一种用于瞬态陡脉冲信号处理的时域-频域联合外推方法

考虑雷电流激励情况下接地网瞬态响应为陡升缓降的特点,提出了一种基于Hermite函数展开改进的时域-频域联合外推方法。时域-频域联合外推方法通过分别对时域早时响应和频域低频响应采样,利用Hermite函数的时域-频域互反性构造外推系统完整的瞬态响应,但其不能处理陡脉冲激励的瞬态响应。文中对激励为陡脉冲的瞬态响应信号进行预处理和后处理工作。信号前处理工作为:在时域和频域内分别进行尺度变换,对瞬态响应波形进行平滑运算和序列补零,有效降低外推系数矩阵的条件数;给出了Hermite函数插值阶数的自适应确定方法;信号后处理工作为:为处理时域信号晚时响应的数值发散问题,文中进一步对信号采用GPOF方法进行平滑。数值算例和测量结果证明了该方法的正确性和有效性;文中算法适用于陡脉冲信号时域-频域的联合外推。

Improved Simultaneous Extrapolation in Sharp Impluse Signals in Time and Frequency Domains

The characteristic of the transient response of the grounding system takes on a fast rising and slow damping with the lightning excitation. An improved simultaneous time and frequency domain extrapolation method is presented based on Hermite function expansion, which takes the above mentioned characteristic of the transient signal into account. using early time response and low-frequency data, the complete electromagnetic response is generated. By using mutually complementary data, simultaneous extrapolation in time and frequency domains are carried out by using the Hermite polynomials as the basis function. However, the extrapolation method is not suitable to deal with the transient response with the fast pulse excitation. The improvement for the extrapolation method is to pre- and post-process the transient response data with the fast pulse excitation. As a pre-processed procedure, in order to reduce the condition number of the matrix used for determined the coefficient of basis function, the scale transformation is used in time and frequency domain respectively, and the data in time domain is smoothed and padded with zero. An adaptive algorithm to determine the order of Hermite function is also proposed. As a post-processed step, the transient data are smoothed by using GPOF to obtain a convergent result. The numerical example and the field measurement are presented to illustrate the application of this methodology. The method proposed enhances the ability of the simultaneous time and frequency extrapolation techniques.