各态历经随机风场的降维模拟

Dimension-reduction simulation of ergodic random wind field

从n V-1D平稳过程的统一源谱分解出发,通过定义正交随机变量集的随机函数,得到了n V-1D平稳过程的谱分解降维模型。在此基础上引入双索引频率,进一步给出了各态历经随机风场的降维模型。利用快速Fourier变换(FFT),模拟了某大跨度桥梁水平向各态历经随机风场。研究表明:降维模型的均值函数严格满足无偏性和各态历经性,相关函数近似满足无偏性和各态历经性;对比分析降维方法与传统MonteCarlo方法的模拟结果,前者的均值误差、标准差误差及自功率谱误差均低于后者,相差范围均在1%左右,验证了本文方法的有效性及优越性。

Based on the unified source spectral decomposition representation of the n V-1 D stationary fluctuating wind speed process, with consideration of the stochastic function of orthogonal random variables, the spectral decomposition dimension reduction model of the stochastic fluctuation wind field is proposed in this paper. Then the double-index frequency is introduced to obtain the dimension reduction model of the ergodic stochastic wind field. The research shows that the mean function of this model unconditionally satisfies unbiasedness and ergodicity, while the correlation function approximatively satisfies unbiasedness and ergodicity. Finally, the fast Fouriertransform(FFT) algorithm is used to simulate the horizontal ergodic stochastic wind field acting on a large-span bridge. By comparing the simulation results of the dimension reduction method and the conventional Monte Carlo method, the mean error, standard deviation error and auto-power spectrum error of the former are lower than the latter, and the difference range is about 1%, which verifies the effectiveness and superiority of the proposed method.