Multivariate Multiscale Fuzzy Entropy Research Articles

Refined composite multivariate multiscale fuzzy dispersion entropy: Theoretical analysis and applications

Multivariate multiscale sample entropy (mvMSE) is a popular method to quantify the irregularity of multi-channel time series. However, mvMSE generates either undefined or unreliable results for short-length signals and has a high computational cost. To address these issues, multivariate multiscale dispersion entropy (mvMDE) was recently developed, but it depends on its parameters and overlooks some data information. To address these limitations, we herein propose an extension of fuzzy dispersion entropy (FDE) by incorporating fuzzy set theory, multidimensional embedding reconstruction theory, and dispersion patterns. This leads to the multivariate multiscale FDE (mvMFDE) and refined composite mvMFDE (RCmvMFDE) measures. (RC)mvMFDE is the first multivariate analysis based on Shannon entropy that uses the fuzzification concept. Some sets of time series have been synthesized and analyzed using several concepts in multivariate signal processing to evaluate the advantages of our introduced mvMFDE and RCmvMFDE. The results indicated that the proposed methods are less sensitive to their parameters, signal length, and noise, providing more stable results compared to the existing approaches mvMSE and mvMDE. On multi-channel noise signals and bivariate autoregressive processes, mvMSE, mvMDE, and mvMFDE produced similar finding although mvMFDE exhibited superior discriminative capabilities. When applied to one physiological dataset and two mechanical datasets, RCmvMFDE distinguished the diverse dynamics of multichannel signals exceptionally well.

How to mine the abnormal information of power transformers: An efficient tool for quantifying the fault characteristics via multi-vibration signals

The new power system puts forward higher requirements for the reliability of power equipment. Mining the intrinsic information of equipment operation from massive data is the key challenge to determining fault early warning. The transformer fault diagnosis through vibration signal analysis has gained increasing prominence. However, the vibration signals produced by power transformers exhibit complex nonlinear and multivariate fluctuations due to the interaction of electromagnetic and mechanical factors. Unfortunately, the traditional fault diagnosis models lack the capability to capture extensive global fault information, resulting in inadequate performance in fault identification. This paper proposes the enhanced hierarchical multivariate multiscale fuzzy entropy (EHMvMFE) as an effective method for quantifying defect information in multivariate transformer signals to overcome the challenge. Firstly, the enhanced hierarchical decomposition method and time series coarse-graining theory are introduced into multivariate fuzzy entropy to develop EHMvMFE, which can comprehensively reflect the feature information of multivariate signals from the full range of frequencies. Then, EHMvMFE is utilized to extract the features via multivariate vibration signals of the transformer. Finally, the extreme learning machine is conducted to achieve effective identification of abnormal conditions. The proposed method is applied to two categories of transformer fault cases, and the diagnostic indicators are at least higher than 99.70 % and 91.82 %, which indicates a strong advantage in comparison with other popular models. The approach could be flexibly extended to the fault diagnosis of other power equipment, which is a potentially effective tool for improving the reliability of power systems.

Optimized multivariate multiscale slope entropy for nonlinear dynamic analysis of mechanical signals

Slope entropy (SloEn) is an effective nonlinear dynamic method to represent the complexity of time series, which has been extensively applied to various mechanical signal processing. However, it is only applicable to the analysis of single-channel time series at a single scale. Additionally, thresholds γandδ of SloEn can affect the division of symbols. To address these limitations, this paper firstly develops multivariate SloEn (mvSloEn) and extends it to multiscale mvSloEn (mvMSloEn), which not only accounts for the correlation of time series complexity within and across channels, but also mirrors the complexity of multi-channel time series over multiple scales. Furthermore, the sea-horse optimization-mvMSloEn (SHO-mvMSloEn) is proposed through utilizing the sea-horse optimizer (SHO) to fine-tune the thresholds for improved performance. Finally, the proposed SHO-mvMSloEn is applied to three real-world datasets and the highest classification accuracies are all over 98 %, superior to the existing multivariate multiscale dispersion entropy (mvMDE), multivariate multiscale fuzzy entropy (mvMFE), and multivariate multiscale sample entropy (mvMSE), which demonstrates that the proposed SHO-mvMSloEn always exhibits the best feature extraction capability.

A new rotating machinery fault diagnosis method for different speeds based on improved multivariate multiscale fuzzy distribution entropy

A new rotating machinery fault diagnosis method for different speeds based on improved multivariate multiscale fuzzy distribution entropy

Which Multivariate Multi-Scale Entropy Algorithm Is More Suitable for Analyzing the EEG Characteristics of Mild Cognitive Impairment?

So far, most articles using the multivariate multi-scale entropy algorithm mainly use algorithms to analyze the multivariable signal complexity without clearly describing what characteristics of signals these algorithms measure and what factors affect these algorithms. This paper analyzes six commonly used multivariate multi-scale entropy algorithms from a new perspective. It clarifies for the first time what characteristics of signals these algorithms measure and which factors affect them. It also studies which algorithm is more suitable for analyzing mild cognitive impairment (MCI) electroencephalograph (EEG) signals. The simulation results show that the multivariate multi-scale sample entropy (mvMSE), multivariate multi-scale fuzzy entropy (mvMFE), and refined composite multivariate multi-scale fuzzy entropy (RCmvMFE) algorithms can measure intra- and inter-channel correlation and multivariable signal complexity. In the joint analysis of coupling and complexity, they all decrease with the decrease in signal complexity and coupling strength, highlighting their advantages in processing related multi-channel signals, which is a discovery in the simulation. Among them, the RCmvMFE algorithm can better distinguish different complexity signals and correlations between channels. It also performs well in anti-noise and length analysis of multi-channel data simultaneously. Therefore, we use the RCmvMFE algorithm to analyze EEG signals from twenty subjects (eight control subjects and twelve MCI subjects). The results show that the MCI group had lower entropy than the control group on the short scale and the opposite on the long scale. Moreover, frontal entropy correlates significantly positively with the Montreal Cognitive Assessment score and Auditory Verbal Learning Test delayed recall score on the short scale.

Fault diagnosis of bearing based on refined piecewise composite multivariate multiscale fuzzy entropy

As one of the key components of the train, the condition of the bearing is related to the train's safe operation. The vibration signal of the bearing is usually nonlinear and nonstationary, which makes it difficult to extract fault features and leads to low diagnostic accuracy. Entropy theory can effectively measure the change of nonlinearity and complexity of the vibration signal. However, the conventional entropy algorithm cannot extract the characteristics of a multi-channel signal simultaneously. A bearing fault diagnosis method based on refined piecewise composite multivariate multiscale fuzzy entropy (RPCMMFE) and convolutional neural network (CNN) is proposed. The proposed method can fully extract fault features and improve fault diagnosis accuracy. Firstly, based on multivariate multiscale fuzzy entropy (MMFE), RPCMMFE is proposed by introducing refined theory and piecewise composite theory. Then, the RPCMMFE of different fault signals is calculated, and RPCMMFE is considered to be a feature vector that acts as an input into the CNN for fault diagnosis. Finally, it is verified by two groups of experiments. The experimental results show that the features extracted by this method have better stability and discrimination ability and can identify bearing faults more accurately. The average accuracy rates are 99% and 99.17%, respectively.

Multivariate Multiscale Cosine Similarity Entropy and Its Application to Examine Circularity Properties in Division Algebras

The extension of sample entropy methodologies to multivariate signals has received considerable attention, with traditional univariate entropy methods, such as sample entropy (SampEn) and fuzzy entropy (FuzzyEn), introduced to measure the complexity of chaotic systems in terms of irregularity and randomness. The corresponding multivariate methods, multivariate multiscale sample entropy (MMSE) and multivariate multiscale fuzzy entropy (MMFE), were developed to explore the structural richness within signals at high scales. However, the requirement of high scale limits the selection of embedding dimension and thus, the performance is unavoidably restricted by the trade-off between the data size and the required high scale. More importantly, the scale of interest in different situations is varying, yet little is known about the optimal setting of the scale range in MMSE and MMFE. To this end, we extend the univariate cosine similarity entropy (CSE) method to the multivariate case, and show that the resulting multivariate multiscale cosine similarity entropy (MMCSE) is capable of quantifying structural complexity through the degree of self-correlation within signals. The proposed approach relaxes the prohibitive constraints between the embedding dimension and data length, and aims to quantify the structural complexity based on the degree of self-correlation at low scales. The proposed MMCSE is applied to the examination of the complex and quaternion circularity properties of signals with varying correlation behaviors, and simulations show the MMCSE outperforming the standard methods, MMSE and MMFE.

A MVMD–MMFE algorithm and its application in the flow patterns identification of horizontal oil–water two-phase flow

Abstract Aiming to extract the main information features of fluid multivariate conductance signals and identify the flow patterns under different flow velocities, we present a multichannel time series analysis algorithm based on the multivariate variational mode decomposition (MVMD) and multivariate multiscale fuzzy entropy (MMFE). Firstly, by simulating a multichannel complex signal and performing a series of sensitivity experiments within various noise intensities, we prove the feasibility of the MVMD in chaotic time series. Then, we employ the MVMD to decompose multivariate conductance signals into the intrinsic mode function (IMF) and calculate the MMFE of the IMFs for different flow patterns. Meanwhile, the multivariate empirical mode decomposition (MEMD) is also applied on the comparison of signal decomposition. Finally, we discuss the classification consequence under different mode values k to realize the optimal decomposition. The experimental results show that the MVMD–MMFE algorithm can extract the main information of fluid multichannel signals and distinguish three horizontal oil–water flow patterns effectively, which provides an idea for studying the nonlinear characteristics of the chaotic system.

Variational Embedding Multiscale Diversity Entropy for Fault Diagnosis of Large-Scale Machinery

The large-scale machinery generally requires multiple accelerometers for condition monitoring. The multichannel vibration signals carry a wealth of fault information. Synchronous fault feature extraction using multichannel signals will significantly improve the diagnostic performance. The multivariate entropy method is able to synchronously extract the fault features from multiple sensors, but how to recognize the single fault occurring on different channels remains unexplored. In this article, we propose a novel feature extraction method called variational embedding multiscale diversity entropy, which constructs the phase space with different structures. The proposed variational phase space construction strategy will generate a different probability distribution for each channel, which results in a better separability for multichannel feature extraction. Combined with the random forest classifier, a novel fault diagnosis scheme is developed for condition monitoring of the large-scale machinery. One simulated signal and two experimental data are designed to validate the effectiveness of the proposed strategy. The results demonstrate that the proposed method has the best multichannel feature extraction ability compared with three existing methods: multivariate multiscale sample entropy, multivariate multiscale fuzzy entropy, and multivariate multiscale permutation entropy.

Using the Features Extracted From the Ambient Noise Cross-Correlation Function to Evaluate the Performance of Broadband Seismograph

Broadband seismographs are used to collect seismic data over an extended period. Temperature, pressure, and humidity are field variables that can have an impact on the broadband seismograph’s performance as well as the accuracy of observational data. Variations in performance, geological structure, and noise source will cause the cross-correlation function of seismic ambient noise to alter. To evaluate the effectiveness of seismographs, we propose to use the whole cross-correlation function as well as the positive and negative time waveforms for feature extraction. The cross-correlation function is decomposed to evaluate the phase variations using Local Mean Decomposition (LMD) and Variational Mode Decomposition (VMD). This is followed by the calculation of the Multivariate Multiscale Fuzzy Entropy Partial Mean (MMFEPM). Wavelet Packet Decomposition (WPD) and MMFEPM are used to evaluate phase variations in the positive and negative time waveforms. WPD combined with Wavelet Feature Scale Entropy (WFSE) is chosen to evaluate the amplitude variations of the cross-correlation function and its positive and negative waveforms. The results show that the proposed methods can identify time offsets within 0.025-2.5s and amplitude variations of 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-16</sup> , which provide a new direction for evaluating the performance of seismographs using ambient noise.

Refined Composite Multivariate Multiscale Fractional Fuzzy Entropy: Measuring the Dynamical Complexity of Multichannel Financial Data

Refined composite multivariate multiscale fractional fuzzy entropy (RCmvMFFE), which aims to sensitively discriminate different short noisy multichannel financial data, is proposed as a new measure to quantify the complexity dynamics of multichannel time series in this work. To better comprehend the RCmvMFFE measure, the dynamical complexity analyses of multichannel synthetic dataset are comparatively studied with multivariate multiscale fuzzy entropy (mvMFE), refined composite multivariate multiscale fuzzy entropy (RCmvMFE), and refined composite multivariate multiscale fractional fuzzy entropy (RCmvMFFE). Then, these measures are firstly employed to explore actual multichannel financial index series to the best of our knowledge. The empirical analyses report that RCmvMFFE measure is able to deeply and sensitively dig up the market information hidden in the multichannel financial data and can better discriminate markets in different area compared to the traditional measures to some extent.

Rotating machinery fault diagnosis based on multivariate multiscale fuzzy distribution entropy and Fisher score

With evaluating the randomness and the nonlinear dynamic change of time sequence effectively, multiscale fuzzy distribution entropy (MFDE) is proposed to extract fault features from vibration signal. However, it is unsuitable for multivariate signals, which contain more abundant fault information. Through changing the coarse-grained and calculation process of MFDE, a novel entropy named as multivariate multiscale fuzzy distribution entropy (MMFDE) is proposed, which not only has the characteristics of MFDE, but also considers the within- and cross-channel correlations. By applying MMFDE to two kinds of simulation signals, the results show the proposed entropy is stable and reliable. A novel fault diagnosis method for rotating machinery is proposed by extracting fault features with MMFDE, selecting sensitive ones with Fisher score (FS), and identifying working state with support vector machine (SVM). Two experiments show the better diagnosis performance of the proposed rotating machinery fault diagnosis method than the related methods with the accuracy of 98.95% and 96.80% respectively.

Complexity Analysis of Three-Dimensional Fractional-Order Chaotic System Based on Entropy Theory

Complexity analysis of fractional-order chaotic system is an interesting topic in recent years. How to measure the complexity of fractional-order chaotic system correctly and effectively is the basis of its theoretical analysis and engineering application. In this paper, complexity analysis of three-dimensional fractional-order chaotic system based on multivariate multiscale fuzzy entropy (mvMFE), multivariate multiscale sample entropy (mvMSE) and multivariate multiscale dispersion entropy (mvMDE) respectively is proposed. In the case of single parameter change, different entropy such as mvMFE, mvMSE and mvMDE are used to analyze how complexity varies with parameter. In the case of two parameters change, the change of complexity is analyzed by the chromatomap which takes two parameters as independent variable, and mvMFE, mvMSE, and mvMDE as the dependent variable when the two parameters change simultaneously. Aiming at the performance problem when the complexity of three-dimensional fractional-order chaotic system is analyzed by mvMFE, mvMSE, and mvMDE, the maximum complexity under single parameter and the detection area under two parameters are used as indicators. The result shows that the performance of mvMDE is the best, and the nonlinear term in the mathematical model of fractional-order chaotic system is positively correlated with the complexity of the system. This will provide a new method for measuring the complexity of fractional-order chaotic system, and lay the basis of theoretical analysis and practical application of fractional chaotic system in the fields of image encryption, sound encryption, image compression-encryption technique, and secure communication.

Fuzzy support vector machine with joint optimization of genetic algorithm and fuzzy c-means.

Motor imagery electroencephalogram (MI-EEG) play an important role in the field of neurorehabilitation, and a fuzzy support vector machine (FSVM) is one of the most used classifiers. Specifically, a fuzzy c-means (FCM) algorithm was used to membership calculation to deal with the classification problems with outliers or noises. However, FCM is sensitive to its initial value and easily falls into local optima. The joint optimization of genetic algorithm (GA) and FCM is proposed to enhance robustness of fuzzy memberships to initial cluster centers, yielding an improved FSVM (GF-FSVM). The features of each channel of MI-EEG are extracted by the improved refined composite multivariate multiscale fuzzy entropy and fused to form a feature vector for a trial. Then, GA is employed to optimize the initial cluster center of FCM, and the fuzzy membership degrees are calculated through an iterative process and further applied to classify two-class MI-EEGs. Extensive experiments are conducted on two publicly available datasets, the average recognition accuracies achieve 99.89% and 98.81% and the corresponding kappa values are 0.9978 and 0.9762, respectively. The optimized cluster centers of FCM via GA are almost overlapping, showing great stability, and GF-FSVM obtains higher classification accuracies and higher consistency as well.

뇌전도의 다변량 다중스케일 퍼지 엔트로피 분석에 기반한 감정 인식

뇌전도(Electroencephalogram, EEG) 신호는 뇌 활동의 즉각적이고 지속적인 신호로서, 사람의 감정 상태의 변화를 직접적으로 반영할 수 있기 때문에 감정 분석에 주로 이용된다. 이러한 EEG 신호의 분석 방법 중, 엔트로피(Entropy) 분석은 시계열의 복잡성을 정량화하기 위한 측정법 중 하나이며, 복잡성의 정량적 분석은 비정상적이고 비선형적인 생체 신호의 분석에 유망하다. 본 논문에서는 여러 전극으로부터 기록된 EEG 신호를 사용하여 감정 상태를 분석하기 위해 여러 시간 스케일에서 다변량 시계열의 복잡도를 정량화하는 다변량 다중스케일 퍼지 엔트로피(Multivariate Multiscale Fuzzy Entropy)를 제안한다. 공공 생체신호 데이터베이스인 DEAP의 EEG 데이터를 이용하여 높은/낮은 각성(Arousal) 및 높은/낮은 정서(Valence)의 이진 분류를 통해 감정 상태의 구분의 유효성을 검증하였다.

Monitoring of multi-bolt connection looseness using entropy-based active sensing and genetic algorithm-based least square support vector machine

Abstract Looseness detection of bolted connections is an essential industrial issue that can reduce the maintenance and repair costs caused by joint failures; however, current loosening detection methods mainly focus on the single-bolt connection. Even though several methods, such as the vibration-based method and electro-mechanical impedance (EMI) method, have been employed to detect multi-bolt looseness, while they are easily affected by environmental issues. Therefore, the main contribution of this paper is to detect loosening of the multi-bolt connection through the PZT-enabled active sensing method, which has several merits including easy-to-implement, low cost, and good ability of anti-environment disturbance. Since the current indicator of the active sensing, namely the signal energy is insensitive to multiple damages, we developed a new damage index (DI) based on the multivariate multiscale fuzzy entropy (MMFE). Subsequently, the maximum relevance minimum redundancy (mRMR) was used to select significant features from the MMFE-based DI to construct the new datasets. After feeding the new datasets into the genetic algorithm-based least square support vector machine (GA-based LSSVM), we trained a classifier to detect loosening of the multi-bolt connection. Finally, repeated experiments were conducted to demonstrate the effectiveness of the proposed method, which can guide future investigations on bolt looseness detection.

An integrated method based on refined composite multivariate hierarchical permutation entropy and random forest and its application in rotating machinery

Fault feature extraction of rotating machinery is crucial and challenging due to its nonlinear and nonstationary characteristics. In order to resolve this difficulty, a quality nonlinear fault feature extraction method is required. Hierarchical permutation entropy has been proven to be a promising nonlinear feature extraction method for fault diagnosis of rotating machinery. Compared with multiscale permutation entropy, hierarchical permutation entropy considers the fault information hidden in both high frequency and low frequency components. However, hierarchical permutation entropy still has some shortcomings, such as poor statistical stability for short time series and inability of analyzing multichannel signals. To address such disadvantages, this paper proposes a new entropy method, called refined composite multivariate hierarchical permutation entropy. Refined composite multivariate hierarchical permutation entropy can extract rich fault information hidden in multichannel signals synchronously. Based on refined composite multivariate hierarchical permutation entropy and random forest, a novel fault diagnosis framework is proposed in this paper. The effectiveness of the proposed method is validated using experimental and simulated signals. The results demonstrate that the proposed method outperforms multivariate multiscale fuzzy entropy, refined composite multivariate multiscale fuzzy entropy, multivariate multiscale sample entropy, multivariate multiscale permutation entropy, multivariate hierarchical permutation entropy, and composite multivariate hierarchical permutation entropy in recognizing the different faults of rotating machinery.

Multivariate Multiscale Dispersion Entropy of Biomedical Times Series

Due to the non-linearity of numerous physiological recordings, non-linear analysis of multi-channel signals has been extensively used in biomedical engineering and neuroscience. Multivariate multiscale sample entropy (MSE–mvMSE) is a popular non-linear metric to quantify the irregularity of multi-channel time series. However, mvMSE has two main drawbacks: (1) the entropy values obtained by the original algorithm of mvMSE are either undefined or unreliable for short signals (300 sample points); and (2) the computation of mvMSE for signals with a large number of channels requires the storage of a huge number of elements. To deal with these problems and improve the stability of mvMSE, we introduce multivariate multiscale dispersion entropy (MDE–mvMDE), as an extension of our recently developed MDE, to quantify the complexity of multivariate time series. We assess mvMDE, in comparison with the state-of-the-art and most widespread multivariate approaches, namely, mvMSE and multivariate multiscale fuzzy entropy (mvMFE), on multi-channel noise signals, bivariate autoregressive processes, and three biomedical datasets. The results show that mvMDE takes into account dependencies in patterns across both the time and spatial domains. The mvMDE, mvMSE, and mvMFE methods are consistent in that they lead to similar conclusions about the underlying physiological conditions. However, the proposed mvMDE discriminates various physiological states of the biomedical recordings better than mvMSE and mvMFE. In addition, for both the short and long time series, the mvMDE-based results are noticeably more stable than the mvMSE- and mvMFE-based ones. For short multivariate time series, mvMDE, unlike mvMSE, does not result in undefined values. Furthermore, mvMDE is faster than mvMFE and mvMSE and also needs to store a considerably smaller number of elements. Due to its ability to detect different kinds of dynamics of multivariate signals, mvMDE has great potential to analyse various signals.

Multichannel Complexity Index (MCI) for a multi-organ physiological complexity assessment

Quantitative measurements of multi-organ interplay are crucial for the assessment of multivariate physiological dynamics in health and disease. Nevertheless, current quantification of multivariate complexity for nonlinear physiological processes is limited by reliability issues on short-time series, and parameters sensitivity especially in case of a multiscale analysis. To overcome these limitations, we propose a new tool to characterize the complexity of interacting physiological processes that may have different temporal dynamics: the Multichannel Complexity Index (MCI). This metrics relies on a novel method for the reconstruction of the multivariate phase space, where each series is embedded using its proper time delay. MCI accounts for the estimation of phase space distances using fuzzy rules, and may be computed at two different ranges of time-scale values to investigate short- and long-term dynamics. We validated our algorithm using three-channel white gaussian noise and 1/f noise systems, with different levels of coupling. By applying our approach to these data, we demonstrate that the MCI method allows to discern not only the degree of complexity in the system dynamics, but also the across-channel coupling level. Results on synthetic series from the Henón map and Rössler attractor demonstrate that MCI effectively discerns between different dynamical behaviours, outperforming state of the art metrics such as the Refined Composite Multivariate Multiscale Fuzzy Entropy. On publicly-available physiological series, considering heartbeat dynamics and blood pressure variability, results demonstrate a MCI sensitivity to postural changes(p<10−2 for rest vs. slow-tilt, and p<0.05 for rest vs. rapid-tilt/stand-up conditions), as well as a MCI sensitivity to subjects’ age-range (data gathered while watching Fantasia Disney movie, 1940) with p<10−2 for short scales and p=0.03 for long scales. In conclusion, MCI is a viable tool for an effective multivariate physiological complexity assessment. The Matlab code implementing the proposed MCI algorithm is available online.

An Improved Refined Composite Multivariate Multiscale Fuzzy Entropy Method for MI-EEG Feature Extraction.

Feature extraction of motor imagery electroencephalogram (MI-EEG) has shown good application prospects in the field of medical health. Also, multivariate entropy-based feature extraction methods have been gradually applied to analyze complex multichannel biomedical signals, such as EEG and electromyography. Compared with traditional multivariate entropies, refined composite multivariate multiscale fuzzy entropy (RCmvMFE) overcomes the defect of unstable entropy values caused by the scale factor increase and is beneficial towards obtaining richer feature information. However, the coarse-grained process of RCmvMFE is mean filtered, which weakens Gaussian noise and is powerless against random impulse noise interference. This yields poor quality feature information and low accuracy classification. In this paper, RCmvMFE is improved (IRCmvMFE) by using composite filters in the coarse-grained procedure to enhance filter performance. Median filters are employed to remove the impulse noise interference from multichannel MI-EEG signals, and these filtered MI-EEGs are further smoothed by the mean filters. The multiscale IRCmvMFEs are calculated for all channels of composite filtered MI-EEGs, forming a feature vector, and a support vector machine is used for pattern classification. Based on two public datasets with different motor imagery tasks, the recognition results of 10 × 10-fold cross-validation achieved 99.43% and 99.86%, respectively, and the statistical analysis of experimental results was completed, showing the effectiveness of IRCmvMFE, as well. The proposed IRCmvMFE-based feature extraction method is superior compared to entropy-based and traditional methods.