Model order reduction by dominance of mode sets and optimal modal span
摘要
This study introduces a novel model order reduction technique grounded in modal truncation, featuring the concept of optimal modal spans. It extends traditional modal dominance analysis by evaluating not only individual modes but also the collective influence of mode sets on approximation accuracy. For a specified reduced order, the method identifies the most representative subset of modes by exhaustively analyzing all feasible combinations. The reduced model is further refined through residue optimization, enabling accurate approximations at lower dimensions. The use of optimal modal spans, combined with convex residue fitting, yields reduced-order models that consistently outperform classical truncation approaches. These theoretical gains are formally established and supported by two formulations, one continuous and one discrete, along with numerical experiments that validate the approach and illustrate its practical advantages.