Instrumentation & Measurement Magazine 24-9 - 53

Fig. 8. Recall scores of (a) the KNN classifier and (b) the MLP. The red dots at recall=1 in the left plot are parameters set for which the algorithm overfits the
training data (from [36]).
physical space. This procedure is repeated for different realizations
of the magnetic field errors (the so-called seeds) for a
certain accelerator model, and an average DA can be defined:
N
DA

ave
N  d r  ,
1
i
seed
i1
where ri(θ) stands for the last stable amplitude for seed i in the
direction of angle θ. For design studies, a conservative estimate
is preferred, and the DA is estimated as:
DA r where i N j Nangle
1  
min   ,
i j
,

seed , 1
and ri,j represents the last stable amplitude for the ith seed and
jth angle. DAmin might be strongly influenced by outliers, and
efficient automatic tools to tackle the identification of outliers
would be very useful. Fig. 9 shows examples of DA plots, generated
for two LHC configurations, using sixty seeds, eleven
angles, and 105
simulated turns. The left plot refers to the optics
version 1.3 for the High-Luminosity LHC at top energy,
Fig. 9. (a) DA simulations for the v1.3 HL-LHC configuration and (b) the 2016 LHC configuration. Initial 4D co-ordinates like (x, 0, y, 0) are used, and a polar scan is
carried out on (x, y), only. The markers represent the results of the sixty seeds. In (a), Example of DA computations where an outlier is correctly flagged is marked
in green. In (b), Examples of false positives appear in red. False positive cases are of less concern in this case, as they have an impact on the determination of the
maximum stable amplitude that does not affect DAmin
(from [36]).
December 2021
IEEE Instrumentation & Measurement Magazine
53

Instrumentation & Measurement Magazine 24-9

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