Digital twin (DT) is an emerging technology in the context of digital transformation that enables the monitoring, diagnosis, energy efficiency, and optimization of different systems. The model of DT is a crucial feature for an accurate representation of the physical system. The latter can be complex and dynamic which makes it prone to variability and stochastic behavior. Thus, monitoring through a DT model that gives as an output a single best estimation of the nominal behavior can sometimes be insufficient considering the dynamic properties of the system. For this reason, the current paper intends to present a novel approach for DT modeling through interval models to bound and include the uncertainties inside the model using a statistical approach and Hilbert transform. A case study is presented focusing on the energy consumption of an industrial robot considering the variability of the real process and the measurement noise.