Development of a Mathematical Model of the Optimal Technological Process for Non-Autoclaved Foam Concrete Obtaining

The technological process of obtaining of concrete is a complex dynamic system in which many elements interact. When considering the technological process as a system, it is necessary to take into account its interaction with the external environment and internal relationships of the individual elements of the system. The main source of information that reveals the essence of the technological process as a system is its mathematical model. The paper presents a multifactorial mathematical model of the technological process of obtaining of non-autoclaved foam concrete. The indicators of operational properties that are in demand for customers are selected as quality criteria. They are compressive strength and thermal conductivity. The search for the optimum was carried out according to key technological factors. These are the ratio between Portland cement and sand, the water-solid ratio, the foaming agent consumption and the mixing cycle time. Four-factor mathematical planning in three levels was used to optimize the technological process of foam concrete production. The results of experiments and a detailed step-by-step method of constructing a mathematical model are presented. Due to the fact that the result obtained by the values of the criteria indicators may not always satisfy the customer, the authors propose a method of compromise between the criteria. It is achieved by mutual concessions, i.e. percentage losses of criteria. The main solution method is the lexicographic method or the method of targeted search.