A new component mode synthesis method: Quasi-static mode compensation

A new component mode synthesis method is presented in this paper that combines the computational efficiency of the well-known constraint mode approach with the dynamic compensation accuracy obtained by higher-order expansion methods. Instead of employing static constraint modes, quasi-static modes are used to capture inertial effects of the truncated modes. The method is ideally suited for mid-band frequency analysis in which both high-frequency and low-frequency modes may be omitted. A tuning parameter, designated as the centering frequency, controls the dynamic range of the quasi-static modes. Numerical examples are provided which demonstrate the improved accuracy of the proposed method.     

Phase-Averaged Vortex Train Flow Generated by Plasma DBD Actuator

It will be shown how plasma actuator can generate wall-jet-like flow or train of periodical vortices depending on the generator setting. For generation the high-frequency high-voltage AC is used. Low-frequency modulation of the supply voltage is required to generate vortices. Data acquisition will be performed using time-resolved PIV technique. Phase-averaging will be studied from two different perspectives. Firstly, sampling of phases will be ensured using trigger that is contained in the PIV software and, secondly, phase-averaged flow will be computed from two main modes of POD analysis. The generated flow patterns are to be applied for control of a boundary layer. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

两个模态耦合的Ginzburg-Landau方程的时空混沌同步化

根据数值计算的结果提出了模态耦合的条件,两个方程在高频模态上是耦合的,而在低频模态上是不耦合的．利用了无穷维动力系统理论,证明了两个高频模态耦合的Ginzburg-Landau方程在函数空间中存在吸引域,因而存在连通的、有限维的紧的整体吸引子．驱动方程存在时空混沌．将方程组联系一个截断形式,得到的修正方程组将保持原方程组的动力学行为．高频模态耦合的两个方程在一定的条件下具有挤压性质,证明了可达到完全的时空混沌同步化．在数学上定性解释了无穷维动力系统的同步化现象．研究方法不同于有限维动力系统中通常使用的Liapunov函数方法与近似线性方法．     

A novel hybrid decomposition-ensemble model based on VMD and HGWO for container throughput forecasting

This paper built a hybrid decomposition-ensemble model named VMD-ARIMA-HGWO-SVR for the purpose of improving the stability and accuracy of container throughput prediction. The latest variational mode decomposition (VMD) algorithm is employed to decompose the original series into several modes (components), then ARIMA models are built to forecast the low-frequency components, and the high-frequency components are predicted by SVR models which are optimized with a recently proposed swarm intelligence algorithm called hybridizing grey wolf optimization (HGWO), following this, the prediction results of all modes are ensembled as the final forecasting result. The error analysis and model comparison results show that the VMD is more effective than other decomposition methods such as CEEMD and WD, moreover, adopting ARIMA models for prediction of low-frequency components can yield better results than predicting all components by SVR models. Based on the results of empirical study, the proposed model has good prediction performance on container throughput data, which can be used in practical work to provide reference for the operation and management of ports to improve the overall efficiency and reduce the operation costs.     

基于分解—集成的铁路货运需求预测研究

铁路货运量受到多种因素影响,准确的预测可以为铁路行业未来规划的编制提供重要的参考依据,也可以使铁路部门制定符合当前货运市场的运输政策。货运量数据具有非线性、不平稳的特点,利用传统的单一预测模型进行预测,很难描述整体特征,预测精度有待提高。本文基于分解—集成的原则,利用变分模态分解算法将货运量分解为高频和低频模态,针对各模态特点,分别建立预测模型,将得到的预测结果加总起来作为最终货运量的预测值。实证表明,分解—集成预测方法与传统的单一预测模型相比,提高了预测的准确率,可以很好地应用在铁路货运量需求预测的研究中。     

A second-order accurate three sub-step composite algorithm for structural dynamics

In this paper, a novel three sub-step composite algorithm with desired numerical properties is developed. The proposed method is a self-starting, unconditionally stable and second-order accurate implicit algorithm without overshoot. Particularly, the second-order accuracy in time is achieved in its final form, but it is not required in each sub-step. Its unique algorithmic parameter is analyzed to achieve the unconditional stability and it shares the identical effective stiffness matrix inside three sub-steps to save the computational cost in linear analyses. The same as the Bathe algorithm, the proposed algorithm is always L-stable, meaning that the spurious high-frequency modes can be effectively eliminated. Three numerical examples are simulated to illustrate the superiority of the proposed algorithm over some existing implicit algorithms. The first numerical simulation, solving a linear single-degree-of-freedom system, shows less period elongation errors and the second-order accuracy of the present scheme. The second one, a clamped-free bar excited by the end load, shows the ability of effectively damping out the unexpected high-frequency modes. The last example solves the nonlinear mass-spring system with variable degree-of-freedoms and illustrates that the composite sub-step algorithm can save more computational cost than the traditional implicit algorithm when the integration step size is selected appropriately.     

基于傅里叶分析法的股票市场超高频数据相关性分析

股票市场超高频数据具有交易间隔随机性的特点,传统的皮尔逊相关性度量不能够直接使用原始交易数据,需要通过插值得到均匀、同步的抽样序列.傅里叶分析法不需要对原始数据进行插值,能更精确地度量时间序列的相关性.将傅里叶分析法用于我国金融市场股票收益率的相关性分析中,对皮尔逊相关分析和傅里叶分析法的度量效果进行了比较.     

Nonlinear low frequency water waves in a cylindrical shell subjected to high frequency excitations – Part II: Theoretical analysis

In Part I of this work (Comm. Nonlin. Sci. Numer. Simulat. 18 (2013) 1710–1724), an experimental investigation on nonlinear low-frequency gravity water waves in a cylindrical shell subjected to high-frequency horizontal excitations was reported. To reveal the mechanism of this phenomenon, a theoretical analysis is now presented as Part II of the work. A set of nonlinear equations for two mode interactions is established based on variational principle of fluid-shell coupled system. Theory proofs that for high frequency mode of circumferential wave number m nonlinear interaction exits only with gravity wave modes of circumferential wave number zero or 2m. Multi-scale analysis reveals that appearance of such phenomenon is due to Hopf bifurcation of the dynamic system. Curves of critic excitation force with respect to excitation frequency are obtained by analysis. Theoretical results show good qualitative and quantitative agreement with experimental observations.     

On the Influence of High-Frequency Excitation on Systems with Dynamic Friction

By imposing high-frequency vibrations to a system, the characteristics of dry friction for low sliding velocities can be smoothed and, consequently, undesired friction induced phenomena such as stick-slip motion can be quenched. Many studies have been published so far, most of them focussing on the reduction of friction between metal surfaces and using classical Coulomb friction models. Within this contribution the effect of high-frequency excitation on dry friction taking into account dynamic friction models will be discussed. To this end, the friction law suggested by Dahl is used and the resulting friction characteristics are compared to those obtained for the classical Coulomb friction model. Using Dahl's friction model, a reduction of the smoothing effect is observed. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

基于卡方检验分析的随书光盘管理绩效的研究

为研究图书馆随书光盘资源的管理绩效,本文分析了随书光盘的管理模式的特点和卡方检验用于随书光盘管理绩效分析的原理,采用问卷调查法获得读者随书光盘使用情况的数据,并采用单因素和多因素方法进行了随书光盘的管理绩效分析。结果显示,随书光盘的使用率较高,随书光盘管理模式对读者随书光盘的使用方式具有显著的影响,读者更多地选择网络阅读与下载方式,随书光盘的网络管理模式具有更大绩效。因此,卡方检验可以作为随书光盘管理绩效的量化评价方法,为随书光盘管理提供理论依据,高校图书馆需要加强随书光盘网络管理的建设,提高随书光盘的信息服务质量。     

Synergies among students’ thinking modes and representation types in linear algebra: employing statistical implicative analysis

In this work, students’ thinking modes and representation types in linear algebra are investigated through statistical implicative analysis techniques. Specifically, our research question considers the implicative relationships between students’ thinking modes and representation types of linear algebra. The participants were 74 undergraduate linear algebra students enrolled in the department of mathematics education of a government university located in western Turkey. The data was collected using six paper-and-pencil tasks, relating to a context of linear equations, matrix algebra, linear combination, span, linear independency–dependency and basis. A document analysis technique was used to analyze the data within a theoretical lens of thinking modes and representation types. To delineate similarity diagrams, hierarchical trees, and implicative models (which will be detailed in the paper), an R version of Cohesion Hierarchical Implicative Classification software was used. According to the results, students’ analytic structural thinking modes on linear combination and span and linear independency significantly imply the use of algebraic and abstract representations. The results also confirm that the notions of linear combination and span and linear dependency/independency are core elements for theoretical thinking and are needed for learning linear algebra.     

基于高频波动率模型与R-vine copula的行业资产组合风险测度研究

相较于低频波动率模型,高频波动率模型在单资产的波动和风险预测中均取得了更好效果,因此如何将高频波动率模型引入组合风险分析具有重要的理论和现实意义。本文以沪深300指数中的6种行业高频数据为例,运用滚动时间窗技术建立9类已实现波动率异质自回归(HAR-RV-type)模型刻画行业指数波动,同时使用R-vine copula模型描述行业资产间相依结构,进一步结合均值-CVaR模型优化行业资产组合投资比例,构建组合风险的预期损失模型,并通过返回测试比较不同风险模型的精度差异。研究结果表明:将HAR族高频波动率模型引入组合风险分析框架,能够有效预测行业资产组合风险状况;高频波动率预测的准确性将进而影响组合风险测度效果,跳跃、符号跳跃变差以及符号正向、负向跳跃变差均有助于提高行业组合风险的预测精度。     

Normalization of sunspot cycles and eigen mode analysis

The smoothed monthly sunspot numbers of the previous 22 complete sunspot cycles are normalized in time domain, and then an eigen mode analysis is carried out to draw the principle factors (or components) in the cycles. The results show that the main characteristics of the solar cycles can be described fairly well by the first 5 eigen modes. The obtained eigen modes are used to predict the declining phase of cycle 23 on the basis of the data prior to its maximum. The prediction indicates that cycle 23 will last for 127 months to December 2006, with the minimum of 6.2.     

A Generalized Single Linkage Method for Estimating the Cluster Tree of a Density

The goal of clustering is to detect the presence of distinct groups in a dataset and assign group labels to the observations. Nonparametric clustering is based on the premise that the observations may be regarded as a sample from some underlying density in feature space and that groups correspond to modes of this density. The goal then is to find the modes and assign each observation to the domain of attraction of a mode. The modal structure of a density is summarized by its cluster tree; modes of the density correspond to leaves of the cluster tree. Estimating the cluster tree is the primary goal of nonparametric cluster analysis. We adopt a plug-in approach to cluster tree estimation: estimate the cluster tree of the feature density by the cluster tree of a density estimate. For some density estimates the cluster tree can be computed exactly; for others we have to be content with an approximation. We present a graph-based method that can approximate the cluster tree of any density estimate. Density estimates tend to have spurious modes caused by sampling variability, leading to spurious branches in the graph cluster tree. We propose excess mass as a measure for the size of a branch, reflecting the height of the corresponding peak of the density above the surrounding valley floor as well as its spatial extent. Excess mass can be used as a guide for pruning the graph cluster tree. We point out mathematical and algorithmic connections to single linkage clustering and illustrate our approach on several examples. Supplemental materials for the article, including an R package implementing generalized single linkage clustering, all datasets used in the examples, and R code producing the figures and numerical results, are available online.     

Selective Damping for Weakly Coupled FE-MD models

When dynamic problems are of interest, the high-frequency waves reflected from the coupling boundary will pollute the solution in the MD domain quickly and render the results from the multiscale model meaningless. In this contribution, we show that by applying artificial damping only to the high-frequency part of the displacement field in the coupling domain in the weak coupling method can significantly reduce the reflections in the MD domain while not affecting the low-frequency part that can be transmitted into the FE domain. The frequency analysis shows the errors in the magnitudes and phases of wave components are orders of magnitudes smaller than that in the bridging domain model or undamped weak coupling model. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

The effect of vertical vibration on the onset of thermocapillary convection in a horizontal liquid layer

The effect of vertical vibration on the onset of Marangoni convection in a horizontal layer of a viscous incompressible uniform liquid with a free surface and a hard (solid) or soft (impermeable and stress-free) wall is investigated. In the case of harmonic vibration, a dispersion relation is constructed in explicit form using continued fractions. From this, equations are obtained for determining the critical values of the parameters for all three main types of loss of stability. Neutral curves of the monotonic and oscillatory instability are constructed, for fixed frequency and amplitude of the vibration, in the form of a graph of the Marangoni number against the wave number. The regions of parametric resonances, corresponding to synchronous and subharmonic modes are determined. The frequency values for which a high-frequency asymptotic form is reached are obtained. The long-wave Marangoni oscillatory instability is investigated, and it is shown that in this case the Marangoni numbers are negative and depend only on the Prandtl and Biot numbers.     

Electrical analogous in viscoelasticity

In this paper, electrical analogous models of fractional hereditary materials are introduced. Based on recent works by the authors, mechanical models of materials viscoelasticity behavior are firstly approached by using fractional mathematical operators. Viscoelastic models have elastic and viscous components which are obtained by combining springs and dashpots. Various arrangements of these elements can be used, and all of these viscoelastic models can be equivalently modeled as electrical circuits, where the spring and dashpot are analogous to the capacitance and resistance, respectively. The proposed models are validated by using modal analysis. Moreover, a comparison with numerical experiments based on finite difference time domain method shows that, for long time simulations, the correct time behavior can be obtained only with modal analysis. The use of electrical analogous in viscoelasticity can better reveal the real behavior of fractional hereditary materials.     

Second kind integral equation formulation for the mode calculation of optical waveguides

We present a second kind integral equation (SKIE) formulation for calculating the electromagnetic modes of optical waveguides, where the unknowns are only on material interfaces. The resulting numerical algorithm can handle optical waveguides with a large number of inclusions of arbitrary irregular cross section. It is capable of finding the bound, leaky, and complex modes for optical fibers and waveguides including photonic crystal fibers (PCF), dielectric fibers and waveguides. Most importantly, the formulation is well conditioned even in the case of nonsmooth geometries. Our method is highly accurate and thus can be used to calculate the propagation loss of the electromagnetic modes accurately, which provides the photonics industry a reliable tool for the design of more compact and efficient photonic devices. We illustrate and validate the performance of our method through extensive numerical studies and by comparison with semi-analytical results and previously published results.     

小Bond数条件下圆柱贮箱中液体晃动的模部分析

运用模部分析方法考察了小Bond数条件下圆柱贮箱中弯曲静液面对液体晃动模态的重构作用.研究表明,圆柱贮箱中的液体作小幅晃动时,参与晃动的各阶基本模态的正交性若仅由Bessel模部来给出,则弯曲静液面将使各阶模态加权耦合,形成新的特征模态;参与晃动的各阶基本模态的正交性若由三角函数模部来给出,则弯曲静液面将独立改变各阶模态的固有频率,各阶模态之间不耦合.运用新的重构模态来研究圆柱贮箱中液体的横向受迫晃动,给出了其模态选择特征.