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<p>In this paper, a novel Bayesian estimation (BE) model and greedy optimization algorithm of sensor selection in Bayesian estimation (GOAB) are proposed for compressed sensing dynamic mode decomposition (CSDMD) to accurately reconstruct flow fields from sparse sensors data. The prior information of parameters and noise in compressed sensing can be obtained by dynamic mode decomposition (DMD) of full-state flow data and singular value decomposition of the DMD noise matrix. The Bayesian estimation operator for the reconstruction process is derived using maximum a posteriori estimation. In this paper, optimal sensors are selected by maximizing a new objective function of the Bayesian estimation operator, where the DMD noise matrix is approximated as a reduction matrix with a simple criterion. Four examples of flow field reconstruction are considered to demonstrate the accuracy of the algorithm. The result shows that the proposed method (BE and GOAB, called BE-GOAB for short) is effective in flow fields reconstruction of CSDMD, and is superior to the traditional least square estimation and its sensor selection algorithm.</p>

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Optimization of sensor selection and Bayesian estimation for compressed sensing dynamic mode decomposition

  • 期刊论文

  • 发表日期：

    2026年7月4日

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  • Wenwei Jiang,
  • Huayu Liu,
  • Jinxing Ding,
  • Chenhao Tan,
  • Yuntao Zhou,
  • Kai Yang,
  • Xiaowei Gao

摘要

In this paper, a novel Bayesian estimation (BE) model and greedy optimization algorithm of sensor selection in Bayesian estimation (GOAB) are proposed for compressed sensing dynamic mode decomposition (CSDMD) to accurately reconstruct flow fields from sparse sensors data. The prior information of parameters and noise in compressed sensing can be obtained by dynamic mode decomposition (DMD) of full-state flow data and singular value decomposition of the DMD noise matrix. The Bayesian estimation operator for the reconstruction process is derived using maximum a posteriori estimation. In this paper, optimal sensors are selected by maximizing a new objective function of the Bayesian estimation operator, where the DMD noise matrix is approximated as a reduction matrix with a simple criterion. Four examples of flow field reconstruction are considered to demonstrate the accuracy of the algorithm. The result shows that the proposed method (BE and GOAB, called BE-GOAB for short) is effective in flow fields reconstruction of CSDMD, and is superior to the traditional least square estimation and its sensor selection algorithm.