Bearing Fault Diagnosis Using Refined Composite Generalized Multiscale Dispersion Entropy-Based Skewness and Variance and Multiclass FCM-ANFIS

Bearing vibration signals typically have nonlinear components due to their interaction and coupling effects, friction, damping, and nonlinear stiffness. Bearing faults affect the signal complexity at various scales. Hence, measuring signal complexity at different scales is helpful to diagnosis of bearing faults. Numerous studies have investigated multiscale algorithms; nevertheless, multiscale algorithms using the first moment lose important complexity data. Accordingly, generalized multiscale algorithms have been recently introduced. The present research examined the use of refined composite generalized multiscale dispersion entropy (RCGMDispEn) based on the second moment (variance) and third moment (skewness) along with refined composite multiscale dispersion entropy (RCMDispEn) in bearing fault diagnosis. Moreover, multiclass FCM-ANFIS, which is a combination of adaptive network-based fuzzy inference systems (ANFIS), was developed to improve the efficiency of rotating machinery fault classification. According to the results, it is recommended that generalized multiscale algorithms based on variance and skewness be examined for diagnosis, along with multiscale algorithms, and be used to achieve an improvement in the results. The simultaneous usage of the multiscale algorithm and generalized multiscale algorithms improved the results in all three real datasets used in this study.     

Application of Generalized Composite Multiscale Lempel–Ziv Complexity in Identifying Wind Turbine Gearbox Faults

Wind turbine gearboxes operate in harsh environments; therefore, the resulting gear vibration signal has characteristics of strong nonlinearity, is non-stationary, and has a low signal-to-noise ratio, which indicates that it is difficult to identify wind turbine gearbox faults effectively by the traditional methods. To solve this problem, this paper proposes a new fault diagnosis method for wind turbine gearboxes based on generalized composite multiscale Lempel–Ziv complexity (GCMLZC). Within the proposed method, an effective technique named multiscale morphological-hat convolution operator (MHCO) is firstly presented to remove the noise interference information of the original gear vibration signal. Then, the GCMLZC of the filtered signal was calculated to extract gear fault features. Finally, the extracted fault features were input into softmax classifier for automatically identifying different health conditions of wind turbine gearboxes. The effectiveness of the proposed method was validated by the experimental and engineering data analysis. The results of the analysis indicate that the proposed method can identify accurately different gear health conditions. Moreover, the identification accuracy of the proposed method is higher than that of traditional multiscale Lempel–Ziv complexity (MLZC) and several representative multiscale entropies (e.g., multiscale dispersion entropy (MDE), multiscale permutation entropy (MPE) and multiscale sample entropy (MSE)).     

中子预辐照损伤对钨中氢滞留行为影响机制的多尺度模拟

高温等离子体作用下的中子辐照损伤和氢氦滞留行为一直是聚变堆钨基材料面临的两个关键问题,尤其是预辐照损伤对氢氦滞留的协同作用。鉴于制约因素的复杂性和实验上的困难,相关基础问题的理论研究至关重要。我们基于发展的顺序多尺度模拟方法研究了多晶钨的中子预辐照损伤及其对低能（20 eV）氢注入下缺陷动力学演化和氢滞留分布的影响。通过定量对比有无中子预辐照的多晶钨中氢的滞留行为,我们发现中子预辐照损伤产生的稳定空位团簇作为新的氢捕获点,加剧了氢在近表面处的滞留和表面损伤,限制了其向深度的扩散,从而导致了低能氢滞留量的急剧增加。相关结果将直接为实际等离子体环境下聚变堆钨基材料的辐照损伤和氢氦效应提供理论指导与预测。     

Multiscale entropy analysis of complex physiologic time series

There has been considerable interest in quantifying the complexity of physiologic time series, such as heart rate. However, traditional algorithms indicate higher complexity for certain pathologic processes associated with random outputs than for healthy dynamics exhibiting long-range correlations. This paradox may be due to the fact that conventional algorithms fail to account for the multiple time scales inherent in healthy physiologic dynamics. We introduce a method to calculate multiscale entropy (MSE) for complex time series. We find that MSE robustly separates healthy and pathologic groups and consistently yields higher values for simulated long-range correlated noise compared to uncorrelated noise.     

Multiscale Weighted Permutation Entropy Analysis of Schizophrenia Magnetoencephalograms

Schizophrenia is a neuropsychiatric disease that affects the nonlinear dynamics of brain activity. The primary objective of this study was to explore the complexity of magnetoencephalograms (MEG) in patients with schizophrenia. We combined a multiscale method and weighted permutation entropy to characterize MEG signals from 19 schizophrenia patients and 16 healthy controls. When the scale was larger than 42, the MEG signals of schizophrenia patients were significantly more complex than those of healthy controls (p<0.004). The difference in complexity between patients with schizophrenia and the controls was strongest in the frontal and occipital areas (p<0.001), and there was almost no difference in the central area. In addition, the results showed that the dynamic range of MEG complexity is wider in healthy individuals than in people with schizophrenia. Overall, the multiscale weighted permutation entropy method reliably quantified the complexity of MEG from schizophrenia patients, contributing to the development of potential magnetoencephalographic biomarkers for schizophrenia.     

Multiscale Permutation Lempel–Ziv Complexity Measure for Biomedical Signal Analysis: Interpretation and Application to Focal EEG Signals

This paper analyses the complexity of electroencephalogram (EEG) signals in different temporal scales for the analysis and classification of focal and non-focal EEG signals. Futures from an original multiscale permutation Lempel–Ziv complexity measure (MPLZC) were obtained. MPLZC measure combines a multiscale structure, ordinal analysis, and permutation Lempel–Ziv complexity for quantifying the dynamic changes of an electroencephalogram (EEG). We also show the dependency of MPLZC on several straight-forward signal processing concepts, which appear in biomedical EEG activity via a set of synthetic signals. The main material of the study consists of EEG signals, which were obtained from the Bern-Barcelona EEG database. The signals were divided into two groups: focal EEG signals (n = 100) and non-focal EEG signals (n = 100); statistical analysis was performed by means of non-parametric Mann–Whitney test. The mean value of MPLZC results in the non-focal group are significantly higher than those in the focal group for scales above 1 (p < 0.05). The result indicates that the non-focal EEG signals are more complex. MPLZC feature sets are used for the least squares support vector machine (LS-SVM) classifier to classify into the focal and non-focal EEG signals. Our experimental results confirmed the usefulness of the MPLZC method for distinguishing focal and non-focal EEG signals with a classification accuracy of 86%.     

A mesoscopic model of the intermixing during nanoenergetic materials processing

A general mesoscopic model for the simulation of thin-film vapor deposition applied to energetic materials, specifically bimetallic multilayers, is presented. We describe the setup of this mesoscopic simulator developed in the frame of a multiscale study by implementing ab initio data into a set of differential equations. We present numerical results relative to the formation of barrier layers as a result of interdiffusion between successive bimetallic AlNi multilayers. The key role of the vacancies species created during deposition is highlighted.     

多尺度多变量模糊熵分析

多尺度多变量样本熵评价同步多通道数据的多变量复杂度, 是非线性动态相互关系的一种反映, 但其统计稳定性差, 且不适用于非线性非平稳信号. 研究利用模糊隶属度函数代替模式相似判断的硬阈值准则, 并分析模糊隶属度函数形式的影响; 研究利用多变量经验模态分解算法进行多尺度化, 并对比其处理效果. 仿真试验表明, 模糊隶属度函数的引入可以有效提高算法的统计稳定性, 所构造的物理模糊隶属度函数的性能最为显著; 基于多变量经验模态分解算法的多尺度化过程可更有效地捕获信号的不同尺度成分, 从而更敏感地区分具有不同复杂度的信号. 对临床试验数据的分析支持以上结论, 且结果提示随着年龄增加或心脏疾病的发生, 心率变异性和心脏舒张间期变异性的多变量复杂度以不同的方式降低: 年龄增加会使低尺度熵值降低, 表示近程相关性的丢失; 而心脏疾病会同时影响各个尺度的熵值, 即同时丢失了近程和长时相关性. 该结论可用于指导心血管疾病的无创预警研究. 关键词： 多变量复杂度 多尺度多变量模糊熵 物理模糊隶属度函数 多变量经验模态分解     

Bridging the scales in nano engineering and science

This review article describes various multiscale approaches, development of which was spurred by the emergence of nanotechnology. The multiscale approaches are grouped into two main categories: information-passing and concurrent. In the concurrent multiscale methods both, the discrete and continuum scales are simultaneously resolved, whereas in the information-passing schemes, the discrete scale is modelled and its gross response is infused into the continuum scale. Most of the information-passing approaches provide sublinear computational complexity, (i.e., scales sublinearly with the cost of solving a fine scale problem), but the quantities of interest are limited to or defined only on the coarse scale. The issues of appropriate scale selection and uncertainty quantification are also reviewed.     

Sound absorption performance of gradiently slit-perforated double-porosity materials

A gradiently slit-perforated double-porosity material is proposed by introducing macro-scale periodic gradient slit-perforations into traditional porous materials with singleporosity.This material is one kind of multiscale material since it includes two scales of matrix micro-pore size and slit-perforation size.A theoretical model is developed for the sound absorption of the gradiently slit-perforated double-porosity material.In the model,the material is divided into lots of thin layers and each layer is approximated to be straight slit-perforated material.The equivalent density and dynamic compressibility of each thin layer are given by using the low or high permeability contrast double-porosity theory.Then the sound pressure and particle velocity relations between adjacent thin layers are obtained by employing the transfer matrix method.Finally,the surface acoustic impedance and the sound absorption of the gradiently slit-perforated porous material can be calculated.A finite element model is further established to validate the accuracy of the theoretical model.In the considered frequency range of 100-3000 Hz,the simulation results agree well with theoretical results.The influence of multiscale structural parameters on the sound absorption performance of the porous materials is analyzed theoretically and numerically.It is proved that the multiscale structure design can significantly improve the sound absorption performance of porous materials.Compared to the slit-perforation gradient,the slit-perforation width plays a more significant influence on sound absorption.The sound absorption enhancement mechanism of the multiscale structure design is revealed by the analysis of the sound pressure and energy dissipation distributions in the material.This work provides a multiscale structural design method for improving the sound absorption performance of traditional porous materials at broadband frequency.     

Dynamic behavior of temperature field in a buoyancy-driven turbulent fire

We study the dynamic behavior of temperature field in a buoyancy-driven turbulent fire from the viewpoints of symbolic dynamics, complex networks, and statistical complexity. The permutation entropy and the horizontal visibility network entropy allow us to capture the subtle changes in temperature fluctuations. The possible existence of deterministic chaos in temperature fluctuations, as well as in streamwise flow velocity fluctuations [Takagi et al., Phys. Rev. E 96 (2017) 052223], is clearly verified using the multiscale complexity-entropy causality plane.     

Multiscale entropy based study of the pathological time series

This paper studies the multiscale entropy （MSE） of electrocardiogram＇s ST segment and compares the MSE results of ST segment with that of electrocardiogram in the first time. Electrocardiogram complexity changing characteristics has important clinical significance for early diagnosis. Study shows that the average MSE values and the varying scope fluctuation could be more effective to reveal the heart health status. Particularly the multiscale values varying scope fluctuation is a more sensitive parameter for early heart disease detection and has a clinical diagnostic significance.     

Modified DFA and DCCA approach for quantifying the multiscale correlation structure of financial markets

We use multiscale detrended fluctuation analysis (MSDFA) and multiscale detrended cross-correlation analysis (MSDCCA) to investigate auto-correlation (AC) and cross-correlation (CC) in the US and Chinese stock markets during 1997–2012. The results show that US and Chinese stock indices differ in terms of their multiscale AC structures. Stock indices in the same region also differ with regard to their multiscale AC structures. We analyze AC and CC behaviors among indices for the same region to determine similarity among six stock indices and divide them into four groups accordingly. We choose S&P500, NQCI, HSI, and the Shanghai Composite Index as representative samples for simplicity. MSDFA and MSDCCA results and average MSDFA spectra for local scaling exponents (LSEs) for individual series are presented. We find that the MSDCCA spectrum for LSE CC between two time series generally tends to be greater than the average MSDFA LSE spectrum for individual series. We obtain detailed multiscale structures and relations for CC between the four representatives. MSDFA and MSDCCA with secant rolling windows of different sizes are then applied to reanalyze the AC and CC. Vertical and horizontal comparisons of different window sizes are made. The MSDFA and MSDCCA results for the original window size are confirmed and some new interesting characteristics and conclusions regarding multiscale correlation structures are obtained.     

Neurofeedback Training Based on Motor Imagery Strategies Increases EEG Complexity in Elderly Population

Neurofeedback training (NFT) has shown promising results in recent years as a tool to address the effects of age-related cognitive decline in the elderly. Since previous studies have linked reduced complexity of electroencephalography (EEG) signal to the process of cognitive decline, we propose the use of non-linear methods to characterise changes in EEG complexity induced by NFT. In this study, we analyse the pre- and post-training EEG from 11 elderly subjects who performed an NFT based on motor imagery (MI–NFT). Spectral changes were studied using relative power (RP) from classical frequency bands (delta, theta, alpha, and beta), whilst multiscale entropy (MSE) was applied to assess EEG-induced complexity changes. Furthermore, we analysed the subject’s scores from Luria tests performed before and after MI–NFT. We found that MI–NFT induced a power shift towards rapid frequencies, as well as an increase of EEG complexity in all channels, except for C3. These improvements were most evident in frontal channels. Moreover, results from cognitive tests showed significant enhancement in intellectual and memory functions. Therefore, our findings suggest the usefulness of MI–NFT to improve cognitive functions in the elderly and encourage future studies to use MSE as a metric to characterise EEG changes induced by MI–NFT.     

基于三次样条插值的图像多尺度方向边缘重构

为了检测小结构的轮廓以及大目标的边缘,将多尺度边缘检测与小波变换有机地结合起来,利用小波分析方法来研究信号的多尺度边缘特征。针对图像信号的多尺度边缘检测和重构问题,利用二进小波变换的多尺度分析特性,定义了图像在水平和垂直方向的多尺度边缘。同时,利用三次样条插值算法,提出了一种由二进小波变换在水平和垂直方向的极值重构图像信号的算法。实验结果显示多尺度重建方法与著名的交替投影算法相比,算法复杂度低,图像重建速度提高了20倍,而且重建图像质量较好,其峰值信噪比提高了1 dB以上。     

Highly scalable discrete-particle simulations with novel coarse-graining: accessing the microscale

ABSTRACT

Simulating energetic materials with complex microstructure is a grand challenge, where until recently, an inherent gap in computational capabilities had existed in modelling grain-scale effects at the microscale. We have enabled a critical capability in modelling the multiscale nature of the energy release and propagation mechanisms in advanced energetic materials by implementing, in the widely used LAMMPS molecular dynamics (MD) package, several novel coarse-graining techniques that also treat chemical reactivity. Our innovative algorithmic developments rooted within the dissipative particle dynamics framework, along with performance optimisations and application of acceleration technologies, have enabled extensions in both the length and time scales far beyond those ever realised by atomistic reactive MD simulations. In this paper, we demonstrate these advances by modelling a shockwave propagating through a microstructured material and comparing performance with the state-of-the-art in atomistic reactive MD techniques. As a result of this work, unparalleled explorations in energetic materials research are now possible.     

Multiscale Entropy under the Inverse Gaussian Distribution： Analytical Results

The multiscale entropy （MSE） reveals the intrinsic multiple scales in the complexity of physical and physiological signals, which are usually featured by heavy-tailed distributions. However, most research results are pure experimental search. Recently, Costa et al. have made the first attempt to present the theoretical basis of MSE, but it only supports the Gaussian distribution [Phys Rev. E 71 （2005） 021906]. We present the theoretical basis of MSE under the inverse Gaussian distribution, a typical model for physiological, physical and financial data sets. The analysis allows for uncorrelated inverse Gaussian process and 1/f noise with the multivariate inverse Gaussian distribution, and then provides a reliable foundation for the potential applications of MSE to explore complev nhwical and Dhwical time series.     

Multiscale finite element methods for high-contrast problems using local spectral basis functions

In this paper we study multiscale finite element methods (MsFEMs) using spectral multiscale basis functions that are designed for high-contrast problems. Multiscale basis functions are constructed using eigenvectors of a carefully selected local spectral problem. This local spectral problem strongly depends on the choice of initial partition of unity functions. The resulting space enriches the initial multiscale space using eigenvectors of local spectral problem. The eigenvectors corresponding to small, asymptotically vanishing, eigenvalues detect important features of the solutions that are not captured by initial multiscale basis functions. Multiscale basis functions are constructed such that they span these eigenfunctions that correspond to small, asymptotically vanishing, eigenvalues. We present a convergence study that shows that the convergence rate (in energy norm) is proportional to (H/Λ₁)^1/2, where Λ₁ is proportional to the minimum of the eigenvalues that the corresponding eigenvectors are not included in the coarse space. Thus, we would like to reach to a larger eigenvalue with a smaller coarse space. This is accomplished with a careful choice of initial multiscale basis functions and the setup of the eigenvalue problems. Numerical results are presented to back-up our theoretical results and to show higher accuracy of MsFEMs with spectral multiscale basis functions. We also present a hierarchical construction of the eigenvectors that provides CPU savings.