HARMONIC COMPONENT EXTRACTION FROM A CHAOTIC SIGNAL BASED ON EMPIRICAL MODE DECOMPOSITION METHOD

A novel approach of signal extraction of a harmonic component from a chaotic signal generated by a Duffing oscillator was proposed. Based on empirical mode decomposition (EMD) and concept that any signal is composed of a series of the simple intrinsic modes, the harmonic components were extracted from the chaotic signals. Simulation results show the approach is satisfactory.     

Multifractal detrended fluctuation analysis based on optimized empirical mode decomposition for complex signal analysis

Nonlinear Dynamics - Multifractal detrended fluctuation analysis (MFDFA) is a powerful tool to uncover nature of complex signals. However, MFDFA runs into difficulties in determining the type of...     

基于经验模态概率分布的光纤陀螺信号处理

为了抑制光纤陀螺随机漂移,基于改进的经验模态分解(EMD)和新型模态筛选标准提出了一种自适应的区间阈值滤波方法。首先分析加入高斯噪声对 EMD 分解结果的影响,提出有界噪声辅助以改善 EMD 分解质量,然后针对本征模态函数的概率分布特征提出了基于样本熵的模态筛选标准,最后采用数据驱动的阈值选择方法实现自适应的区间阈值滤波。为了验证算法的有效性,采集一款干涉型光纤陀螺静态漂移信号进行实验分析,结果表明本文方法较基于平稳小波变换和 EMD 的阈值滤波有更好的去噪效果。仿真分析表明该去噪算法减小了捷联惯性导航系统的航向角误差,均方根误差较     

基于参考信号的广义特征值分解盲源分离算法及其在北斗多路径效应削弱中的应用

多路径误差是北斗导航定位系统高精度动态监测的主要误差源。针对北斗导航定位系统多路径误差的特性,结合广义特征值盲源分离方法的优势,提出一种基于参考信号的广义特征值盲源分离算法来削弱多路径效应的影响。首先将前一天的原始坐标残差序列通过奇异谱分析方法进行去噪,其结果作为初始参考信号;然后将当天的原始坐标残差序列进行经验模式分解方法分解,分解得到的IMF分量作为虚拟观测数据,利用广义特征值盲源分离算法获取当天多路径误差信号;最后,利用仿真数据和连续10天的实际观测数据进行试验分析,结果表明利用该方法建立的多路径误差改正模型能有效地了削弱多路径的影响,北、东、天三个方向精度分别提高了78.8%、35.3%、90.1%。提出的模型在一定程度上解决了固定多路径模型随着时间推移重复性减小且有效性降低的问题。     

基于集合经验模态分解-小波阈值方法的爆破振动信号降噪方法

为了更好地消除混杂在爆破信号中的噪声,引入一种基于集合经验模态分解和小波阈值共同作用的降噪方法。首先将信号进行集合经验模态分解,然后选择含噪的模态函数分量进行小波阈值降噪处理,最后把处理后的分量和未处理的分量进行叠加,重构的信号即为降噪信号。该方法不仅能有效的去除噪声,还能使爆破波形保留其真实性和完整性。     

A ship motion forecasting approach based on empirical mode decomposition method hybrid deep learning network and quantum butterfly optimization algorithm

Studies of the shallow water waves are active, possessing the applications in ocean engineering, marine environment, atmospheric science, etc. In this paper, we investigate a (3+1)-dimensional shallow water wave equation with time-dependent coefficients. Hirota method and symbolic computation help us work out (1) a bilinear form, (2) N-soliton solutions with N being a positive integer, (3) the higher-order breather solutions, (4) periodic-wave solutions and (5) hybrid solutions composed of one first-order breather and one soliton/two solitons. Moreover, we provide some nonlinear phenomena described by the associated solutions. All of the obtained results are determined via the time-dependent coefficients of that equation.

     

Determination of turbulence properties by using empirical mode decomposition on periodic and random perturbed flows

Stationary and non-stationary grid-generated turbulence was studied using a complementary technique that combines empirical mode decomposition (EMD) and triple-decomposition. Non-stationary conditions were generated by superimposing periodic and random fluctuations on the original flow. Empirical mode decomposition (EMD) was applied as a filter to separate these fluctuations from the turbulent velocity component. Triple-decomposition was then used and the turbulent intensity, the integral length scales and the Power Spectral Density of the velocity were determined. How to use EMD in order to optimize this decomposition is discussed. Finally, the properties of the turbulence are compared to those characterized without addition of fluctuations and a good agreement is found.     

变分模态分解在爆破信号趋势项去除中的应用

爆破工程中,信号趋势项的准确去除对提高爆破振动信号分析的精度具有重要意义。针对经验模态分解（empirical mode decomposition,EMD）识别法存在的模态混叠和端头效应等缺陷,提出了基于变分模态分解（variational mode decomposition,VMD）去除信号趋势项的方法,即VMD法。叙述了VMD法识别爆破信号趋势项原理,并进行了仿真实验,结果表明：趋势项频率对分解效果的影响相对较小,当趋势项频率处于1～5 Hz之间时,频率对分解效果的影响基本保持不变;振幅对分解效果影响显著,且振幅越小,VMD法的分解效果越差。当趋势项振幅超过原始爆破信号最大振幅的1/3时,VMD法分解效果较好。最后,应用VMD法和EMD法对含有趋势项的实测爆破振动信号进行处理,认为相比于EMD法,VMD法处理后的信号基本一致且不存在端点效应,在爆破信号趋势项去除领域中具有更加广泛的适用性。

     

动能定理应用探讨

应用动能定理解质点系运动问题时，不能随意假定质点系的始末状态，而必须全过程进行分析。本给出了一个只考虑想象中的、并不存在的始末状态而得出错误结论的例子。     

Application of the dynamic mode decomposition to experimental data

The dynamic mode decomposition (DMD) is a data-decomposition technique that allows the extraction of dynamically relevant flow features from time-resolved experimental (or numerical) data. It is based on a sequence of snapshots from measurements that are subsequently processed by an iterative Krylov technique. The eigenvalues and eigenvectors of a low-dimensional representation of an approximate inter-snapshot map then produce flow information that describes the dynamic processes contained in the data sequence. This decomposition technique applies equally to particle-image velocimetry data and image-based flow visualizations and is demonstrated on data from a numerical simulation of a flame based on a variable-density jet and on experimental data from a laminar axisymmetric water jet. In both cases, the dominant frequencies are detected and the associated spatial structures are identified.     

Topological entropy and geometric entropy and their application to the horizontal visibility graph for financial time series

Seismic wave control is very important both in civil and mechanical engineering. Common passive methods for isolating a building or a device include base isolators and tuned mass dampers. In the present paper, a time-varying controllable spring is considered as a vibration isolator for a linear mechanical system. The controller works as follows: When the seismic movement is active, the velocity of the moving mass is monitored as the reference velocity. When such reference velocity is positive, the stiffness is reduced; when it is negative, the stiffness is increased. Numerical investigations show that the controller is capable of filtering seismic excitation close to the natural frequency of the controlled system and reducing the total seismic energy transfer up to 5 times. The role played by the gravity in the active vibration filtering is pointed out by showing that no filtering action can be observed in gravity-free simulations. Moreover, control effectiveness has been proven for a measured seismic signal, showing its robustness in presence of noise.     

基于小波包能量谱爆炸参量对爆破振动信号能量分布的影响

基于现场实测爆破振动数据,根据爆破振动信号具有短时非平稳的特点,采用小波包分析技术对不同爆炸参量(爆心距、最大段药量和微差雷管段数)下产生的爆破振动信号进行小波包能量谱分析,获得了爆破振动信号不同频带的能量分布,研究了不同爆炸参量下的爆破振动信号能量分布特征,从爆破振动信号能量角度探讨了不同爆炸参量下爆破地震波的衰减规律,为研究爆破地震效应提供了一种新的分析技术。     

厚度振动模式下背衬结构PZT的声能特性

为了充分利用埋入混凝土中压电陶瓷所激励的声能,采用了一种在压电陶瓷圆片结构的一面设置金属背衬的方法将压电陶瓷双侧的声能集中到一侧,提高了声指向性和声能。实验表明:该方法能使同距离下压电陶瓷圆片轴向声能提高10倍以上,并且得到了声能的相对增量随背衬厚度和声激励频率之积变化的特性曲线。声信号的谱分析还表明:背衬没有改变声信号的主频和主峰区间的频率带宽;当声激励频率为谐振频率79kHz时,最优背衬厚度为2.4mm;当声激励频率f为60kHz～100kHz时,接收端声能相对较大,适合用于实际的压电埋入式超声无损检测。     

基于区域分解的并行有限元程序及其在水下爆炸中的应用

基于MPI标准定义的消息传递接口实现了显式动力学有限元程序的并行计算.通过基于Hilbert空间填充曲线的区域分解算法,实现各区域的独立运算和区域之间共享数据的相互通信.利用程序对水下爆炸自由场中的冲击波传播规律进行了数值模拟,并通过对不同进程数下的并行加速比进行测试,验证了程序的并行效率.     

Wada index based on the weighted and truncated Shannon entropy

Nonlinear Dynamics - The Wada index based on the weighted and truncated Shannon entropy is presented in this paper. The proposed Wada index can detect if a given basin boundary is a Wada boundary....     

On the two-phase Stefan problem with interfacial energy and entropy

Archive for Rational Mechanics and Analysis -     

Eigenfunction expansion method and its application to two-dimensional elasticity problems based on stress formulation

This paper proposes an eigenfunction expansion method to solve twodimensional （2D） elasticity problems based on stress formulation. By introducing appropriate state functions, the fundamental system of partial differential equations of the above 2D problems is rewritten as an upper triangular differential system. For the associated operator matrix, the existence and the completeness of two normed orthogonal eigenfunction systems in some space are obtained, which belong to the two block operators arising in the operator matrix. Moreover, the general solution to the above 2D problem is given by the eigenfunction expansion method.     

RECURRENT NEURAL NETWORK MODEL BASED ON PROJECTIVE OPERATOR AND ITS APPLICATION TO OPTIMIZATION PROBLEMS

The recurrent neural network (RNN) model based on projective operator was studied. Different from the former study, the value region of projective operator in the neural network in this paper is a general closed convex subset of n-dimensional Euclidean space and it is not a compact convex set in general, that is, the value region of projective operator is probably unbounded. It was proved that the network has a global solution and its solution trajectory converges to some equilibrium set whenever objective function satisfies some conditions. After that, the model was applied to continuously differentiable optimization and nonlinear or implicit complementarity problems. In addition, simulation experiments confirm the efficiency of the RNN.