Kurtosis Methods Research Articles

Stock Liquidity and Return Distribution in Emerging Market

Purpose: This study aims to illustrate the relationship between the liquidity of a stock and the return distribution of all companies listed on the Indonesian Stock Exchange. Design/methodology/approach: The correlation between stock liquidity and return distribution, represented using skewness and kurtosis methods, was determined by the author through two-way tests using line regression (fixed cross-section regression) and machine learning (random forest regressor) for Indonesia data Stock exchange from 2014 to 2023. Findings: The results indicate a connection between stock liquidity and return distribution. When evaluating stock liquidity, the zero return days technique gives a more significant relationship, while the kurtosis of return method gives a more significant return distribution. It is impossible to determine with absolute certainty whether the correlation is positive or negative; it depends on how stock liquidity and return distribution are measured. Research limitations/implications: The correlation between stock liquidity and return distribution cannot be characterized as an absolute relationship due to the intricacy and variety of approaches used to measure it. Practical implications: The kurtosis of return has a better relationship with stock liquidity, and “zero return day” and “relative spread” are still more strongly correlated with the return distribution. Originality/value: As the first study to use machine learning and linear regression to examine the relationship between stock liquidity and return distribution, this paper expands the body of knowledge. Second, it examines which return distribution – skewness or kurtosis – has a stronger correlation with stock liquidity. Third, we examine which liquidity metrics—relative spread, Amihud liquidity, price impact ratio, and zero return days—are most related to the return distribution.

Features of measurement uncertainty evaluation during calibration of digital ohmmeters

The scheme for transferring the size of the unit of resistance during the calibration of digital ohmmeters at direct current is considered. The procedure for the measurement uncertainty evaluation is described: recording the measurement model and its refinement, evaluation of input and measured values, evaluation of standard uncertainties of the input and measured values, evaluation of the expanded uncertainty. The refined model includes the dependence of the resistance of the reference resistor on temperature and a correction to the drift of the resistance value of the reference resistor since its last calibration. To evaluate the expanded uncertainty, the kurtosis method was used. An uncertainty budget has been made, including the kurtosis of input and measured values. The use of the Excel package makes it possible to implement, based on this budget, a program for automation of measurement uncertainty calculations. An example of the measurement uncertainty evaluation during the calibration of a digital ohmmeter of type 2318 at a point of 1 mOhm using an electrical resistance coil R310 with an accuracy class of 0.01 is considered. The influence of nonlinearity of the measurement model on the estimates of the numerical value of the measurand and its combined standard uncertainty is studied. To verify the results, the distribution law of the measurand was modelled by the Monte Carlo method. An algorithm for determining the expanded uncertainty using the NIST Uncertainty Machine web application for the missing confidence level of 0.9545 is proposed. The comparison of the results of the measurement uncertainty evaluation by the kurtosis and Monte Carlo methods has shown their good agreement.

Body-Worn Sensors for Recognizing Physical Sports Activities in Exergaming via Deep Learning Model

Obesity and laziness are some of the common issues in the majority of the youth today. This has led to the development of a proposed exergaming solution where users can play first-person physical games. This research study not only proposes a solution for physical fitness in the form of a game using wearable sensors but also proposes a multi-purpose system that provides different applications when trained for the domain-specific dataset. Critical tasks of gesture recognition and depiction in virtual reality can be applied to many applications in the domains of crime detection, fitness, healthcare, online learning, and sports. In particular, the proposed system enables a user to perform, detect, and depict different gestures in the virtual reality game. First, the system pre-processes input data by applying a median filter to overcome the anomalies. Then, features are extracted through a convolutional neural network, power spectral density, skewness, and kurtosis methods. Further, the system optimizes different features by using the grey wolf optimization. Lastly, the feature set which is optimized is fed to a recurrent neural network for classification. When Compared to the traditional methods, the suggested system gives better results while being easier to use. The IMSporting behaviors (IMSB) dataset includes badminton and other physical activities, the WISDM dataset includes common locomotor motions, and the ERICA dataset which includes a variety of exercises, were used in the experimentation. According to experimental findings, the suggested approach outperformed current methods, which showed detection accuracies of 85.01%, 88.46%, and 93.18% over the IMSB, WISDM, and ERICA datasets, respectively.

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.

Fluidization dynamic characteristics of carbon nanotube particles in a tapered fluidized bed

These picture shows the energy contribution of micro-, meso- and macro-structures at different operating conditions in the TFB without distributor. Energy contribution of micro-, meso- and macro-structures at different particle size. In this work, a tapered fluidized bed (TFB) without a distributor for fluidizing carbon nanotube (CNT) was applied for improving the dead zone, blockage, and fracture of distributor, which occurred in actual production. Experiments were performed under different superficial gas velocities, static bed heights, CNT agglomerate size, and positions of pressure probe. To obtain multi-perspective and multi-scale understanding of fluidization dynamics of gas–CNT flow in the TFB without a distributor, the standard deviation, skewness, kurtosis, wavelet decompositions and homogeneous index analysis methods were adopted. Some noticeable phenomena were observed. Particle movements including inter-particle, gas–particle and particle–wall dominate dynamic characteristics. The amplitudes of pressure fluctuations of coarse agglomerated multi-walled CNT were more sensitive to the gas velocity than that of fine agglomerated multi-walled CNT. The sensitively of energy contribution of the meso- and macro-structures was that the sensitivity of the measured position was less than the sensitivity of the energy contribution by the changes of particle size, and the sensitivity of the energy contribution by the changes of particle size was less than the energy contribution by the changes of gas velocity. The fluidization quality of coarse agglomerated multi-walled CNT was better than that of fine agglomerated multi-walled CNT, which was verified by the skewness and wavelet analysis.

Feature extraction of latent fault components of rolling bearing based on self-learned sparse atomics and frequency band entropy

As the key rotating parts in machinery, it is crucial to extract the latent fault features of rolling bearing in machinery condition monitoring to avoid the occurrence of sudden accidents. Unfortunately, the latent fault features are hard to extract by using the traditional signal processing method such as envelope demodulation because the effect of envelope demodulation is influenced strongly by the degree of background noise. Sparse decomposition, as a new promising method being able of capturing the latent fault feature components buried in the vibration signal, has attracted a lot of attentions, especially the predefined dictionary-based sparse decomposition methods. However, the feature extraction effect of the predefined dictionary-based sparse decomposition depends on whether the prior knowledge of the analyzed signal is sufficient or not. To overcome the above problems, a feature extraction method of latent fault components of rolling bearing based on self-learned sparse atomics and frequency band entropy is proposed in the article. First, a self-learned sparse atomics method is applied on the early weak vibration signal of rolling bearing and several self-learned atomics are obtained. Then, the self-learned atomics owing bigger kurtosis values are selected and used to reconstruct the vibration signal to remove the other interference signals. Subsequently, the frequency band entropy method is used to analyze the reconstructed vibration signal, and the optimal parameter of band-pass filter could be calculated. At last, the reconstructed vibration signal is filtered using the optimal band-pass filter, envelope demodulation on the filtered signal is applied, and better fault feature is extracted. The feasibility and effectiveness of the proposed method are verified through the vibration data of the accelerated fatigue life test of rolling bearing. Besides, the analysis results of the same vibration data using Autogram and spectral kurtosis methods are also presented to highlight the superiority of the proposed method.

Time-frequency synthesis analysis for complex signal of rotating machinery via variational mode manifold reinforcement learning

The transient signal caused by localized fault in rotating machinery always contains complex modulation information with heavy background noise distributed, which brings much difficulties for fault feature identification in the application of rotating machinery fault diagnosis. Focusing on the sensitive feature extraction from these complex signals, this paper proposes a novel variational mode manifold reinforcement learning (VM2RL) to adaptively construct time-frequency synthesis analysis for enhancement of transient features. First, a method of adaptive variational mode decomposition (VMD) is employed to divide the raw spectrum of the given signal into several sub-bands with different frequency modulation information. Second, an improved time-frequency manifold (ITFM) learning is introduced to gain the topological manifold structure from those sub-distributions in time-frequency domain. Then, a sound-enhanced signature of transient features on the whole time-frequency plane can be synthesized by combining those sub-TFMs from each modulated segment back to the corresponding frequency band. Finally, the time-frequency envelope spectrum for fault diagnosis is further obtained through statistically evaluating their amplitude distribution. Among them, short-frequency Fourier transform (SFFT) is introduced to transform local frequency bands into a series of TFDs which improves the computational efficiency of TFM learning. In this manner, the desired transient distribution on full time-frequency plane can be automatically reconstructed by VM2RL with manifold reinforced in a data-driven way. A simulation study and two experimental signals are both analyzed here, and fast spectral kurtosis and conventional VMD methods are also used to verify its effectiveness. Meanwhile, a quantitative analysis has been provided to further illustrate its superiority in the application of complex signal fault of rotating machinery.

Sparse Envelope Spectra for Feature Extraction of Bearing Faults Based on NMF

Periodic impulses and the oscillation response signal are the vital feature indicators of rolling bearing faults. However, finding the suitable feature frequency band is usually difficult due to the interferences of other components and multiple resonance regions. According to the characteristics of non-negative matrix factorization (NMF) on a spectrogram, the feature extraction method from a sparse envelope spectrum for rolling bearing faults is proposed in this paper. On the basis of the time–frequency distribution (TFD) of the periodic transient oscillations, the basic matrix can be interpreted as the spectral bases, and the time weight matrix corresponding to spectral bases can be extracted by NMF. Because the bases and the weights have a one-to-one correspondence, the frequency band filtering with the basic component and the time domain envelope of the weight vector are calculated respectively. Then, the sparse envelope spectrum can be derived by the inner product of the above results. The effectiveness of the proposed method is verified by simulations and experiments. Compared with band-pass filtering and spectral kurtosis methods, and considering the time weights and corresponding the spectral bases for the periodic transient oscillations, the weak fault-rated feature can be enhanced in the sparse spectrum, while other components and noise are weakened. Therefore, the proposed method can reduce the requirement of selecting frequency band filtering.

Weak fault diagnosis of rolling bearing under variable speed condition using IEWT-based enhanced envelope order spectrum

In order to achieve status identification of rolling bearing at early fault stage under variable speed conditions, a method called IEWT-based enhanced envelope order spectrum is proposed by improving empirical wavelet transform (IEWT) using cuckoo search algorithm (CSA) and combing IEWT with the compute order tracking (COT) approach and singular value ratio spectrum (SVRS) denoising technology. The inherent deficiencies of traditional EWT limit its application in fault signal processing significantly. In order to address this issue, the support interval of an empirical wavelet is adaptively determined by CSA to ensure the accuracy of signal decomposition, and an IEWT method is proposed. For a given bearing fault signal under fluctuating speed conditions, firstly COT is utilized as a preprocessing technology to convert the original time domain signal into the resampled angle domain signal without special hardware. Then, IEWT is used to separate the informative component effectively from the resampled signal. Due to the weak features and the heavy noises in the early fault signal, IEWT is unable to remove the whole interference contained in the separated component directly. Thus, SVRS denoising technology is applied on the envelope signal of the separated signal to further enhance the potential impulsive features and suppress the residual noises. Finally, the fault type of rolling bearing can be determined by analyzing the obtained enhanced envelope order spectrum. Both the simulated and the experimental signals are used to verify the effectiveness of the proposed method, and the comparisons between the proposed method and the EEWT, the EMD, and the spectral kurtosis methods are carried out. The results indicate the proposed method possesses significant advantages in bearing weak fault diagnosis under variable speed condition.

Wide frequency band electrochemical noise measurement and analysis of a Li/SOCl2 primary battery

Electrochemical noise of a primary LiSOCl2 battery was measured in a wide frequency band during discharge at a constant value resistor. Power spectral density calculation method was used as the first stage of data analysis. Measurements with two analog to digital converter speed rates made it possible to carry out precision analysis in more than five order wide frequency bands starting from 2.5 kHz down to 17 mHz. It was shown that each power spectral density spectrum consists of two regions. Each of them possesses linear frequency dependence with its own slope. They intercept in the frequency band from 10 Hz down to 0.1 Hz depending on the state of charge value. Dispersion and high-order moments such as kurtosis and skewness calculation methods were applied to analyze electrochemical noise data as alternate analysis techniques. It was found that dispersion calculation can give useful information about electrochemical noise evolution during discharge process for the investigated battery type.

A new l0-norm embedded MED method for roller element bearing fault diagnosis at early stage of damage

Minimum entropy deconvolution (MED) has been widely applied to extract the repetitive transients. Its effectiveness for bearing fault diagnosis, however, might be undermined by the drawbacks: 1) it prefers a solution of a single impulse under the harsh working conditions, and 2) it is sensitive to the length of inverse filters. To overcome such limitations, a novel l0-norm embedded MED method is proposed for early bearing fault diagnosis in this paper. The performances of l0-norm regularized solution are first detailedly discussed with different smooth functions. Subsequently, the approximate hyperbolic tangent function (AHTF) with a better steepness is selected as the smooth function to estimate the l0-norm. The l0-norm regularized solution is then incorporated into the iterative de-convolving procedure of MED as it can suppress interferences of singular impulses and wipe the noise component off the raw signal. As a result, the reliabilities of iterative de-convolving procedure of MED are enhanced via feeding the l0-norm regularized solution. Simulated studies and experimental verifications are performed to demonstrate the superiorities of the proposed method by comparing with the conventional MED, SL0-MED and spectral kurtosis (SK) methods. The comparison results illustrate that the proposed method is more effective for weak feature extraction using different lengths of inverse filters. The fault characteristic frequency can be easily identified on the envelope spectra of the signal processed by the proposed method with comparison of the qualitative and quantitative analysis results.

Comparison of beta-kurtosis and kurtosis methods for troubleshooting the performance of a transmission vehicle using vibrating frequencies

One of the main methods in maintenance and repair is a preventive maintenance method that is often more effective. The requirements of this method are to monitor the performance of machinery during operation. One of the car's functions that is monitored in this way is its vibra-tions. In this paper, a mathematical model of vibration analysis of a passenger car gearbox is presented based on Beta-Kurtosis and Kurtosis methods. In the next step, the data and test settings for the gearbox are based on the accelerometer installation to record the vibrations of the gearbox. To verify the accuracy of the proposed method, the results of the vibrational analysis of the car gearbox in four modes of a healthy gearbox, defective gearbox in the shaft end bearing, gear shaft failure on the gear shaft, simultaneous failure of the bearing and gearbox on the gear shaft were compared. Also, the results are compared for both Kurtosis and Beta-Kurtosis methods. The results show that both of the proposed methods are very accurate in identifying faults in the gearbox and determining the type of fault.

Emg Signal Classification Using Fuzzy Logic

Electromyography (EMG) signals are an important technique in the control applications of prostatic hand. These signals, which are measured from the skin surface, are used to perform movements such as wrist flexion / extension, forearm supination / pronation and hand opening / closing of prosthetic devices. In this study, root mean square, waveform length and kurtosis methods were applied to extracted EMG signals from flexor carpi radialis and extensor carpi radialis muscles by using two channel surface electrodes. A fuzzy logic based classification method has been applied to classify the extracted signal features. With this method, classification for different gripping movements has been successfully accomplished.

Compound faults detection in gearbox via meshing resonance and spectral kurtosis methods

Kurtosis-based impulsive component identification is one of the most effective algorithms in detecting localized faults in both gearboxes and rolling bearings. However, if localized faults exist in both gear tooth and rolling bearing simultaneously it is difficult to tell the differences between the two types of defects. As such, this study proposes a new method to solve the problem by using the meshing resonance and spectral kurtosis (SK) algorithms together. In specific, the raw signal is first decomposed into different frequency bands and levels, and then the corresponding Kurtogram and MRgram are calculated via the fault SK analysis and the meshing index. Furthermore, the resonance frequency bands induced by localized faults of the gear tooth and rolling bearing are separately identified by comparing the Kurtogram and the MRgram. Finally, the compound faults are respectively detected using envelope analysis. The effectiveness of the proposed method has been validated via both simulated and experimental gearboxes vibration signals with compound faults.

Micro-seismic monitoring in mines based on cross wavelet transform

Time Delay of Arrival (TDOA) estimation methods based on correlation function analysis play an important role in the micro-seismic event monitoring. It makes full use of the similarity in the recorded signals that are from the same source. However, those methods are subjected to the noise effect, particularly when the global similarity of the signals is low. This paper proposes a new approach for micro-seismic monitoring based on cross wavelet transform. The cross wavelet transform is utilized to analyse the measured signals under micro-seismic events, and the cross wavelet power spectrum is used to measure the similarity of two signals in a multi-scale dimension and subsequently identify TDOA. The offset time instant associated with the maximum cross wavelet transform spectrum power is identified as TDOA, and then the location of micro-seismic event can be identified. Individual and statistical identification tests are performed with measurement data from an in-field mine. Experimental studies demonstrate that the proposed approach significantly improves the robustness and accuracy of micro-seismic source locating in mines compared to several existing methods, such as the cross-correlation, multi-correlation, STA/LTA and Kurtosis methods.

DETERMINATION AND EVALUATION OF RAILWAY AGGREGATE SUB-BALLAST GRADATION AND OTHER PROPERTIES VARIATION

The use of high quality aggregate mixture, proper technological parameters of laying and compacting as well as the required thickness of the mixture ensures railway sub-ballast layer properties. In this paper gradation, den­sity and water permeability of 49 produced random samples of aggregate sub-ballast (ASB) mixture which were taken from the stockpile in the plant and from the uncompacted railway layer are investigated. The statistical parameters of the ASB mixture quality indicators and histograms with theoretical curves of normal distribution are presented as well. Their conformity to normal distribution was tested through the use of skewness, kurtosis, Pearson, Shapiro-Wilk and Kolmogorov-Smirnov methods. Regression analysis was employed to determine the dependence of standard deviation of percent passing on the mean percent passing through the sieves. In this paper a new method of determining the homo­geneity of ASB according to the variation of gradation using the maximum standard deviation value of this dependence was employed. The minimum size n was calculated with the permissible relative error of 5%, 10%, 15% and 20%. The obtained research findings revealed that due to segregation processes the homogeneity of ASB mixture from the point of its production to application has decreased by about 38%.

A Joint Kurtosis-Based Adaptive Bandstop Filtering and Iterative Autocorrelation Approach to Bearing Fault Detection

This paper reports a bearing fault detection method based on kurtosis-based adaptive bandstop filtering (KABS) and iterative autocorrelation (IAC). The interferences in the bearing signal can be removed by KABS filtering, whereas IAC is employed for noise reduction and signal enhancement. In the KABS method, two window-merging schemes are proposed to identify the frequency bands potentially containing interferences and to preserve those covering fault frequencies. Issues related to the selection of the number of autocorrection iterations are also discussed. The proposed method can be used for bearing fault detection in a low signal-to-noise ratio (SNR) and low signal-to-interference ratio (SIR) environment. The implementation of the proposed method does not require prior knowledge of the fault-excited resonant frequency. The performance of the proposed method has been examined by simulation analysis, with favorable comparisons to the Hilbert enveloping, energy operator, and spectrum kurtosis methods. Its effectiveness in bearing fault detection has also been demonstrated using experimental data.

A comparative analysis of structural damage detection techniques by wavelet, kurtosis and pseudofractal methods

The aim of this paper is to compare wavelet, kurtosis and pseudofractal based techniques for structural health monitoring in the presence of measurement noise. A detailed comparison and assessment of these techniques have been carried out in this paper through numerical experiments for the calibration of damage extent of a simply supported beam with an open crack serving as an illustrative example. The numerical experiments are deemed critical due to limited amount of experimental data available in the field of singularity based detection of damage. A continuous detectibility map has been proposed for comparing various techniques qualitatively. Efficiency surfaces have been constructed for wavelet, kurtosis and pseudofractal based calibration of damage extent as a function of damage location and measurement noise level. Levels of noise have been identified for each technique where a sudden drop of calibration efficiency is observed marking the onset of damage masking regime by measurement noise.

Vibration in Grease Lubricated Bearing Systems

In this study a dynamic bearing apparatus is designed, developed and used to evaluate noise and vibration of bearings lubricated with various greases under different operating conditions. Eight different greases are evaluated for their vibration and noise characteristics. The threshold, kurtosis and mean square methods are used to quantify grease vibration and rank the greases based on their bearing vibration. The results indicate that ultra-filtered greases exhibit the lowest bearing vibration in the mid-frequency range amongst all greases tested. Presented at the 55th Annual Meeting Nashville, Tennessee May 7–11, 2000

Adaptive filtering of sound pressure signals for monitoring machinery in noisy environments

An experimental evaluation of the ability of sound pressure microphones to diagnose different machinery conditions in noisy environments was performed. An adaptive filtering (ANC) routine was incorporated to reduce the noise. The detection process utilized frequency spectra of the data, along with cepstrum and kurtosis methods of analysis. Two different machine components were monitored: ball bearings in a ball bearings test stand and milling bits in a milling machine. The effect of the placement of the microphones on the ANC routine to reduce the background noise in the signal was investigated and found to influence the results. The results show that the sound pressure microphones could not reliably diagnose ball bearing condition but could diagnose the milling machine bit condition.