Modelamiento aproximado de sistemas dinámicos a través del operador de Koopman

Abstract

Systems modeling has enabled better understanding and solving of complex real-world problems, which are computationally expensive. In this context, data-driven modeling employs surrogate modeling approaches to reduce problem dimensionality and improve computational efficiency. This work focuses on data-driven modeling of nonlinear dynamic systems, to obtain models that allow the detection and diagnosis of faults in dynamic multiple-input multiple-output (MIMO) systems. The starting point of the research is the Koopman operator, whose application is explored in combination with different Dynamic Mode Decomposition (DMD) approaches. The modeling methodology of this research involves evaluating methods such as Hankel Alternative View of Koopman (HAVOK) and Hankel-DMDc, to obtain a correct model for fault detection in MIMO systems. The results obtained from this research, in a test system composed of a system of two interconnected tanks, show that the developed model achieves an adequate adjustment concerning the real behavior of the system and allows not only an effective prediction of its dynamics but also a correct leak detection.