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Abstract
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.
Highlights
Time series analysis and forecasting are sometimes essential methods for conquering topology control issues, traffic control issues existed in sensor networks
We propose the flexible multiscale entropy (FMSE) to applying time series analysis in solving topology and traffic control problems in sensor networks
We have introduced the entropy metrics that are used to measure the complexity and paper introduces a new function for measuring and accumulating the similarity between time series predictability of time series
Summary
Time series analysis and forecasting are sometimes essential methods for conquering topology control issues, traffic control issues existed in sensor networks. One field that has received relatively little attention so far is the measurement of predictability or complexity of time series generated by sensor networks. In paper [9], the authors demonstrated that multiscale entropies provide new information about time series. We further propose a novel method based on multiscale entropies, which is capable of discriminating the difference between noise and interference in the empirical time series. The proposed method is evaluated on both synthetic and real time series, and all of the results demonstrate that the proposed method has a significant improvement in reliability and stability of measuring complexity and predictability of time series.
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