Multivariate Multiscale Entropy Research Articles

Robust Fault Diagnosis of Rolling Bearings Using Multivariate Intrinsic Multiscale Entropy Analysis and Neural Network Under Varying Operating Conditions

olling bearings are crucial components in mechanical, civil and aerospace engineering. The practical working conditions of rolling bearings are complex and tough, hence fault diagnosis of rolling bearings under varying operating conditions is very challenging. This paper proposes a robust fault diagnosis approach of rolling bearings using multivariate intrinsic multiscale entropy analysis and neural network under varying operating conditions. The proposed approach deals with multivariate signal collected from multi-sensor acquisition system to capture much dynamical characteristic information. Multivariate intrinsic multiscale entropy analysis consists of adaptive projection intrinsically transformed multivariate empirical mode decomposition with adaptive noise (APIT-MEMD-AN) and improved multivariate multiscale sample entropy (IMMSE) with smoothed coarse graining process. Intrinsic mode functions (IMFs) obtained by APIT-MEMD-AN depict dynamical properties of multivariate signals. IMMSE of certain orders IMFs are adopted as input values of back propagation (BP) neural network to achieve fault classification of rolling bearings. APIT-MEMD-AN and IMMSE endow the proposed approach with the underlying adaptivity and robustness, making the proposed approach a fully data driven and robust method. Theoretical derivations, numerical simulations and experimental results verify the effectiveness and superiority of the proposed approach. The research work demonstrates the proposed approach is promising in fault diagnosis of rotary machinery under varying operating conditions.

An investigation of oil–water two-phase flow instability using multivariate multi-scale weighted permutation entropy

The present study is devoted to the investigation of oil–water two-phase flow instability using multivariate multi-scale weighted permutation entropy (MWMPE). Four typical multivariate multi-scale entropies, namely MWMPE, multivariate multi-scale permutation entropy (MMPE), multivariate multi-scale sample entropy (MMSE) and multivariate multi-scale approximate entropy (MMAE) are applied in Lorenz system with the addition of different kinds of noises. The comparison results indicate that MWMPE presents the superiorities of being sensitive to the variation in scale, showing a monotonous increasing trend as well as the best anti-noise ability. Accordingly, with the fluctuating signals from an eight-electrode rotating electrical field conductance sensor used for the measurement of oil–water flows, we extract MWMPE for the whole experimental flow conditions, in terms of which the effects of mixture velocity and water-cut on oil–water two-phase flow instability are illuminated. Our research provides an effective method for uncovering the underlying evolution instability of the flow structures in oil–water flows.

Ore particle size classification model based on bi-dimensional empirical mode decomposition

The frequency domain information of ore multi-scale image is difficult to distinguish boundary and texture details of ore objects, and hard to apply to particle size detection. Particle size classification model based on Bi-dimensional empirical mode decomposition (BEMD) is proposed, which is applied to particle detection of multi-size scenarios. Different size fraction ore images’ local frequencies are extracted by BEMD reflecting the edge and texture features. The instantaneous frequencies of each high-frequency images are statistic with image multivariate multiscale entropy, and the entropy ranges can be mapped into the particle size distribution. Three different size fraction images are used to verify the accuracy of the proposed method. The experimental results show that the validity and accuracy of our proposed model is better than other methods in multi-scenario ore particle size detection.

Multivariate multiscale distribution entropy of financial time series

The complexity of time series has become necessary to understand the dynamics of the control system. In this paper, the multivariate multiscale distribution entropy (MMSDE) is introduced as a new method to assess the complexity of dynamical systems such as financial systems, physiological systems, etc. Distribution entropy (DE) takes full advantage of the information hidden in the state–space by the estimation of the probability density of distances among vectors. Based on this, MMSDE can quantify the complexity of multivariate time series from multiple time scales. We test the performance of this method with simulated data. Results show that MMSDE has less dependence on parameters and the test of short time series is very effective. As for the real data, we explore the high dimensional series that are composed of opening price, closing price, volume of stocks data including US stock indices and Chinese stock indices. MMSDE can quantify the change in the complexity of the stock market data. In addition, we get richer information from MMSDE and gain some features about the difference between the U.S. and Chinese stock indexes.

Multivariate multiscale fractional order weighted permutation entropy of nonlinear time series

In this letter, multivariate multiscale fractional permutation entropy (MMFPE) and multivariate weighted multiscale fractional permutation entropy (MWMFPE) have been proposed to provide insights for the study of time series. When measuring the dynamics of complex systems, the MMFPE and MWMFPE methods are sensitive to the signal evolution. Meanwhile, they can provide some analysis of complexity over multiple time series as well as multiple channel signals. We perform these methods on synthetic tri-variate time series to explore some of the interesting properties, especially for negative information and information deception. It can be seen that more complex system is more likely to be deceptive. The amplitude information of time series which is taken into account in the MWMFPE can weaken this deception. The methods are also employed to the closing prices and trade volume of financial stock markets from different areas. According to the MWMFPE results, the indices can be divided into three groups: (1) CAC40, HSI, NASDAQ, S&P500, (2) N225, and (3) ShenCheng, implying that it has a capacity to distinguish these financial stock market.

A new method for tolerance estimation of multivariate multiscale sample entropy and its application for short-term time series

Multivariate multiscale sample entropy (MMSE) is a robust method to detect the complexity of multivariate system. It is evaluated for a certain value of tolerance parameter r which is mainly calculated from common acknowledged range. This kind of selection of r is not suitable for short-term time series and may lead to the unreliable detection. To reduce the impact of limited range of r, we apply cumulative histogram method to estimate the range of r. It is data-driven and needs no parameters. Moreover, we use secondary statistics, AvgMMSE and SDMMSE rather than the single value of MMSE to detect the complexity of signals and differentiate them. Several time series, either generated from chaotic or stochastic systems, are analyzed to demonstrate the approach. The core achievement of this experiment is the stability and classification for short-term time series. Then we apply this method to financial time series. Empirical results show that the proposed method is vigorous enough to classify different stock indices over different periods.

Health Degradation Monitoring and Early Fault Diagnosis of a Rolling Bearing Based on CEEMDAN and Improved MMSE.

Rolling bearings play a crucial role in rotary machinery systems, and their operating state affects the entire mechanical system. In most cases, the fault of a rolling bearing can only be identified when it has developed to a certain degree. At that moment, there is already not much time for maintenance, and could cause serious damage to the entire mechanical system. This paper proposes a novel approach to health degradation monitoring and early fault diagnosis of rolling bearings based on a complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN) and improved multivariate multiscale sample entropy (MMSE). The smoothed coarse graining process was proposed to improve the conventional MMSE. Numerical simulation results indicate that CEEMDAN can alleviate the mode mixing problem and enable accurate intrinsic mode functions (IMFs), and improved MMSE can reflect intrinsic dynamic characteristics of the rolling bearing more accurately. During application studies, rolling bearing signals are decomposed by CEEMDAN to obtain IMFs. Then improved MMSE values of effective IMFs are computed to accomplish health degradation monitoring of rolling bearings, aiming at identifying the early weak fault phase. Afterwards, CEEMDAN is performed to extract the fault characteristic frequency during the early weak fault phase. The experimental results indicate the proposed method can obtain a better performance than other techniques in objective analysis, which demonstrates the effectiveness of the proposed method in practical application. The theoretical derivations, numerical simulations, and application studies all confirmed that the proposed health degradation monitoring and early fault diagnosis approach is promising in the field of prognostic and fault diagnosis of rolling bearings.

Weighted multivariate composite multiscale sample entropy analysis for the complexity of nonlinear times series

Multivariate multiscale sample entropy (MMSE) has recently been proposed to evaluate complexity of time series. However, the results of estimation of complexity by MMSE method may be inaccurate as the coarse-graining procedure reduces the length of the time series at a large scale. In addition, MMSE has some limitations, mainly its inability to detect abrupt changes in the signal and ignore the difference between distinct patterns. In order to overcome those above limitations of MMSE, this paper introduces the weighted multivariate composite multiscale sample entropy (WMCMSE) as a measure to characterize the complexity of nonlinear time series. And we illustrate the necessity of WMCMSE method by comparing WMCMSE results with multivariate multiscale sample entropy (MMSE), weighted multivariate multiscale sample entropy (WMMSE), multivariate composite multiscale sample entropy (MCMSE) on random series. Then, WMCMSE method is employed to study the complexity of traffic speed and volume time series of Beijing Ring 2, 3, 4 roads, which are from August 11th to October 20th, 2012. The results of WMCMSE show that the WMCMSE method can distinguish the behavior of the flow time series, which means that we can detect the congested traffic system. We found that road condition of ring 2, 3, 4 road is very different. Compared to the ring 4 road, the values of the WMCMSE of the ring 2 and 3 roads are higher, indicating that the traffic flow on Ring 2 and Ring 3 road are more complex compared to Ring 4 road. The higher the complexity, the more traffic jams. Government departments can judge the traffic congestion of that time period and that road according to the complexity differences between different time periods and different roads, and then take different measures.

Multivariate empirical mode decomposition and multiscale entropy analysis of EEG signals from SSVEP-based BCI system

The steady-state visual evoked potential (SSVEP)-based Brain-Computer Interface (BCI) has been employed in the brain-controlled wheelchair system for patients with severe dyskinesia disease. However, a long-time operation brings about users fatigue, leading to a decrease of performance of the BCI system in practical applications. The characterization of the fatigued mechanism and the improvement of the SSVEP classification accuracy remains a challenging problem of significant importance. In this letter, we first conduct SSVEP experiments to acquire the EEG signals during both normal and fatigued states. Then we develop a novel framework, which integrates the advantages of multivariate empirical mode decomposition (MEMD) and Support Vector Machine (SVM), for improving the SSVEP classification accuracy, especially during the fatigued state. The results suggest that the novel framework enables us to obtain a higher SSVEP classification accuracy compared with the method without MEMD. Furthermore, in order to reveal the fatigued behavior, we use the multivariate multiscale sample entropy (MMSE) to analyze the multi-channel EEG signals corresponding to normal and fatigued states. We interestingly find that the MMSE values in the fatigued state are lower than that in the normal state, which reflects the increase of regularity in SSVEP signals during the fatigued state. That is, a greater synchronization of neural assemblies is required to realize cognitive impairment when fatigue happens. The knowledge for the understanding of the brain fatigued behavior underlying SSVEP-based BCI experiments is gained by our analysis.

A multiple-fan active control wind tunnel for outdoor wind speed and direction simulation.

This article presents a new type of active controlled multiple-fan wind tunnel. The wind tunnel consists of swivel plates and arrays of direct current fans, and the rotation speed of each fan and the shaft angle of each swivel plate can be controlled independently for simulating different kinds of outdoor wind fields. To measure the similarity between the simulated wind field and the outdoor wind field, wind speed and direction time series of two kinds of wind fields are recorded by nine two-dimensional ultrasonic anemometers, and then statistical properties of the wind signals in different time scales are analyzed based on the empirical mode decomposition. In addition, the complexity of wind speed and direction time series is also investigated using multiscale entropy and multivariate multiscale entropy. Results suggest that the simulated wind field in the multiple-fan wind tunnel has a high degree of similarity with the outdoor wind field.

Wii Balanced Board-Based Utilization for the Human Body Center of Pressure for the Falling Detection via Multivariate Empirical Mode Decomposition and Multivariate Multi-scale Entropy

Wii Balanced Board-Based Utilization for the Human Body Center of Pressure for the Falling Detection via Multivariate Empirical Mode Decomposition and Multivariate Multi-scale Entropy

A Refined Composite Multivariate Multiscale Fuzzy Entropy and Laplacian Score-Based Fault Diagnosis Method for Rolling Bearings

The vibration signals of rolling bearings are often nonlinear and non-stationary. Multiscale entropy (MSE) has been widely applied to measure the complexity of nonlinear mechanical vibration signals, however, at present only the single channel vibration signals are used for fault diagnosis by many scholars. In this paper multiscale entropy in multivariate framework, i.e., multivariate multiscale entropy (MMSE) is introduced to machinery fault diagnosis to improve the efficiency of fault identification as much as possible through using multi-channel vibration information. MMSE evaluates the multivariate complexity of synchronous multi-channel data and is an effective method for measuring complexity and mutual nonlinear dynamic relationship, but its statistical stability is poor. Refined composite multivariate multiscale fuzzy entropy (RCMMFE) was developed to overcome the problems existing in MMSE and was compared with MSE, multiscale fuzzy entropy, MMSE and multivariate multiscale fuzzy entropy by analyzing simulation data. Finally, a new fault diagnosis method for rolling bearing was proposed based on RCMMFE for fault feature extraction, Laplacian score and particle swarm optimization support vector machine (PSO-SVM) for automatic fault mode identification. The proposed method was compared with the existing methods by analyzing experimental data analysis and the results indicate its effectiveness and superiority.

Multivariate Multiscale Symbolic Entropy Analysis of Human Gait Signals

The complexity quantification of human gait time series has received considerable interest for wearable healthcare. Symbolic entropy is one of the most prevalent algorithms used to measure the complexity of a time series, but it fails to account for the multiple time scales and multi-channel statistical dependence inherent in such time series. To overcome this problem, multivariate multiscale symbolic entropy is proposed in this paper to distinguish the complexity of human gait signals in health and disease. The embedding dimension, time delay and quantization levels are appropriately designed to construct similarity of signals for calculating complexity of human gait. The proposed method can accurately detect healthy and pathologic group from realistic multivariate human gait time series on multiple scales. It strongly supports wearable healthcare with simplicity, robustness, and fast computation.

Evaluation of effects of balance training from using wobble board-based exergaming system by MSE and MMSE techniques

Balance is an important criterion in assessing health. The lack of exercise of most young people leads to an increased risk of balance abnormity as part of irregular lifestyles. This paper examines the effect of training with an interactive exercise game on young people’s balance after 1 month. The experiment and analysis followed a three-stage design. Initially, gait function testing was conducted to determine a datum point for the situation at the outset; next, a Gym Top balance trainer was used for training; finally, balance was measured with a force plate and center of pressure signals were collected. Differences in balance before and after training were analyzed with multiscale entropy and multivariate multiscale entropy methods. 12 healthy young people were recruited for the experiment. Statistical analysis of the gait test observations revealed that the number of times of standing and sitting increased significantly after training. Multiscale entropy analysis showed that the multiscale entropy curve was higher after training than before training. Multivariate multiscale entropy analysis showed that balance after training was greater than before training. These results demonstrate that the balance of young people was improved after training with a balance trainer eight times a month.

Characterizing dynamics of absence seizure EEG with spatial-temporal permutation entropy

Abstract Characterizing transient brain dynamics prior to seizures is a main challenge in absence epilepsy study. As brain is a chaos dynamical system, many complexity based methods have been used to track the dynamical changes of absence seizure EEG. However, most of these methods treat multichannel EEG recordings as a set of individual time series, which will inevitably lead to the loss of crucial cross-channel correlation in the epileptic network. Recently, a spatial-temporal permutation entropy method called multivariate multiscale permutation entropy (MMPE) was proposed to measure the complexity of multichannel data. In this study, MMPE was applied to multichannel EEG for characterizing dynamics of absence seizure. It was found that the pre-ictal EEG exhibited a significant lower MMPE value than interictal EEG, and a significant higher MMPE value than the ictal EEG, indicating that the complexity of multichannel EEG decreased in the transition of brain activities. This finding confirmed the existence of a pre-seizure state in absence epilepsy. The identification ability of MMPE was tested against its original univariate complexity measures: permutation entropy (PE) and multiscale permutation entropy (MSPE), and another multivariate multiscale entropy: multivariate multiscale sample entropy (MMSE). After evaluating the performance by four classifiers (Decision Tree, K-Nearest Neighbor, Discriminant Analysis, Support Vector Machine), MMPE can achieve accuracy of 87.2% at least, which is about 15%, 12%, and 10% higher than that of PE, MSPE and MMSE. Hence, this work supports the view that EEG has a detectable change prior to an absence seizure, and MMPE could be considered as a candidate precursor of the impending absence seizures.

Feature extraction and classification method for switchgear faults based on sample entropy and cloud model

This study proposes a fault diagnosis method for extracting and classifying the fault features of switchgears in accordance with the monitoring data of three-phase voltage and current, temperature, humidity, and flashing from the smart breaker and sensors. The fault features are calculated using multivariate multiscale sample entropy (MMSE) for the data mining of multivariate monitoring process. The similarity measure of the composite delay vectors of multivariate time series in MMSE is improved by introducing a cloud model to soften the similar tolerance criterion. The modified MMSE is defined as multivariate multiscale cloud sample entropy (MMCSE). The MMCSE features of switchgear monitoring data can be achieved in different time scales in describing various switchgear faults. Subsequently, a classification method based on fuzzy support vector machine (FSVM) is further adopted to identify different types of switchgear faults using the MMCSE features. In addition, a dropping semi-normal membership cloud model is applied to modify the uncertainty quantification of the relationship among fault samples in FSVM. The effectiveness of the proposed method is validated with the monitoring data in a 10 kV switchboard.

Sample Entropy, Univariate, and Multivariate Multi-Scale Entropy in Comparison with Classical Postural Sway Parameters in Young Healthy Adults.

The present study aimed to compare various entropy measures to assess the dynamics and complexity of center of pressure (COP) displacements. Perturbing balance tests are often used in healthy subjects to imitate either pathological conditions or to test the sensitivity of postural analysis techniques. Eleven healthy adult subjects were asked to stand in normal stance in three experimental conditions while the visuo-kinesthetic input was altered. COP displacement was recorded using a force plate. Three entropy measures [Sample Entropy (SE), Multi-Scale Entropy (MSE), and Multivariate Multi Scale Entropy (MMSE)] describing COP regularity at different scales were compared to traditional measures of COP variability. The analyses of the COP trajectories revealed that suppression of vision produced minor changes in COP displacement and in the COP characteristics. The comparison with the reference analysis showed that the entropy measures analysis techniques are more sensitive in the incremented time series compared to the classical parameters and entropy measures of original time series. Non-linear methods appear to be an additional valuable tool for analysis of the dynamics of posture especially when applied on incremental time series.

Multivariate multiscale entropy of financial markets

In current process of quantifying the dynamical properties of the complex phenomena in financial market system, the multivariate financial time series are widely concerned. In this work, considering the shortcomings and limitations of univariate multiscale entropy in analyzing the multivariate time series, the multivariate multiscale sample entropy (MMSE), which can evaluate the complexity in multiple data channels over different timescales, is applied to quantify the complexity of financial markets. Its effectiveness and advantages have been detected with numerical simulations with two well-known synthetic noise signals. For the first time, the complexity of four generated trivariate return series for each stock trading hour in China stock markets is quantified thanks to the interdisciplinary application of this method. We find that the complexity of trivariate return series in each hour show a significant decreasing trend with the stock trading time progressing. Further, the shuffled multivariate return series and the absolute multivariate return series are also analyzed. As another new attempt, quantifying the complexity of global stock markets (Asia, Europe and America) is carried out by analyzing the multivariate returns from them. Finally we utilize the multivariate multiscale entropy to assess the relative complexity of normalized multivariate return volatility series with different degrees.

Multivariate weighted multiscale permutation entropy for complex time series

In this paper, we propose multivariate multiscale permutation entropy (MMPE) and multivariate weighted multiscale permutation entropy (MWMPE) to explore the complexity of the multivariate time series over multiple different time scales. First, we apply these methods to the simulated trivariate time series which is compose of white noise and 1/f noise to test the validity of multivariate methods. The standard deviations of weighted methods are bigger because of containing more amplitude information, while the standard deviations of multivariate method are smaller than the method for single channel. Hence, it can be found that MWMPE shows a better distinguish capacity, while it is able to measure the complexity of the multichannel data accurately and reflect more information about the multivariate time series as well as holds a better robustness. Then MMPE and MWMPE methods are employed to the financial time series: closing prices and trade volume, from different area. It can be verified that the methods for multichannel data analyze the properties of multivariate time series comprehensively. The entropy values taking the weight into account for both the multichannel and single channel amplify the local fluctuation and reflect more amplitude information. The MWMPE maintain the fluctuation characteristic of SCWMPE of both price and volume. The MWMPE results of these stock markets can be divided into three groups: (1) S&P500, FTSE, and HSI, (2) KOSPI, and (3) ShangZheng. The weighted contingency also shows the difference of inhomogenity of the distributions of ordinal patterns between these groups. Thus, MWMPE method is capable of differentiating these stock markets, detecting their multiscale structure and reflects more information containing in the financial time series.

A Multivariate Multiscale Fuzzy Entropy Algorithm with Application to Uterine EMG Complexity Analysis

The recently introduced multivariate multiscale entropy (MMSE) has been successfully used to quantify structural complexity in terms of nonlinear within- and cross-channel correlations as well as to reveal complex dynamical couplings and various degrees of synchronization over multiple scales in real-world multichannel data. However, the applicability of MMSE is limited by the coarse-graining process which defines scales, as it successively reduces the data length for each scale and thus yields inaccurate and undefined entropy estimates at higher scales and for short length data. To that cause, we propose the multivariate multiscale fuzzy entropy (MMFE) algorithm and demonstrate its superiority over the MMSE on both synthetic as well as real-world uterine electromyography (EMG) short duration signals. Based on MMFE features, an improvement in the classification accuracy of term-preterm deliveries was achieved, with a maximum area under the curve (AUC) value of 0.99.