Multi-Objective Particle Swarm Optimization of Sensor Distribution Scheme with Consideration of the Accuracy and the Robustness for Deformation Reconstruction

Abstract

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.

Isogeometric iFEM Analysis of Thin Shell Structures

“…The integrations given in Equations ( 27) and ( 28) can be suitably calculated through the Gauss quadrature method, for which the area-integral of a function is defined as weighted sum of the function values evaluated at predefined Gauss points. Since the B α (α = m, b) matrices are continuous in the element domain, all Gauss points required for full integration over the mid-surface of the iKLS element can be directly used when performing the area integration in Equation (27). On the contrary, the experimental section strains, E and K, may not be available in the continuous form, as given in Equation (28).…”

“…Alternatively, the area integration in Equation ( 28) can be performed by employing full-integration points and assuming that the E i and K i values at the Gauss points have an identical average-value in the element domain. Note that, finally, if such discrete experimental values are somehow missing, then small weighting coefficients can be assigned to their associated analytical counterparts when calculating Equation (27).…”

“…Furthermore, inverse-beam element formulations were presented for shape sensing of thin/thick beams [ 2 , 22 ]. These inverse elements were numerically and experimentally verified [ 23 , 24 , 25 ] and sensor placement optimizations were proposed for beam models [ 26 , 27 ]. Lately, various iFEM formulations [ 28 , 29 , 30 ] were proposed by utilizing kinematic relations of refined zigzag theory [ 31 ] for the shape and stress sensing of multilayered composite and sandwich plates/shells.…”

Two-Step Calibration Method for Inverse Finite Element with Small Sample Features

“…This method uses a transformation filter based on the kernel correlation function filter, which improves the robustness of the model. In [ 17 ], a double objective optimization model was established, considering both accuracy and robustness in the reconstruction of beams by using the inverse finite element method. It improved the reconstruction accuracy and robustness.…”

Dynamic Deformation Reconstruction of Variable Section WING with Fiber Bragg Grating Sensors

“…Based on the theory of ZigZag and the idea of inverse finite element, Cerracchio constructed the deformation reconstruction model of plate element for composite sandwich structure [13]. Yong Zhao et al have studied the effect of sensor distribution on the reconstruction accuracy in the process of inverse finite beam element reconstruction, and realized the 3D deformational reconstruction of the wing like frame structure [14,15,16]. Xinglin Pan et al have deeply studied the effect of measurement strain error on reconstruction accuracy in the process of static deformation reconstruction of beam structure, and put forward the error correction using fuzzy network [17].…”