用特征正交分解的桥墩处水波动模拟

Simulation for Stochastic Wave of Water Particles Around Bridge Piers by Using Spectral Representation Method with Proper Orthogonal Decomposition(POD)

定义了随机向量过程的特征正交分解,推导了特征正交分解型谱表示法的模拟表达式,该算法可用FFT加速。结合桥墩基础处不同深度水质点波动速度和速度的功率谱密度矩阵仅具有一个独立特征值的特点,推导了随机波动模拟的简化计算公式,简化公式具有较高的计算效率。通过对一个实际桥梁桩基础不同深度处的水质点随机波动速度进行模拟,验证了所提方法的有效性。

Proper orthogonal decomposition （POD） of random multivariate processes was defined firstly. Then, a series of practical expression of the spectral representation method on the basis of POD was given, which can be accelerated by FFT, It can be shown that the power spectral density matrix of velocities and/or accelerations process of water particles in stochastic waves had only one non-nil independent eigenvalue and eigenvector, As a consequence, the equations of the simulation of stochastic wave could be simplifiod. Compared with original spectral representation method, higher computation efficiency might be attained. Finally, by simulation of stochastic waves around an actual bridge pier foundation, the algorithm proposed in this paper was verified.