Estimation of dynamic structural displacements using fiber Bragg grating strain sensors

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Shape sensing methods: Review and experimental comparison on a wing-shaped plate (2018, methodology): “On the other hand, the accuracy of the Modal Method depends on the number of modes used.”
Wing Shape Sensing from Measured Strain (2015, methodology): “From equations (2) through (4), all the DOF in the structure can be computed using equation (5): { ( )} = ( ) ( ) = { ( )} (5)”
A quadrilateral inverse-shell element with drilling degrees of freedom for shape sensing and structural health monitoring (2016, methodology): “[16] reconstructed the response of a beam, which was subjected to dynamic excitation, by using vibration mode shapes.”
Displacement field estimation for a two-dimensional structure using fiber Bragg grating sensors (2009, methodology): “Kang et al [6] investigated the reconstruction method of the structural deformation of one-dimensional (1D) beam structures using a displacement–strain-transformation (DST) matrix and four fiber Bragg grating (FBG) sensors.”
Strain-Based Deformation Shape-Estimation Algorithm for Control and Monitoring Applications (2013, methodology): “As in the FOSS approach, it uses FBGs to obtain strain measurements from the structure to predict the deformation shape based on the following equation [22,23]:”