Saltation-consistent event-aware digital twins for uncertainty transport in non-smooth dynamical systems

Non-smooth mechanical systems challenge prediction not only because their trajectories contain impacts, frictional transitions, and unilateral constraints, but because these events reorganize state propagation, sensitivity, uncertainty, and control authority. Existing digital-twin, hybrid-systems, Bayesian-estimation, and reduced-order frameworks each address part of that difficulty, yet they are usually developed on separate mathematical layers and therefore become least reliable precisely where engineering decisions are most event-sensitive. This paper introduces an event-aware mechanics and inference architecture for non-smooth dynamical systems in which event surfaces are treated as first-class transport interfaces rather than as numerical exceptions. Starting from a high-fidelity hybrid mechanical model with unilateral contact, friction, and measure-valued impulses, we derive saltation-consistent transport laws for sensitivities and covariance, formulate forced Bayesian correction at mechanically determined event times, and establish reduced-order error bounds that isolate jump mismatch as a distinct approximation channel. The resulting framework couples full-order mechanics, event-aware uncertainty propagation, online parameter updating, and reduced-order approximation within a single mathematically consistent architecture. Benchmarks involving impact, stick-slip, and shock-response dynamics show that event-aware transport preserves post-event state accuracy, concentrates parameter information in short event windows, and improves reduced-order fidelity during discontinuity-dominated transients. The central advance is the identification of event surfaces as the structural interfaces through which mechanics, inference, uncertainty transport, and control are coupled in non-smooth digital twins.