Truncation Criterion Of Covariance-modes And Variance-compensation Technique In Proper Orthogonal Decomposition Method

The Proper Orthogonal Decomposition (POD) is an optimal decomposition of random fields in terms of an energy representation. It is a tool for data compression and characteristic analysis of extractable. The principle of POD is deduced separately by the concept of Rayleigh quotient and its extreme property, principal component analysis method in this article. The wind tunnel tests of a spherical shell roof when the rise-to-span is 1:4 and 1:6 are conducted by using the synchronous multi-pressure scanning system. Based on the POD technique, the wind pressure field of the roof has been reconstructed by the adoption of variance ratio and energy ratio as the truncation criterion with the control of the first several proper modes. The statistics characteristic of the reconstructed wind pressure, including the mean value, root mean square value, peak value, time-history curves as well as the power spectrum has carried on the comparison, and carried on the comparison with the measured pressures. When we adopt the variance ratio as the truncation criterion, in order to assure the results that the variance ratio of the fluctuating wind-pressure coefficient around all measured point is equal, use the variance ratio on the reconstruction measured points' fluctuating wind-pressure coefficient, and the method for technology of the variance ratio compensation is proposed. The variance ratio compensation technology is utilized to modify the reconstructed wind pressure, and compared with the reconstructed result before revised.On calculation for responses, the author uses the variance ratio as the truncation criterion to select an appropriate mode number combined with Complete-Quadratic-Combination method, then shrink steps to process the root mean square response to all the measured points of the roof structure. In order to increase the calculation precision, the results are compared with those model numbers by shrinking step through energy ratio as truncation criterion. The variance ratio compensation technology is also utilized to modify the wind-induced response, and compared with the response before revised. When the model number is assured to be invariable, increase the calculation precision of CQC (Complete-Quadratic-Combination) response and make sure of the calculation precision, the possibility of increasing the calculation efficiency is discussed.