Approximation of Functions in Multi-criterial Synthesis of Composite Materials

Abstract

Abstract A prerequisite for the synthesis of composite materials as complex systems is the principles of the control paradigm of Peace and the effectiveness of mathematics (for any reality and any given (not absolute) accuracy, there is a mathematical structure that describes this reality with this accuracy; the converse is also true (homomorphism, arbitrarily close to isomorphism between reality and mathematical structures)).The proposed methodology for managing the identification process (design of composites) includes the process of human choice: the probabilistic nature of the control; the main reason for the inadequacy of a purely analytical research procedure. Here, the optimization of the control of the properties of the composite is carried out experimentally on the model as a result of the approximation of the response function: not the generalized functional is approximated, but the particular criteria of which it consists. The development of composite materials is carried out on the basis of evaluating the parameters of the formation of operational properties. The parameters of each of the kinetic processes of the formation of the physical and mechanical characteristics of the material were taken as particular criteria. Kinetic processes are asymptotic for the composites under study and contain extremum and inflection points. A method is used to approximate multidimensional table-defined functions by generalized polynomials of a particular form. In the parametric identification of kinetic processes, their parameters are considered basic. Approximating models of the main properties are presented. Vector optimization of properties (selection of recipes, technologies and methods of material quality control) is carried out by overcoming ambiguities of goals using linear convolution, introducing benchmarks, building Pareto sets, etc. The expediency of using a systematic approach (the hierarchical structure of properties and the hierarchical structure of the composite proper) to the design of building materials as complex systems is shown. The research results are introduced as prototypes of new identification systems in the development of composite materials with adjustable structure and properties, in contrast to the replication of reference applied developments of identification theory in various industries.