风场模拟中AR模型的若干问题

Some issues on AR models for wind field simulation

自回归(AR)模型具有计算量小,模拟速度快等优良特性,在风场模拟中得到了广泛应用。本文对AR模型进行了系统的研究,将脉动风场模拟中广泛应用的AR模型归为两大类,对模型中的参数从理论上进行了合理的解释。对两种模型模拟脉动风场时涉及到的Wiener-Khintchine公式的变换形式,通过分析对其进行了修正,指出算法上可以采用FFT技术来计算互相关矩阵的元素以提高计算效率。提出了AR模型编程中偶然发现的自回归顺序问题,算例表明两种不同方法的风速时程样本及其无偏自相关估计和自功率谱估计均有较大的影响,希望能引起更多同行对该问题的注意。尽管标量过程AR模型简单且易于掌握,但不能考虑时滞问题。相比之下,理论分析和数值实验都证明,向量过程的AR模型在精度总体要高于标量过程的AR模型,但其运算时间也相应增多。

AR（Auto-Regressive） model is widely used in wind field simulation due to its outstanding performance on amount of computation and its efficiency in computation. In this paper, AR model is more systemic studied. It can be classified into two kinds of AR models as scalar and vector process. Reasonable explanation about parameters in the model has been carried on from the theoretical view. Modifications are performed on Wiener-Khintchine deduced formulas involved in both AR model of vector process and of scalar quantity which were applied into fluctuating wind field. It is found that FFT technique can be used in the calculation of elements of correlation matrix to get high computation efficiency. The problem of auto-regressive sequence found in programming by chance is put forward. Numerical examples show that sequence has more effects on the results of wind velocity time history sample and its unbiased auto-relation estimate and power spectrum estimate. It is hoped that more professions to pay attention on the sequence problem. AR model of scalar quantity is simpler and handled easily but doesn＇t consider time-lag when simulating spatial correlation wind field. Relatively, AR model of vector process is more precise than that of scalar, which is also verified by both theoretical analysis and numerical trial, but this model needs more computating time due to the operation on big matrix and assembly of matrix.