Statistical methods for fibre-optic sensor networks
File(s)
Author(s)
Jammayrac, Amaury
Type
Thesis
Abstract
Given the decrease of sensor cost and the rise of computation power, more structures
will be built with an integrated network of sensors to track and monitor their short- and
long-term state. The statistical research potential around this type of data is immense
and this thesis is a contribution.
This thesis is based on a speci c type of bre-optic sensor network installed on a bridge.
The sensors extract changes of strain at di erent spatial locations on the bridge and have
a covariance structure which has speci c properties. The main one is a latent structure
which appears when the changes of strains are projected to a speci c space of lower
dimension. This latent structure is rarely described in the literature, and this thesis
provides a theoretical framework to describe and reproduce it.
This theoretical framework relies on circulant matrices, and develops the concept of
Lagged Cosines matrix, which uses cosine waves with similar amplitude and frequency,
and di erent phases. The Lagged Cosines matrix is then incorporated as the deterministic
component of a newly de ned stochastic model, called the Lagged Cosines model.
This model is tted to the data from the sensor network. Based on the results of this
t, two main features are inferred from the sensor network and from the response of the
bridge to a train crossing it. First, a deep periodic structure is discovered and analysed in
the sensor network when the bridge is \at rest". Second, when a train crosses the bridge,
the Lagged Cosines model extracts what is de ned as a collective response of the bridge
which characterises the changes of strain at di erent spatial locations, which leads to a
method of anomaly detection.
will be built with an integrated network of sensors to track and monitor their short- and
long-term state. The statistical research potential around this type of data is immense
and this thesis is a contribution.
This thesis is based on a speci c type of bre-optic sensor network installed on a bridge.
The sensors extract changes of strain at di erent spatial locations on the bridge and have
a covariance structure which has speci c properties. The main one is a latent structure
which appears when the changes of strains are projected to a speci c space of lower
dimension. This latent structure is rarely described in the literature, and this thesis
provides a theoretical framework to describe and reproduce it.
This theoretical framework relies on circulant matrices, and develops the concept of
Lagged Cosines matrix, which uses cosine waves with similar amplitude and frequency,
and di erent phases. The Lagged Cosines matrix is then incorporated as the deterministic
component of a newly de ned stochastic model, called the Lagged Cosines model.
This model is tted to the data from the sensor network. Based on the results of this
t, two main features are inferred from the sensor network and from the response of the
bridge to a train crossing it. First, a deep periodic structure is discovered and analysed in
the sensor network when the bridge is \at rest". Second, when a train crosses the bridge,
the Lagged Cosines model extracts what is de ned as a collective response of the bridge
which characterises the changes of strain at di erent spatial locations, which leads to a
method of anomaly detection.
Version
Open Access
Date Issued
2022-03
Date Awarded
2022-08
Copyright Statement
Creative Commons Attribution NonCommercial Licence
License URL
Advisor
Adams, Niall
Cohen, Edward
Publisher Department
Mathematics
Publisher Institution
Imperial College London
Qualification Level
Doctoral
Qualification Name
Doctor of Philosophy (PhD)