A unified framework for enhancing inverse finite element method through strain pre-extrapolation and sensor placement optimization - Li, Kelu; Xiao, Longfei; Wei, Handi; Kou, Yufeng; Shan, Meng (Mechanical systems and signal processing, 2025)
•A novel framework is developed to enhance iFEM accuracy and robustness with limited sensors.•A new strain pre-extrapolation technique, GPR-MCKF, is proposed, accounting for spatio-temporal correlation in measurements.•The FIM of extrapolated strain is derived as an objective function, linking GPR-MCKF and SPO.•SPO results mainly depend on structural geometry and are insensitive to other factors, such as loading conditions.•Numerical and experimental tests confirm the framework’s effectiveness, robustness, and general applicability. The inverse finite element method (iFEM) is a powerful tool for shape sensing, but its effectiveness is often constrained by economic and spatial constraints that prevent sensor coverage. This paper presents a unified framework to enhance iFEM, comprising two key components. The first is a novel strain pre-extrapolation method, GPR-MCKF, which incorporates both spatial and temporal correlations from measurement data. To reduce the computational demand of Gaussian process regression (GPR) when handling large datasets, maximum correntropy Kalman filtering (MCKF) is used to handle temporal correlation, based on the space–time separability of the kernel and the state-space equation of Gaussian process. The second component is a sensor placement optimization (SPO) method with general applicability, introducing an innovative objective function based on the Fisher information matrix (FIM) of the extrapolated strain. This objective function links the two components. Moreover, with constant noise levels and a fixed kernel function, this objective function depends solely on the measurement locations, meaning the results of SPO are determined exclusively by the structural geometry. This objective function, combined with the number of sensors, forms a bi-objective optimization problem, which is solved using the multi-objective Lichtenberg algorithm (MOLA). Finally, numerical and experimental examples validate the framework’s effectiveness, robustness, and general applicability in shape sensing with limited sensors, demonstrating its potential for practical applications to complex and large-scale structures.