Time series forecasting methods and their applications to particle accelerators

Particle accelerators are complex facilities that produce large amounts of structured data and have clear optimization goals as well as precisely defined control requirements. As such they are naturally amenable to data-driven research methodologies. The data from sensors and monitors inside the accelerator form multivariate time series. With fast preemptive approaches being highly preferred in accelerator control and diagnostics, the application of data-driven time series forecasting methods is particularly promising. This review formulates the time series forecasting problem and summarizes existing models with applications in various scientific areas. Several current and future attempts in the field of particle accelerators are introduced. The application of time series forecasting to particle accelerators has shown encouraging results and promise for broader use, and existing problems such as data consistency and compatibility have started to be addressed.

Figure 1

Illustration of an MLP.

Figure 2

Illustration of an RNN cell in folded and unfolded versions.

Figure 3

The structure and updating scheme of an ERNN cell.

Figure 4

The structure and updating scheme of an LSTM cell.

Figure 5

The ROC curve (left) and precision-recall curve (right) of the rf classifier baseline, rf with PCA and rf with FFT models applied on the beam loss dataset (from [61], Fig. 7).

Figure 6

The ROC curves for training and testing with the same (left) and different (right) errant types (from [63], Figs. 14 and 15).

Figure 7

Generation of recurrence plot from a signal with fixed $\epsilon =2$ (from [66], Fig. 7).

Figure 8

Examples of recurrence plots (bottom row) generated from the original signals (top row) by the RPCNN model. From left to right: uncorrelated stochastic data, data starting to grow, and stochastic data with a linear trend (from [66], Fig. 8).

Figure 9

The RPCNN model structure. The positive and negative classes of samples are taken either close to (orange) or far from (green) the interlocks. Each of the 376-time series is transformed into recurrence plots and fed into the CNN. The model output is a probability value (adapted from [66], Figs. 5 and 8).

Figure 10

The ROC curves of an ensemble of RPCNN classifiers. The blue line shows the best classifier with $\mathrm{AUC}=0.71$, the green line is the mean curve, and the shaded area is the 95% confidence interval of different model initialization profiles. The dashed line is the separatrix, left of which there is a positive beam time saved. The inset is enlarged on the gray-shaded region (from [66], Fig. 11).

Figure 11

Recorded waveforms and window taking of the CEBAF SRF fault forecasting model (from [71], Fig. 2).

Figure 12

ROC curves of classifying samples taken at different times before the SRF faults against normal samples (from [71], Fig. 5).

Figure 13

(a) and (b) show the $R^2$-score against different forecast horizons, where (a) is the result of the 2017 training set and (b) is the 2018 testing set. More specifically, the central lines and shaded areas are the mean and envelope of the $R^2$-score of 1000 bootstrapped predictions, respectively. (c) shows the prediction result of Fill 6050 from the KF4 model with a $2\sigma$ confidence band, and (d) is the values of the corresponding four input variables for (c). The horizons are 200 s in 2017 and 300 s in 2018 (from [74], Figs. 8 and 10).

Figure 14

Linear regression result of energy stability. The dashed line splits the training (left) and test (right) data (from [78], Fig. 6).

Figure 15

Possible setup for time series prediction. Each grid denotes a time step; the time window is taken within one shot of the electron pulse. The gray areas are the input of the model, used as a predictors to predict the target, while $N$ denotes the number of input features. The green areas are the target value expected to be predicted at each time step. (a) Predictors (gray) and target (green) are different variables, while the left and right plots show whether to include the present predictors to predict the present target. (b) Target is included as predictor. In the right plot, past predictions of the target (blue) are used in the testing dataset (from [78], Figs. 4 and 5).