Variation of wave action: Modulations of the phase shift for strongly nonlinear dispersive waves with weak dissipation

Strongly nonlinear dispersive waves described by a general Klein—Gordon equation with slowly varying coefficients and a dissipative perturbation are analyzed using the method of multiple scales. We use the exact equation of wave action. The spatial and temporal slow modulations of the phase shift are shown to be governed by a new equation, which results from linearization of the wave action, its flux, and its dissipation due to perturbations of the slow parameters: frequency and wave number (vector). This result extends to nonlinear partial differential equations, the quite recent work by the authors on nonlinear oscillations governed by ordinary differential equations.     

Non-linear responses of suspended cables to primary resonance excitations

We investigate the non-linear forced responses of shallow suspended cables. We consider the following cases: (1) primary resonance of a single in-plane mode and (2) primary resonance of a single out-of-plane mode. In both cases, we assume that the excited mode is not involved in an autoparametric resonance with any other mode. We analyze the system by following two approaches. In the first, we discretize the equations of motion using the Galerkin procedure and then apply the method of multiple scales to the resulting system of non-linear ordinary-differential equations to obtain approximate solutions (discretization approach). In the second, we apply the method of multiple scales directly to the non-linear integral-partial-differential equations of motion and associated boundary conditions to determine approximate solutions (direct approach). We then compare results obtained with both approaches and discuss the influence of the number of modes retained in the discretization procedure on the predicted solutions.     

A comparison of three perturbation methods for non-linear hyperbolic waves

Simple wave solutions of non-linear hyperbolic equations are studied by using the method of renormalization, the analytic method of characteristics, and the method of multiple scales. It is shown that the results of the method of renormalization depend on whether the potential function or the velocity is normalized. This arbitrariness does not occur when using either the analytic method of characteristics or the method of multiple scales. However, special consideration must be given in determining the potential from the velocity obtained by the analytic method of characteristics. No such consideration is needed when the method of multiple scales is applied. The first term obtained for the potential by the method of multiple scales contains a cumulative term in addition to a non-cumulative term. This first-order term is shown to yield the equal area rule for shock waves, and the slope of an equipotential line is the arithmetic mean of the slope of the characteristic in the unperturbed medium and the slope of the characteristic at the point under consideration.     

Nonlinear free transverse vibrations of in-plane moving plates: Without and with internal resonances

In this paper, nonlinear free transverse vibrations of in-plane moving plates subjected to plane stresses are investigated. The Hamilton principle is applied to derive the governing equation and the associated boundary conditions. The method of multiple scales is employed to analyze the nonlinear partial differential equation. The solvability conditions are established in the cases without internal resonance and with 3:1 or 1:1 internal resonances. Some numerical examples are presented to demonstrate the effects of in-plane moving speeds on the frequencies. The nonlinear frequencies of the in-plane moving plate without internal resonances are numerically calculated. The relationship between the nonlinear frequencies and the initial amplitudes is showed at different in-plane moving speeds and the nonlinear coefficients, respectively. It is feasible to investigate resonances without the modes not involved in the resonances. The effects of the related parameters are demonstrated for the case of 3:1 and 1:1 internal resonances, respectively. The differential quadrature scheme is developed to solve numerically the governing equation and confirm results via the method of multiple scales.     

热环境中的光传输与光学校正仿真

对折射率不均匀分布的窗口中的光线传输进行了分析,利用光线追迹得到的光程差再现了光波通过窗口后的波前图。通过研究图像获取和处理方法,提出了用相位互异散斑(PDS)技术进行图像补偿和校正由大气扰动造成的波前变形。结果表明,图像的清晰度和对比度得到了提高。     

The breakdown of Navier—Stokes hydrodynamics in small periodic systems

The results of direct particle simulations of 2-dimensional, convective flow are compared with truncated solutions of the Navier—Stokes equation, and show that the Navier—Stokes predictions are quite accurate throughout the transient development of the flow, if the correct value of the viscosity is used. The viscosity determines the steady values of the flow velocities, and the Navier—Stokes predictions are accurate for systems with multiple k vector forcing. At higher values of the fields, there is a limiting value of the forcing for which the character of the response matches the character of the forcing. Beyond this point there is a breakdown in hydrodynamic behaviour where the particle nature of the fluid dominates. Both multiphase solid and fluid regions are observed, plus cavitation, depending upon the forcing and the system geometry.     

基于变分模态分解-传递熵的脑肌电信号耦合分析

皮层肌肉功能耦合是大脑皮层和肌肉组织间的相互作用, 脑肌电信号的多尺度耦合特征可以体现皮层-肌肉间多时空的功能联系. 本文引入变分模态分解并与传递熵结合, 构建变分模态分解-传递熵模型应用于脑肌间耦合研究. 首先基于变分模态分解将同步采集的脑电(EEG) 和肌电(EMG) 信号分别进行时频尺度化, 然后计算不同时频尺度间的传递熵值, 获取不同耦合方向(EEG→EMG 及EMG→EEG) 上不同尺度间的非线性耦合特征. 结果表明, 在静态握力输出条件下, 皮层与肌肉beta (15—35 Hz) 频段间的耦合强度最为显著; EEG→EMG 方向上脑电与肌电高gamma (50—72 Hz) 频段的耦合强度总体上高于EMG→EEG 方向.研究结果揭示皮层-肌肉功能耦合具有双向性, 且脑肌间不同耦合方向上、不同频段间的耦合强度有所差异.因此可利用变分模态分解-传递熵方法定量刻画大脑皮层与肌肉各时频段之间的非线性同步特征及功能联系.     

Parametrically excited non-linear multidegree-of-freedom systems with repeated natural frequencies

A method for analyzing multidegree-of-freedom systems having a repeated natural frequency subjected to a parametric excitation is presented. Attention is given to the ordering of the various terms (linear and non-linear) in the governing equations. The analysis is based on the method of multiple scales. As a numerical example involving a parametric resonance, panel flutter is discussed in detail in order to illustrate the type of results one can expect to obtain with this analysis. Some of the analytical results are verified by a numerical integration of the governing equations.     

Feature separation using ICA for a one-dimensional time series and its application in fault detection

Principal component analysis (PCA) is a method that transforms multiple data series into uncorrelated data series. Independent component analysis (ICA) is a method that separates multiple data series into independent data series. Both methods have been used in fault detection. However, both require signals from at least two separate sensors. To overcome this requirement and utilize the fault detection capability of ICA and PCA, we propose to use wavelet transform to pre-process the data collected from a single sensor and then use the coefficients of the wavelet transforms at different scales as input to ICA and PCA. The effectiveness of this method is demonstrated by applying it to both a simulated signal series and a vibration signal series collected from a gearbox. The results show that the method of combining wavelet transform and ICA works better than the method of combining wavelet transform and PCA for impulse detection based on a one-dimensional vibration data series.     

拉曼光谱和MLS-SVR的食用油脂肪酸含量预测研究

为实现食用植物油中饱和脂肪酸、油酸、亚油酸含量的快速预测,对一批纯食用油以及不同比例两两混合油共91个样品进行了拉曼光谱检测,在800～2 000 cm-1范围内,通过基于寻峰算法的自动确定支点的基线拟合方法,对获得的光谱数据进行预处理,提取八个特征峰作为拉曼光谱的特征值。以这些特征值为输入,以样品油中实际饱和脂肪酸、油酸、亚油酸含量为输出,运用偏最小二乘回归(PLS)和多输出最小二乘支持向量回归机(MLS-SVR)方法,分别建立了可以同时预测三种脂肪酸含量的数学模型,结果表明MLS-SVR方法具有较好的效果。将MLS-SVR模型的预测结果与气相色谱法结果相比较,可得到三种脂肪酸的预测均方根误差分别为0.496 7%,0.840 0%和1.019 9%,相关系数分别为0.813 3,0.999 2和0.998 1;对未知样品三种脂肪酸的预测均方根误差不超过5%。表明,拉曼光谱和MLS-SVR相结合的食用油脂肪酸含量预测方法,具有快速、简便、无损、准确等优点,为食用油脂肪酸含量分析提供了一种可行的方法。     

小波变换在变压器励磁涌流识别中的应用

为防止励磁涌流导致变压器的差动保护误动作,本文提出了一种以小波系数分布为判据的励磁涌流识别的新方法。该方法以小波变换中多分辨分析为理论依据,通过小波变换后对所得二尺度上的小波系数进行提取,计算其方差变化率来表示小波系数的变化情况,并设定合理的阀值,来对励磁涌流与故障电流进行区分。应用MATLAB工具箱搭建变压器励磁涌流与故障电流仿真模型,进行大量仿真,仿真试验结果表明,该方法能够快速有效的对励磁涌流与故障电流进行识别判断,克服了传统方法的不足,保证差动保护的正确动作,具有很高的应用前景。     

一类准周期参激非线性相对转动动力系统的稳定性与时滞反馈控制

建立了一类含准周期参数激励和时滞反馈的相对转动非线性系统的动力学方程. 采用多尺度法求解1/2亚谐波主参数共振下的分岔响应方程,并分析了系统的稳定性. 在求解非受控系统的定常解的基础上,通过讨论系统的动力学特性,研究了准周期参数激励对系统响应的影响. 采用时滞反馈控制的方法对系统分岔和极限环(域)进行控制,数值模拟的结果表明通过改变时滞参数可以实现对系统分岔的控制,并能有效地控制极限环(域)的幅值和稳定性. 关键词： 相对转动 准周期参激 时滞反馈 极限环     

Temporal scales of auditory objects underlying birdsong vocal recognition

Vocal recognition is common among songbirds, and provides an excellent model system to study the perceptual and neurobiological mechanisms for processing natural vocal communication signals. Male European starlings, a species of songbird, learn to recognize the songs of multiple conspecific males by attending to stereotyped acoustic patterns, and these learned patterns elicit selective neuronal responses in auditory forebrain neurons. The present study investigates the perceptual grouping of spectrotemporal acoustic patterns in starling song at multiple temporal scales. The results show that permutations in sequencing of submotif acoustic features have significant effects on song recognition, and that these effects are specific to songs that comprise learned motifs. The observations suggest that (1) motifs form auditory objects embedded in a hierarchy of acoustic patterns, (2) that object-based song perception emerges without explicit reinforcement, and (3) that multiple temporal scales within the acoustic pattern hierarchy convey information about the individual identity of the singer. The authors discuss the results in the context of auditory object formation and talker recognition.     

精确研究NbN分子d~1∑~+—b~1∑~+电子态跃迁的P线系发射光谱

本文利用最近建立的能精确求解双原子分子P线系发射光谱的物理新公式,研究了NbN分子从电子态d~1∑~+向b~1∑~+电子态跃迁中(1,1)跃迁带的P支发射光谱.获得的计算结果不仅很好地重现了已知低转动态的实验谱线数据,同时也预言了该跃迁带包含转动量子数J=80在内的高振转激发态的精确P线系发射光谱.该方法在理论上为实验技术难以精确测量的双原子分子体系提供了一种获得精确的高激发态谱线数据的物理新方法.从而可以为那些需要NbN分子高激发态跃迁谱线的研究工作提供必要的数据.     

Variational principles for two kinds of extended Korteweg—de Vries equations

Variational principles are constructed using the semi-inverse method for two kinds of extended Korteweg—de Vries (KdV) equations, which can be regarded as simple models of the nonlinear oceanic internal waves and atmospheric long waves, respectively. The obtained variational principles have also been proved to be correct.     

Intelligent Fault Diagnosis of Rolling-Element Bearings Using a Self-Adaptive Hierarchical Multiscale Fuzzy Entropy

The fuzzy-entropy-based complexity metric approach has achieved fruitful results in bearing fault diagnosis. However, traditional hierarchical fuzzy entropy (HFE) and multiscale fuzzy entropy (MFE) only excavate bearing fault information on different levels or scales, but do not consider bearing fault information on both multiple layers and multiple scales at the same time, thus easily resulting in incomplete fault information extraction and low-rise identification accuracy. Besides, the key parameters of most existing entropy-based complexity metric methods are selected based on specialist experience, which indicates that they lack self-adaptation. To address these problems, this paper proposes a new intelligent bearing fault diagnosis method based on self-adaptive hierarchical multiscale fuzzy entropy. On the one hand, by integrating the merits of HFE and MFE, a novel complexity metric method, named hierarchical multiscale fuzzy entropy (HMFE), is presented to extract a multidimensional feature matrix of the original bearing vibration signal, where the important parameters of HMFE are automatically determined by using the bird swarm algorithm (BSA). On the other hand, a nonlinear feature matrix classifier with strong robustness, known as support matrix machine (SMM), is introduced for learning the discriminant fault information directly from the extracted multidimensional feature matrix and automatically identifying different bearing health conditions. Two experimental results on bearing fault diagnosis show that the proposed method can obtain average identification accuracies of 99.92% and 99.83%, respectively, which are higher those of several representative entropies reported by this paper. Moreover, in the two experiments, the standard deviations of identification accuracy of the proposed method were, respectively, 0.1687 and 0.2705, which are also greater than those of the comparison methods mentioned in this paper. The effectiveness and superiority of the proposed method are verified by the experimental results.     

The Measurement of the Separation of Fine Solid Particles in Multiwir Packings

In this paper, a new type of packing for the separation of solid particles from gases is presented. The so called Multiwir (multiple vortex) [1, 2] packings (see Figure 1) consist of multiple adjacent layers of strips spaced uniformly. As the layers are placed oblique to each other, the incoming gas stream passes the packings in the form of a large number of smaller streams which cross each other spatially and thus induce rotational motion in each other. Under centrifugal forces and due to turbulent and electrostatic effects, the particles settle on the surfaces of the strips where they are collected. In this paper, some of the experimental results are described obtained in the investigation of Multiwir-packings, consisting of metal or plastic strips, with different limestone aerosols and feed particle size distributions with particles smaller than approximately 3 μm and 10 μm. The following results have been obtained: — the Multiwir separator should be used for the removal of fine particles. Particles smaller than 10 μm in size can only be collected if special precautions are used, — the efficiency of the separator is dominated by the gas velocity, the geometry of the packing, the material of the strips and the size distribution of the feed material, — the smaller the feed particles are, the smaller the distance between adjacent strips should be, — the reduction of the distance between adjacent strips is limited however by an increase of the pressure drop across the packing, — adhesion between particles and strip surface strongly influences the performance of the packing. The surface of the strips should therefore be wetted, for example with a thin oil film, — the collection of small particles can be further improved if the feed particles are charged electrostatically in front of the packing, — the total grade efficiency of the packings investigated lies between T₀ = 0.6 and 0.9. Extremely good results have been obtained with perforated plastic strips. Simplified mathematical models have been used to describe the phenomenon of particle deposition in Multiwir packings due to inertia effects and turbulent diffusion.     

Multiple master length scales for stable atmospheric boundary layer

Summary A new method of derivation of characteristic turbulence length scales is analysed in a procedure that seems to be a more adequate way of determining stable boundary layer master length scales. The novel feature of this derivation is a provision formultiple length scales, one for each different spacial direction. In its general formulation, these multiple master length scales show a form similar to earlier proposals by Blackadar and his followers.     

Parametric Representation of 3D Grain Ensembles in Polycrystalline Microstructures

As a straightforward generalization of the well-known Voronoi construction, Laguerre tessellations have long found application in the modelling, analysis and simulation of polycrystalline microstructures. The application of Laguerre tessellations to real (as opposed to computed) microstructures—such as those obtained by modern 3D characterization techniques like X-ray microtomography or focused-ion-beam serial sectioning—is hindered by the mathematical difficulty of determining the correct seed location and weighting factor for each of the grains in the measured volume. In this paper, we propose an alternative to the Laguerre approach, representing grain ensembles with convex cells parametrized by orthogonal regression with respect to 3D image data. Applying our algorithm to artificial microstructures and to microtomographic data sets of an Al-5 wt% Cu alloy, we demonstrate that the new approach represents statistical features of the underlying data—like distributions of grain sizes and coordination numbers—as well as or better than a recently introduced approximation method based on the Laguerre tessellation; furthermore, our method reproduces the local arrangement of grains (i.e., grain shapes and connectivities) much more accurately. The additional computational cost associated with orthogonal regression is marginal.     

基于多尺度传递熵的脑肌电信号耦合分析

神经运动控制中脑肌电同步特征可以反映皮层与肌肉之间的功能联系. 为定量研究脑电和肌电信号在不同时间尺度上的同步耦合特征, 提出多尺度传递熵方法实现静态握力输出下的脑肌电耦合分析: 对同步采集的头皮脑电信号(EEG) 和表面肌电信号(EMG)进行多尺度化, 计算不同尺度因子下EEG与EMG间的传递熵值, 获取不同耦合方向(EEG→EMG及EMG→EEG)上的非线性脑肌电耦合特征; 进一步计算功能频段下的显著性面积指标, 定量分析不同尺度下皮层肌肉功能耦合强度的差异. 分析结果显示, 静态握力输出时beta频段(15–35 Hz)皮层肌肉功能耦合特征显著, 且beta2频段(25–35 Hz)在不同尺度上EEG→EMG方向的耦合强度大于EMG→EEG方向, 耦合强度最大值和方向间耦合强度差异显著值均出现于较高时间尺度. 研究结果揭示: 皮层肌肉功能耦合具有双向性, 且耦合强度在不同时间尺度和不同功能频段上有所差异, 可利用多尺度传递熵定量刻画大脑皮层与肌肉之间的非线性同步特征及功能联系.