Contact-Free Sensing of Stability in Vector Fields of Vibratory Dynamical Systems

This article introduces a contact-free sensing (CFS) framework for stability analysis of vibratory dynamical systems via extracted motion vector fields (EMVf) inherent in near infrared (NIR) video frame sequences. Unlike traditional stability metrics (e.g., Amer et al., Lyapunov, and Gromov–Hausdorff), the CFS approach uses the Krantz criterion to measure stability via a required versus actual upper bound on the eigenvalues of the motion vector fields extracted from NIR frame sequences. The experimental results use the CFS framework to demonstrate a reduction in the maximum eigenvalue from${\boldsymbol{\left| \lambda_{\text{max}} \right|>1}}$(unstable EMVf before modulation) to${\boldsymbol{\left| \lambda_{\text{max}} \right| \leq 1}}$(stable EMVf) after modulation. The main novelties in contract-free monitoring of vibratory systems reported in this article are as follow: 1) adjustable time lag between system motion recorded in NIR video frame sequences, 2) ease with which vibratory motion instability is detected whenever the maximal eigenvalue of an EMVf exceeds a required upper bound limit, and 3) straightforward means of measuring the difference between Hamilton characteristics of recorded EMVfs that occur at different times. This noncontact method eliminates sensor-induced artifacts and offers real-time stability for industrial applications in vibratory mechanical (e.g., bounded vibration of a pile driver monitored with an NIR camera) and biomechanical systems (e.g., bounded variation in rehabilitating walker motion).