大跨度屋盖结构在非定常非高斯风压场作用下动力响应快速算法研究

A reasonable wind loading model is a key factor for ensuring the accuracy of the wind-induced response of large-span roof structures. In this project, the computational methods for the dynamic response of roof structures based on the unsteady non-Gaussian wind pressure field models are studied. First, the wind pressure field models are established by wind tunnel experiments. Second, a four-parameter exponential translation model is used, and a modal correction technique is proposed to improve the data extrapolation accuracy, therefore a new method is proposed for simulation of the stochastic wind pressure fields. Third, a new method combining the wavelet packet transform and the particle swarm optimization (PSO) algorithm is proposed for the adjustment and optimization of the stochastic wind pressure fields. Fourth, a fictitious Gaussian process and its cubic polynomial are introduced to express the wind pressure process, and based on the theorem of the higher-order joint moments of a Gaussian stochastic vector and the theory of structural stochastic vibration, the equations for the wind pressure field and the structural response are derived including the expressions for the power spectra, the higher-order spectra, in particular the bispectrum and trispectrum, the third order moment, and the fourth order moment of the structural response. Further, a numerical solution technique, some explicit computation formulae, and the multiple fast Fourier transform (FFT) technique are combined in the proposed algorithm to improve the efficiency. Therefore, a new frequency-domain method is proposed for computing the dynamic response of structures subjected to the unsteady non-Gaussian wind pressure fields. This project is of significance for developing the theories and techniques for the wind resistance analysis of roof structures with engineering applications, improving both the accuracy of structural dynamic response and the computational efficiency, and studying the reliability analysis methods for the stochastic vibration of structures subjected to the unsteady non-Gaussian wind pressure fields.

合理的风荷载模型是保证大跨屋盖结构风振响应分析结果精度的关键因素。本项目研究基于非定常非高斯风压场模型的屋盖结构动力响应计算方法。通过风洞试验建立风压场模型；采用四参数指数函数模型，提出模态修正方法提高数据外推精度，从而建立随机风压场模拟的新方法；提出小波包时频变换和粒子群搜索算法相结合的随机风压场调整优化的新方法；引入虚拟高斯过程及其三次多项式表示风压过程，根据高斯随机向量高阶联合矩定理和结构随机振动理论，推导出风压场基本方程及结构响应功率谱、双谱和三阶矩、三谱和四阶矩的计算公式，采用数值求解、显式计算和多重快速傅里叶变换结合的算法提高效率，从而建立非定常非高斯风压场作用下结构动力响应频域分析的新方法。本项目的完成对于发展和完善屋盖抗风分析理论和方法并指导工程实践、提高屋盖结构动力响应的计算精度和效率，以及研究基于非定常非高斯风压场模型的结构风振可靠性分析方法，具有重要意义。

合理的风荷载模型是保证大跨屋盖结构风振响应分析结果精度的关键因素，而风洞试验是研究风荷载特性的有效途径。（1）设计、制作9个屋盖结构刚性模型，涵盖球面网壳、柱面网壳、矩形平屋面和U形平屋面等四种屋盖类型，分别进行风洞试验，采集大量的风压时程数据，经过数据处理，获得屋盖的平均风压系数、相应的局部体型系数的分布，为实际结构抗风分析提供参考依据。下一步将建立屋盖风压自谱模型、相干函数模型。（2）基于CFD数值模拟中的大涡模拟技术，利用布置粗糙元的方法产生适用于建筑结构脉动风压场数值模拟的入流边界条件，从而提出一种流场入口边界条件的模拟生成方法。（3）将标准三次多项式模型、本征正交分解法和B样条曲面插值结合起来，提出大跨度屋盖结构非高斯风压场模拟的新方法——结合法。通过工程算例分析，证实了该方法的有效性以及对于大规模模拟的适用性，并且从算法上分析了所提出新方法高效率、省内存的原因和优势。（4）推导出两个随机信号的小波包能量与功率谱之间的关系，在此基础上提出基于小波包分析的随机信号自谱和互谱估计的新方法，进而提出背景与共振响应时程分离的计算步骤。以一个体育场的大跨度索膜屋盖结构为工程算例，首先进行风振响应时域分析，得到所有节点的位移和所有单元的内力，然后运用基于小波包时频变换的随机信号功率谱计算方法得出各种响应信号的功率谱，最后获得了背景和共振响应时程。（5）以一个典型的双伞形膜屋盖结构为研究对象，生成了非高斯随机风压场样本，然后将所生成的样本作用于这个膜结构屋盖上，得到结构不同构件的响应时程，继而获得了可满足设计要求的各类构件的整体风振响应系数，并得出一些有益的结论。（6）进行了非定常非高斯风压场作用下屋盖结构动力响应频域分析法研究，取得初步成果。. 本项目的完成对于发展和完善屋盖抗风分析理论和方法并指导工程实践、提高屋盖结构动力响应的计算精度和效率，具有重要意义。