大跨度桥梁各态历经脉动风场的数值模拟分析

Numerical study on ergodic fluctuating wind field of long-span bridge

基于本征正交分解(proper orthogonal decomposition,POD)的谱表示法,结合大跨度桥梁脉动风场的特点,推导出一种以互谱密度矩阵为POD对象的脉动风场模拟简化公式.采用以能量评判为准则的误差精确公式,对特征值合理截断阶数进行估计.引入双索引频率,实现了模拟样本的各态历经性.采用快速傅里叶变换(fast Fourier transform,FFT)对算法加速,给出了简化模拟公式在FFT算法下的具体表达式,便于程序编制.利用该法模拟了一座大跨度铁路连续刚构桥的主梁脉动风场,所得样本自功率谱和互功率谱均与目标谱吻合良好,验证了该方法的有效性和正确性.对算法的合成速度进行了分析,指出控制算法速度的关键在于矩阵的正交分解.

On the basis of the spectral representation method with proper orthogonal decomposition （POD）, considering the features of fluctuating wind field of long-span bridges, a reduction simulated formula of fluctuating wind field, which considered the cross-spectral density matrix as the POD object, was deduced. The equation of end error calculation based on the energy criterion was adopted to estimate the rational truncation item number of eigenvalues. And by introducing the double-indexing of the frequencies, the simulation of ergodic time domain series was achieved. Also, the Fast Fourier Transform was adopted to improve calculation efficiency, and the improved formula based on the Fast Fourier Transform was deduced in order to program expediently. In addition, the algorithm was applied to simulate the beam stochastic wind field of a long-span railway continuous rigid frame bridge. The auto-power spectral density and cross-power spectral density of the simulated time domain samples show good agreement with target spectrum, which can verify the effectiveness and correctness of the algorithm. Finally, the algorithm resultant velocity of wind field was analyzed. Results indicate that the key point of influencing the algorithm calculation efficiency is the POD velocity of matrix.