【作者】 王敦华；

【导师】 田玉基；

【作者基本信息】 北京交通大学 ， 结构工程， 2009， 硕士

【摘要】 本征正交分解(POD)是以能量表述的随机场最优分解,是一种数据压缩和特征萃取的工具。本文分别运用Mercer定理、瑞利商概念及其极值性质推导了POD原理。并利用POD分解技术,仅采用前若干阶本征模态对超高层建筑表面的风压场进行了重建,对重建结果及规律进行了分析。根据风洞试验同步测量的风压数据,利用POD技术对超高层未布置测压点位置的风压时间序列进行了预测。文中分别采用曲面插值、反距离插值、B样条插值、三次样条插值及双线性插值五种方法得到预测点位置上的本征模态值。结合由原风压场协方差分析得到的主坐标和上述新本征模态值,获得未布置测压点位置的风压时间序列。通过在时间域和频率域内五种插值方法预测出的风压与实测风压的比较,得出三次样条插值的预测精度最高,稳定性最好,曲面插值预测效果次之,同时也说明了利用POD技术预测超高层建筑表面风压场是有效的。最后,应用归一化POD技术对原始风压场进行了进一步的细化,把脉动风压时间序列分解为方差和归一化后的时间序列。在风压场的预测中,每种插值方法对方差和归一化后的时间序列影响不同,应用归一化POD技术可选择不同的插值方法分别预测,克服了局部风压预测不准确的缺点,提高了预测精度。更多还原

【Abstract】 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 Mercer theorem and the concept of Rayleigh quotient and its extreme property in this article. Based on the Proper Orthogonal Decomposition, the surface of high-rise building wind pressure field is reconstructed with only a number of eigen modes , Analysis and summarization is also made to law of the reconstruction.Combined with simultaneous measurement wind pressure data of wind tunnel tests, the POD technique has been used to predict the wind pressure time series on the high-rise building where the pressure taps are not distributed. Surface interpolation, inverse distance interpolation, B-spline interpolation, cubic spline interpolation and bilinear interpolation five methods are employed to obtain the values of the proper modes on high-rise building where wind pressure time series are to be predicted. using the principal coordinates from the covariance analysis of the original pressure field and the new proper mode values, the wind pressure time series on the high-rise building without the pressure taps are acquired. In the time domain and frequency domain comparison of prediction by five interpolation methods with the measured wind pressure, we can see that the result of the cubic spline interpolation is the highest prediction accuracy and stability of the best, followed by surface interpolation prediction, also that the POD in the prediction of the surface wind field .on high-rise building is effective.Finally, Application of normalized POD technology , the original field pressure is further refined, The fluctuating wind pressure time series is decomposed into variance and normalized the time series, In the prediction of wind pressure field, the each interpolation method has different impact in two parts, with the help of normalized POD technology, the best interpolation method is choose to predict each part, that overcomes the disadvantage of inaccurate in partial pressure prediction and improves prediction accuracy.更多还原