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Author:

Zhang, Mingming (Zhang, Mingming.) | Bai, Simeng (Bai, Simeng.) | Xia, Aiguo (Xia, Aiguo.) | Tuo, Wei (Tuo, Wei.) | Lv, Yongzhao (Lv, Yongzhao.)

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Scopus SCIE

Abstract:

The balance between accuracy and computational complexity is currently a focal point of research in dynamical system modeling. From the perspective of model reduction, this paper addresses the mode selection strategy in Dynamic Mode Decomposition (DMD) by integrating an embedded fractal theory based on fractal dimension (FD). The existing model selection methods lack interpretability and exhibit arbitrariness in choosing mode dimension truncation levels. To address these issues, this paper analyzes the geometric features of modes for the dimensional characteristics of dynamical systems. By calculating the box counting dimension (BCD) of modes and the correlation dimension (CD) and embedding dimension (ED) of the original dynamical system, it achieves guidance on the importance ranking of modes and the truncation order of modes in DMD. To validate the practicality of this method, it is applied to the reduction applications on the reconstruction of the velocity field of cylinder wake flow and the force field of compressor blades. Theoretical results demonstrate that the proposed selection technique can effectively characterize the primary dynamic features of the original dynamical systems. By employing a loss function to measure the accuracy of the reconstruction models, the computed results show that the overall errors of the reconstruction models are below 5%. These results indicate that this method, based on fractal theory, ensures the model's accuracy and significantly reduces the complexity of subsequent computations, exhibiting strong interpretability and practicality.

Keyword:

box counting dimension reduced order model fractal dimension dynamic mode decomposition correlation dimension

Author Community:

  • [ 1 ] [Zhang, Mingming]Beijing Univ Technol, Sch Math Stat & Mech, Beijing 100124, Peoples R China
  • [ 2 ] [Bai, Simeng]Beijing Univ Technol, Sch Math Stat & Mech, Beijing 100124, Peoples R China
  • [ 3 ] [Xia, Aiguo]Beijing Aeronaut Technol Res Ctr, Beijing 100076, Peoples R China
  • [ 4 ] [Tuo, Wei]Beijing Aeronaut Technol Res Ctr, Beijing 100076, Peoples R China
  • [ 5 ] [Lv, Yongzhao]Beijing Aeronaut Technol Res Ctr, Beijing 100076, Peoples R China

Reprint Author's Address:

  • [Bai, Simeng]Beijing Univ Technol, Sch Math Stat & Mech, Beijing 100124, Peoples R China;;[Xia, Aiguo]Beijing Aeronaut Technol Res Ctr, Beijing 100076, Peoples R China;;

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Source :

FRACTAL AND FRACTIONAL

Year: 2024

Issue: 6

Volume: 8

5 . 4 0 0

JCR@2022

Cited Count:

WoS CC Cited Count:

SCOPUS Cited Count: 1

ESI Highly Cited Papers on the List: 0 Unfold All

WanFang Cited Count:

Chinese Cited Count:

30 Days PV: 0

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