Dynamic Mode Decomposition Approach for Estimating the Shape of a Cable

Abstract

Abstract This study investigates the dynamic behavior of a flexible cable with heterogeneous stiffness using a data-driven approach. The study aims to develop accurate models that describe intricate structures with rigid or flexible components. To achieve this, reflective markers were attached to the cable at equal spacing and the motion was manually excited and captured using an 8 camera setup and OptiTrack’s Motive software. Cable displacement data at marker locations were used as initial conditions for various Dynamic Mode Decomposition (DMD) models. The performance of the data-driven cable model is compared against the performance of the DMD modeling approach, fitting the dynamics of single- and multidegree-of-freedom systems with added white noise. In this work, the authors have considered using time delays and Wavelets-based DMD. The study found that the wavelet-based DMD (WDMD) model was the most accurate method for reconstructing the response of the cable in the test cases. Researchers suggest that this data-driven approach can be applied to predict the dynamic behavior of nonlinear systems, with potential applications in civil engineering, aerospace, and robotics. Overall, this study presents a promising approach for developing accurate models of complex structures with rigid or flexible components. The findings of this study may be valuable in designing structures that can withstand dynamic loads and vibrations.