ВЛАСТИВОСТІ УМОВНИХ ЛІНІЙНИХ ЦИКЛОСТАЦІОНАРНИХ ВИПАДКОВИХ ПРОЦЕСІВ З ДИСКРЕТНИМ ЧАСОМ У ЗАДАЧАХ ЕНЕРГЕТИЧНОЇ ІНФОРМАТИКИ

• Date: 2023
• Main Authors: Mykhailo Fryz, Leonid Scherbak
• Format: Article
• Language: English
• Published: General Energy Institute of the National Academy of Sciences of Ukraine 2023
• Subjects: математична модель; енергетична інформатика; умовний лінійний випадковий процес; циклостаціонарний процес; білий шум; характеристична функція.
• Online Access: https://systemre.org/index.php/journal/article/view/17
• Journal Title: System Research in Energy

Modern challenges in the energy industry require comprehensive research in the fieldof energy informatics, which combines computer science, control systems, and energy managementsystems within a single methodology. An important area of energy informatics is the study of problemsof systems and processes modeling in energy, including energy loads and consumption. Linear andconditional linear random processes (CLRP) are mathematical models of signals represented as the sumof a large number of random impulses occurring at random times. The energy consumption, vibrationsignals of energy objects, etc. can be modeled using this approach. A variant of the CLRP modelwith discrete time, taking into account the cyclic properties of energy consumption, has been investigatedin the paper. The goal is to justify the conditions for the discrete-time CLRP to be a periodicallycorrelated random process, as well as a cyclostationary process. It has been shown thatthe corresponding conditions depend on the periodicity of the probability distributions of the kernel andthe generating white noise of the CLRP representation. To achieve the goal, the propertiesof mathematical expectation and covariance function of CLRP, as well as the method of characteristicfunctions, have been used. The paper proves that the discrete-time CLRP is a periodically correlatedrandom sequence if the generating white noise has periodic mathematical expectation and variance, andthe kernel is a periodically correlated random field. Based on the analysis of the multivariatecharacteristic function, it has been proven that the discrete-time CLRP is cyclostationary ifthe 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 importantfor mathematical modeling, simulation, statistical analysis, and forecasting of energy consumption.