任意分布ST方法及其在随机场线耦合中的应用

Stochastic Testing method of arbitrary distributions and application in random field line coupling analysis

摘要:

随机测试(ST)方法是一种不确定性量化方法，已有的ST方法还不能处理具有任意分布随机变量的情况。通过Gram-Schmidt正交化算法为任意分布随机变量构建混沌多项式基底，对ST方法进行拓展，使其可用于任意分布随机变量的情况。将拓展后的ST方法用于传输线场线耦合分析中。在场线耦合的计算中，由于辐射场的不确定性，入射波极化角、方位角与仰角存在不确定性，因此传输线的响应也呈现出不确定性，导致随机场线耦合问题。针对输入参数服从任意分布的情况，应用ST方法对传输线场线耦合响应进行不确定性量化。对模型的输出响应进行多项式混沌展开，通过求解展开系数得到模型响应的统计信息。结合单随机变量和多随机变量场线耦合算例，得到传输线电压响应的统计信息。最后对比蒙特卡罗模拟方法，验证了ST方法的正确性和高效性。

Abstract:

Stochastic Testing(ST) method is an uncertainty quantification method. The existing ST methods are still unable to handle situations with arbitrarily distributed variables. This paper uses the Gram-Schmidt orthogonalization algorithm to construct a chaotic polynomial basis for arbitrarily distributed random variables to extend ST method. The extended ST method is applied to the field line coupling analysis of transmission lines. In the calculation of field line coupling, due to the uncertainty of the radiation field, there is uncertainty in the polarization angle, azimuth angle, and elevation angle of the incident wave, resulting in uncertainty in the response of the transmission line, leading to the problem of random field line coupling. For the case where the input parameters follow an arbitrary distribution, ST method is applied to quantify the uncertainty of the coupling response of the transmission line field. Performing polynomial chaos expansion on the output response of the model and solving the expansion coefficients, statistical information of the model response is obtained. Combining the field line coupling examples of single random variable and multi-random variable, the statistical information of transmission line voltage response is obtained. Compared with Monte Carlo Simulation(MCS) method, the correctness and efficiency of the ST method are verified.