Some problems of proper orthogonal decompostion in application to reconstruction of wind pressure field for reticulated spherical domes

Abstract eng:
Various applications of the Proper Orthogonal Decomposition (POD) method in a random field are briefly reviewed, and a discrete form of POD derivation is presented. Three conditions inherent in the derivation are utilized to classify POD into four types. A new treatment of non-uniformly distributed taps is proposed. Different treatments lead to different optimal problems with different physical meanings. The POD technique is adopted to reconstruct the wind pressure field for reticulated spherical domes with different mesh size and shape, and compared with those obtained from a wind tunnel test model. Even in the case of non-uniformly distributed taps, POD modes should not be divided by the tributary area before interpolation. It is considered that the geometry information (tributary area) is inherent in the eigenvector. The interpolation is within the column space of the eigenvector matrix. The errors of reconstructed time history of wind pressure coefficient are not only due to those of scattered data interpolation of POD modes but also due to the density of taps on a test model. Linear interpolation causes much bigger errors than cubic interpolation. The error of POD mode interpolation increases as the corresponding eigenvalue decreases. The real POD modes are smoother than the interpolated ones.

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