雷电流幅值累积概率分布曲线拟合方法

Curve Fitting Method of Cumulative Probability Distribution of Lightning Current Magnitude

为从雷电流幅值累积概率分布的统计散点中准确获得分布公式的参数,以残差平方和作为拟合结果优劣的衡量标准,提出了3种雷电流幅值累积概率分布曲线的拟合方法,即＂中值电流＂法、线性变换法和Levenberg-Marquardt法,前两者计算过程简单易于实现,后者鲁棒性强,计算开销也最大。计算实例表明：Levenberg-Marquardt法的拟合残差平方和最小,拟合曲线最贴近统计散点,＂中值电流＂法次之,线性变换法的拟合残差平方和较前两者高出1-2个数量级;Levenberg-Marquardt法迭代步数依赖于给定的初值,采用IEEE的推荐参数作初值,经过4-6轮迭代即可得到终值;将＂中值电流＂法的拟合结果作为初始值代入Levenberg-Marquardt法中,形成混合拟合方法,可加速迭代过程,保持拟合效果不变的前提下减少约26%的运算时间。综上,建议使用＂中值电流＂法与Levenberg-Marquardt法相结合的混合方法进行拟合。

In order to derive an accurate parameter from statistical data of cumulative probability distribution（CPD） of lightning current magnitude（LCM）, we proposed 3 curve fitting methods by taking the residual square sum（RSS） as a measurement of fitting goodness, namely ＂median current＂ method, linear transformation method, and Levenberg-Marquardt method. The former two have a simple procedure and are easy to implement, while the latter one is of good robust and large computation cost. Case study reveals that the Levenberg-Marquardt method achieves the smallest RSS and its resultant fitting curve lies closest to statistica1 l data, while ＂median current＂ method achieves the second small RSS and linear transformation method achieves 10-100 times RSS greater than the other two. It is also indicated that the iteration procedure of the Levenberg-Marquardt method depends on initial value, and usually takes 4-6 iterations to obtain final outcome with the parameter recommended by IEEE as initial value. Furthermore, by substituting the outcome from the ＂median current＂ method（as an initial value）into the Levenberg-Marquardt method, a hybrid one can be formed, which accelerates iteration procedure, and reduces operation time by about 26% with the same outcome. In conclusion, a hybrid method combining ＂median current＂ method and Levenberg-Marquardt algorithm is recommended.