Floquet纤维几何与非线性气动弹性颤振附近离流形瞬态的更高阶约化坐标

中文摘要 AI 辅助

为吸引极限环附近的状态分配约化坐标需要正确的不变纤维几何。从伴随Floquet模式获得的经典一阶相位-等稳定图沿强稳定商纤维投影，而保留慢丛的度量正交补通常不沿此投影。我们在局部证明，满足线性化半共轭关系的图留下O(delta^2)的不变性残差，而沿非不变补的投影通常留下O(delta)项。对于非线性气动弹性极限环，度量法向与强稳定方向相差48.5至71.7度，且度量法向扰动包含一阶保留相位和慢幅值分量。用强稳定纤维替换度量法向，将测量的残差标度从delta^1.01变为delta^1.87，且无需拟合参数。随后，我们测试了学习得到的更高阶修正，其线性化固定在伴随Floquet图上，其对称性精确，其约化流固定。尽管它们降低了登记的固定归一化潜在残差，但事后幅值重新校准和针对伴随Floquet目标的未来一致性移动或逆转了排名。由于学习到的映射已共享基线的第一阶规范，且未来目标由基线图提供，这些诊断既未确立独立的正面也未确立负面的更高阶结果。因此，在该基准中，正确的一阶Floquet几何是必要的，而学习修正的额外预测价值仍未被可用的表示依赖诊断所识别。

英文摘要

Assigning reduced coordinates to states near an attracting limit cycle requires the correct invariant-fibre geometry. The classical first-order phase-isostable chart obtained from adjoint Floquet modes projects along the strong-stable quotient fibre, whereas a metric-orthogonal complement of the retained slow bundle generally does not. We prove locally that a chart satisfying the linearised semiconjugacy relation leaves an O(delta^2) invariance residual, while projection along a non-invariant complement generically leaves an O(delta) term. For a nonlinear aeroelastic limit cycle, the metric-normal and strong-stable directions differ by 48.5 to 71.7 degrees, and metric-normal perturbations contain first-order retained phase and slow-amplitude components. Replacing the metric normal by the strong-stable fibre changes the measured residual scaling from delta^1.01 to delta^1.87 without fitted parameters. We then test learned higher-order corrections whose linearisation is pinned to the adjoint-Floquet chart, whose symmetry is exact, and whose reduced flow is fixed. Although they reduce the registered fixed-normalisation latent residual, post-hoc amplitude recalibration and adjoint-Floquet-targeted future consistency move or reverse the ranking. Because the learned maps already share the baseline's first-order gauge and the future target is supplied by the baseline chart, these diagnostics establish neither an independent positive nor negative higher-order result. Correct first-order Floquet geometry is therefore necessary in this benchmark, while the additional predictive value of the learned correction remains unidentified by the available representation-dependent diagnostics.

发表机构

• William Wright Technology Centre (W-Tech)（威廉·赖特技术中心）
• School of Mechanical & Aerospace Engineering（机械与航空航天工程学院）
• Queen’s University Belfast（贝尔法斯特女王大学）

机构由 AI 辅助整理，请以论文原文为准。