Fractional analytics hidden in complex industrial time series data: a case study on supermarket energy use

Time series data of complex industrial system doesn't subject Gaussian distribution due to its sharp spikes and heavy-tailed characteristic. Finding the latent features and rules for these data is a meaningful topic. Here the industrial data analysis is discussed under the fractional thinking with an actual supermarket energy system as example. The cooling system in supermarket always exhibits many non-Gaussian behaviors which are hard to capture by traditional data analytic methods. This paper shows that the novel fractional-order perspective is suitable for the real industrial data. Hurst exponent and fractal theory are used to study the long-range dependency characteristic from the supermarket energy data. It is found that the α-stable distribution better match with the probability density of row data compared with the traditional Gaussian distribution (integer-order) firstly. Then rescaled range method (R/S) is adopted to get the Hurst exponent which can estimate the long-range dependency existing in these process variables. Furthermore, the fractal feature of time series is estimated by comparing the slope of different scaling function under different order according to multifractal detrended fluctuation analysis (MFDFA). The non-Gaussian statistical characteristics, Hurst exponents and fractal feature of supermarket data are derived by comparing the results under different parameters. The practical application results show that the fractional order thinking can deeply mine the latent information hidden in the process data and has a significant advantage in data analytics domain.