室内振荡温度场的Koopman模态分解
Koopman Mode Decomposition of Oscillatory Temperature Field inside a Room
摘要：
Koopman模式分解（Koopman mode decomposition，KMD）是一种非线性时间序列分析技术，能够将复杂的时空动力学数据分解为具有单一频率的多个模式，称为Koopman模式（Koopman modes，KM）。我们将KMD应用于室内温度场振荡动力学的测量数据，这是我们日常生活中普遍存在的复杂现象，在节能空调中具有明确的技术动机。为了表征不仅振荡场（标量场），而且相关的热通量（矢量场），我们引入了温度梯度的概念，使用KM的空间梯度。通过直接从数据中估计温度梯度，我们表明KMD能够提取嵌入在振荡温度场中的热通量的独特结构，与空调相关。
英文摘要：
Koopman mode decomposition (KMD) is a technique of nonlinear time-series analysis capable of decomposing data on complex spatio temporal dynamics into multiple modes oscillating with single frequencies, called the Koopman modes (KMs). We apply KMD to measurement data on oscillatory dynamics of a temperature field inside a room that is a complex phenomenon ubiquitous in our daily lives and has a clear technological motivation in energy-efficient air conditioning. To characterize not only the oscillatory field (scalar field) but also associated heat flux (vector field), we introduce the notion of a temperature gradient using the spatial gradient of a KM. By estimating the temperature gradient directly from data, we show that KMD is capable of extracting a distinct structure of the heat flux embedded in the oscillatory temperature field, relevant in terms of air conditioning.
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