Abstract：Electron density is one of the key fundamental parameters of plasma discharges. Hβ 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 Hβ 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 Hβ 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.
Key words：Optical emission spectroscopy; Electron density; Stark broadening; Random forests; Gas temperature
张婷琳，唐 龙，彭东宇，汤 昊，姜盼盼，刘博通，陈传杰. 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[J]. 光谱学与光谱分析, 2024, 44(10): 2778-2784.
ZHANG Ting-lin, TANG Long, PENG Dong-yu, TANG Hao, JIANG Pan-pan, LIU Bo-tong, CHEN Chuan-jie. A Diagnostic Method for Electron Density of Plasmas by
Machine-Learning Combined With Stark Broadening. SPECTROSCOPY AND SPECTRAL ANALYSIS, 2024, 44(10): 2778-2784.
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