  The increasing automation in many areas of the Industry expressly demands to
design efficient machine-learning solutions for the detection of abnormal
events. With the ubiquitous deployment of sensors monitoring nearly
continuously the health of complex infrastructures, anomaly detection can now
rely on measurements sampled at a very high frequency, providing a very rich
representation of the phenomenon under surveillance. In order to exploit fully
the information thus collected, the observations cannot be treated as
multivariate data anymore and a functional analysis approach is required. It is
the purpose of this paper to investigate the performance of recent techniques
for anomaly detection in the functional setup on real datasets. After an
overview of the state-of-the-art and a visual-descriptive study, a variety of
anomaly detection methods are compared. While taxonomies of abnormalities (e.g.
shape, location) in the functional setup are documented in the literature,
assigning a specific type to the identified anomalies appears to be a
challenging task. Thus, strengths and weaknesses of the existing approaches are
benchmarked in view of these highlighted types in a simulation study. Anomaly
detection methods are next evaluated on two datasets, related to the monitoring
of helicopters in flight and to the spectrometry of construction materials
namely. The benchmark analysis is concluded by recommendation guidance for
practitioners.
