed method is verified by analyzing the vibration signals of the broken gear-wear composite fault of the gears in the actual gearbox. Compared with the improved empirical mode decomposition method, the superiority of the proposed method is further highlighted.

Blind Deconvolution Technique Based on Improved Correlated Generalized Lp/Lq Norm for Extracting Repetitive Transient Feature

Since minimum correlated generalized Lp/Lq deconvolution (MCG-Lp/Lq-D) cannot simultaneously have a good sensing ability to repetitive fault impulses and a strong robustness to noise when processing low SNR signals, a new deconvolution method, minimum improved correlated generalized Lp/Lq deconvolution (MICG-Lp/Lq-D), is proposed in this article. The proposed method is designed based on a novel norm, the improved correlated generalized Lp/Lq (ICG-Lp/Lq) norm. The ICG-Lp/Lq norm not only has the low-order statistics form that is similar to the correlated generalized Lp/Lq (CG-Lp/Lq) norm used in MCG-Lp/Lq-D, but also has the high shift-order signal correlation construction similar to the correlated kurtosis (CK) norm used in maximum correlated kurtosis deconvolution (MCKD). This guarantees that the proposed norm is robust enough to strong noise and can improve its sensing ability for repetitive impulses simultaneously. This feature of the ICG-Lp/Lq norm ensures that MICG-Lp/Lq-D can suppress outliers and extract weak impacts when processing low SNR signals. Simulated and experimental case studies verify the performance of the proposed method. The results indicate that the proposed method is robust enough to strong noise and very sensitive to repetitive impulses simultaneously, which indeed overcomes the aforementioned defects of MCG-Lp/Lq-D. Therefore, MICG-Lp/Lq-D can be considered a promising tool for detecting repetitive impulses.

A Novel Three-Step Classification Approach Based on Time-Dependent Spectral Features for Complex Power Quality Disturbances

Power quality events caused by renewable-energy integration are usually associated with complex disturbances; therefore, their type identification is the primary task of subsequent pollution control. This study proposes a novel three-step classification approach based on time-dependent spectral features (TDSFs) for the classification of complex power quality disturbances (PQDs). First, the improved complete ensemble empirical mode decomposition with adaptive noise (ICEEMDAN) is adopted to decompose the PQDs into several intrinsic mode functions (IMFs). The related IMFs are selected by correlation coefficient and kurtosis. Then the eight eigenvalues of each IMF are extracted, including TDSFs. Finally, the eigenvalue dimension of each IMF is reduced by linear discriminant analysis (LDA). Moreover, the classifier of the adaptive k-nearest neighbor with excluding outliers (AdaKNNEO) can confirm the PQDs type. To verify the effectiveness of the proposed approach, a series of simulations and hardware experiments are conducted. The overall result shows robustness and high accuracy of the proposed method, and especially for the complex PQDs, it possesses the highest entirely correct of 96% compared to other advanced methods.

Early Fault Diagnosis of Shaft Crack Based on Double Optimization Maximum Correlated Kurtosis Deconvolution and Variational Mode Decomposition

Aiming at the problem that the vibration energy of shaft crack early weak fault is small and the feature extraction was difficult, the fault diagnosis method of cuckoo search, maximum correlation kurtosis deconvolution and variational mode decomposition (CS-MCKD-VMD) was proposed to diagnose the early weak fault of shaft cracks. Firstly, considering the periodic characteristics of fault signal, MCKD was used to highlight the fault signal, and the kurtosis correlation of deconvolution signal processed by MCKD were enhanced. Then, VMD could be used to decompose the harmonic signal, and VMD was used to process the deconvolution signal to generate some intrinsic mode functions (IMF), and the correlation coefficient method was used to calculate the components with the maximum correlation. At the same time, in order to improve the correlation of parameters in MCKD and VMD, CS was used to optimize the parameters to reduce the error of human selection. Thirdly, the optimal component was calculated by the fast spectral kurtosis (FSK), and the envelope spectrum was obtained by filtering the optimal component with the parameters obtained. Finally, the simulation and experimental results show that the transfer frequency and its 2 and 3 times frequency were prominent in the envelope spectrum, which was consistent with the analysis of shaft crack fault mechanism, Therefore, it was proved that the CS-MCKD-VMD method can effectively extract the early weak fault features of shaft cracks.

Feature Extraction Based on EWT With Scale Space Threshold and Improved MCKD for Fault Diagnosis

Aiming at the problem of feature extraction of non-stationary, non-linear and weak fault signals, a new feature extraction method based on empirical wavelet transform (EWT) with scale space threshold (STEWT) and improved maximum correlation kurtosis deconvolution (MCKD) with power spectral entropy and grid search (PGMCKD), namely STEWT-PGMCKD is proposed for rolling bearing faults in this paper. In the proposed STEWT-PGMCKD method, the scale space threshold method is designed to solve the problems of falling into local extremum and mode over decomposition caused by the local-max-min band decomposition method of EWT, which is used to decompose the frequency band of signal, and the correlation analysis is carried out between the decomposed modal components and the original signal to retain the modal components with high correlation. Then an adaptive MCKD based on power spectral entropy is proposed to solve the problem that the signal processing effect of MCKD is affected by filter size L and deconvolution period T. Nextly, the parameters of the MCKD are optimized by grid search method. Finally, the power spectrum analysis of the enhanced signal is carried out to realize the feature extraction and fault diagnosis. The experiment results show that the proposed STEWT-PGMCKD method can effectively extract the weak fault information and accurately realize the fault diagnosis for rolling bearings.

The Traverse Symplectic Correlation-Gram (TSCgram): A New and Effective Method of Optimal Demodulation Band Selection for Rolling Bearing

Resonance demodulation is a commonly used method to obtain fault information, whose main challenge is to seek a suitable frequency band for demodulation. Autogram is a recently proposed method for optimal demodulation frequency band (ODFB) selection, in which the frequency domain is divided by a binary tree structure. However, the frequency band information obtained by Autogram is easily missed. To solve this issue, a 1/3 binary tree structure is employed to segment the frequency domain and improve the segmentation accuracy of Autogram. Despite this, the frequency bands with different position information cannot be fully obtained through the above-mentioned structure yet. In this article, the traverse symplectic correlation-gram (TSCgram) is proposed to overcome the shortcomings existing in Autogram and based on that, a novel fault diagnosis method for rolling bearing is proposed. First, the frequency domain of the raw vibration signal of rolling bearing is accurately divided through the traversal segmentation structure. Then, the concept of symplectic correlation is introduced to reduce the interference of noise, as well as other unrelated components on the traditional kurtosis, thus further improving the accuracy of ODFB detection. Finally, the band position corresponding to the maximum symplectic correlation kurtosis (SCK) value is chosen as the ODFB for fault diagnostics of rolling bearing. Also, the proposed method is applied to the simulated and measured data analysis by comparing it with fast kurtogram and Autogram methods. The comparison and analysis results indicate that the fault diagnostic effect of the proposed TSCgram method is better than the comparing methods.

Research on Fault Extraction Method of CYCBD Based on Seagull Optimization Algorithm

Maximum cyclostationarity blind deconvolution (CYCBD) can recover the periodic impulses from mixed fault signals comprised by noise and periodic impulses. In recent years, blind deconvolution has been widely used in fault diagnosis. However, it requires a preset of filter length, and inappropriate filter length may cause the inaccurate extraction of fault signal. Therefore, in order to determine filter length adaptively, a method to optimize CYCBD by using the seagull optimization algorithm (SOA) is proposed in this paper. In this method, the ratio of SNR to kurtosis is used as the objective function; firstly, SOA is used to search the optimal filter length in CYCBD by iteration, and then it uses the optimal filter length to perform CYCBD; finally, the frequency‐domain waveform is determined through Fourier transformation. The method proposed is applied to the fault extraction of a simulated signal and a test vibration signal of the closed power flow gearbox test bed, and the fault frequency is successfully extracted, in addition, using maximum correlation kurtosis deconvolution (MCKD) and multipoint optimal minimum entropy deconvolution adjusted (MOMEDA) to compare with CYCBD‐SOA, which validated availability of the proposed method.

Fault Diagnosis of Rolling Bearing based on Permutation Entropy Optimized Maximum Correlation Kurtosis Deconvolution

An improved MCKD algorithm was proposed as an adaptive parameter selection approach. In this method, the optimal filter length of the MCKD algorithm was determined by the maximum permutation entropy value and the optimal fault period of the MCKD algorithm was determined by the maximum kurtosis value. The determined optimal filter length and optimal fault period were verified by simulation signals of the bearing as well as fault experimental signals of the inner and outer rings. Results demonstrate that in early fault diagnosis, the improved MCKD algorithm based on permutation entropy can extract faint characteristic information of early fault of rolling bearing effectively. It can highlight fault pulse signals which are covered by noises and get more ideal results than the minimum entropy deconvolution algorithm.

Rolling Element Fault Diagnosis Based on VMD and Sensitivity MCKD

In order to improve the diagnosis accuracy and solve the weak fault signal of rolling element of rolling bearings due to long transmission path, a novel fault diagnosis method based on variational mode decomposition (VMD) and maximum correlation kurtosis deconvolution (MCKD), namely VMD-MCKD-FD is proposed for rolling elements of rolling bearings in this paper. In the proposed VMD-MCKD-FD, the vibration signal of rolling element of rolling bearings is decomposed into a series of Intrinsic Mode Functions (IMFs) by using VMD method. Then the number of modes with outstanding fault information is determined by Kurtosis criterion in order to calculate the deconvolution period T. The periodic fault component of reconstructed signal is enhanced by using sensitivity MCKD method. Finally, the power spectrum of the reconstructed signal is analyzed in detail in order to obtain the fault frequency and diagnose the rolling element fault of rolling bearings. The simulation signal and actual vibration signal are selected to verify the effectiveness of the VMD-MCKD-FD method. The experimental results show that the VMD-MCKD-FD method can effectively diagnose the rolling element fault of rolling bearings and obtain better fault accuracy.

Rolling Bearing Sub-Health Recognition via Extreme Learning Machine Based on Deep Belief Network Optimized by Improved Fireworks

Rolling bearings, as the main components of the large industrial rotating equipment, usually work under complex conditions and are prone to break down. It can provide a certain theoretical basis for identifying the sub-health state of the industrial equipment by the analysis from the incipient weak signals. Thus, a sub-health recognition offline algorithm based on Refined Composite Multiscale Dispersion Entropy (RCMDE) and Deep Belief Network-Extreme Learning Machine (DBN-ELM) optimized by Improved Firework Algorithm (IFWA) is proposed. First of all, in light of the drawbacks that it is easy to fall into local optima and cross the boundary for exploding fireworks in Firework Algorithm (FWA), Cauchy mutation and adaptive dynamic explosion radius factor coefficient is introduced into IFWA. Secondly, Maximum Correlation Kurtosis Deconvolution (MCKD) optimized by the improved parameters is used to process the incipient vibration signals with nonlinearity, nonstationary, and IFWA is used to adaptively adjust to the period T and the filter length L in MCKD(IFWA-MCKD). Then, each sequence of signals is further extracted the feature-RCMDE to rich sample diversity. Finally, combining the powerful unsupervised learning capability from DBN and the generalization capability from ELM, DBN-ELM can be established. What's more, in order to avoid the interference of human on the parameters, IFWA is used to optimize the number of hidden nodes in DBN-ELM, and the IFWA-DBN-ELM is established. It shows that the algorithm has the higher sub-health recognition accuracy, better robustness and generalization, which has a better industrial application prospect.

Multistage Fault Feature Extraction of Consistent Optimization for Rolling Bearings Based on Correlated Kurtosis

Fault diagnosis of rolling bearings is not a trivial task because fault-induced periodic transient impulses are always submerged in environmental noise as well as large accidental impulses and attenuated by transmission path. In most hybrid diagnostic methods available for rolling bearings, the problems lie in twofolds. First, most optimization indices used in the individual signal processing stage do not take the periodical characteristic of fault transient impulses into consideration. Second, the individual stages make use of different optimization indices resulting in inconsistent optimization directions and possibly an unsatisfied diagnosis. To solve these problems, a multistage fault feature extraction method of consistent optimization for rolling bearings based on correlated kurtosis (CK) is proposed where maximum correlated kurtosis deconvolution (MCKD) is employed to attenuate the influence of transmission path followed by tunable Q factor wavelet transform (TQWT) to further enhance fault features by decomposing the preprocessed signals into multiple subbands under different Q values. The major contribution of the proposed approach is to consistently use CK as an optimization index of both MCKD and TQWT. The subband signal with the maximum CK which is an index being able to measure the periodical transient impulses in vibration signal yields an envelope spectrum, from which fault diagnosis is implemented. Simulated and experimental signals verified the effectiveness and advantages of the proposed method.

Features Method for Selecting VMD Parameters based on Spectrum without Modal Overlap

Variation Mode Decomposition (VMD) can decompose a complex set of signals into the form of a sum of multiple amplitude modulated FM eigenmode functions (IMFs). Compared with EMD decomposition, the VMD method has a strict mathematical model foundation, which further avoids modal overlap and has higher computational efficiency. Therefore, VMD has been widely used in engineering. Different from the adaptive decomposition of the signal by EMD, the VMD method needs to preset mode parameter K and the second penalty factor α in the VMD decomposition before decomposing the signals. In the case of reasonable parameter setting, VMD method shows better robustness, otherwise it will greatly affect the accuracy of decomposition results. In this paper, the influence of the two parameters on the decomposition effect is discussed by combining the correlation coefficient, kurtosis index and spectrum graph. Based on the problem that these two important parameters are difficult to select, a constraint rule and screening strategy without modal overlap is proposed. According to the parameter selection strategy, mode parameter K and the second penalty factor α are automatically selected to ensure that modal overlap does not occur, Signal decomposition shall be as detailed and accurate as possible. By decomposing the bearing data, the rationality of the parameter selection strategy is proved. A new idea is put forward for the research of VMD.

A Reliable Prognosis Approach for Degradation Evaluation of Rolling Bearing Using MCLSTM.

Prognostics and health management technology (PHM), a measure to ensure the reliability and safety of the operation of industrial machinery, has attracted attention and application adequately. However, how to use the monitored information to evaluate the degradation of rolling bearings is a significant issue for its predictive maintenance and autonomic logistics. This work presents a reliable health prognosis approach to estimate the health indicator (HI) and remaining useful life (RUL) of rolling bearings. Firstly, to accurately capture the degradation process, a novel health index (HI) is constructed based on correlation kurtosis for different iteration periods and a Gaussian process latency variable model (GPLVM). Then, a multiple convolutional long short-term memory (MCLSTM) network is proposed to predict HI values and RUL values. Finally, we perform experimental datasets of rolling bearings, demonstrating that the presented method surpasses other state-of-the-art prognosis approaches. The results also confirm the feasibility of the presented method in industrial machinery.

Field distribution characteristics of vortex beams passing through the non-Gaussian random rough surface

Based on the theory of angular spectrum representation, the non-Gaussian rough surface is simulated by Johnson transfer system, and the field distribution characteristics of Laguerre-Gaussian vortex beams passing through the random non-Gaussian rough surface are studied. The effects of the direction correlation length, kurtosis, skewness and root mean square roughness of non-Gaussian rough surface on the field distribution of the vortex beam are analyzed. The range of the root mean square roughness is studied when the intensity distribution of the vortex beam passing through the random rough surface changes, and the corresponding experiment is carried out. The experimental data are compared with the simulation results. The results show that when the direction correlation length of non-Gaussian rough surface is 20 mm, the skewness is 0.001, the kurtosis is 6, and the root mean square roughness is more than 0.12 mm, the intensity distribution of the Laguerre-Gaussian beam passing through the random surface no longer keeps the hollow distribution, and the corresponding phase singularity disappears.

A novel ITD-GSP-based characteristic extraction method for compound faults of rolling bearing

Abstract The diagnosis of compound faults of rolling bearing is extremely difficult due to the nonlinearity and non-stationary of signal. With the purpose of extracting the compound faults from rolling bearings of aero-engine, efforts were made to integrate Intrinsic Time-scale Decomposition (ITD) and Graph Signal Processing (GSP), namely the ITD-GSP methodology. A PR component (obtained by ITD algorithm) with minimum Laplacian Energy (LE) index is chosen as the optimal rotational component to identify types of compound fault of rolling bearing. The result indicates that the proposed ITD-GSP methodology can precisely and effectively provide the characteristic frequency of compound faults no matter in which direction of sensors (vertical and horizontal) and which type of compound faults of rolling bearing. On the contrary, the mainstream schemes of fault analysis using ITD algorithm (correlation coefficients or kurtosis as the basis to screen optimal rotational component) cannot.

Early diagnosis of bearing faults using decomposition and reconstruction stochastic resonance system

Weak vibration signals generated by faults in rolling element bearings are often masked by high levels of background noise, which leads to inaccurate fault detection. To overcome the masking, a stochastic resonance based on decomposition and reconstruction method is employed for early bearing fault diagnosis. First, theoretical analysis is performed to confirm the requirement for signal preprocessing. Subsequently, a novel cross correlation kurtosis is defined as an index to obtain an optimal intrinsic mode function after empirical mode decomposition. Finally, the preprocessed signal is clarified via a stochastic resonance method and reconstructed for bearing fault diagnosis. Combined with ensemble bagged trees-based machine learning, the decomposition and reconstruction stochastic resonance method was beneficial for detecting fault signals from incoming noisy vibration signals using simulated and actual vibration signals. According to the results, the proposed method was superior to traditional stochastic resonance method and variational mode decomposition with the k-number method.

COMPOUND FAULT DIAGNOSIS OF BEARINGS USING AN IMPROVED SPECTRAL KURTOSIS BY MAXIMUM CORRELATION KURTOSIS DECONVOLUTION (MCKD).

This paper discusses the use of Maximum Correlation kurtosis deconvolution (MCKD) method as a pre-processor in fast spectral kurtosis (FSK) method in order to find the compound fault characteristics of the bearing, by enhancing the vibration signals. FSK only extracts the resonance bands which have maximum kurtosis value, but sometimes it might possible that faults occur in the resonance bands which has low kurtosis value, also the faulty signals missed due to noise interference. In order to overcome these limitations FSK used with MCKD, MCKD extracts various faults present in different resonance frequency bands; also detect the weak impact component, as MCKD also dealt with strong background noise. By obtaining the MCKD parameters like, filter length & deconvolution period, we can extract the compound fault feature characteristics.

Fault feature extraction of rotating machinery using a reweighted complete ensemble empirical mode decomposition with adaptive noise and demodulation analysis

Fault feature extraction is crucial to detect failures as earlier as possible in fault diagnosis of rotating machinery. Due to the influence of environment noise and interference, the signal to noise ratio (SNR) of fault feature is relatively low in the measured signal. Complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN) is an improved method based on EEMD, which has been extensively applied to signal de-noising. The key problem for CEEMDAN is to determine the fault-related degree of a decomposed intrinsic mode function (IMF), especially in the presence of both Gaussian and non-Gaussian noises or interferences. However, most of the traditional assessment criterions are developed to describe the statistical parameters of IMFs, e.g. correlation coefficient and kurtosis, which ignore the specific characteristics of the fault and are easily affected by noise components. Therefore, a new criterion is proposed to quantify the fault-related degree of a vibration signal, in which the ratio of periodic modulation components caused by fault to the generalized interferences is defined. Then, a reweighted and reconstruction strategy of the decomposed IMFs is presented to obtain the de-noised signal based on the new criterion. Furthermore, in order to detect the fault-related modulation features in multi-frequency scales, a time-frequency representation (TFR) based demodulation analysis is employed, which guarantees an accurate extraction of the fault feature at the early stage of fault. The effectiveness of the proposed fault diagnosis method comparing to traditional methods are demonstrated by both numerical simulation and experimental studies. The results show that the proposed method achieves a better performance in terms of SNR improvement and fault feature detection, it can successfully detect the fault features in the presence of Gaussian and non-Gaussian noises.

Data processing of pulsation signals based on local wave decomposition and teager energy

Nonstationary and nonlinear signals are often encountered in the research and development of turbomachinery. One such example is the pulsating strain signal measured during engine ramping to find the maximum resonant strain in the application. Because the pulse signal may come from different interference sources, it is difficult to detect weak useful signal in the background of noise. In order to solve this problem, a new method based on local wave decomposition (LWD) and Teager energy is proposed. According to the local characteristics of the vibration signal, the optimal prediction operator of the transformed sample is constructed by selecting the appropriate square error minimization criterion, so that the second generation wavelet basis function can fit the local characteristics of the vibration signal. The adaptive second generation wavelet is used as the prefilter to improve the effect of LWD decomposition. Then the correlation kurtosis is used to select the sensitive internal model function (IMFs). Finally, the Teager energy operator algorithm is applied to the selected sensitive IMF to identify the characteristic frequency. The validity of the method is verified by the measured strain signal of a turbocharger turbine as an example.