机器学习与斯塔克展宽法结合的等离子体电子密度诊断方法

A Diagnostic Method for Electron Density of Plasmas by Machine-Learning Combined With Stark Broadening

电子密度是等离子体基本参数之一。H_(β)是基于斯塔克展宽的发射光谱法最常用的谱线。在大气压条件下,范德瓦尔斯展宽对H_(β)谱线加宽的贡献突出,它与等离子体的气体温度有关。为了提取斯塔克展宽,需要利用分子的转动温度预先确定气体温度,因而其结果必然存在一定的误差,从而导致在谱线的非线性参数拟合中将气体温度的误差传递给电子密度。提出了一种基于机器学习的随机森林回归模型与基于发射光谱的斯塔克展宽法相结合的电子密度光谱诊断方法。通过与传统最小二乘法的误差特性进行对比发现,该方法具有更好的鲁棒性和泛化性能,能够精确且快速地诊断电子密度。通过在气体温度中引入随机偏差,利用谱线展宽模型仿真出不同等离子体状态下的H_(β)谱线,将其作为机器学习的训练数据集。将每组带温度偏差的谱线强度分布与对应的电子密度构成样本集,对随机森林模型进行训练,使模型得到最小均方误差的超参最小叶节点和决策树数量分别为2和100。在模拟中,考虑到气体温度的诊断误差,将带温度偏差的光谱数据作为模型输入,预测出电子密度。研究表明,经训练后的随机森林模型对电子密度的预测结果与真实值之间的平均相对误差小于3%。利用气体温度误差范围为0~±10%的光谱测试集对模型进行评估,随着温度误差增大,模型预测结果比最小二乘法的结果更好。当气体温度误差为±10%时,模型预测电子密度的均方误差相比于最小二乘法降低了30%以上。在光谱数据训练集中,当训练数据集引入的偏差范围为0~±10%时,模型的预测均方误差达到最小,鲁棒性优于最小二乘法,而当训练数据集所含偏差超过±10%时,模型的预测结果较差。另外,利用训练好的随机森林模型分析H_(β)谱线所需的时间远远小于最小二乘拟合法。

Electron density is one of the key fundamental parameters of plasma discharges.H_(β)is the most used spectral line for spectroscopic diagnosis based on the Stark broadening method.The van der Waals broadening,which is related to the gas temperature,makes an important contribution to the broadening of the H_(β)line at atmospheric pressure.To extract the Stark broadening width,the gas temperature should be determined in advance from the rotational temperature of molecules,resulting in inevitable errors in measuring.During the nonlinear parameters fitting processes of a spectral line,the errors in gas temperature will transfer to electron density measurement.This work proposes combining a random forest regression model based on machine learning and a Stark broadening method based on optical emission spectroscopy.Compared with the error characteristic of the traditional least square method,this method is found to have a good performance in robustness and generalization capability so that it could diagnose the electron density of plasma more precisely and quickly.Because of the different states of plasma discharges,the training set of H_(β)standard theoretical line used for the machine learning is simulated by the model of spectral line broadening,in which the random errors are introduced into the gas temperature.A sample set,combined with the spectral line's intensity distribution with each group's temperature deviation and the corresponding electron density,is employed to train the random forest model.The hyperparameters(i.e.,the minimum number of leaf nodes and the number of decision trees)that minimize the mean square error of the model are set to 2 and 100,respectively.It is found that the average relative error between the results predicted by the random forests regression model,which is well-trained,and the actual values are less than 3%.The model was evaluated by a test set of spectral data with a temperature error range of 0~±10%.With the increase in temperature error,the prediction results of the random forest model are better than those of the least squares method.When the error of gas temperature is±10%,the mean squared error of predicted electron density is reduced by more than 30%compared with the least squares method.In the training set of spectral data,when the error of gas temperature introduced into the training set is in the range of 0~±10%,the minimum mean squared error of electron density is achieved,and the robustness of the model is better than that of the least squares method.However,the prediction results of the model become inaccurate when the temperature error introduced into the training set is beyond±10%.In addition,the time spent analyzing the spectral line by the model,which is well-trained,is much less than that by the least square method.