A Stochastic Hybrid Systems Framework for Probabilistic Digital Failure Twin Modeling Considering Multiple Dependent Failure Processes

While Digital Twins (DT) are increasingly utilized to simulate complex systems, most existing models focus exclusively on nominal behavior, overlooking the failure dynamics essential for reliability modeling. To address this limitation, we propose a hierarchical Digital Failure Twin (DFT) framework designed to model failure behaviors emerging from multiple dependent processes. At the component level, we employ a Stochastic Hybrid System (SHS) approach: stochastic differential equations represent continuous degradation, while discrete transitions capture abrupt failure events and their mutual interactions. These component-level behaviors are then integrated into a system-level digital twin to analyze the impact of component failures on overall system performance. To facilitate efficient simulation and reliability assessment, we propose a semi-analytical method based on conditional moment dynamics and first-order second-moment (FOSM) approximation. This SHS-based method provides a unified analytical framework for evaluating both gradual degradation and sudden shocks. We demonstrate the efficacy of this approach through a robotic arm case study, modeling the impacts of motor-level wear and catastrophic failures caused by shocks. Numerical results indicate that our framework effectively captures complex dependencies among failure modes, offering accurate reliability estimates with significantly reduced computational overhead compared to traditional simulation methods.

Keywords: Digital failure twin, Stochastic hyrid systems, multiple dependent failure process, robotic arm.