利用两个现成的老的机器学习方法，随机森林RF和人工神经网络ANN，对付解决一个老问题，电磁铁阵列的磁场生成问题，这是电磁驱动的一个新的发文章的点，可以用来学习简单idea的实现。
用随机森林和人工神经网络对用于医疗应用的电磁导航系统建模
Modeling Electromagnetic Navigation Systems for Medical Applications using Random Forests and Artificial Neural Networks [1]
Paper Link
Authors: Yu, Ruoxi, et al.
2020, IEEE International Conference on Robotics and Automation (ICRA)
0. 摘要 Abstract
随机树和神经网络这两个机器学习方法的表现都好于最新的线性多极子电磁模型根均方误差减少了40%-87%，在高电流区域，有等同于90%的误差减少。
RF and ANN methods outperformed the state-of-the-art linear multipole electromagnetic model. They reduced the root average square error by 40% to 87%. At high current regions, 90% error reduction.
2. 建模理论 Modeling methods
我们使用在一定量的电磁铁电流时的来自于磁链密度传感器的稳定状态测量训练机器学习模型。
We use steady state measurements from magnetic flux density sensors at a number of currents to train the machine learning models.
手头的任务是给定电流下，预测在特定位置的生成3D磁场磁链密度。
The task at hand is to predict the generated 3D magentic flux density at a specific position.
考虑在三个预测场分量之间的可能的关系，RF和ANN被使用来进行这多输出回归任务。
Considering the relationship among three predicted field components, RF and ANN are used to perform the multi-output regression task.
3. 实验 Experiments
总共3590组电流被生成，每组电流生成时产生的磁场都有119个磁传感器测量，共有427210个磁场sample被记录。
因为线圈的低速动态响应，高频噪音对生成磁场的影响很小。尽管如此，电流测量的数值在一个测量窗口内求平均平滑。磁场测量也被平均来减少测量噪音的影响。
Due to the low dynamic response of the coils, the effect of such high-frequency noise has little effect on the generated magnetic fields. Nonetheless, the current measurements are smoothed by averaging values over the measurement window. The magnetic field measurements are averaged to reduce the effect of measurement noise.
RF模型是用scikit-learn包做的，ANN是用Keras包做的。
为了评估模型的预测性能，两个通用的最优拟合标准被使用来比较测量和预测磁场。包含R方分和根均方误差。R方分值为1表明模型预测完美符合测量，而RMSE接近0表示是一个好模型。
To evaluate the prediction performance of the models, two general goodness-of-fit metrics are used to compare the measured and predicted magnetic field, including R 2 R^{2} R2 and the root mean square error (RMSE). An R 2 R^{2} R2 value of 1 1 1 indicates that the model predictions perfectly fit the measurements, whereas a RMSE close to 0 suggests a good model.
R 2 = 1 − ∑ j = 1 N ( b j − b ^ j ) 2 ∑ j = 1 N ( b j − b ˉ j ) 2 R^{2}=1-\frac{\sum_{j=1}^{N}{(\mathbf{b}^{j}-\hat{\mathbf{b}}^{j})^{2}}}{\sum_{j=1}^{N}{(\mathbf{b}^{j}-\bar{\mathbf{b}}^{j})^{2}}} R2=1−∑j=1N(bj−bˉj)2∑j=1N(bj−b^j)2
R M S E = ∑ j = 1 N ( b j − b ^ j ) 2 N RMSE=\sqrt{\frac{\sum_{j=1}^{N}{(\mathbf{b}^{j}-\hat{\mathbf{b}}^{j})^{2}}}{N}} RMSE=N∑j=1N(bj−b^j)2
[1]: Yu, Ruoxi, et al. “Modeling Electromagnetic Navigation Systems for Medical Applications using Random Forests and Artificial Neural Networks.” 2020 IEEE International Conference on Robotics and Automation (ICRA). IEEE, 2020.