Dynamic shape estimation by modal approach using fiber Bragg grating strain sensors

Abstract

A possible approach to meet the increasing performance requirements of lightweight structures in various engineering fields is the application of smart structures. One of the functions, which are required, is the observation of the structures' shape. During operation, however, the monitoring of displacement fields is difficult. This paper discusses the displacement field estimation of a dynamically excited plate using fiber Bragg grating strain sensors. Using a modal approach, it is possible to derive a transformation matrix to estimate the displacement field using only a few strain measurements. To reduce systematic estimation errors due to residual modes, a parameter study was performed and the sensor location optimized using the condition number of the transformation matrix as an objective function. An experiment with an optimized sensor configuration including 16 fiber Bragg grating strain sensors was performed to verify the method and the simulation results..H\ZRUGV shape estimation, fiber Bragg grating (FBG), modal approach, displacement-strain relationship, sensor locations ,1752'8&7,21The observation of structural displacements in smart structures is of great interest in various application fields such as tooling machines (1) , airplane wings (2) , or high-precision-and space-reflectors (3) . Since the displacement field is difficult to be measure in a lot of applications, especially during operation, strain data can be used to estimate the displacement field. Various methods for the shape estimation can be found in literature: calibration methods (4) , the use of transfer functions (5) , least-square-fitting algorithms (6) or a modal approach (7) , which is used here. An advantage of this method is the possibility to estimate the displacement field of a structure using strain data from a few discrete positions. A disadvantage is the systematic estimation error due to the residual modes which introduce temporal aliasing. One of the topics of this study is to minimize this error using an appropriate sensor distribution.In order to achieve an improvement of the estimation quality, a parameter study shall show different relationships between designated estimation variables and the estimation quality. Using the information of the parameter study, the sensor locations will be optimized. The effectiveness of the determined sensor locations will be proven by simulations and an experiment.The strain sensing was enabled by multiplexed fiber Bragg grating strain sensors (FBG). They fit well to the mentioned applications, since they are lightweight themselves, immune to electromagnetic disturbances, easy to integrate into composite structures and enable sensing at many positions using only a single fiber.The displacement of a structure can be expressed by using an infinite number of displacement mode shapesφ and the strain by an infinite number of strain mode shapes ψ . Both can be multiplied with the corresponding weighting factors,

Fibre Optic Sensors for Structural Health Monitoring of Aircraft Composite Structures: Recent Advances and Applications

“…Several authors have used this modal-based algorithm and strain measurements obtained by means of FBG sensors for shape reconstruction. Kang et al [ 109 ] and Rapp et al [ 110 ] used measured strain data and strain-to-displacement transformations to estimate dynamic structural displacements, Rapp et al [ 111 ] estimated the displacements of a 2D structure using its mode shapes, and Kim et al investigated shape reconstruction for rotating structures [ 112 ].…”

Fiber optic sensor networks in smart structures

“…The same approach can be used to express dynamic strain fields. Since the modal coordinates q of the deformation and strain fields correspond, they provide the relationship between the strains and deformations, which can be expressed in the following equation: transformation matrix [SDT] (4,5) . As one can see, it is possible to estimate a full state vector including an arbitrary number N of deformations {w}, using a small number M of strains {ε}.…”

Displacement, Strain and Failure Estimation for Multi-Material Structure Using the Displacement-Strain Transformation Matrix

“…The displacement-strain transformation method has been actively studied since the early 2000s. At the beginning of the study, deformation predictions for one-dimensional beam shapes [14] and two-dimensional plates were conducted [15]. After that, the deformation predictions were obtained by gradually expanding its application range to rotating structures [16] and actual wind turbine blades [17].…”