基于神经网络曲线拟合的电晕电流数学模型研究

Investigation on Mathematic Model of Corona Current Based on the Curve Fitting by Artificial Neural Network

为求解电晕电流的通用数学模型,利用人工神经网络能以任意精度逼近任意函数的能力,设计了2层BP神经网络,分别对实测的具有双指数函数、Gaussian函数及不规则脉冲形式的电晕电流进行拟合。结果表明,当神经元数目取5-10时,便能对不同类型的电晕电流波形进行高精度拟合,拟合误差量级可达10-4,拟合时间约为2-10 s,通过提取网络的权值、阈值参数可得到电流的解析表达式。该方法得到的电流表达式具有统一的结构,不依赖于电流波形,可作为电晕电流的通用数学模型。

In order to study the general mathematic model for corona currents, we designed a back propagation artificial neural network（BPNN） consisting of two layers which can approximates to an arbitrary function with an arbitrary accuracy to fit the measured corona currents. Theses current waveforms are represented by double exponential function, Gaussian function, and random irregular pulses. The results indicate that the BPNN can fit the experiment corona current waveforms with a high accuracy when the neuron number is selected from 5 to 10. Compared with the measured current waveforms, the error of mean square（MSE） of the fitting current waveforms can arrive 10-4 and the calculation time is about 2 to 10 seconds by the BPNN method. The analytical expressions for the corona currents can be achieved via extracting the weights and thresholds parameters of the BPNN. The expressions can be used as the general mathematic model for corona currents because the expressions have the same structure and the structure is independent of the waveform.