Digital twins improve the performance of heavy equipment and decrease its operational costs. To be effective, they must run along decades of a real machine lifecycle. Ensuring coherence between a real machine and its digital twin over such a long period is a challenging task that has not yet been well-studied. This task involves preserving the design and operational data and periodic execution of digital twin software that processes such data. The circumstances of heavy equipment operation complicate the task. This paper considers the problem of digital twin data and software management in light of the unique challenges related to heavy equipment. It presents an experimental case study for running digital twins of mobile log cranes using a data model and a microservices-based architecture developed by the authors. The results demonstrate the capability of the architecture for running physics-based digital twins of heavy equipment in a heterogeneous execution environment consisting of local, edge, and cloud computing resources.

The conjecture of Fliess concerning commutative context-free languages is disproved using a counterexample.