Optimal Sensor Placement for Inverse Finite Element Reconstruction of Three-Dimensional Frame Deformation

Abstract

The inverse finite element method (iFEM) for the 3D framework deformation reconstruction was introduced. As the process of iFEM did not require a priori knowledge, such as the modal shape, the loading, and the elastic-inertial material information of the structure, it presented high potential in the framework deformation reconstruction. With the current research, it was observed that the key step in the deformation reconstruction of the frame structure with iFEM was the section strains computing of the beam element from the surface strain measurements. The corresponding stability was severely affected by the placement of strain sensors. Therefore, it was necessary to discover a suitable sensor placement to maintain the stability of section strains computing. For this problem, one optimal model of sensor placement was proposed in this paper. Firstly, the well-separated eigenvalues were applied as the optimization target to construct the optimal model. Following, an optimal sensor placement was obtained through the optimal placement model solution, with the particle swarm optimization (PSO) method. Finally, the effectiveness of optimal placement was verified though the accuracy comparison of iFEM deformation reconstruction of a wing-like frame subjected to various loads for different schemes of sensor placement.

Real-Time Monitoring of the Position and Orientation of a Radio Telescope Sub-Reflector with Fiber Bragg Grating Sensors

“…For the end-node loads, the section stains e1ε(xi), e4ε(xi), e5ε(xi), and e6ε(xi) are constant, while e2ε(xi) and e3ε(xi) are linear. In References [18,19], the section strains are expressed as: e1ε(xi)=a1e2ε(xi)=a2xi+a4e4ε(xi)=m1a2e6ε(xi)=a6…”

“…al, discussed the influence of the above ill-posed problem on the estimation of the beam structural deformation by Equation (7), and constructed an optimal placement model of strain sensors to maintain the stability and accuracy of the estimation of the beam structural deformation. Using the sensor placement scheme obtained from the aforementioned optimal placement model, the deformation of the beam/frame structure can be accurately and steadily reconstructed even if differences exist for strain sensor placement and strain measurement [18,19]. In this paper, the placement of strain sensors is quoted from References [18,19] (refer to Table 1).…”

“…Using the sensor placement scheme obtained from the aforementioned optimal placement model, the deformation of the beam/frame structure can be accurately and steadily reconstructed even if differences exist for strain sensor placement and strain measurement [18,19]. In this paper, the placement of strain sensors is quoted from References [18,19] (refer to Table 1). The coordinate of every sensor in Table 1 is in the coordinate system of Figure 4, which is a local coordinate system (refer to Figure 6).…”

“…On the basis of the iFEM framework and the kinematic assumptions of Timoshenko beam theory, Gherlone et al formulated a robust inverse finite beam element for the purpose of sensing three-dimensional (3D) deformation of a beam/frame structure [15,17]. In References [18,19], the optimal placement of sensors was researched by Zhao et al to maintain the stability and accuracy of deformation reconstruction using iFEM with an inverse beam element. The experimental validations showed that iFEM is able to accurately and effectively estimate the deformations of a three-dimensional frame/shell/plate, and even the composite structure undergoing static and/or dynamic damped harmonic excitations without any knowledge of material, inertial, loading, or damping structural properties [20].…”

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

“…This method can establish the model independently, regardless of the position of the sensor, but it requires more model information. In [ 14 , 15 ], an optimized sensor layout model based on eigenvalue analysis was proposed, in order to improve the robustness of the reconstruction model. In [ 16 ], Islam et al proposed a robust object tracking method based on a dynamic learning rate.…”