Improving empirical models of complex technological objects under conditions of uncertainty

This paper proposes a method for improving empirical models of complex technological objects with insufficient information about the input and output values of an object's parameters. It has been established that most methods for constructing empirical models require knowledge of the statistical characteristics of the input and output values of an object. When modeling complex non-reproducible stochastic processes that evolve over time, information about the parameters and structure of an object is usually not available. A method has been proposed where input and output values are treated as fuzzy quantities with a triangular membership function. Since at some points in the region, the triangular membership function is undifferentiated, it is inconvenient to use it in its typical form to solve the problem of optimal control. Therefore, it is proposed to approximate it with the Gaussian membership function. It is shown that such an approximation is reduced to finding one parameter, which is determined by the least squares method. Its value practically does not depend on the magnitude of the uncertainty interval while the value characterizing the accuracy of approximation is a monotonously increasing function that has a linear character. This makes it possible to define the main operations on fuzzy numbers and derive an empirical model for the case of a polynomial "base" model. The resulting model is linear in its parameters, so a genetic algorithm can be used to find them. It is shown that genetic algorithms can be used in the construction of empirical polynomial models when input parameters are interpreted as fuzzy numbers. Thus, it can be argued that when constructing an empirical model of an object that is affected by external disturbances that cannot be measured, it is advisable to approximate all input quantities with a triangular Gaussian membership function