Fast basin stability estimation for dynamic systems under large perturbations with sequential support vector machine

Abstract

The vulnerability of real-world dynamic systems or processes to large perturbations has nullified the conventional linear stability analysis. Despite the theoretical advance on computation of Lyapunov functions for dynamics analysis, they oftentimes enlist subtle construction technique and confounding process, and thus lack broad applications. As a global stability measure, basin stability utilizes the volume of the basin of attraction to quantify the stability of system dynamics, and has been thrown to sharp relief recently. Concretely, the perturbation manifests as a distribution of the initial conditions of system states. Monte Carlo simulation, or the Bernoulli trials of the time-domain simulation at the accessible realization of initial conditions, is the state of the art to quantify basin stability. However, this inevitably involves daunting computational budget. At its core, basin stability estimation is a classification problem on each sampling point in the state space at the onset of the possibly large perturbation. Hence, we propose a sequential support vector machine (SVM) framework to efficiently locate the stability boundaries and delineate the basin of attraction. The high-fidelity time-domain simulation is only called upon those sampling points that are predicted by SVM to be close to the boundaries, and the SVM as well as the boundaries are sequentially updated with the addition of those newly evaluated sampling points. This innovative sequential approach reduces over 90% of the computational cost in the conventional time-domain simulation.