Optimising Parameters in Recurrence Quantification Analysis of Smart Energy Systems

Abstract

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.

Investigating Robustness of Energy Management Maps for SMEs

“…Several experiments with missing data, noise and different data resolution were run, in order to assess the robustness of the methods developed in [4]. We found that in the majority of the cases, the method is robust to the aforementioned tests.…”

“…This is especially true with emerging areas of applications such as 30 min resolution electric energy data. The optimal selection of parameters for energy usage data was discussed in [4].…”

“…In this section we assess the robustness of the algorithms determining the time delay and embedding dimension [4]. We estimate the two parameters using i) longer periods of data, Figure 13a, and ii) using three weeks' data rolling over the available period, i.e.…”

“…Finding the optimal radius is a time-consuming process (see [4]). For this reason we focus only on two training periods; a four and a five week period starting from the 12th of May 2018.…”

“…In this article, we are investigating robustness of the recently proposed Recurrence Quantitive Analysis (RQA) ( [1], [2]) based method (for further details see [3], [4]) for energy management of SMEs. The method consists of two phases, the training phase where the map(s) of 'usual' behaviour is obtained, and the operational phase where the new data is tested against the existing map.…”