Floquet branch optimization for spectrally efficient representations of periodic systems
Résumé
Analysis and simulation of linear time–periodic systems entail significant memory and computational costs, owing to the need to describe time-varying quantities (time-varying system matrices, periodic eigenvectors… ). This challenge is compounded in many applications that require multiple system resolutions, such as design assessment with many load cases, uncertainty quantification analyses, and random vibration simulations. We propose exploiting the infinitely many available Floquet representations of linear time–periodic systems using spectral quantifiers to obtain spectrally optimized representations with enhanced sampling properties. These representations permit the simulation of linear time–periodic systems with reduced memory allocation and computation time. To achieve this, we introduce several spectral quantifiers for Floquet representations and formulate a multi-objective spectral optimization problem whose solution yields the desired spectrally-optimized representations. This multi-objective problem is solved using a heuristic approach, a multi-objective Genetic algorithm. Our benchmark and numerical tests show memory allocation savings ranging from ~90% to ~50% , on different settings. In multi-run scenarios, we also demonstrate significant computational time advantages as the number of runs increases. These results suggest substantial computational improvements in simulating linear time–periodic systems using our proposed framework; the implications are faster simulations under the described scenarios, and expanded capabilities owing to memory efficiency in multi-run simulation.