Aguirre Luis A, Letellier Christophe
Departamento de Engenharia Eletrônica, Universidade Federeal de Minas Gerais, Avenida Antônio Carlos 6627, 31270-901 Belo Horizonte MG, Brazil.
Phys Rev E Stat Nonlin Soft Matter Phys. 2011 Jun;83(6 Pt 2):066209. doi: 10.1103/PhysRevE.83.066209. Epub 2011 Jun 22.
Investigation of observability properties of nonlinear dynamical systems aims at giving a hint on how much dynamical information can be retrieved from a system using a certain measuring function. Such an investigation usually requires knowledge of the system equations. This paper addresses the challenging problem of investigating observability properties of a system only from recorded data. From previous studies it is known that phase spaces reconstructed from poor observables are characterized by local sharp pleatings, local strong squeezing of trajectories, and global inhomogeneity. A statistic is then proposed to quantify such properties of poor observability. Such a statistic was computed for a number of bench models for which observability studies had been previously performed. It was found that the statistic proposed in this paper, estimated exclusively from data, correlates generally well with observability results obtained using the system equations. It is possible to arrive at the same order of observability among the state variables using the proposed statistic even in the presence of noise with a standard deviation as high as 10% of the data. The paper includes the application of the proposed statistic to sunspot time series.
非线性动力系统可观测性特性的研究旨在提示利用特定测量函数从系统中能获取多少动力学信息。此类研究通常需要了解系统方程。本文解决了仅从记录数据研究系统可观测性特性这一具有挑战性的问题。从先前的研究可知，由不良可观测量重构的相空间具有局部尖锐褶皱、轨迹局部强烈挤压以及全局不均匀性的特征。然后提出一种统计量来量化这种不良可观测性的特性。针对一些先前已进行可观测性研究的基准模型计算了这种统计量。结果发现，本文提出的仅从数据估计的统计量与使用系统方程获得的可观测性结果总体上具有良好的相关性。即使存在标准差高达数据10%的噪声，使用所提出的统计量也能够在状态变量之间得出相同的可观测性顺序。本文还包括了所提出的统计量在太阳黑子时间序列中的应用。
