Geometric nonlinear shape sensing using the calibration matrix method

Structural Health Monitoring (SHM) is increasingly being considered for predictive maintenance of aircrafts. This study investigates the use of strain and displacement measurements obtained from a limited number of sensors as input to a calibration matrix (CM) algorithm to compute the shapes of structures undergoing geometric nonlinear (GNL) structural deformation. To evaluate CM, GNL benchmark problems from the literature were expanded with sensors at specific locations on these structures. Two problems used for GNL inverse finite element methods (iFEM) in the literature were implemented as well, for comparison. Each problem was modeled using ABAQUS and subjected to significant deformations, resulting in strain and displacement measurements from simulated sensors. A novel GNL CM variant is presented that converts virtual sensor data into accurately reconstructed strain/displacement distributions and applied loads, achieving superior accuracy for the two state-of-the-art GNL iFEM problems. The accuracy was assessed for each problem based on the number and type of sensors employed. Under noiseless conditions, the presented method achieves a force reconstruction error of 1% or less for all problems utilizing 96 strain sensors and of 2% or less for all but one problem when employing 96 displacement sensors or a combination of strain and displacement sensors. A displacement error of 0.34% or less is achieved for all benchmark problems, using just 32 sensors of either type. When subjected to noise, the accuracy is comparable or better than the iFEM results with 96 sensors of either type for all but one of the benchmark problems, and superior when using a greater number of sensors, reaching median errors of less than 1%. A median force error of 2.5% is reached with 720 strain sensors when subject to 10% noise. This level of accuracy is achieved for both isotropic and composite laminate materials, and for structures undergoing buckling deformation.