Abstract
The article shows the way to implement a quasilinear mathematical model of flow distribution in pipeline engineering networks that is effective in a wide range of changes in the multidimensional random vector of loads at network nodes and provides reliable determination of the parameters of the probability distribution functions of flows in active and passive network elements. The proposed model consists of determining the matrix of generalized network parameters-the load distribution coefficients along the branches of the circuit, calculated at the point corresponding to the mathematical expectation of the node loads. Based on the obtained model, the convergence of the results obtained with the results of simulation of engineering networks is proved using a numerical experiment on an electronic computer. The effectiveness of the developed model, the corresponding algorithms and a set of programs for an electronic computer is shown - the value of the criterion of reduced costs for parametric optimization of engineering networks can be reduced by 5-7% compared to the methods used in practice. The possibility of obtaining at the design stage the equivalent hydraulic characteristics of engineering networks in the form corresponding to the data of experimental measurements of pressures at the nodes of real complex engineering networks is proved.
Highlights
The main task of mathematical modelling of engineering networks in this work is to assess the reliability of the mathematical model of stochastic flow distribution proposed in [1, 2]
We propose ways to implement a quasilinear mathematical model of flow distribution in pipeline engineering networks, which determines the matrices of generalized network parameters – load distribution coefficients along the branches of the scheme, calculated at a point corresponding to the mathematical expectation of node loads
Based on the model obtained in the work, the convergence of the obtained results with the results of simulation modelling of engineering networks is proved by numerical experiment on an electronic computer
Summary
The main task of mathematical modelling of engineering networks in this work is to assess the reliability of the mathematical model of stochastic flow distribution proposed in [1, 2]. Three calculation schemes of the utility network are used, shown in Figures 1, 2 and 3. It is easy to see that these calculation schemes differ in their dimensionality, the number of nodes and branches, which allows us to objectively reveal the advantages of the mathematical model on networks of varying complexity
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