Best practice guidelines for the dynamic mode decomposition from a wind engineering perspective

This paper distills the serial work of Li et al. (2022a, 2022b, 2022c, 2023b, 2023a, 2021, 2020a) into a practice guide for the Dynamic Mode Decomposition (DMD) with a particular emphasis on the quick learning and adaptation of the technique from a wind engineering perspective. The guide begins with discussions of the DMD's connections with the Koopman, Fourier & Laplace, the Proper Orthogonal Decomposition, and machine learning theories. Then, based on 1.5 × 10⁶ core hours of parametric investigations on paradigmatic cases, recommendations that broadly apply to bluff-body wind engineering problems—especially regarding the input sequence—are formulated. In the temporal aspect, results highlight the DMD's preference for steady, stationary, equilibrium, or quasi-equilibrium systems, and suggest a sampling resolution 15–20 times the frequency of the dynamics of interest. Emphasis is also placed on the necessity of the Stabilization state for sampling convergence while avoiding the input of overdetermined systems. In the spatial aspect, high-dimensional, mean-subtracted data with minimal interpolation and noise proved to yield better Koopman models. Different input variables, though derived from the same system, may also result in non-unique Koopman modes depending on their nonlinear richness. Finally, two open-source MATLAB algorithms have been discussed and made open-source to facilitate the easy dissemination and usage for wind engineers. Via pedagogical examples, Algorithm 1 outlines a standard procedure to check for sampling convergence, and Algorithm 2 performs the similarity-expression DMD and visualizes the outputs.