anomalous samples from the entire set of ObsBox data in view of more detailed analyses. At this stage, each bunch is considered as independent, implying that phenomena like coupled-bunch instabilities are disregarded, which greatly simplifies the cluster identification as this then applies to a univariate time series. After having determined the clustering, one can proceed with a Hierarchical Clustering Algorithm [49] to identify iteratively and link clusters in a form of a dendrogram. The experience gathered so far is that signals with similar patterns are, for the most part, clustered together, although some issues have been observed, linked with the fact that the designed clustering algorithm does not allow for a partial match of the time series. In summary, there is an enormous potential for ML techniques to correctly identify false triggers, thus allowing for a more efficient and detailed study of the relatively few data sets that contain instability data. Pressure Readings and Heating Detection Charged particles stored in a high-energy, high-intensity accelerator ring may generate heating in the surrounding equipment due to electron cloud effects [50], particles lost on the beam surroundings [51], synchrotron radiation effects [52], and beam-induced RF heating due to impedance effects [53]. In a high-vacuum environment, temperature increase may lead to outgassing [54] that appears as a pressure increase in vacuum gauges, and Beam-induced heating can be directly measured by means of temperature probes. However, standard vacuum monitoring is more widespread and systematic than temperature monitoring, e.g., more than 1200 vacuum gauges are distributed along LHC ring circumference [56]. Pattern analysis of the vacuum gauges readings after each LHC fill to identify abnormal behavior is a time-consuming and heavy task. Furthermore, there is no reliable technique to convert the vacuum measurements into equivalent temperature values. The pressure readings produced by the vacuum gauges are analyzed by a newly developed automatic classification algorithm in view of detecting heating patterns from an anomalous pressure increase. Fig. 7 shows the time evolution of the pressure of a Beam 2 vacuum gauge situated in Sector 4-5 of the LHC, in the vicinity of the stand-alone magnets D4 and Q5. Sudden changes in pressure readings are clearly visible and may be linked with outgassing generated by a temperature rise. Note that we disregard the underlying physical phenomenon inducing the temperature rise as only its effects are considered. To speed up finding the anomalous gauge readings, the classifier selects a subset of all gauges containing such signals, i.e., the classifier should aim at a high recall score, defined as the fraction of true positives detected from the total number of positive cases. More than 700 vacuum gauge readings were labelled as anomalous through human expert supervision, and a data set containing 700 time series of 3000 time steps each was created. 52 Fig. 7. Typical data (pressure readings and beam intensity) used to estimate beam heating effects from pressure readings of a Beam 2 vacuum gauge situated in Sector 4-5 of the LHC, in the vicinity of the stand-alone magnets D4 and Q5, during a physics fill of the 2015 run. The sudden pressure increases may indicate a beam-induced heating effect close to the vacuum gauge (from [36]). A PCA was then performed, resulting in the retention of only 12 features that retain no particular physical meaning but explain 99.9% of the full data set variance, hence without leading to a significant loss of information. A K-Nearest Neighbour Classifier (KNN) followed by a Multi-Layer Perceptron (MLP) were then trained on the resulting data set containing only these 12 features (see [36] for details). The performance of the KNN and MLP classifiers was evaluated by means of a 4-fold cross-validation approach [57], applied when training each model. The 4-fold technique implemented Stratified splitting [58], the folds being built by preserving the percentage of samples for each class. Fig. 8a shows the results of the parameter set scan maximising the recall for the KNN. The red dots, corresponding to recall=1 in the KNN classifier, are parameter sets for which the algorithm overfits the training data, i.e., it behaves extremely well on training data, but poorly on the test data. At index 7 in the plot, one can find the best parameter set, i.e., the first set of parameters that does not overfit the training set, for which recall=0.60 ± 0.09. The results of the MLP scan over the network parameters is shown in Fig. 8b. The best parameter set is achieved at index 0, corresponding to a network made of 2 hidden layers with 176 neurons per layer. For the neural network, recall=0.86 ± 0.10, an improvement of 35% with respect to the KNN case. Hence, a rather simple Neural Network features interesting recall scores, thus motivating the test of more refined ML techniques on this task, such as Convolutional Neural Network and ensemble methods (see [36]). Digression: ML Learning Applied to Simulated Measurements of Dynamic Aperture This section is devoted to the presentation and discussion of applications of ML to numerical simulations, hence not beam measurements, of nonlinear beam dynamics. Among various concepts that can be used to describe nonlinear beam dynamics, that of Dynamic Aperture (DA) is particularly useful. It is the radius of the smallest sphere inscribed in the connected volume in phase space where bounded motion over a given time interval occurs [59]. Tracking simulations are used to estimate the DA by probing the evolution of a certain set of initial conditions, usually uniformly distributed in polar coordinates in normalized IEEE Instrumentation & Measurement Magazine December 2021

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