Degradation modelling of chaotic systems via random walks in phase space

Accurately predicting long-term degradation in chaotic systems remains a fundamental challenge due to their sensitive dependence on initial conditions and non-periodic dynamics. Conventional numerical models, which rely on fine time-step integration, are computationally demanding and prone to cumulative errors. Here we present a phase-space random walk framework for degradation modeling in chaotic systems. The approach characterizes local degradation velocity distributions through short-time averaging and reconstructs the long-term evolution as stochastic transitions across phase-space regions. Validation on chaotic electronic and mechanical systems demonstrates that the method improves computational efficiency by over two orders of magnitude while maintaining prediction errors below five percent. The analysis further reveals that chaotic systems experience transitions among dynamic regimes with varying degrees of chaos during degradation. This framework provides an efficient and generalizable way to modeling complex degradation processes, offering a other insights into the reliability design of electronic, mechanical, and mechatronic systems.