Multi-criteria optimization of geopolymer foam composition

Abstract

This study presents an approach to synthesizing a mathematical model for determining the composition of geopolymer foams. The focus is on improving the accuracy of multicriteria optimization for metakaolin-based geopolymer composite composition. Experimental data on the physical and mechanical properties of geopolymers are digitized to establish the computational basis for these calculations. Optimization criteria include density, porosity, compressive strength, flexural strength, Young's modulus, volumetric heat capacity, thermal diffusivity, and thermal conductivity. In addition, parameters such as shrinkage, processability, adsorption, adhesion, and economic aspects are also considered. The proposed format aims to fine-tune the geopolymer composite formulation by using the developed model for multi-criteria analysis of technological and physical-mechanical properties of foamed geopolymer composite materials (FGCM). A synthesis of mathematical models including the main criterion, suboptimization, generalized criterion, lexicographic optimization, sorting of alternatives, interval values, and decision tree methods was used to develop methods for multi-criteria optimization of the composition of foamed geopolymers. The study additionally uses the method of criteria convolution, in which the indices of specific criteria are modified in the form of a ratio scale to clarify the limits and boundaries of changes in the composition of the geopolymer mixture. This minimizes contradictory conclusions and expert opinions and highlights the extreme values for each group of parameters. By filtering the raw information, the accuracy of estimates is improved. The exclusivity of the proposed model for determining the composition of foamed geopolymers lies in the possibility of selecting the necessary formulation by mathematical processing of digitized information of the results of measurements of physical-mechanical and operational-technological properties according to the proposed innovative algorithms and schemes. Compared to existing methods, the focus of the proposed method allows for solving problems that are inaccessible to direct observation. This is due to the discovery of hidden information about the interaction of structural and strength parameters. Combining subjective and objective elements of the choice of the optimal geopolymer formulation, the proposed methodology of information processing allows for improving the quality of determining the optimal composition of the geopolymer mixture. The results of multicriteria optimization for foamed geopolymer indicate that the optimal component composition of the geopolymer matrix, within the selected range of variation, consists of 100g metakaolin, 90g potassium activator, 5g silica fume, 100g silica sand, 7g basalt fiber, and 3g aluminum. These proportions yield the best mechanical, thermal, and technological properties.