Sandia National Laboratories, Albuquerque, New Mexico 87185, USA.
Department of Aeronautics and Astronautics, University of Washington, Seattle, Washington 98195, USA.
Chaos. 2022 Jul;32(7):073131. doi: 10.1063/5.0097973.
The information impulse function (IIF), running Variance, and local Hölder Exponent are three conceptually different time-series evaluation techniques. These techniques examine time-series for local changes in information content, statistical variation, and point-wise smoothness, respectively. Using simulated data emulating a randomly excited nonlinear dynamical system, this study interrogates the utility of each method to correctly differentiate a transient event from the background while simultaneously locating it in time. Computational experiments are designed and conducted to evaluate the efficacy of each technique by varying pulse size, time location, and noise level in time-series. Our findings reveal that, in most cases, the first instance of a transient event is more easily observed with the information-based approach of IIF than with the Variance and local Hölder Exponent methods. While our study highlights the unique strengths of each technique, the results suggest that very robust and reliable event detection for nonlinear systems producing noisy time-series data can be obtained by incorporating the IIF into the analysis.
信息脉冲函数（IIF）、运行方差和局部赫尔德指数是三种概念上不同的时间序列评估技术。这些技术分别检查时间序列中的局部信息含量变化、统计变化和逐点平滑度。本研究使用模拟数据模拟随机激励的非线性动力系统，探讨了每种方法在正确区分瞬态事件和背景的同时定位时间的能力。通过改变时间序列中的脉冲大小、时间位置和噪声水平，设计并进行了计算实验来评估每种技术的功效。我们的研究结果表明，在大多数情况下，与方差和局部赫尔德指数方法相比，IIF 的基于信息的方法更容易观察到瞬态事件的第一次出现。虽然我们的研究强调了每种技术的独特优势，但结果表明，通过将 IIF 纳入分析，可以为产生噪声时间序列数据的非线性系统获得非常稳健和可靠的事件检测。
