Intelligent Asset Management of Aging Infrastructure: Unveiling Non-Linear Degradation and Negative Resilience via Massive-Scale SDE Simulations

Abstract

Conventional infrastructure asset management relies heavily on continuous, linear degradation models, which often fail to capture sudden macroscopic failures. This study computationally explores these limitations by investigating non-linear degradation processes under specified boundary conditions. We propose a stochastic differential equation (SDE) framework incorporating jump processes and specular reflection boundaries to model the macroscopic irreversibility of structural decay. To illustrate this framework’s behavior, large-scale Monte Carlo simulations involving up to 1,000,000 cohorts were conducted. The computational results numerically demonstrate that, entirely by model construction, continuous drift and diffusion are explicitly prevented from breaching the imposed reflection boundaries. Consequently, absorption at the failure state is driven exclusively by the jump term. Rather than claiming this as an absolute physical necessity or a mathematical proof of real-world degradation, this study aims to computationally illustrate the macroscopic consequences of imposing such strict boundary rules. Furthermore, the simulations show that under these specific reflection constraints, environmental noise cannot mathematically extend the system lifespan—a restricted dynamic we call “negative resilience.” Acknowledging the absence of empirical validation and alternative boundary comparisons, these exploratory findings serve as a theoretical baseline to understand boundary-driven jump-diffusion behavior, highlighting the inherent limitations of relying purely on continuous predictive models.