通过柯普曼算子的有限维逼近对旋转爆震燃烧器中的非线性动力学进行数据驱动建模
Data Driven Modeling of Nonlinear Dynamics in a Rotating Detonation Combustor via Finite Dimensional Approximations of the Koopman Operator
AI总结：
研究旋转爆震燃烧器非线性动力学，利用动态模态分解变体构造柯普曼算子有限维逼近，引入时延嵌入克服标准DMD局限，减轻传感器噪声影响，基于DMD模型深入了解不同运行模式动力学。
AI中文摘要：
旋转爆震燃烧器（RDC）是一种在推进和发电应用中提高效率的有前景的技术。RDC的动力学由环形燃烧室内持续传播的爆震波控制，可观察到多种运行模式，包括反向旋转波之间的非线性相互作用和驻波模式的出现。柯普曼算子理论提供了一个框架，通过在可观测量空间而非状态空间中表示系统演化来全局线性化非线性动力系统。本文利用应用于高速视频数据的动态模态分解（DMD）变体构造柯普曼算子的有限维逼近，该数据捕捉了柏林工业大学RDC中爆震波的自然火焰发光度。通过引入时延嵌入作为可观测量字典，克服了标准DMD方法的局限性，特别是在驻波模式的精确重建和捕捉非线性相互作用方面。此外，还提出了一种减轻光度测量中传感器噪声影响的技术。最后表明，基于DMD的模型通过将重建信号分解为其特征，深入了解了不同运行模式的动力学。
英文摘要：
A Rotating Detonation Combustor (RDC) is a promising technology for increasing efficiency in propulsion and power generation applications. The dynamics of the RDC are governed by continuously propagating detonation waves within an annular combustion chamber. Multiple operating modes can be observed, including nonlinear interactions between counter-rotating waves and the emergence of standing wave patterns. Koopman operator theory provides a framework to globally linearize nonlinear dynamical systems by representing their evolution in the space of observables rather than states. In this work, finite-dimensional approximations of the Koopman operator are constructed using variants of Dynamic Mode Decomposition (DMD) applied to high-speed video data capturing the natural flame luminosity of the detonation waves in the RDC at the Technical University (TU) Berlin. By introducing time-delay embeddings as a dictionary of observables, this approach overcomes the limitations of standard DMD methods, particularly for accurate reconstruction of standing wave patterns and for capturing nonlinear interactions. In addition, a technique is presented to mitigate the influence of sensor noise in the luminosity measurements. Finally, it is shown that the DMD-based models provide insight into the dynamics of different operating modes by decomposing the reconstructed signal into its characteristic features.
