Research on Sensor Layout Strategy Based on Inverse Finite Element Deformation Reconstruction Using an Enhanced NSGA-III Algorithm

Strain sensor placement strongly influences the accuracy and cost of deformation reconstruction with the inverse finite element method (iFEM). This study develops a common sensor layout for several loading regimes by coupling the four-node inverse shell element with a Lichtenberg-inspired local search embedded in the Non-dominated Sorting Genetic Algorithm III (LA-NSGA-III). At a prescribed sensor count, the layout is optimized by simultaneously minimizing reconstruction residuals for multiple training loads. The method is assessed using DTLZ benchmarks and a plate example under equal objective-evaluation budgets, with separate controls for the multi-load formulation and the local search operator. Across 20 paired plate runs with 23 sensor sites, the proposed search reduces the mean joint training residual by 18.65% relative to NSGA-III, with mean displacement errors of 0.73% and 0.77% for the two training loads. Additional pressure, torsional and off-center force cases, a withheld combined load, strain noise, and sensor loss are used to assess a fixed layout under changing conditions. A cantilever plate test demonstrates strain-based displacement reconstruction, with laser peak displacement measurements used to calibrate the FE reference model. The method supports the offline design of a single sensor layout for iFEM reconstruction under multiple anticipated loading conditions, reducing the need to reposition sensors when the load changes.