PROPERTIES OF DISCRETE-TIME CONDITIONAL LINEAR CYCLOSTATIONARY RANDOM PROCESSES IN THE PROBLEMS OF ENERGY INFORMATICS

Abstract

Modern challenges in the energy industry require comprehensive research in the field of energy informatics, which combines computer science, control systems, and energy management systems within a single methodology. An important area of energy informatics is the study of problems of systems and processes modeling in energy, including energy loads and consumption. Linear and conditional linear random processes (CLRP) are mathematical models of signals represented as the sum of a large number of random impulses occurring at random times. The energy consumption, vibration signals of energy objects, etc. can be modeled using this approach. A variant of the CLRP model with discrete time, taking into account the cyclic properties of energy consumption, has been investigated in the paper. The goal is to justify the conditions for the discrete-time CLRP to be a periodically correlated random process, as well as a cyclostationary process. It has been shown that the corresponding conditions depend on the periodicity of the probability distributions of the kernel and the generating white noise of the CLRP representation. To achieve the goal, the properties of mathematical expectation and covariance function of CLRP, as well as the method of characteristic functions, have been used. The paper proves that the discrete-time CLRP is a periodically correlated random sequence if the generating white noise has periodic mathematical expectation and variance, and the kernel is a periodically correlated random field. Based on the analysis of the multivariate characteristic function, it has been proven that the discrete-time CLRP is cyclostationary if the generating white noise is a cyclostationary process and the kernel is a cyclostationary random field. The properties of discrete-time conditional linear cyclostationary random processes are important for mathematical modeling, simulation, statistical analysis, and forecasting of energy consumption. Keywords: mathematical model, energy informatics, conditional linear random process, cyclostationary process, white noise, characteristic function.