Matematyczne modelowanie sieci wodociągowych

W wyniku przeprowadzonych rozważań wykazano możliwość zastosowania modeli hybrydowych w procesie programowania rozległych systemów zaopatrzenia w wodę. Model hybrydowy ma charakter strukturalny, jest powtarzalny, dyskretny w stanie. Model hybrydowy systemu zaopatrzenia w wodę pozwala na projektowanie nowych systemów, ocenę pracy i analizę działania całego i poszczególnych elementów istniejących systemów wodociągowych. Niniejsza praca ma charakter wstępny, studialny, a w dalszych jej częściach podjęta zostanie próba implementacji hybrydowego modelu systemu zaopatrzenia w wodę.

Many existing water supply systems in Poland is not in the satisfactory condition. In such conditions, it becomes problematic to prepare a properly functioning water and wastewater management system in the area. Computer systems equipped with applications that allow for the proper, efficient design of water supply and sewage systems, and analysis of running of existing ones using various types of mathematical models, including hybrid models, can be helpful in solving mentioned problems. There fore, it is advisable to undertake the work and research on models of water supply systems in order to know more deeply their structure and to rationalize designing, use and operation of those systems. As a result, the final results of the work in this area should contribute to improving knowledge of water systems, the relationship between individual basic elements of those systems, facilitating designing and operation of water supply systems and increase their level of reliability, which in turn will improve water supply to users . To date, no computer studies have been conducted on models of networks using a hybrid neuro-mathematical models. Most of the research and dissertations were based on existing mathematical models of water supply networks. Formulae described in this paper do not include many characteristics of biological neurons. First of all, these are static models, in which delay times which result from the dynamics of the system were excluded. Effects of synchronization or frequency modulation function of the biological neuron are not also included. Despite these limitations networks built using such simplified mathematical models show many features that are characteristic to biological systems. As a result of considerations, the possibility of hybrid models application in the programming process of extensive water supply systems was proved. Hybrid model is structural in nature, is repetitive, discrete in state. Hybrid model of water supply system allows to design new systems, evaluation of the work and analysis of running of the whole and individual elements of existing water supply systems. This work is preliminary, studial, and its further parts will be concerned on the attempt of implementation of a hybrid model of water supply system.