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Koopman Mode Decomposition of Oscillatory Temperature Field inside a Room

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Document pages: 8 pages

Abstract: Koopman mode decomposition (KMD) is a technique of nonlinear time-seriesanalysis capable of decomposing data on complex spatio temporal dynamics intomultiple modes oscillating with single frequencies, called the Koopman modes(KMs). We apply KMD to measurement data on oscillatory dynamics of atemperature field inside a room that is a complex phenomenon ubiquitous in ourdaily lives and has a clear technological motivation in energy-efficient airconditioning. To characterize not only the oscillatory field (scalar field) butalso associated heat flux (vector field), we introduce the notion of atemperature gradient using the spatial gradient of a KM. By estimating thetemperature gradient directly from data, we show that KMD is capable ofextracting a distinct structure of the heat flux embedded in the oscillatorytemperature field, relevant in terms of air conditioning.

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