A wavelet-based dynamic mode decomposition for modeling mechanical systems from partial observations

Dynamic mode decomposition (DMD) has emerged as a popular data-driven modeling approach to identifying spatio-temporal coherent structures in dynamical systems, owing its strong relation with the Koopman operator. For systems external forcing, identified model should not only be suitable for specific forcing function but generally approximate input-output behavior of underlying dynamics. A novel methodology those classes is proposed present work, using wavelets conjunction dynamic (ioDMD). Our non-intrusive constructs numerical models directly from trajectories full model's inputs and outputs, without requiring full-model operators. These are generated by running simulation or observing original systems' response an experimental framework. Hence, applicable whose internal state vector measurements available. Instead, data few output locations accessible, often case practice. The methodology's applicability explained finite element beam model. WDMD provides linear state-space representation system corresponding input functions. developed then used simulate beam's towards different types method further validated on set modal analysis simple free-free beam, demonstrating efficacy appropriate candidate practical despite having no access treating black-box.