Percolation of entropy functionals on cayley tree graphs as a method of order-disorder character diagnostics of complex structures

The problem of long-range action identification of classical quartet, honeycomb, and simplex lattices and bihexagonal Duneau-Katz lattice has been solved. The percolation problem is considered in terms of entropy functional on Cayley tree graphs. Long-range order is described not only by hyperbolic percolation entropy dependence with γ ≤ 1 and zero-order asymptotic entropy; the residual entropy of system ordering can also be observed in some cases.     

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)).     

仿生鳍条姿态测量及其误差分析

在复杂环境下齿轮箱信号往往会淹没在噪声信号中,特征向量难以提取。为了有效的进行故障诊断,提出了基于最大相关反褶积(MCKD)总体平均经验模态分解(EEMD)近似熵和双子支持向量机(TWSVM)的齿轮箱故障诊断方法。首先采用MCKD方法对强噪声信号进行滤波处理,在采用EEMD方法对齿轮箱信号进行分解,分解后得到本征模函数(IMF)分量进行近似熵求解,得到齿轮特征向量,最后将其输入到TWSVM分类器中进行故障识别。仿真实验表明,采用MCKD-EEMD方法能够有效的提取原始信号,与其他分类器相比,TWSVM的计算时间短,分类效果好等优点。     

基于MCKD-EEMD近似熵和TWSVM的齿轮箱故障诊断

在复杂环境下齿轮箱信号往往会淹没在噪声信号中,特征向量难以提取;为了有效地进行故障诊断,提出了基于最大相关反褶积(MCKD)总体平均经验模态分解(EEMD)近似熵和双子支持向量机(TWSVM)的齿轮箱故障诊断方法;首先采用MCKD方法对强噪声信号进行滤波处理,在采用EEMD方法对齿轮箱信号进行分解,分解后得到本征模函数(IMF)分量进行近似熵求解,得到齿轮特征向量,最后将其输入到TWSVM分类器中进行故障识别;仿真实验表明,采用MCKD-EEMD方法能够有效地提取原始信号,与其他分类器相比,TWSVM的计算时间短,分类效果好等优点。     

Application of the maximum entropy method in ultrasound nondestructive testing for scatterer imaging with allowance for multiple scattering

The possibility of solving the inverse scattering problem with allowance for the effect of multiple scattering between the scatterers by the least-squares method that minimizes the solution’s residual is considered. Since the problem is ill-posed, Tikhonov’s regularization is efficient with the entropy of the estimate of the measured field taken as the stabilizing functional, which is the essence of the maximum entropy method. The method is implemented in its multifrequency version. Results of the application of the maximum entropy method in numerical experiments are provided with images reconstructed in different frequency ranges in the presence of white noise.     

基于符号熵特征提取方法的特种品质鸡蛋近红外光谱鉴别分析

特种品质鸡蛋的快速、无损、准确鉴别是目前急需解决的问题。提出利用符号熵特征提取方法进行特种品质鸡蛋的近红外光谱鉴别。选择普通鸡蛋、柴鸡蛋、富硒蛋和富锌蛋作为研究对象,测得其在12 000～4 000cm-1范围内近红外漫反射光谱,基于符号聚合近似算法进行符号化表示,提取符号光谱序列的符号熵作为特征向量,然后设计纠错编码支持向量机多类分类器对光谱进行定性鉴别。算法参数变化时,符号熵特征表现出很好的鲁棒性,最高识别率达100%。研究结果表明利用近红外方法鉴定特种品质鸡蛋是可行的,同时符号熵可作为一种新的近红外光谱特征提取方法。     

Fault Recognition of Rolling Bearings Based on Parameter Optimized Multi-Scale Permutation Entropy and Gath-Geva

To extract fault features of rolling bearing vibration signals precisely, a fault diagnosis method based on parameter optimized multi-scale permutation entropy (MPE) and Gath-Geva (GG) clustering is proposed. The method can select the important parameters of MPE method adaptively, overcome the disadvantages of fixed MPE parameters and greatly improve the accuracy of fault identification. Firstly, aiming at the problem of parameter determination and considering the interaction among parameters comprehensively of MPE, taking skewness of MPE as fitness function, the time series length and embedding dimension were optimized respectively by particle swarm optimization (PSO) algorithm. Then the fault features of rolling bearing were extracted by parameter optimized MPE and the standard clustering centers is obtained with GG clustering. Finally, the samples are clustered with the Euclid nearness degree to obtain recognition rate. The validity of the parameter optimization is proved by calculating the partition coefficient and average fuzzy entropy. Compared with unoptimized MPE, the propose method has a higher fault recognition rate.     

Image quality improvement in ultrasonic nondestructive testing by the maximum entropy method

We consider the possibility of solving the inverse scattering problem in the linear approximation (in the form of a convolution equation) by reducing it to a system of linear algebraic equations and minimizing the residual. Since the problem is an ill-posed one, the Tikhonov regularization proves useful. The possibility of using the entropy of the image estimate as a stabilizing functional is considered, which is the key idea of the maximum entropy method. The single-frequency and multifrequency versions of the method are realized. The advantage of the maximum entropy method over the conventional linear methods of solving the inverse scattering problem is shown. The superresolution and sidelobe suppression abilities of the maximum entropy method are demonstrated. The method is shown to be stable to measurement noise and multiplicative interference in the form of aperture decimation. Examples of the image reconstruction by the maximum entropy method from model and experimental data are presented.     

Rolling Bearing Fault Diagnosis Based on VMD-MPE and PSO-SVM

The goal of the paper is to present a solution to improve the fault detection accuracy of rolling bearings. The method is based on variational mode decomposition (VMD), multiscale permutation entropy (MPE) and the particle swarm optimization-based support vector machine (PSO-SVM). Firstly, the original bearing vibration signal is decomposed into several intrinsic mode functions (IMF) by using the VMD method, and the feature energy ratio (FER) criterion is introduced to reconstruct the bearing vibration signal. Secondly, the multiscale permutation entropy of the reconstructed signal is calculated to construct multidimensional feature vectors. Finally, the constructed multidimensional feature vector is fed into the PSO-SVM classification model for automatic identification of different fault patterns of the rolling bearing. Two experimental cases are adopted to validate the effectiveness of the proposed method. Experimental results show that the proposed method can achieve a higher identification accuracy compared with some similar available methods (e.g., variational mode decomposition-based multiscale sample entropy (VMD-MSE), variational mode decomposition-based multiscale fuzzy entropy (VMD-MFE), empirical mode decomposition-based multiscale permutation entropy (EMD-MPE) and wavelet transform-based multiscale permutation entropy (WT-MPE)).     

二维广义模糊熵图像阈值分割法

针对一维广义模糊熵不能有效处理含噪图像的分割问题,在二维灰度直方图上定义了图像的二维隶属度函数,提出了二维广义模糊熵阈值分割法.该方法不仅考虑了图像的点灰度值,同时考虑了图像像素的邻域平均灰度值,能更好地利用图像中的信息.为了提高二维广义模糊熵阈值法的运行速度、解决参量选取问题,结合粒子群优化搜索方法,设计了嵌套式的优化过程.实验表明,二维广义模糊熵阈值分割法对噪音图像有更好的适应性.     

Quantitative Identification of Internal and External Wire Rope Damage Based on VMD-AWT Noise Reduction and PSO-SVM

As a common load-bearing component, mining wire rope produces different types of damage during a long period of operation, especially in the case of damage inside the wire rope, which cannot be identified by the naked eye, and it is difficult to accurately detect such damage using the present technology. In this study we designed a non-destructive testing device based on leakage magnetism, which can effectively detect the internal defects of wire rope damage, and carried out simulation analysis to lay a theoretical foundation for the subsequent experiments. To address the noise reduction problem in the design process, a variational mode decomposition–adaptive wavelet thresholding noise reduction method is proposed, which can improve the signal-to-noise ratio and also calculate the wavelet energy entropy in the reconstructed signal to construct multi-dimensional feature vectors. For the quantitative identification of system damage, a particle swarm optimization–support vector machine algorithm is proposed. Moreover, based on the signal following the noise reduction step, seven different feature vectors, namely, the waveform area, peak value, peak-valley value, wavelet energy entropy classification, and identification of internal and external damage defects, have been determined. The results show that the device can be used to effectively identify internal damage defects. In addition, the comparative analysis showed that the algorithm can reduce the system noise and effectively identify internal and external damage defects with a certain superiority.     

On information,negentropy and thermostatistics

The interrelation between some basic concepts of information, theory and thermodynamics has been studied on the basis of the statistical measures of entropy and information. The problems studied are the negentropy principle of information, a minimax information principle of thermal equilibrium and the role of information correlation in the derivation of a functional equation characterising the statistical equilibrium of a system.     

基于信息熵的变星光谱快速识别方法

变星对人类研究宇宙的起源与发展具有重要意义,对于变星研究的困难首先源于对变星的筛选和识别,即如何从海量恒星光谱数据中有效识别变星光谱。传统的异常数据定义试图通过不同的方式寻找异常数据与一般模式之间的偏差,进而予以定量分析和筛选。然而,这种方法的时间复杂度过大,且结果存在不可理解和无法解释的问题。文章利用熵可以反映系统有序程度与稳定程度的特性,引入信息熵作为衡量数据集一般模式的标准,提出了基于信息熵的变星光谱快速识别方法。该方法显著降低了算法的时间复杂度,有效地消除了人为主观因素对识别结果的影响。采用国家天文台提供的Sloan数字巡天数据实验验证了该方法的可行性和有效性。     

Acoustic classification of Australian anurans based on hybrid spectral-entropy approach

A new hybrid method for automated frog sound identification, using spectral centroid, Shannon entropy and Rényi entropy is proposed. The advantage of using entropy based information theoretic approach for analyzing complexity of bioacoustics signals in animal vocalization is discussed. Sound samples from nine species of Microhylidae frogs are first segmented into syllables. Fourier spectral centroid, Shannon entropy and Rényi entropy of the syllables are then determined. Finally, nonparametric k-th nearest neighbour (k-NN) classifier is used to recognize the frog species based on these three extracted features. Result shows that the k-NN classifier based on these selected features is capable to identify the species of the frogs with an average accuracy of 98%. It is found that the accuracy reduces significantly only when the noise levels higher than −20 dB.     

经验模态分解法在光纤光栅围栏报警系统中的应用

为了解决基于FBG传感器的光纤围栏报警系统中多个FBG传感器在同时受扰时,定位报警信号难的问题,实现对报警信号的有效识别和判断,提出了一种基于经验模态分解（EMD）和小波包特征熵算法的分析方法。利用经验模态分解法对于信号的突变性敏感和有效保留以及其特有的自适应性分解特性,首先对报警信号进行经验模态分解,再结合小波包分解,得到小波包系数提取其信号的能量分布,再做归一化得到信号的能量分布特征向量,进而运用相关性分析实现对报警信号的识别和判断。通过建立实验模型,对采集到的报警信号做了分析,证明了该方法对于解决光纤围栏报警系统中FBG传感器的级联判断报警信号的有效性。     

两相流流型多尺度熵及动力学特性分析

研究了几种典型非线性时间序列的多尺度熵特征,在此基础上分析了由插入式阵列电导传感器采集的144种流动条件下的垂直上升气液两相流电导波动信号.研究结果表明：利用小尺度下样本熵的变化速率特征可以分辨三种典型流型（泡状流、段塞流、混状流）,而大尺度下样本熵的波动特征可以反映各种流型的动力学特性.泡状流随机可变特性表现为大尺度下样本熵的高值及振荡特征;段塞流气塞与液塞的间歇性运动表现为大尺度下样本熵的低值及平稳性;混状流极不稳定的振荡运动特性表现为介于泡状流及段塞流之间的熵值特点,并在更大尺度时熵值逐渐接近泡状流 关键词： 样本熵 多尺度熵 气液两相流 动力学特性     

基于最大熵模型的导师-学生关系推测

导师-学生关系是科研合作网络中重要的关系类型之一, 准确识别此类关系对促进科研交流与合作、评审回避等有重要意义. 以论文合作网络为基础, 依据学生发表论文时通常与导师共同署名的现象, 抽象出能够反映导师-学生合作关系的特征, 提出了基于最大熵模型的导师-学生关系识别算法. 利用DBLP中1990-2011年的论文数据进行实例验证, 结果显示: 1)关系类型识别结果的准确率超过95%; 2)导师-学生关系终止时间的平均误差为1.39年. 该方法在识别关系时避免了特征之间相互独立的约束, 准确率优于其他同类识别算法, 且建模方法对识别社交网络中的其他关系类型也具有借鉴意义. 关键词： 社交网络 关系识别 最大熵模型 特征选择     

一种基于单元信息熵的目标匹配改进算法

为解决图像信息熵无法有效进行图像匹配的问题,将图像单元信息熵和投影特征相结合,定义了图像单元信息熵,并提出了一种基于单元投影信息熵的图像匹配方法.在单元信息熵的基础上,在各个单元格内进行单元信息熵投影计算,然后按照一定的测度进行计算,从而实现图像的匹配.采用网格分层的搜索算法,加快搜索速度,提高其工程实用性.实验证明:该算法具有良好的抗几何失真能力和抗辐射失真的能力,以及很好的抗噪声干扰的能力,可以准确的进行目标匹配.     

An Evaluation of Entropy Measures for Microphone Identification

Research findings have shown that microphones can be uniquely identified by audio recordings since physical features of the microphone components leave repeatable and distinguishable traces on the audio stream. This property can be exploited in security applications to perform the identification of a mobile phone through the built-in microphone. The problem is to determine an accurate but also efficient representation of the physical characteristics, which is not known a priori. Usually there is a trade-off between the identification accuracy and the time requested to perform the classification. Various approaches have been used in literature to deal with it, ranging from the application of handcrafted statistical features to the recent application of deep learning techniques. This paper evaluates the application of different entropy measures (Shannon Entropy, Permutation Entropy, Dispersion Entropy, Approximate Entropy, Sample Entropy, and Fuzzy Entropy) and their suitability for microphone classification. The analysis is validated against an experimental dataset of built-in microphones of 34 mobile phones, stimulated by three different audio signals. The findings show that selected entropy measures can provide a very high identification accuracy in comparison to other statistical features and that they can be robust against the presence of noise. This paper performs an extensive analysis based on filter features selection methods to identify the most discriminating entropy measures and the related hyper-parameters (e.g., embedding dimension). Results on the trade-off between accuracy and classification time are also presented.     

Variational wave functions in calculations of the forces of oscillators in atoms and ions

The present article discusses the quality of wave functions obtained within the framework of different variational methods. The advantages of the minimax method, which incorporates the ordinary variational method, are discussed. Using as an example the calculation of the force of oscillators, it is shown that a consistent set of complete wave functions determined within the framework of the minimax method yields better agreement with the force of oscillators calculated by means of the length and velocity methods than does the ordinary variational method. Tomsk State University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 5, pp. 114–119, May, 1998.