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Optimal FBG Sensor Deployment via Gaussian Quadrature Formula
for Measurement of Displacement of Laterally Loaded Piles
Le déploiement optimal des capteurs à fibres optiques, par la formule de la quadrature de Gauss,
pour la mesure du déplacement des pieux chargés latéralement
Jung Y.-H., Na S.-U., Mok Y.
Dept. of Civil Engineering, Kyung Hee University, Republic of Korea
ABSTRACT: A new approach to sensor deployment for measurement of lateral displacement of piles is introduced. To monitor a pile
loaded by lateral loads, the multiplexed Fiber-optic Bragg Grating (FBG) sensors are used. For enhanced accuracy of measurement
under budgetary limitation, optimal position of the FBG sensors inscribed along an intact optic fiber line is crucial. Herein, ideal test
conditions under which test results could be verified through theoretical solutions were created. The integration points of the Gaussian
quadrature formula were employed to determine the optimal positions to place sensors. By using differential equations on pile
displacement subjected to lateral load, the measured and calculated displacements were compared. The comparative analysis shows
that positioning sensors based on theoretical Gaussian quadrature formula reduces measurement errors. To minimize the errors in
estimating lateral displacement under general in-situ conditions, a suggestion for the FBG sensor deployment has been given.
RESUME : Une nouvelle approche de déploiement des capteurs à fibres optiques pour la mesure du déplacement latéral des pieux est
présentée. Pour surveiller un pieu chargé latéralement, les capteurs multiplexeurs à fibres optiques avec réseau de Bragg (Fiber-Optic
Bragg Grating : FBG) sont utilisés. L'emplacement optimal des capteurs FBG inscrits le long d'une ligne intacte de fibre optique est
crucial afin d’assurer une bonne précision de mesure, à un coût optimisé. Les conditions idéales d'essai dans lesquelles les résultats
peuvent être vérifiés par des solutions théoriques ont été créées. Les points d’intégration de la formule de la quadrature de Gauss ont
été utilisés pour déterminer les meilleurs emplacements des capteurs. En utilisant les équations différentielles des déplacements d’un
pieu soumis à une charge latérale, les résultats des mesures et du calcul ont été comparés. L'analyse comparative montre que
l'approche du déploiement des capteurs sur la base théorique de la formule de la quadrature de Gauss fonctionne très bien. Une
suggestion du déploiement des capteurs FBG est donnée afin de minimiser les erreurs d’estimation du déplacement latéral sous les
conditions générales
in situ.
KEYWORDS: Gaussian quadrature, Sensor placement, Lateral-loaded Pile, Measurements
1 INTRODUCTION
FBG sensors have been widely applied to structural monitoring
because optical sensors can overcome many limitations of
existing electric sensors such as electronic interference and low
durability. In addition, there is an advantage that it is possible
for one strand of optical fiber to be inscribed with many sensors
and used as a multi-point sensor. In regard to monitoring super-
structures such as railroad bridges that are frequently exposed to
electromagnetic waves, the FBG sensor is successfully used for
the long-term maintenance system (Chung et al. 2005).
To measure the performance of geotechnical structures such
as piles, FBG sensors are superior to other electric sensors
because typically the measurement for geotechnical structures
should be performed in adverse environments such as high
confinement, strong chemical corrosion, and narrow space.
Recently, there were several attempts to measure the
performance of piles. Lee, et al. (2004) have attached FBG
sensors to cast-in-place concrete piles and measured the vertical
load transfer process, thus presenting the usability of FBG
sensors in geotechnical structures. Habel and Krebber (2011)
have used fiber-optic acoustic emission sensors to measure AE
signals related to the shock waves of concrete pile heads, thus
evaluating the soundness of concrete piles. However, few are
cases that have systematically analyzed and verified the use of
FBG sensors in geotechnical structures.
Compared to the conventional point-located sensors, FBG
sensors multiplexed on a single strand of fiber has a great
advantage in its small occupancy of space for attachment and
installation. Despite such advantages, the use of FBG sensors
has not prevailed because inscribing one FBG grating on an
optic fiber is still more expensive than buying a conventional
strain gage sensor. Therefore, minimizing the number of sensors
and optimizing sensor positions are the most urgent issue for
successful deployment of FBG sensors in the industry.
Sensors can generally be placed in an area of interest either
deterministically or randomly. The choice of the deployment
scheme depends highly on the type of sensors, application and
the environment that the sensors will operate in. Without any
preferance of interest, sensors would be placed uniformly along
the pile, whereas those simple schemes do not consider any cost
effectiveness or optimazation to reduce measurement errors.
In this study, a new deployment scheme for multiplexed
FBG sensors on the single optical fiber strand is introduced. The
Gaussian quadrature formula has been employed to minimize
the error in measuring the displacement of a laterally loaded pile.
A model cantilever beam is used to simulate the pile. The
applicability of the Gaussian quadrature formula for optimizing
sensor positions has been confirmed by comparing applied and
computed displacements.
Three different strategies for placing
sensors along the aluminum bar which represents a laterally
loaded pile are developed, and accordingly eight different
schemes of the sensor placement are configured. One end of the
bar specimen is clamped, and the other is displaced by using the
calipers. The maximum displacement is calculated by
integrating the slopes and moments at the FBG sensor positions,
and compared with the actual magnitude of applied
displacement to suggest its geotechnical applicability.
