Montoya Angela, Habtour Ed, Moreu Fernando
Sandia National Laboratories, Albuquerque, NM 87185, USA.
William E. Boeing Department of Aeronautics & Astronautics, University of Washington, Seattle, WA 98195, USA.
Entropy (Basel). 2020 Oct 23;22(11):1199. doi: 10.3390/e22111199.
A system's response to disturbances in an internal or external driving signal can be characterized as performing an implicit computation, where the dynamics of the system are a manifestation of its new state holding some memory about those disturbances. Identifying small disturbances in the response signal requires detailed information about the dynamics of the inputs, which can be challenging. This paper presents a new method called the Information Impulse Function (IIF) for detecting and time-localizing small disturbances in system response data. The novelty of IIF is its ability to measure relative information content without using Boltzmann's equation by modeling signal transmission as a series of dissipative steps. Since a detailed expression of the informational structure in the signal is achieved with IIF, it is ideal for detecting disturbances in the response signal, i.e., the system dynamics. Those findings are based on numerical studies of the topological structure of the dynamics of a nonlinear system due to perturbated driving signals. The IIF is compared to both the Permutation entropy and Shannon entropy to demonstrate its entropy-like relationship with system state and its degree of sensitivity to perturbations in a driving signal.
系统对内部或外部驱动信号干扰的响应可被描述为执行一种隐式计算，其中系统的动态特性表现为其新状态保留了有关这些干扰的一些记忆。识别响应信号中的小干扰需要有关输入动态特性的详细信息，这可能具有挑战性。本文提出了一种称为信息脉冲函数（IIF）的新方法，用于检测和对系统响应数据中的小干扰进行时间定位。IIF的新颖之处在于它能够通过将信号传输建模为一系列耗散步骤，在不使用玻尔兹曼方程的情况下测量相对信息含量。由于通过IIF可以实现信号中信息结构的详细表达，因此它非常适合检测响应信号中的干扰，即系统动态特性。这些发现基于对非线性系统因扰动驱动信号而产生的动态拓扑结构的数值研究。将IIF与排列熵和香农熵进行比较，以证明其与系统状态的类似熵的关系以及对驱动信号中扰动的敏感程度。
