Interval Analysis For The Identification Of Nonlinear Models In Static Systems
Andriy Serhiyovych Melnyk
Department of Computer Science, West Ukrainian National University, Ukraine
Abstract
The article addresses a significant scientific problem – the development of identification methods for interval nonlinear models of static characteristics of complex objects with acceptable computational complexity. It examines the challenges associated with identifying the parameters and structure of nonlinear models of static characteristics. The proposed solutions reduce the complexity of the modelling process while ensuring the derivation of adequate models with guaranteed accuracy, determined by experimental results in the form of interval values of the modelled characteristics. A parameter identification approach for interval nonlinear models is presented, which reformulates the problem as minimizing the quadratic deviation between the modelled characteristics of a static object and the experimental intervals. Although this approach expands the optimization parameter space by introducing additional coefficients into the objective function to ensure consistency between experimental data and calculations, it also enables the development of efficient optimization procedures. For structural identification, a method based on analyzing the gradient of the objective function of the optimization problem is proposed, allowing for the directed selection of structural elements during the synthesis of an interval nonlinear model. A novel structural identification method for nonlinear interval models and an algorithm for its implementation have been developed. Experimental examples confirm the high convergence and efficiency of the proposed approach. The proposed methods for nonlinear model identification based on interval data analysis will contribute to the advancement of applied research in national security, environmental monitoring, medicine, and other fields where mathematical models serve as the foundation for decision-making.