Wind and Structures

Techno-Press (테크노프레스)
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Mathematical explanation on the POD applications for wind pressure fields with or without mean value components

  • Zhang, Jun-Feng (School of Civil Engineering, Zhengzhou University) ;
  • Ge, Yao-Jun (State Key Laboratory for Disaster Reduction in Civil Engineering, Tongji University) ;
  • Zhao, Lin (State Key Laboratory for Disaster Reduction in Civil Engineering, Tongji University) ;
  • Chen, Huai (School of Civil Engineering, Zhengzhou University)
  • Received : 2015.10.22
  • Accepted : 2016.08.21
  • Published : 2016.10.25
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Abstract

The influence mechanism of mean value components, noted as $P_0$, on POD applications for complete random fields $P_C(t)$ and fluctuating random fields $P_F(t)$ are illustrated mathematically. The critical philosophy of the illustration is introduction of a new matrix, defined as the correlation function matrix of $P_0$, which connect the correlation function matrix of $P_C(t)$ and $P_F(t)$, and their POD results. Then, POD analyses for several different wind pressure fields were presented comparatively as validation. It's inevitable mathematically that the first eigenmode of $P_C(t)$ resembles the distribution of $P_0$ and the first eigenvalue of $P_C(t)$ is close to the energy of $P_0$, due to similarity of the correlation function matrixs of $P_C(t)$ and $P_0$. However, the viewpoint is not rigorous mathematically that the first mode represents the mean pressure and the following modes represent the fluctuating pressure when $P_C(t)$ are employed in POD application. When $P_C(t)$ are employed, POD results of all modes would be distorted by the mean value components, and it's impossible to identify $P_0$ and $P_F(t)$ separately. Consequently, characteristics of the fluctuating component, which is always the primary concern in wind pressure field analysis, can only be precisely identified with $P_0$ excluded in POD.

Keywords

Acknowledgement

Supported by : National Science Foundation of China

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