Simulation of fluctuating wind velocity at given position on moving high-speed train
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摘要: 以修正Karman风速谱为目标谱, 基于最小信息准则确定线性滤波法自回归模型的阶数, 采用线性滤波法和谐波叠加法模拟了高速列车随车移动点的脉动风速时间历程, 并验证了模拟结果的可靠性, 对比了2种方法模拟脉动风速均值、方差、幅频、相频等特征变量以及风速分布规律的差异, 并分析了2种方法的计算效率。分析结果表明: 采用2种方法得到的脉动风速功率谱密度均围绕目标谱波动; 脉动风速均值约为0, 由于随机数的使用, 使得脉动风速峰值在个别时间点存在差异, 且在低频区域得到的仿真谱差异可能超过50%;不同风向角下计算所得脉动风速均值的差异小于2%, 且脉动风速的分布规律几乎一致; 当列车运行速度为80m·s-1, 且距地面高度10m处平均风速为25m·s-1时, 2种方法得到的脉动风速峰值均值间的差异小于1%, 表明2种方法均适用于模拟高速列车随车移动点的脉动风速; 2种方法所得脉动风速幅值均随脉动风速频率的增大而减小, 相位在-π~π内波动, 脉动风速分布在-3~3m·s-1内的差异仅为0.48%;采用2种方法所得脉动风速点数满足高斯分布, 且高斯分布拟合系数最大差异为3.15%;采用线性滤波法模拟所得脉动风速波动比谐波叠加法大7.89%, 其稳定性劣于谐波叠加法; 采用线性滤波法的计算时间约为谐波叠加法的1/9, 其计算效率远高于谐波叠加法。Abstract: The modified Karman wind spectrum was employed as the target spectrum. The order of the autoregressive model for the linear filtering method (LFM) was determined by using the Akaike information criterion (AIC), and the reliability of the simulation results was verified. The LFM and the harmonic superposition method (HSM) were used to simulate the fluctuating wind velocity at a given position on a moving high-speed train. The characteristic variables of fluctuating wind velocity, such as mean values, variances, amplitudes, phase frequencies and distributions calculated by the two methods were compared. The computational efficiencies of these two methods were analyzed. Analysis result shows that the power spectrum densities of fluctuating wind velocity obtained from the two methods fluctuate around the target power spectrum. The mean value of fluctuating wind velocity is approximately 0. Due to the existence of random number, there is a difference in the peak values of fluctuating wind velocity at certaintime, and the differences in the simulated power spectrums within low frequency area may exceed 50%. Under different yaw angles, the difference in the mean values of fluctuating wind velocity between the two methods is less than 2%, and the distribution rules are quite similar. When the train speed is 80 m·s-1 and the average wind velocity at the height of 10 mabove ground level is 25 m·s-1, the difference in the average peak values of fluctuating wind velocity between HSM and LFM is less than 1%. Both the two methods are suitable for simulating the fluctuating wind velocity at a given position on a moving high-speed train. With the increase of the frequency of fluctuating wind velocity, the amplitude of fluctuating wind velocity decreases and the phase fluctuates in the range of-πtoπ. The difference in the fluctuating wind velocity distributions in the range of-3 to 3 m·s-1 is 0.48%. The point numbers of fluctuating wind velocity obtained by the two methods both correspond to the Gaussian distribution, and the maximum difference in the Gaussian distribution fitting coefficients is 3.15%. The variance of the fluctuating wind velocity obtained from LFM is 7.89% larger than that obtained from HSM, therefore, LFM is less stable than HSM. The running time of LFM is approximately 1/9 that of HSM, therefore, its calculation efficiency is much higher than that of HSM.
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图 2 脉动风速仿真功率谱与目标谱对比
Figure 2. Comparison of simulated power spectrums and target spectrum of fluctuating wind velocity
图 3 不同风向角时脉动风速对比
Figure 3. Comparison of fluctuating wind velocities with different yaw angles
图 4 两种方法所得脉动风速均值和方差对比
Figure 4. Comparison of mean values and variances of fluctuating wind velocities obtained from two methods
图 5 两种方法所得脉动风速幅值谱和相位谱对比
Figure 5. Comparison of amplitude spectrums and phase spectrums of fluctuating wind velocity obtained from two methods
表 2 高斯分布拟合系数的分布区间
Table 2. Distribution intervals of Gaussian distribution fitting coefficients
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