# METHOD FOR CALCULATION OF DISPERSIONS OF DEPENDENT VARIABLES OF A STOCHASTIC MODEL OF QUASI-STATIONARY OPERATING MODES OF THE MAIN WATER PIPELINE

## Authors

• Olha Matviienko Kharkіv National University of Radio Electronics, Ukraine
• Nataliia Manchynska Kharkiv National University of Radio Electronics, Ukraine

## Keywords:

stochastic model, dispersion, main water conduit, quasi-stationary regime, deterministic equivalent

## Abstract

The subject of research in the article is a stochastic model of quasi-stationary modes of operation of water supply and distribution systems, which adequately describes the actual operating modes of the water supply system for a given time interval and can be used as a basic model for setting and solving problems of optimal stochastic control of the development and operation of supply and distribution systems. water. The goal of the work is to develop a method for calculating estimates of the dispersions of dependent variables depending on the given values of mathematical expectations and dispersions of independent variables for a stochastic model of quasi-stationary modes of operation of the main water conduit as a subsystem of the water supply and distribution system. To achieve this goal, it is necessary to solve the following tasks: to build a deterministic equivalent of a stochastic model of quasi-stationary modes of operation of the main water conduit; calculate estimates of mathematical expectations of dependent variables; calculate estimates of variances of dependent variables. To calculate estimates of the variances of dependent variables depending on the variances of independent variables, we will use the method of statistical linearization. To obtain estimates of mathematical expectations of dependent variables, the deterministic equivalent of the stochastic model of quasi-stationary modes of operation of the main water conduit is solved by the modified Newton method. The following results are obtained: a method for calculating estimates of the dispersions of dependent variables for a stochastic model of quasi-stationary modes of operation of the main water conduit. Conclusions: the paper proposes an approximate method for calculating the statistical properties of dependent variables depending on the statistical properties of the parameters and independent variables of the stochastic model of quasi-stationary modes of operation of the main water conduit. The proposed method is based on the construction of a deterministic equivalent of a stochastic model of quasi-stationary modes of operation of the main water conduit and its use for calculating estimates of variances of dependent variables depending on the given values of mathematical expectations and variances of independent variables. Compared with the simulation method, the proposed approximate method does not require significant time and computational resources. The use of the proposed method was demonstrated by an example.

## Author Biographies

### Olha Matviienko, Kharkіv National University of Radio Electronics

PhD (Engineering Sciences),Associate Professor

Senior Lecturer

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2023-04-17

## Section

MATHEMATICAL MODELING & COMPUTATIONAL METHODS