Sliding-Window Matrix Pencil Method for Design Optimization with Limit-Cycle Oscillation Constraints

This paper introduces a novel approach to constrain limit-cycle oscillations in design optimization. The approach builds upon a limit-cycle oscillation constraint that bounds the recovery rate to equilibrium, circumventing the need for bifurcation diagrams. Previous work demonstrated the constraint using approximate recovery rates obtained by evaluating the system state velocity for prescribed states. This work proposes a fully nonlinear matrix pencil method that accurately evaluates the recovery rate based on transient simulations. The proposed method captures the amplitude variation in the recovery rate using a short time window that slides along the time history of a quantity of interest. This sliding-window matrix pencil method is first verified for a typical section model. Sensitivity analyses identify guidelines to obtain accurate recovery rates efficiently. The system is then optimized subject to limit-cycle oscillation, flutter, and side constraints, and the results are compared with the ones based on approximate recovery rates. The sliding-window matrix pencil method allows the optimizer to produce a less conservative design while preventing limit-cycle oscillations at desired operating conditions and amplitudes. The approach introduced in this paper can facilitate the inclusion of limit-cycle oscillation considerations in the design phase of a broad class of nonlinear systems.