Year: 2026
Type: article
Abstract: In nonlinear systems, escape from a safe basin constitutes a critical instability mechanism that often leads to catastrophic outcomes, such as structural collapse or ship capsize. In one of the possible (and, arguably, most dangerous) scenarios, the escape occurs when a transient perturbation displaces the system state across the stable manifold of a dynamic saddle in the phase space. Predicting the proximity to this boundary remains a significant challenge, especially in systems for which governing equations are unavailable. This paper introduces the transient beating frequency as a novel, data-driven marker for predicting basin escape. We demonstrate that when a system is perturbed close to the basin boundary but remains within the safe potential well, its transient slow-flow envelope exhibits a pronounced beating behavior. We analytically prove that this beating frequency decreases and intersects zero with a vertical tangent precisely at the amplitude of the unstable saddle. Exploiting this mathematical constraint, we develop an estimation algorithm to extrapolate the location of the saddle from a single, safe transient trajectory. The proposed methodology is validated through two diverse numerical case studies: a 2-DoF softening model of a floating offshore wind turbine, demonstrating practical applicability in capsize prediction, and a 21-DoF finite element model of a hardening clamped-clamped von Kármán beam, proving the method’s scalability to high-dimensional systems. The results confirm that the algorithm successfully and accurately estimates the amplitude of the unstable periodic orbit using only localized transient data, establishing the decrease of the transient beating frequency as an effective early warning marker for predicting dynamic-saddle escapes in engineering systems.
Authors: Giuseppe Habib, Oleg V. Gendelman
Language: English
Subfield: Global and Planetary Change
Field: Environmental Science
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $4,040
Award: G770953265
OpenAlex ID: W7168483214