-
对于旨在实现高参数和长脉冲运行的磁约束聚变装置而言, 基于离子温度实时测量的等离子体反馈控制至关重要, 而电荷交换复合光谱是等离子体离子温度的基本测量手段. 本文提出了一种基于神经网络的电荷交换复合光谱诊断数据快速分析方法, 并对其跨参数区间的外推能力进行研究. 该研究使用中国环流器二号A装置HL-2A的12.2×104个光谱数据及离线解谱获得的离子温度标签值构成数据集. 模型基于卷积神经网络, 相对于标签值实现了拟合优度$ {R}^{2}{\mathrm{约}}0.92 $的效果, 在推理阶段单光谱耗时小于1 ms, 相比传统方法加速了100—1000倍. 在外推能力方面, 提出基于低温度实验数据生成高温度的合成光谱数据的方法, 并通过在只包含离子温度2 keV以下的训练集中添加大约5%的合成数据, 大幅增加了模型在外推参数区间(2—4 keV)分析的准确性, 并将模型在3—4 keV区间测试的误差降低了约60%. 该研究证明了在磁约束核聚变领域利用合成数据提升人工智能算法性能的可行性.
Real-time measurement and feedback control of key plasma parameters are critical for future fusion reactor operation, with ion temperature being a vital control target as part of the triple product for fusion ignition. However, plasma diagnostics often require complex data analysis. A widely used method of obtaining ion temperature $ {T}_{{\mathrm{i}}} $ from charge exchange recombination spectrum (CXRS) is iterative spectral fitting, which is time-consuming and requires expert intervention during data analysis. On top of that, frequent human expert intervention is required in traditional iterative fitting. Therefore, the traditional method cannot meet the demand for real-time $ {T}_{{\mathrm{i}}} $ measurement. Neural network (NN), which can learn the underlying relationships between the measured spectra and $ {T}_{{\mathrm{i}}} $, is a promising approach to cope with this problem. In fact, NN approach has been widely adopted in the field of magnetically confined plasma. Previous study in JET has achieved a satisfactory accuracy for inferring $ {T}_{{\mathrm{i}}} $ from CXRS spectra compared with the traditional fitting results. Recently, the study of disruption prediction has achieved great progress with the help of deep NNs. However, these researches are conducted on steadily-operating devices; for NN models, the data distribution of training set is similar to that of test set. This is not the case for newly-built tokamak like HL-3 nor for future fusion reactors such as ITER. For new devices, there will be a period for the plasma parameters to rise from low to high ranges. In this case, it is crucial to investigate the ability of NN model to extrapolate based on low parameter training data. A traditional neural network (TNN)-based model is proposed to accelerate the analysis of spectral data of CXRS, with a focus on investigating the ability of the model to extrapolate to much higher $ {T}_{{\mathrm{i}}} $ range. The dataset contains about 122000 spectral data, as well as their corresponding $ {T}_{{\mathrm{i}}} $ inferred from offline iterative process. The results demonstrate that the TNN-based model achieves excellent analysis of $ {T}_{{\mathrm{i}}} $ as indicated by a coefficient of determination (R²) of 0.92, and reduces the inference time for analyzing a single spectrum to less than 1 ms, reaching 100–1000 times faster than traditional spectral fitting methods. However, the performance of the data-driven neural network model is limited by challenges such as insufficient data and imbalanced data distribution, which further deteriorates the ability to extrapolate. Generally, data with higher $ {T}_{{\mathrm{i}}} $ account for a small portion of the total dataset. In our study, only about 5% of the spectra correspond to $ {T}_{{\mathrm{i}}} > 2{\mathrm{ }}\;{\mathrm{k}}{\mathrm{e}}{\mathrm{V}} $ (ranging from 2 to 4 keV). However, they reflect the temperature of central plasma, which is more important for assessing the performance of plasma. To overcome this limitation, this study synthesizes high-temperature data based on experimental data from discharges with $ {T}_{{\mathrm{i}}} $ in low-temperature range. By incorporating 5% synthetic data into the training set only consisting of data with $ {T}_{{\mathrm{i}}} < 2\;{\mathrm{ }}{\mathrm{k}}{\mathrm{e}}{\mathrm{V}} $, the ability of model to extrapolate is extended to the whole range of $ {T}_{{\mathrm{i}}} < 4\;{\mathrm{k}}{\mathrm{e}}{\mathrm{V}} $. The average relative error (ARE) of the model within the training data in the range of $ {3\;{\mathrm{ }}{\mathrm{k}}{\mathrm{e}}{\mathrm{V}} < T}_{{\mathrm{i}}} < 4\;{\mathrm{k}}{\mathrm{e}}{\mathrm{V}} $ decreases from 35% to below 15%, corresponding to a reduction of approximately 60% relative to the ARE before adding synthetic data. This approach demonstrates the feasibility of using synthetic data to enhance the performance of artificial intelligence algorithms in the field of magnetic confinement fusion. These findings provide valuable ideas for developing the real-time ion temperature measurement and feedback control of future high-parameter fusion devices. Furthermore, the study lays a foundation for investigating high-performance across-device characteristic, such as machine learning-based disruption prediction and tearing mode control. -
Keywords:
- plasma /
- neural network /
- extrapolation capability /
- spectral diagnostic
-
图 1 HL-2A装置CXRS光谱诊断示例 (a) CXRS诊断系统示意图; (b)离子温度为3.1和1.4 keV下光谱及其分解结果
Fig. 1. The CXRS diagnostic system and measured spectra in HL-2A: (a) Diagram of CXRS diagnostic system; (b) spectra and their decomposition results at ion temperature of 3.1 and 1.4 keV.
图 3 神经网络模型结构, 其中实线箭头连接的地方表示残差连接
Fig. 3. The architecture of the CNN-based model, where the solid arrow is connected, the residual connection is represented.
图 4 神经网络模型的标签与预测值散点图, 图中黑色虚线为横坐标与纵坐标值相等的线
Fig. 4. The scatter plot of label and output of the CNN-based model, the black dotted line in the figure is the line where the horizontal coordinate and the vertical coordinate are equal.
图 5 神经网络模型的标签与预测结果对比 (a)标签与预测离子温度不同时刻剖面对比; (b)标签与预测离子温度不同位置时间演化对比
Fig. 5. The label against the output ion temperature of the CNN-based model: (a) Ti profiles in different time; (b) time evolution of Ti at different radius.
图 6 光谱曲线及对应的IG曲线(炮号34339, 810 ms). 神经网络对输入的IG曲线呈现近似“M”型, 且与高斯峰的位置准确吻合, 呈现出检测高斯峰的行为
Fig. 6. The spectrum and IG graph of the spectrum in 810 ms of shot No. 34339. The neural network presents an approximate “M” shape to the input IG curve, and it is exactly consistent with the position of the Gaussian peak, showing the behavior of detecting the Gaussian peak
图 7 Ti在0—2 keV参数区间训练的神经网络模型外推到更高温度参数区间的表现
Fig. 7. The performance of the CNN-based model trained on dataset with Ti in 0–2 keV on test set in higher Ti range.
图 8 合成谱线的流程图及谱线示例.
Fig. 8. Examples of synthetic spectrum, along with the flow chart of the synthesizing process.
图 9 $ {T}_{{\mathrm{i}}} $在0—2 keV区间训练的神经网络模型外推到更高温度参数区间的表现
Fig. 9. Performance of the CNN-based model trained on dataset with $ {T}_{{\mathrm{i}}} $ between 0–2 keV on data with higher $ {T}_{{\mathrm{i}}} $.
图 10 训练集有、无合成训练数据的神经网络模型在不同离子温度区间的平均相对误差MRE表现对比
Fig. 10. Comparison of the MRE in various $ {T}_{{\mathrm{i}}} $ ranges of CNN-based models w/ or w/o synthetic training data.
表 1 CNN层的参数配置
Table 1. Configuration of the CNN layers.
编号 核数量 核宽度 激活函数 池化 池化步长 池化宽度 1 32 3 gelu[23] — — — 2 32 3 最大 2 2 3 32 3 — — — 4 32 3 — — — 5 64 3 最大 2 2 6 64 3 — — — 7 64 3 — — — 8 128 5 最大 2 2 9 128 3 — — — 10 128 3 — — — 11 128 3 最大 — 全局 
下载: 导出CSV
表 2 模型训练过程的超参数配置及相关说明
Table 2. Hyper-parameters of the CNN-based model.
参数(英文名) 值 说明 高斯噪声(Gaussian noise) μ = 0, σ = 0.01 添加高斯噪声对训练集进行数据增强 批次尺寸(Batch size) 128 随机梯度下降过程中的批次数据个数 早停机制(Early stopping) 20 经过一定轮次的训练若效果不再提升则视为训练完成 神经元屏蔽(Dropout) 0.2 全连接层中神经元输出在训练过程中随机置零的比例, 以减少过拟合
下载: 导出CSV
表 3 模型的拟合效果及速度评估
Table 3. Performance of the model.
训练集 测试集/keV $ {R}^{2} $ MRE 推理耗时/
(ms·单光谱–1)无合成数据 0—2 0.92 14% 0.59
(平均值)0.67
(99%)无合成数据 0—4 0.86 15% 有合成数据 0—4 0.93 13%
下载: 导出CSV
-
[1] Lister J B, Bruzzone P L, Costley A E, Fukuda T, Yu G, Mertens V, Moreau D, Oikawa T, Pitts R A, Portone A, Vayakis G, Wesley J, Yoshino R 2000 Nucl. Fusion 40 1167
Google Scholar
[2] Gormezano C, Sips A C C, Luce T C, Ide S, Becoulet A, Litaudon X, Isayama A, Hobirk J, Wade M R, Oikawa T, Prater R, Zvonkov A, Lloyd B, Suzuki T, Barbato E, Bonoli P, Phillips C K, Vdovin V, Joffrin E, Casper T, Ferron J, Mazon D, Moreau D, Bundy R, Kessel C, Fukuyama A, Hayashi N, Imbeaux F, Murakami M, Polevoi A R, St John H E 2007 Nucl. Fusion 47 S285
Google Scholar
[3] Hellermann M G V, Mandl W, Summers H P, Weisen H, Wolf R 1990 Rev. Sci. Instrum. 61 3479
Google Scholar
[4] Seraydarian R P, Burrell K H 1986 Rev. Sci. Instrum. 57 2012
Google Scholar
[5] 何小雪, 陈文锦, 魏彦玲, 刘亮, 王诗琴, 余德良 2024 核聚变与等离子体物理 44 477
He X X, Chen W J, Wei Y L, Liu L, Wang S Q, Yu D L 2024 Nucl. Fusion Plasma Phys. 44 477
[6] 张镱 2015 硕士学位论文(合肥: 中国科学技术大学)
Zhang Y 2015 M. S. Thesis (Hefei: University of Science and Technology of China
[7] Svensson J, Hellermann M V, König R W T 1999 Plasma Phys. Controlled Fusion 41 315
Google Scholar
[8] Bishop C M, Roach C M 1992 Rev. Sci. Instrum. 63 4450
Google Scholar
[9] Abbate J, Conlin R, Kolemen E 2021 Nucl. Fusion 61 046027
Google Scholar
[10] Zheng G H, Yang Z Y, Liu S F, Ma R, Gong X W, Wang A, Wang S, Zhong W L 2024 Nucl. Fusion 64 126041
Google Scholar
[11] Yang Z, Xia F, Song X, Gao Z, Wang S, Dong Y 2021 Nucl. Fusion 61 126042
Google Scholar
[12] Yang Z, Xia F, Song X, Gao Z, Li Y, Gong X, Dong Y, Zhang Y, Chen C, Luo C, Li B, Zhu X, Ji X, Li Y, Liu L, Gao J, Liu Y 2022 Fusion Eng. Des. 182 113223
Google Scholar
[13] Seo J, Kim S, Jalalvand A, Conlin R, Rothstein A, Abbate J, Erickson K, Wai J, Shousha R, Kolemen E 2024 Nature 626 8000
[14] Duan X R, Xu M, Zhong W L, et al. 2024 Nucl. Fusion 64 112021
Google Scholar
[15] Duan X R, Xu M, Zhong W L, et al. 2022 Nucl. Fusion 62 042020
Google Scholar
[16] Donné A J H, Costley A E, Barnsley R, et al. 2007 Nucl. Fusion 47 S337
Google Scholar
[17] Wei Y L, Yu D L, Liu L, Ida K, von Hellermann M, Cao J Y, Sun A P, Ma Q, Chen W J, Liu Y, Yan L W, Yang Q W, Duan X R, Liu Y 2014 Rev. Sci. Instrum. 85 103503
Google Scholar
[18] He X X, Yu D L, Yan L W, Liu L, Chen W J, Wei Y L, He X F, Ma Q, Shi Z B, Liu Y, Yang Q W, Xu M, Duan X R 2020 Rev. Sci. Instrum. 91 053504
Google Scholar
[19] 王彦飞, 朱悉铭, 张明志, 孟圣峰, 贾军伟, 柴昊, 王旸, 宁中喜 2021 70 095211
Google Scholar
Wang Y F, Zhu X M, Zhang M Z, Meng S F, Chai H, Wang Y, Ning Z X 2021 Acta Phys. Sin. 70 095211
Google Scholar
[20] Fei N Y, Gao Y Z, Lu Z W, Xiang T 2021 2021 IEEE/CVF International Conference on Computer Vision Electric Network, October 11—17, 2021 pp142—151
[21] He K M, Zhang X Y, Ren S Q, Sun J 2015 arXiv: 1512.03385 [cs. CV]
[22] He M, Yang Z, Liu S, Xia F, Zhong W 2024 Plasma Phys. Controlled Fusion 66 105019
Google Scholar
[23] Hendrycks D, Gimpel K 2016 arXiv: 1606.08415 [cs. LG]
[24] Loshchilov I, Hutter F 2017 arXiv: 1711.05101 [cs. LG]
[25] Yushmanov P N, Takizuka T, Riedel K S, Kardaun O J W F, Cordey J G, Kaye S M, Post D E 1990 Nucl. Fusion 30 1999
Google Scholar
[26] Sundararajan M, Taly A, Yan Q 2017 arXiv: 1703.01365 [cs. LG]
下载:
计量
- 文章访问数: 267
- PDF下载量: 2
- 被引次数: 0
