共查询到19条相似文献,搜索用时 187 毫秒
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螺旋桨鸣音的混沌动力特性研究 总被引:2,自引:0,他引:2
利用混沌动力学方法研究螺旋桨鸣音信号时间序列,估计时间序列的相空间重构最佳参数,并提出其具有混沌动力特性,分析了系统拓扑维数的边界和生成系统所必须独立变量的个数,还计算分析了重构相空间中吸引子轨迹随时间演化的发散情况。分析计算结果表明:螺旋桨鸣音信号时间序列可以选取最佳延迟时间tD=1、最小嵌入维数dE=8进行相空间重构,其混沌吸引子的关联维数为5.1579、最大Lyapunov指数为0.0771,此研究结果可以为螺旋桨鸣音现象的进一步研究提供理论基础。 相似文献
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提出一种多变量混沌时间序列相空间重构的条件熵扩维方法.首先使用互信息法求解每个变量的时间延迟,其次按条件熵最大原则逐步扩展相空间的嵌入维数,使得重构坐标从低维到高维的转换保持较强的独立性,最终的重构相空间具有较低的冗余度,为多变量时间序列的预测构造了有效的模型输入向量.通过对几个经典多变量混沌时间序列进行数值实验,结果表明该方法比单变量预测和已有多变量预测方法具有更好的预测效果,说明了该重构方法的有效性.
关键词:
多变量混沌时间序列
相空间重构
条件熵
神经网络预测 相似文献
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根据混沌动力系统的相空间延迟坐标重构理论,基于支持向量机的强大的非线性映射能力, 建立了混沌时间序列的支持向量机预测模型,并在统计学习理论的基础上采用最小二乘方法来训练预测模型,利用该模型对嵌入维数与模型的均方根误差的关系进行了探讨.最后利用Mackey-Glass时间序列和变参数的Ikeda 时间序列对该模型进行了验证,结果表明,该预测模型能精确地预测混沌时间序列,而且在混沌时间序列的嵌入维数未知时也能取得比较好的预测效果.这一结论预示着支持向量机是一种研究混沌时间序列的有效方法.
关键词:
混沌时间序列
支持向量机
最小二乘法 相似文献
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鉴于径向基函数(RBF)神经网络模型在非线性预测方面的优良性能, 提出了利用该预测模型对混沌时间序列相空间重构的两个关键参数——延迟时间和嵌入维数进行联合估计的方法, 并以客观的评价指标为依据给出其最优估计值. 以Lorenz系统为例进行数值分析, 得到RBF单步及多步预测模型中嵌入维数和延迟时间的最佳参数估计值, 并在原模型中对估计值进行校验. 结果表明, 该方法可以有效地估计出嵌入维数和延迟时间, 从而显著提高预测精度. 相似文献
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空调系统负荷非线性变化,单独利用人工神经网络方法进行预测,受到样本数量少等的限制,精度一般都比较低。空调系统负荷时间序列包含了参与空调系统动态变化的全部变量的信息,可以利用相空间重构技术提取和恢复出系统原来的规律。重构后的相空间具有与实际动力系统相同的几何性质,这样就可以大大增加样本数。相空间重构受嵌入维数m和延迟时间τ的影响,确定这两个重构参数的最佳数值是非常重要的。建立了基于相空间重构技术的神经网络空调负荷预测模型,在嵌入维数m和延迟时间τ分别取不同的值时,利用这个模型对相同时间段的空调负荷进行预测,选择预测误差最小时对应的参数为最佳相空间重构参数,对应的预测值为最佳预测结果。结果表明,这个方法有很好的效果,具有简化计算复杂性等特点。 相似文献
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Phase space reconstruction is the first step to recognizing
the chaos from observed time series. On the basis of differential
entropy, this paper introduces an efficient method to estimate the
embedding dimension and the time delay simultaneously. The
differential entropy is used to characterize the disorder degree of
the reconstructed attractor. The minimum value of the differential
entropy corresponds to the optimum set of the reconstructed
parameters. Simulated experiments show that the original phase space
can be effectively reconstructed from time series, and the
accuracy of the invariants in phase space reconstruction is greatly
improved. It provides a new method for the identification of chaotic
signals from time series. 相似文献
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MaxEnt inference algorithm and information theory are relevant for the time evolution of macroscopic systems considered as
problem of incomplete information. Two different MaxEnt approaches are introduced in this work, both applied to prediction
of time evolution for closed Hamiltonian systems. The first one is based on Liouville equation for the conditional probability
distribution, introduced as a strict microscopic constraint on time evolution in phase space. The conditional probability
distribution is defined for the set of microstates associated with the set of phase space paths determined by solutions of
Hamilton’s equations. The MaxEnt inference algorithm with Shannon’s concept of the conditional information entropy is then
applied to prediction, consistently with this strict microscopic constraint on time evolution in phase space. The second approach
is based on the same concepts, with a difference that Liouville equation for the conditional probability distribution is introduced
as a macroscopic constraint given by a phase space average. We consider the incomplete nature of our information about microscopic
dynamics in a rational way that is consistent with Jaynes’ formulation of predictive statistical mechanics, and the concept
of macroscopic reproducibility for time dependent processes. Maximization of the conditional information entropy subject to
this macroscopic constraint leads to a loss of correlation between the initial phase space paths and final microstates. Information
entropy is the theoretic upper bound on the conditional information entropy, with the upper bound attained only in case of
the complete loss of correlation. In this alternative approach to prediction of macroscopic time evolution, maximization of
the conditional information entropy is equivalent to the loss of statistical correlation, and leads to corresponding loss
of information. In accordance with the original idea of Jaynes, irreversibility appears as a consequence of gradual loss of
information about possible microstates of the system. 相似文献
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Magnetic resonance absorption lineshapes can have subtle dependencies on the model parameters that specify the lineshape. To quantify how the model parameters influence the lineshape, it is useful to study simple model systems for which analytical expressions are available. We propose that information theory is a useful tool to quantify how well model parameters may be inferred from a noisy signal. Information theory also allows us to assess the importance of missing parameters from an incomplete model. We do this by monitoring the magnitude of a partition function determined from a suitably defined probability mass function as the model parameters are varied. The optimum parameter set makes the partition function a maximum, which establishes a computable criterion for determining the best model parameter set. Given the availability of a partition function, one may define thermodynamic functions such as the entropy. The optimum parameter set in this interpretation corresponds to the state of maximum entropy. In this work, we observe that at sufficiently low signal to noise ratio, the entropy landscape has no clear maximum, while a related quantity, the Fisher information, always has a clear minimum at the optimum parameter set. The qualitative information we are able to gather from the entropy landscapes is also difficult to assess when the parameters are far from their optimum values, at least for the model system studied here. 相似文献
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阐述了以表述信息演化规律的信息(熵)演化方程为核心的非平 衡统计信息理论.推导出了 Shannon信息(熵)的非线性演化方程,引入了统计物理信息并 推导出了它的非线性演化方程.这两种信息(熵)演化方程一致表明:统计信息(熵)密度 随时间的变化率是由其在坐标空间(和态变量空间)的漂移、扩散和减损(产生)三者引起 的.由此方程出发,给出了统计信息减损率和统计熵产生率的简明公式、漂移信息流和扩散 信息流的表达式,证明了非平衡系统内的统计信息减损(或增加)率等于它的统计熵产生( 或减少)率、信息扩散与信息减损同时
关键词:
统计信息(熵)演化方程
统计信息减损率
统计熵产 生率
信息(熵)流
信息(熵)扩散
动态互信息 相似文献
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XING Xiusan 《中国科学G辑(英文版)》2006,49(1):1-37
In recent years we extended Shannon static statistical information theory to dynamic processes and established a Shannon dynamic
statistical information theory, whose core is the evolution law of dynamic entropy and dynamic information. We also proposed
a corresponding Boltzmman dynamic statistical information theory. Based on the fact that the state variable evolution equation
of respective dynamic systems, i.e. Fokker-Planck equation and Liouville diffusion equation can be regarded as their information
symbol evolution equation, we derived the nonlinear evolution equations of Shannon dynamic entropy density and dynamic information
density and the nonlinear evolution equations of Boltzmann dynamic entropy density and dynamic information density, that describe
respectively the evolution law of dynamic entropy and dynamic information. The evolution equations of these two kinds of dynamic
entropies and dynamic informations show in unison that the time rate of change of dynamic entropy densities is caused by their
drift, diffusion and production in state variable space inside the systems and coordinate space in the transmission processes;
and that the time rate of change of dynamic information densities originates from their drift, diffusion and dissipation in
state variable space inside the systems and coordinate space in the transmission processes. Entropy and information have been
combined with the state and its law of motion of the systems. Furthermore we presented the formulas of two kinds of entropy
production rates and information dissipation rates, the expressions of two kinds of drift information flows and diffusion
information flows. We proved that two kinds of information dissipation rates (or the decrease rates of the total information)
were equal to their corresponding entropy production rates (or the increase rates of the total entropy) in the same dynamic
system. We obtained the formulas of two kinds of dynamic mutual informations and dynamic channel capacities reflecting the
dynamic dissipation characteristics in the transmission processes, which change into their maximum—the present static mutual
information and static channel capacity under the limit case where the proportion of channel length to information transmission
rate approaches to zero. All these unified and rigorous theoretical formulas and results are derived from the evolution equations
of dynamic information and dynamic entropy without adding any extra assumption. In this review, we give an overview on the
above main ideas, methods and results, and discuss the similarity and difference between two kinds of dynamic statistical
information theories. 相似文献
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A simple second quantization model is used to describe a two-mode Bose-Einstein condensate (BEC), which can be written in terms of the generators of a SU(2) algebra with three parameters. We study the behavior of the entanglement entropy and localization of the system in the parameter space of the model. The phase transitions in the parameter space are determined by means of the coherent state formalism and the catastrophe theory, which besides let us get the best variational state that reproduces the ground state energy. This semiclassical method let us organize the energy spectrum in regions where there are crossings and anticrossings. The ground state of the two-mode BEC, depending on the values of the interaction strengths, is dominated by a single Dicke state, a spin collective coherent state, or a superposition of two spin collective coherent states. The entanglement entropy is determined for two recently proposed partitions of the two-mode BEC that are called separation by boxes and separation by modes of the atoms. The entanglement entropy in the boxes partition is strongly correlated to the properties of localization in phase space of the model, which is given by the evaluation of the second moment of the Husimi function. To compare the fitness of the trial wavefunction its overlap with the exact quantum solution is evaluated. The entanglement entropy for both partitions, the overlap and localization properties of the system get singular values along the separatrix of the two-mode BEC, which indicates the phase transitions which remain in the thermodynamical limit, in the parameter space. 相似文献
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Quantum confinement in an asymmetric double‐well potential through energy analysis and information entropic measure
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Amlan K. Roy 《Annalen der Physik》2016,528(5):412-433
Localization of a particle in the wells of an asymmetric double‐well (DW) potential is investigated here. Information entropy‐based uncertainty measures, such as Shannon entropy, Fisher information, Onicescu energy, etc., and phase‐space area, are utilized to explain the contrasting effect of localization‐delocalization and role of asymmetric term in such two‐well potentials. In asymmetric situation, two wells behaves like two different potentials. A general rule has been proposed for arrangement of quasi‐degenerate pairs, in terms of asymmetry parameter. Further, it enables to describe the distribution of particle in either of the deeper or shallow wells in various energy states. One finds that, all states eventually get localized to the deeper well, provided the asymmetry parameter attains certain threshold value. This generalization produces symmetric DW as a natural consequence of asymmetric DW. Eigenfunctions, eigenvalues are obtained by means of a simple, accurate variation‐induced exact diagonalization method. In brief, information measures and phase‐space analysis can provide valuable insight toward the understanding of such potentials. 相似文献
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Random-injection-based two-channel chaos with enhanced bandwidth and suppressed time-delay signature by mutually coupled lasers: Proposal and numerical analysis
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Simultaneous bandwidth(BW) enhancement and time-delay signature(TDS) suppression of chaotic lasing over a wide range of parameters by mutually coupled semiconductor lasers(MCSLs) with random optical injection are proposed and numerically investigated. The influences of system parameters on TDS suppression(characterized by autocorrelation function(ACF) and permutation entropy(PE) around characteristic time) and chaos BW are investigated. The results show that, with the increasing bias current, the ranges of parameters(detuning and injection strength) for the larger BW(> 20 GHz) are broadened considerably, while the parameter range for optimized TDS(< 0.1) is not shrunk obviously.Under optimized parameters, the system can simultaneously achieve two chaos outputs with enhanced BW(> 20 GHz)and perfect TDS suppression. In addition, the system can generate two-channel high-speed truly physical random number sequences at 200 Gbits/s for each channel. 相似文献
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V. L. Lazarev 《Technical Physics》2010,55(2):159-165
An approach is proposed for studying various systems based on the concept of entropy potentials of their parameters. In this
approach, any state of a system can be described quantitatively using the values of entropy potentials of corresponding parameters.
With such an approach, the states and the evolution processes in the systems being analyzed can be mapped onto the coordinate
space of the “information field” of the system, which makes it possible to simplify the solution of a number of applied problems. 相似文献