Stochastic Multi-phase Modeling and Health Assessment for Systems Based on Degradation Branching Processes

Degradation modeling and health assessment play a critical role in predictive maintenance of engineering systems. In a multi-component system, the degradation of a component may propagate to other components after a random time period, resulting in a multi-phase system-level degradation behavior. Although extensive work has been conducted on system degradation modeling, traditional methods are not adequate to model such degradation and propagation phenomena simultaneously. In this paper, a stochastic multi-phase modeling approach is proposed for such systems based on the degradation branching processes. The statistical properties of general degradation branching processes are analyzed in regards to two common types of system failures. Specially, when each branch of the multi-phase degradation process can be described by a Wiener process, the analytical expressions for system reliability and lifetime distribution are derived after dividing the entire degradation process into multiple phases based on the locations of branching particles. Based on these results, system health assessment can be conducted by incorporating the current degradation state and the importance of each component. Case studies on high-speed train bogie systems and solar panel arrays are provided to demonstrate the effectiveness and practical values of the proposed methods in handling such complex degradation phenomena.