For the inverse finite element method (iFEM), an inappropriate scheme of strain senor distribution would cause severe degradation of the deformation reconstruction accuracy. The robustness of the strain–displacement transfer relationship and the accuracy of reconstruction displacement are the two key factors of reconstruction accuracy. Previous research studies have been focused on single-objective optimization for the robustness of the strain–displacement transfer relationship. However, researchers found that it was difficult to reach a mutual balance between robustness and accuracy using single-objective optimization. In order to solve this problem, a bi-objective optimal model for the scheme of sensor distribution was proposed for this paper, where multi-objective particle swarm optimization (MOPSO) was employed to optimize the robustness and the accuracy. Initially, a hollow circular beam subjected to various loads was used as a case to perform the static analysis. Next, the optimization model was established and two different schemes of strain sensor were obtained correspondingly. Finally, the proposed schemes were successfully implemented in both the simulation calculation and the experiment test. It was found that the results from the proposed optimization model in this paper proved to be a promising tool for the selection of the scheme of strain sensor distribution.
In order to monitor the variable-section wing deformation in real-time, this paper proposes a dynamic reconstruction algorithm based on the inverse finite element method and fuzzy network to sense the deformation of the variable-section beam structure. Firstly, based on Timoshenko beam theory and inverse finite element framework, a deformation reconstruction model of variable-section beam element was established. Then, considering the installation error of the fiber Bragg grating (FBG) sensor and the dynamic un-modeled error caused by the difference between the static model and dynamic model, the real-time measured strain was corrected using a solidified fuzzy network. The parameters of the fuzzy network were learned using support vector machines to enhance the generalization ability of the fuzzy network. The loading deformation experiment shows that the deformation of the variable section wing can be reconstructed with the proposed algorithm in high precision.
When the inverse finite element method (inverse FEM) is used to reconstruct the deformation field of a multi-element structure with strain measurements, strain measurement errors can lower the reconstruction accuracy of the deformation field. Furthermore, the calibration ability of a self-structuring fuzzy network (SSFN) is weak when few strain samples are used to train the SSFN. To solve this problem, a novel two-step calibration method for improving the reconstruction accuracy of the inverse FEM method is proposed in this paper. Initially, the errors derived from measured displacements and reconstructed displacements are distributed to the degrees of freedom (DOFs) of nodes. Then, the DOFs of nodes are used as knots, in order to produce non-uniform rational B-spline (NURBS) curves, such that the sample size employed to train the SSFN can be enriched. Next, the SSFN model is used to determine the relationship between the measured strain and the DOFs of the end nodes. A loading deformation experiment using a three-element structure demonstrates that the proposed algorithm can significantly improve the accuracy of reconstruction displacement.
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