Accelerator beam orbit prediction based on multi-stage cascaded BP neural networks
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摘要: 加速器束流轨道校正对于加速器稳定运行具有非常重要的作用，精确预测加速器束流轨道的变化对于实现束流自动化校准也具有重要意义。通过对束流轨道变化的准确预测，可以为调整加速器控制参数提供可靠的信息，从而实现对束流的精确控制和调节。通过研究束流在直线加速器中等能量传输段的传输过程，利用模拟加速器数据，基于多级级联的反向传播（BP）神经网络搭建了加速器束流轨道预测模型，能够实现对束流轨道参数的预测。结果表明，与采用传统单隐层BP神经网络建立的预测模型相比，多级级联BP神经网络能够实现更高的预测精度与可靠性，为直线加速器中等能量传输段的优化设计和束流轨道自动化校准提供了一种有效的方法。
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关键词:
- 加速器驱动次临界系统 /
- 中等能量传输段 /
- 级联网络 /
- 反向传播神经网络 /
- 束流轨道预测
Abstract: Since accelerator beam orbit correction is crucial for stable operation of accelerators, accurate prediction of the changes of the accelerator beam orbit is also essential for automated beam calibration. Precise predictions of beam orbit changes can provide reliable information for adjusting accelerator control parameters to achieve precise control and regulation of beam orbit. In this paper, based on a multi-stage cascaded back propagation (BP) neural network and simulated accelerator data, the beam transport process in the medium energy transfer section of a linear accelerator is studied and an accelerator beam orbit prediction model is constructed to predict beam orbit parameters. The results show that the proposed multi-stage cascaded BP neural network achieves higher prediction accuracy and reliability than the prediction model built using a traditional single hidden layer BP neural network. This provides an effective method for optimally designing the medium energy transfer section of the linear accelerator and automating the calibration of the beam orbit. -
图 1 CAFe-Ⅱ的MEBT段结构示意图
Figure 1. Schematic diagram of the MEBT-segment structure of CAFe-Ⅱ (Q: quadrupole magnet; M: steering magnet)
图 2 BP神经网络训练过程示意图
Figure 2. Schematic diagram of the BP neural network training process
图 4 BPM2束流位置参数与各转向磁铁关联度示意图
Figure 4. Schematic diagram of the correlation between the BPM2 beam position parameters and the individual steering magnets
图 5 多级级联BP神经网络结构拓扑图
Figure 5. Multi-stage cascaded BP neural network structure topology
图 6 多级级联BP网络模型训练结果
Figure 6. Training results of multi-stage cascaded BP network model
表 1 级联模型中各级BP神经网络结构
Table 1. BP neural network structure at all levels in the cascade model
net input number of neurons in hidden layer output 1 M1, M2 4 BPM2 2 BPM2, M3 4 BPM3 3 BPM3, M4, M5 6 BPM4 4 BPM4 3 BPM5 
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算法1：多级级联BP神经网络算法 输入：Data的训练集和验证集；学习率η；迭代次数Epochs；批次大小Batch Size 1. 在(0,1)范围内随机初始化网络中的连接权和偏置； 2. 构建第一个网络的训练集Data-1:[(M1,M2), BPM2]； 3. for Epochs 4. for all [(M1, M2), BPM2]∈ Data-1 do: 5. 训练第一个网络： 6. 前向传播，根据公式（3）、(4)得到输出${\text{BPM}}_2'$；根据公式（4）计算误差L-1； 7. 定义一个类似指针的变量：start_idx，根据Batch Size标记抽取样本的位置； 8. 取Batch Size个样本的BPM3信息，构建第二个网络的输入[(${\text{BPM}}_2'$, M3),BPM3]； 9. 训练第二个网络：(得到输出$ {\text{BPM}}_3' $；误差L-2) 10. 重复步骤5-8，依次构建并训练第三个和第四个网络； 11. 所有网络完成一个批次训练后，反向传播误差，更新连接权和偏置； 12. end for 13. 每轮训练完成后，利用验证集检验； 14. until 达到停止条件 输出：连接权和偏置确定的4个BP神经网络
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表 2 学习率及迭代次数选择
Table 2. Learning rate and epochs selection
No. learning rate epochs batch size number of neurons in hidden layer passing rate/% prediction accuracy/mm training time/s 1 0.01 1000 64 14 97.2 0.038 286.42 2 0.005 1000 64 14 97.9 0.032 298.74 3 0.001 1000 64 14 95.8 0.047 293.56
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表 3 隐藏层神经元个数及训练批次大小选择
Table 3. Number of hidden layer neurons and training batch size selection
No. learning rate epochs batch size number of neurons in
hidden layerpassing rate/% prediction
accuracy/mmtraining time/s 1 0.005 1000 64 9 97.3 0.036 296.42 2 0.005 1000 128 9 96.9 0.040 267.58 3 0.005 1000 256 9 95.7 0.048 251.24 4 0.005 1000 64 14 97.9 0.032 298.74 5 0.005 1000 128 14 97.2 0.036 263.51 6 0.005 1000 256 14 96.3 0.047 247.14
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表 4 网络模型的预测能力及可靠性
Table 4. Comparison of the predictive power and reliability of network models
net name learning rate epochs batch size prediction accuracy of
BPM5/mmstandard deviation
of sampleresponse
time/sBP neural network 0.005 5000 64 0.151 0.389 0.002 multi-stage cascaded BP neural network 0.005 5000 64 0.135 0.368 0.001
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