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Register a new userOptimising Parameters in Recurrence Quantification Analysis of Smart Energy Systems
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Added by
Georgios Giasemidis Dr
Publication date
2018
fields
Electronic Engineering
and research's language is
English
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Recurrence Quantification Analysis (RQA) can help to detect significant events and phase transitions of a dynamical system, but choosing a suitable set of parameters is crucial for the success. From recurrence plots different RQA variables can be obtained and analysed. Currently, most of the methods for RQA radius optimisation are focusing on a single RQA variable. In this work we are proposing two new methods for radius optimisation that look for an optimum in the higher dimensional space of the RQA variables, therefore synchronously optimising across several variables. We illustrate our approach using two case studies: a well known Lorenz dynamical system, and a time-series obtained from monitoring energy consumption of a small enterprise. Our case studies show that both methods result in plausible values and can be used to analyse energy data.
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The growing study of time series, especially those related to nonlinear systems, has challenged the methodologies to characterize and classify dynamical structures of a signal. Here we conceive a new diagnostic tool for time series based on the concept of information entropy, in which the probabilities are associated to microstates defined from the recurrence phase space. Recurrence properties can properly be studied using recurrence plots, a methodology based on binary matrices where trajec- tories in phase space of dynamical systems are evaluated against other embedded trajectory. Our novel entropy methodology has several advantages compared to the traditional recurrence entropy defined in the literature, namely, the correct evaluation of the chaoticity level of the signal, the weak dependence on parameters, correct evaluation of periodic time series properties and more sensitivity to noise level of time series. Furthermore, the new entropy quantifier developed in this manuscript also fixes inconsistent results of the traditional recurrence entropy concept, reproducing classical results with novel insights.
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The standard chirplet transform (CT) with a chirp-modulated Gaussian window provides a valuable tool for analyzing linear chirp signals. The parameters present in the window determine the performance of CT and play a very important role in high-resolution time-frequency (TF) analysis. In this paper, we first give the window shape analysis of CT and compare it with the extension that employs a rotating Gaussian window by fractional Fourier transform. The given parameters analysis provides certain theoretical guidance for developing high-resolution CT. We then propose a multi-resolution chirplet transform (MrCT) by combining multiple CTs with different parameter combinations. These are combined geometrically to obtain an improved TF resolution by overcoming the limitations of any single representation of the CT. By deriving the combined instantaneous frequency equation, we further develop a high-concentration TF post-processing approach to improve the readability of the MrCT. Numerical experiments on simulated and real signals verify its effectiveness.
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