Neural Nonparametric Stability Indicator for Self-Excited Dynamical Systems

This article introduces a novel methodology employing deep-learning neural networks to estimate Lyapunov functions in dynamic systems accurately. Unlike traditional parametric approaches, our method is model-free, enabling adaptability to various system dynamics without prior assumptions. We also present a new strategy for generating Lyapunov functions using neural networks, enhancing stability assessments’ precision and robustness. The effectiveness of this approach is validated through comparative analysis within a self-excited acoustical system (SAS) applied across diverse materials. This research demonstrates a new approach to differentiate between material stress states and the presence of defects, as evidenced by variations in the potential funnel’s dimensions of the Lyapunov function and specific asymmetries indicative of defective states. Key contributions include the development of a flexible, neural network-based framework for stability assessment and a new application for structural health monitoring. By leveraging this model-free neural approach, we provide a powerful tool for determining the stability of nonlinear dynamical systems and enhancing defect detection processes, significantly advancing control theory and material science.