Hankel-Koopman Finite-Horizon Energy Decomposition of Coupled Experimental Data: A Three-Phase Data-Driven Twin Forecasting Framework

Abstract

This paper introduces a unified three-phase data-driven twin framework for finite-horizon forecasting of physical quantities from coupled experimental measurements. The framework combines a new Hankel--Koopman finite-horizon energy decomposition with orthogonal modes and an inverse-calibrated multi-output nonlinear autoregressive model with exogenous inputs. The nonlinear dynamics are identified and simulated in the Hankel coefficient space over a prescribed calibration window. Candidate models are then evaluated after anti-diagonal recovery and reconstruction of the corresponding trajectories in the physical measurement space. The resulting simulated channel trajectories serve as exogenous inputs to a recursive forecasting model for the quantity of interest. In this way, the proposed framework integrates reduced-order representation, nonlinear dynamical identification, measurement reconstruction, and explainable forecasting. The mathematical analysis specializes Koopman delay-coordinate theory to the serialized multichannel Hankel lift and establishes its compatibility with the shifted Hankel representation. It also proves the orthogonality of the modes and the finite-horizon modal energy decomposition, together with the existence, uniqueness, inverse stability, and forward stability of the identified models under explicitly stated hypotheses. In a solar-power-plant case study, the framework yields consistently high correlations and low relative errors across all considered forecast horizons, demonstrating its ability to preserve the temporal evolution of the quantity of interest during recursive forecasting.