Zhou Renjie, Yang Chen, Wan Jian, Zhang Wei, Guan Bo, Xiong Naixue
School of Computer Science and Technology, Hangzhou Dianzi University, Hangzhou 310018, China.
Key Laboratory of Complex Systems Modeling and Simulation of Ministry of Education, Hangzhou Dianzi University, Hangzhou 310018, China.
Sensors (Basel). 2017 Apr 6;17(4):787. doi: 10.3390/s17040787.
Measurement of time series complexity and predictability is sometimes the cornerstone for proposing solutions to topology and congestion control problems in sensor networks. As a method of measuring time series complexity and predictability, multiscale entropy (MSE) has been widely applied in many fields. However, sample entropy, which is the fundamental component of MSE, measures the similarity of two subsequences of a time series with either zero or one, but without in-between values, which causes sudden changes of entropy values even if the time series embraces small changes. This problem becomes especially severe when the length of time series is getting short. For solving such the problem, we propose flexible multiscale entropy (FMSE), which introduces a novel similarity function measuring the similarity of two subsequences with full-range values from zero to one, and thus increases the reliability and stability of measuring time series complexity. The proposed method is evaluated on both synthetic and real time series, including white noise, 1/f noise and real vibration signals. The evaluation results demonstrate that FMSE has a significant improvement in reliability and stability of measuring complexity of time series, especially when the length of time series is short, compared to MSE and composite multiscale entropy (CMSE). The proposed method FMSE is capable of improving the performance of time series analysis based topology and traffic congestion control techniques.
测量时间序列的复杂性和可预测性有时是为传感器网络中的拓扑和拥塞控制问题提出解决方案的基石。作为一种测量时间序列复杂性和可预测性的方法，多尺度熵（MSE）已在许多领域中得到广泛应用。然而，作为MSE基本组成部分的样本熵，测量时间序列的两个子序列的相似度时只有零或一两种情况，没有中间值，这导致即使时间序列只有微小变化，熵值也会突然变化。当时间序列长度变短的时候，这个问题会变得尤为严重。为了解决这个问题，我们提出了灵活多尺度熵（FMSE），它引入了一种新颖的相似度函数，用于测量两个子序列从零到一的全范围值的相似度，从而提高了测量时间序列复杂性的可靠性和稳定性。我们在合成和实时时间序列上对所提出的方法进行了评估，包括白噪声、1/f噪声和实际振动信号。评估结果表明，与MSE和复合多尺度熵（CMSE）相比，FMSE在测量时间序列复杂性的可靠性和稳定性方面有显著提高，特别是在时间序列长度较短时。所提出的FMSE方法能够提高基于时间序列分析的拓扑和流量拥塞控制技术的性能。
