基于特征系统实现算法的流体控制降阶模型
Reduced order models for control of fluids using the Eigensystem Realization Algorithm
摘要：
在反馈流控制中，挑战之一是开发描述与手头任务相关的流体物理的数学模型，同时忽略流的不相关细节以保持计算上易处理。许多技术目前被用来开发这样的降阶模型，如适当的正交分解（POD），和近似快照为基础的平衡截断，也被称为平衡POD。每种方法都有其优点和缺点：例如，POD模型可以表现出不可预测的行为，表现不佳，但它们可以直接从实验数据中计算出来;近似平衡截断通常会产生比POD更好的模型，但需要伴随模拟的数据，因此不能应用于实验数据。在本文中，我们表明，使用本征系统实现算法（ERA）\citep{JuPa-85}，理论上可以得到完全相同的降阶模型的平衡POD。此外，该模型可以直接从实验数据中获得，而不使用伴随信息。该算法还可以大大提高计算效率时，形成降阶模型从仿真数据。如果伴随信息是可用的，那么平衡POD比ERA有一些优势：例如，它产生的模式是有用的多个目的，该方法已被推广到不稳定的系统。我们还提出了一个修改后的ERA程序，产生的模式没有伴随信息，但对于这个程序，所得到的模型是不平衡的，并不执行以及在例子中。我们提出了一个详细的比较的方法，并说明他们在低雷诺数的流动过去的倾斜平板的例子。
英文摘要：
In feedback flow control, one of the challenges is to develop mathematical models that describe the fluid physics relevant to the task at hand, while neglecting irrelevant details of the flow in order to remain computationally tractable. A number of techniques are presently used to develop such reduced-order models, such as proper orthogonal decomposition (POD), and approximate snapshot-based balanced truncation, also known as balanced POD. Each method has its strengths and weaknesses: for instance, POD models can behave unpredictably and perform poorly, but they can be computed directly from experimental data; approximate balanced truncation often produces vastly superior models to POD, but requires data from adjoint simulations, and thus cannot be applied to experimental data. In this paper, we show that using the Eigensystem Realization Algorithm (ERA) \citep{JuPa-85}, one can theoretically obtain exactly the same reduced order models as by balanced POD. Moreover, the models can be obtained directly from experimental data, without the use of adjoint information. The algorithm can also substantially improve computational efficiency when forming reduced-order models from simulation data. If adjoint information is available, then balanced POD has some advantages over ERA: for instance, it produces modes that are useful for multiple purposes, and the method has been generalized to unstable systems. We also present a modified ERA procedure that produces modes without adjoint information, but for this procedure, the resulting models are not balanced, and do not perform as well in examples. We present a detailed comparison of the methods, and illustrate them on an example of the flow past an inclined flat plate at a low Reynolds number.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
