基于插值技术谐波叠加法的风速场模拟

Simulation of wind velocity fields by resorting to harmonic superposition method based on interpolation technique

风荷载的数值模拟在结构设计中起着非常重要的作用。在土木工程脉动风速时程的各种数值模拟方法中,谐波叠加法最为常用。而且,通过引入FFT和不同插值技术可以在不显著地影响模拟精度的情况下,大大地缩短模拟计算所花费的时间。基于两次多项式、三次多项式、以及两种不同边界条件三次样条函数插值技术的谐波叠加法来模拟一幢100 m高高层建筑上10个点的脉动风速时程,通过均方根误差(Root Mean Square Error,RMSE)和相对误差系数(Error factor,Ef)两项指标来评价不同插值技术与传统谐波叠加法(未引入插值技术)相比较的插值模拟计算精度,并且记录各自所耗费的时间,综合比较模拟效率和精度以找出最为适合的一种插值技术。结果表明:基于第一种边界条件三次样条函数插值技术的谐波叠加法为最佳的模拟方法。

The harmonic superposition method is most widely used in conventional simulation methods for tall buildings, and the time expense for using harmonic superposition method can be significantly shortened by resorting to the FFT technique and various kinds of interpolation techniques without significant loss of accuracy. Square polynomial interpolation technique, cubic polynomial interpolation technique, and two kinds of spline interpolation techniques with different end conditions were adopted to simulate the wind velocity time series at 10 points on a 100-metres high building. The root mean square error (RMSE) and the error factor (E f) were designated as two indices to evaluate the accuracy of these four interpolation techniques, relative to the traditional harmonic superposition method (without introducing the interpolation technique). Their time expenses were recorded respectively. Finally, the best interpolation technique was picked out through comprehensively taking into account both accuracy and time expense.