Effects of the data resolution and quantitative analysis of dynamic mode decomposition

Abstract The dynamic mode decomposition(DMD), based on the Koopman analysis, is a tool capable of spatiotemporal analysis of one-dimensional signals to three-dimensional CFD data. Outputs of the DMD consist of amplitudes, frequencies, decaying rates, and spatial modes. However, the effects of data resolution (size) and the quantitative analysis of the DMD are limited to one-dimensional signal data. In this study, the effects of the data resolution and quantitative analysis using scaling factors 2/√M on the DMD amplitudes and √M on the DMD spatial mode strengths are investigated, with M being the data size. Firstly, proofs of the scaling factors for one-dimensional and two-dimensional data are presented. Second, the effect of data size on amplitudes and spatial mode strengths and their scaled results are confirmed using one-dimensional artificial signal data, two-dimensional artificial signal field, two-dimensional vortex shedding simulation, and a two-dimensional pulsating flow experiment data with various data resolutions. The results show that the amplitude increase proportionally to the size of the data, and the spatial mode strength is inversely proportional to the size of the data in all cases. As a result of applying the scaling factors in one-dimensional artificial signal and two-dimensional artificial signal field data, the amplitudes and spatial modes contain the same values regardless of the change in resolutions. The scaled amplitudes and spatial mode strengths on vortex shedding simulation and two-dimensional laminar pulsating jet show good agreements with slight differences regardless of the resolution change. The proposed scaling factor can be applied to compare data quantitatively obtained with different resolutions.