Quantifying and combining uncertainty for improving the behavior of Digital Twin Systems

TL;DR

This paper tackles the problem of divergence between the physical and digital twins in Digital Twin Systems by explicitly representing and exploiting uncertainty in both twins as random variables with Gaussian assumptions. It introduces a framework where uncertainties are first-class citizens, enabling probabilistic comparisons via a consistency operator and enabling uncertainty-aware control; further, it presents an uncertainty mitigation strategy (MDTS) that averages PT and DT uncertainties to yield a lower effective uncertainty $\mu$ and more accurate control, supplemented by reliability-based resets of the model. The key contributions include (i) formal definitions for uncertainty representation and the consistency operator between random variables, (ii) an architecture for mitigating uncertainty through weighted averaging of PT and DT signals, and (iii) a practical demonstration on an incubator case showing reduced error to ground truth and effective anomaly detection. The findings suggest that uncertainty-aware controllers can improve DTS performance and safety, with potential for broader adoption in adaptive systems where PT and DT uncertainties interact, supported by open-source artifacts for further validation.

Abstract

Uncertainty is an inherent property of any complex system, especially those that integrate physical parts or operate in real environments. In this paper, we focus on the Digital Twins of adaptive systems, which are particularly complex to design, verify, and optimize. One of the problems of having two systems (the physical one and its digital replica) is that their behavior may not always be consistent. In addition, both twins are normally subject to different types of uncertainties, which complicates their comparison. In this paper we propose the explicit representation and treatment of the uncertainty of both twins, and show how this enables a more accurate comparison of their behaviors. Furthermore, this allows us to reduce the overall system uncertainty and improve its behavior by properly averaging the individual uncertainties of the two twins. An exemplary incubator system is used to illustrate and validate our proposal.

Figures (13)

• Figure 1: The experimental incubator (lid open).
• Figure 2: A schematic overview of the incubator digital twin setup.
• Figure 3: Evolution of the incubator box temperature and the heater control of the classical control (Physical Twin). The non smoothness of the temperature curve highlights the presence of stable white noise in the incubator temperature.
• Figure 4: Error of physical twin with respect to measurand system (ground truth), leading to an early switch of the heater.
• Figure 5: evolution of the incubator temperature and the heater control of the uncertainty-aware model based control (Uncertainty-Aware Digital Twin). The uncertainty is represented around the nominal temperature value. It highlights the increase of uncertainty along the simulation.