Measuring the Fidelity of a Physical and a Digital Twin Using Trace Alignments

Digital twins are gaining relevance in many domains to improve the operation and maintenance of complex systems. Despite their importance, most efforts are currently focused on their design, development, and deployment but do not fully address their validation. In this paper, we are interested in assessing the fidelity of physical and digital twins and, more specifically, whether they exhibit twinned behaviors. This will allow engineers to check the suitability of the digital twin for its intended purpose. Our approach assesses their fidelity by comparing the behavioral traces of the two twins. Our contribution is threefold. First, we define a measure of equivalence between individual snapshots capable of deciding whether two snapshots are sufficiently similar. Second, we use a trace alignment algorithm to align the corresponding equivalent states reached by the two twins. Finally, we measure the fidelity of the behavior of the two twins using the level of alignment achieved in terms of the percentage of matched snapshots and the distance between the aligned traces. Our proposal has been validated with the digital twins of four cyber-physical systems: an elevator, an incubator, a robotic arm, and a programmable robotic car. We were able to determine which systems were sufficiently faithful and which parts of their behavior failed to emulate their counterparts. Finally, we compared our proposal with similar approaches from the literature, highlighting their respective strengths and weaknesses related to our own.