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Nonlinear analysis of spatio-temporal analog discrete events and its application

时空模拟离散事件的非线性分析及其应用

基本信息

批准号：
17500136
负责人：
IKEGUCHI Tohru
金额：
$ 2.24万
依托单位：
Saitama University
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
2005
资助国家：
日本
起止时间：
2005 至 2006
项目状态：
已结题

来源：
https://kaken.nii.ac.jp/en/grant/KAKENHI-PROJECT-17500136/
关键词：
nonlinear event dynamics dynamical systems chaos amplitude phase prediction predictability 予測

项目摘要

Several methods have been proposed to analyze complex behavior produced from nonlinear dynamical systems. If we predict behavior produced from such nonlinear dynamical systems, we have to consider nonlinear prediction methods rather than linear prediction methods.In this report, we propose a novel nonlinear modeling framework to analyze complex, possible chaotic event series. We construct a state space by involving the event timing and its amplitude information simultaneously. Thus, we consider that the important and essential information of the dynamical system is not only event sizes or event timings but both of observed event sizes and timings.In addition, we propose a new nonlinear prediction method to realize high predictability for the observed time series of event sizes and timings. Although the nonlinear prediction methods are classified into a global method and a local method, we focused on the local methods in this report. In particular, we adopted the Jacobian matrix estimat … More ion method, one of the local linear methods. Generally, the local linear methods use information of movements of nearby trajectories of a prediction target on an attractor of the nonlinear dynamical systems. Then, in the local linear method, it is very important to estimate the information of the movements as accurately as possible from observed time series data, because if the estimated information is poor, it is difficult to predict future states correctly.To resolve such an important issue, we proposed a new local linear prediction method that introduces the bootstrap replication method, which is called nonlinear bootstrap prediction. The bootstrap method is one of the statistical techniques to estimate statistics of a population from small number of observed data. We propose a new prediction method by combining the basic local linear prediction and the bootstrap method. Then, we showed that the proposed bootstrap nonlinear prediction method is very effective by performing numerical simulations. To evaluate the validity of the prediction method, we generally use a root mean square error. However, we are often asked to estimate a prediction interval in which true future points might be included. We proposed a new method to estimate prediction intervals using a distribution of nonlinear bootstrap predicted points. Then, we evaluate the validity of the proposed interval estimation comparing to an ensemble prediction which is the conventional interval estimation. As results, we show that the bootstrap method is more reasonable to make efficient prediction intervals especially in the case of short term prediction. Less

已经提出了几种方法来分析非线性动力系统产生的复杂行为。如果我们预测这种非线性动力系统产生的行为，我们必须考虑非线性预测方法而不是线性预测方法。在本报告中，我们提出了一种新颖的非线性建模框架来分析复杂的、可能的混沌事件系列。我们通过同时涉及事件时序及其幅度信息来构建状态空间。因此，我们认为动力系统的重要且本质的信息不仅是事件大小或事件时间，而且是观测到的事件大小和时间。此外，我们提出了一种新的非线性预测方法，以实现对事件大小和时间的观测时间序列的高可预测性。尽管非线性预测方法分为全局方法和局部方法，但我们在本报告中重点关注局部方法。特别是，我们采用了雅可比矩阵估计离子方法，局部线性方法之一。通常，局部线性方法使用非线性动力系统吸引子上的预测目标的附近轨迹的运动信息。那么，在局部线性方法中，从观测的时间序列数据中尽可能准确地估计运动信息是非常重要的，因为如果估计的信息很差，就很难正确预测未来的状态。为了解决这个重要问题，我们提出了一种引入引导复制方法的新的局部线性预测方法，称为非线性引导预测。 Bootstrap 方法是从少量观测数据估计总体统计数据的统计技术之一。我们结合基本的局部线性预测和引导方法提出了一种新的预测方法。然后，我们通过数值模拟表明所提出的引导非线性预测方法非常有效。为了评估预测方法的有效性，我们通常使用均方根误差。然而，我们经常被要求估计一个预测区间，其中可能包含真实的未来点。我们提出了一种使用非线性引导预测点的分布来估计预测区间的新方法。然后，我们将所提出的区间估计与作为传统区间估计的集合预测进行比较，评估其有效性。结果表明，引导方法更合理，可以做出有效的预测区间，特别是在短期预测的情况下。较少的