TY - JOUR
T1 - Online dynamic mode decomposition for time-varying systems
AU - Zhang, Hao
AU - Rowley, Clarence Worth
AU - Deem, Eric A.
AU - Cattafesta, Louis N.
N1 - Funding Information:
∗Received by the editors June 5, 2018; accepted for publication (in revised form) by T. Sauer July 4, 2019; published electronically September 12, 2019. https://doi.org/10.1137/18M1192329 Funding: This work was supported by AFOSR through grant FA9550-14-1-0289 and DARPA through award HR0011-16-C-0116. †Mechanical and Aerospace Engineering, Princeton University, Princeton, NJ 08544 (haozhang@princeton.edu, cwrowley@princeton.edu). ‡Mechanical Engineering, Florida State University, Tallahassee, FL 32310 (edeem@fsu.edu, lcattafesta@fsu.edu).
Publisher Copyright:
© 2019 Society for Industrial and Applied Mathematics.
PY - 2019
Y1 - 2019
N2 - Dynamic mode decomposition (DMD) is a popular technique for modal decomposition, ow analysis, and reduced-order modeling. In situations where a system is time varying, one would like to update the system's description online as time evolves. This work provides an efficient method for computing DMD in real time, updating the approximation of a system's dynamics as new data becomes available. The algorithm does not require storage of past data and computes the exact DMD matrix using rank-1 updates. A weighting factor that places less weight on older data can be incorporated in a straightforward manner, making the method particularly well suited to time-varying systems. A variant of the method may also be applied to online computation of \windowed DMD," in which only the most recent data are used. The efficiency of the method is compared against several existing DMD algorithms: for problems in which the state dimension is less than about 200, the proposed algorithm is the most efficient for real-Time computation, and it can be orders of magnitude more efficient than the standard DMD algorithm. The method is demonstrated on several examples, including a time-varying linear system and a more complex example using data from a wind tunnel experiment. In particular, we show that the method is effiective at capturing the dynamics of surface pressure measurements in the ow over a at plate with an unsteady separation bubble.
AB - Dynamic mode decomposition (DMD) is a popular technique for modal decomposition, ow analysis, and reduced-order modeling. In situations where a system is time varying, one would like to update the system's description online as time evolves. This work provides an efficient method for computing DMD in real time, updating the approximation of a system's dynamics as new data becomes available. The algorithm does not require storage of past data and computes the exact DMD matrix using rank-1 updates. A weighting factor that places less weight on older data can be incorporated in a straightforward manner, making the method particularly well suited to time-varying systems. A variant of the method may also be applied to online computation of \windowed DMD," in which only the most recent data are used. The efficiency of the method is compared against several existing DMD algorithms: for problems in which the state dimension is less than about 200, the proposed algorithm is the most efficient for real-Time computation, and it can be orders of magnitude more efficient than the standard DMD algorithm. The method is demonstrated on several examples, including a time-varying linear system and a more complex example using data from a wind tunnel experiment. In particular, we show that the method is effiective at capturing the dynamics of surface pressure measurements in the ow over a at plate with an unsteady separation bubble.
KW - Data-driven modeling
KW - Dynamic mode decomposition
KW - Online methods
KW - Rank-1 updating algorithm
KW - System identification
KW - Time-varying systems
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U2 - 10.1137/18M1192329
DO - 10.1137/18M1192329
M3 - Article
AN - SCOPUS:85072533820
VL - 18
SP - 1586
EP - 1609
JO - SIAM Journal on Applied Dynamical Systems
JF - SIAM Journal on Applied Dynamical Systems
SN - 1536-0040
IS - 3
ER -