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Efficient simulation of fully non-stationary random wind field based on reduced 2D hermite interpolation
Mechanical Systems and Signal Processing ( IF 8.4 ) Pub Date : 2021-03-01 , DOI: 10.1016/j.ymssp.2020.107265
Tianyou Tao , Hao Wang , Kaiyong Zhao

Abstract The spectral representation method (SRM) has been widely used to simulate stationary or non-stationary wind fields for engineering structures. Although several attempts have been made to realize the invoking of Fast Fourier Transform (FFT), the SRM is still very inefficient to simulate the fully non-stationary wind field with a time-varying coherence due to the extremely time-consuming Cholesky decompositions and large memory requirement. In this paper, a reduced 2D Hermite interpolation-enhanced approach is developed to further improve the efficiency of SRM in simulating fully non-stationary wind fields. Central to this approach is the interpolation procedure which requires Cholesky decompositions and storage of cross power spectral density matrix (CEPSD) elements only at interpolation knots. Thus the computational costs of Cholesky decompositions and memory requirement are dramatically decreased. The number of Cholesky decompositions is then fixed with no relation to the segments of frequency and duration of wind samples, which eliminates the Cholesky decomposition as a cause that affects the simulation efficiency. Meanwhile, each element in the decomposed CEPSD matrix is decoupled into products of time- and frequency-dependent functions by the reduced 2D Hermite interpolation, so the FFT can be used to expedite the summation of trigonometric terms. Apart from using FFT, another merit of the proposed approach is that an accelerated FFT algorithm can be incorporated to further improve the simulation efficiency based on the specific decoupled expression of frequency-dependent functions. The parametric analysis shows that the proposed approach is very efficient in comparison with the existing method using proper orthogonal decomposition (POD), and it provides a desired level of simulation accuracy when appropriate interpolation interval is selected. The case study in simulating the fully non-stationary wind field of a long-span cable-stayed bridge demonstrates the effectiveness of the proposed approach with verifications on both evolutionary power spectra and correlation functions.

中文翻译:

基于简化二维 Hermite 插值的全非平稳随机风场高效模拟

摘要 频谱表示法(SRM)已被广泛用于模拟工程结构的稳态或非稳态风场。尽管已经进行了多次尝试来实现快速傅立叶变换 (FFT) 的调用,但由于极其耗时的 Cholesky 分解和大量的时间相干性,SRM 在模拟具有时变相干性的完全非平稳风场方面仍然非常低效。内存要求。在本文中,开发了一种简化的 2D Hermite 插值增强方法,以进一步提高 SRM 在模拟完全非平稳风场方面的效率。这种方法的核心是插值过程,它需要 Cholesky 分解和仅在插值节点处存储交叉功率谱密度矩阵 (CEPSD) 元素。因此,Cholesky 分解的计算成本和内存需求显着降低。然后固定 Cholesky 分解的数量,与风样本的频率和持续时间段无关,这消除了 Cholesky 分解作为影响模拟效率的原因。同时,分解后的 CEPSD 矩阵中的每个元素通过简化的 2D Hermite 插值解耦为时间和频率相关函数的乘积,因此 FFT 可用于加速三角项的求和。除了使用 FFT 之外,所提出的方法的另一个优点是可以结合加速 FFT 算法以进一步提高基于频率相关函数的特定解耦表达式的仿真效率。参数分析表明,与使用适当正交分解 (POD) 的现有方法相比,所提出的方法非常有效,并且在选择适当的插值间隔时可提供所需的仿真精度水平。模拟大跨度斜拉桥完全非平稳风场的案例研究证明了所提出方法的有效性,并验证了演化功率谱和相关函数。
更新日期:2021-03-01
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