仅用一次激励数据，就能预测非线性振子的复杂动态行为。
One-shot learning for the complex dynamical behaviors of weakly nonlinear forced oscillators
- 通过多频演化方法分解响应，从单次激励数据中推导控制方程。
- 模型在单点训练下准确预测软硬化效应与跳跃现象，覆盖宽范围激励水平。
- 适用于微机电系统设计，大幅降低实验数据采集成本。
非线性动力学的外推预测仍是工程中的核心挑战。本研究提出一种一次性学习方法，仅需一次激励时序数据即可识别全局频率-响应曲线，通过学习系统控制方程实现。我们引入MEv-SINDy（多频演化稀疏非线性动力学识别）方法，用于推断非自治、多频系统的控制方程。该方法利用广义谐波平衡法（GHB），将复杂的受迫响应分解为一系列慢变演化方程。我们在两类关键微机电系统（MEMS）上验证了该方法：非线性梁谐振器和MEMS微镜。结果表明，仅在单一点训练的模型，即可准确预测不同激励水平下的软硬化效应与跳跃现象。该方法显著降低了非线性微系统表征与设计的数据采集负担。
原文摘要 · Abstract (English)
Extrapolative prediction of complex nonlinear dynamics remains a central challenge in engineering. This study proposes a one-shot learning method to identify global frequency-response curves from a single excitation time history by learning governing equations. We introduce MEv-SINDy (Multi-frequency Evolutionary Sparse Identification of Nonlinear Dynamics) to infer the governing equations of non-autonomous and multi-frequency systems. The methodology leverages the Generalized Harmonic Balance (GHB) method to decompose complex forced responses into a set of slow-varying evolution equations. We validated the capabilities of MEv-SINDy on two critical Micro-Electro-Mechanical Systems (MEMS). These applications include a nonlinear beam resonator and a MEMS micromirror. Our results show that the model trained on a single point accurately predicts softening/hardening effects and jump phenomena across a wide range of excitation levels. This approach significantly reduces the data acquisition burden for the characterization and design of nonlinear microsystems.
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