Sensor Fusion for Shape Sensing: Theory and Numerical Simulation

Computing global strain distributions in complex aerospace and wind energy structures in quasi-real time is an important challenge for the aerospace and wind energy industry. Shape sensing is being considered as a potential means for obtaining global strain fields of complex structures. This is achieved through the use of inverse finite element methods (iFEM). Traditional shape sensing techniques use a variety of sensors in isolation. These isolated approaches lead to a number of drawbacks, including significant errors in the strain and/or displacement distributions that they determine. This study focuses on reducing these errors by combining data from various sensor types.In order to achieve this objective, a new iFEM approach was developed to improve how shape sensing determines a structure’s deformation from distributed sensors. The method utilizes a procedure that minimizes a quadratic error functional, based on the difference between the theoretical and the measured strains and displacements. The analytical iFEM equations are discretized for use in a numerical model, which is used to analyze simulated sensor data. The simulated data is obtained from a FEM analysis of a structure loaded in bending, torsion and shear, in addition to experiencing combined loads. As with previous inverse methods, the error functional weights were employed to manage missing measurements and Tikhonov regularization was applied to guarantee smoothness of the numerical solution.In this study, it has been shown that the new iFEM methodology can determine the structural deformations to within 1% of the FEM results for each of the load cases. In addition, the methodology is capable of achieving the same accuracy as single sensor type iFEM methods with a smaller total number of sensors. The single sensor type iFEM methods that were considered made use of only strain data or only displacement data. Finally, an experimental setup consisting of a simple cantilever plate structure was constructed in order to experimentally verify the newly developed iFEM algorithm. The experimental strain and displacement data were obtained utilizing a Rayleigh backscattering fiber optic distributed sensing system and MEMS sensors, respectively. Both of these sensor types were mounted on the structure and subjected to the load cases that were simulated in the FEM analysis