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

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

Selection of the Most Probable Best

We consider an expected-value ranking and selection problem where all k solutions' simulation outputs depend on a common uncertain input model. Given that the uncertainty of the input model is captured by a probability simplex on a finite support, we define the most probable best (MPB) to be the solution whose probability of being optimal is the largest. To devise an efficient sampling algorithm to find the MPB, we first derive a lower bound to the large deviation rate of the probability of falsely selecting the MPB, then formulate an optimal computing budget allocation (OCBA) problem to find the optimal static sampling ratios for all solution-input model pairs that maximize the lower bound. We devise a series of sequential algorithms that apply interpretable and computationally efficient sampling rules and prove their sampling ratios achieve the optimality conditions for the OCBA problem as the simulation budget increases. The algorithms are benchmarked against a state-of-the-art sequential sampling algorithm designed for contextual ranking and selection problems and demonstrated to have superior empirical performances at finding the MPB