A dedicated sensing approach for structural thermoelastic displacement fields: demonstrated on a cantilever plate

Thermal deformation is a critical issue in thin-walled and plate-like structures. Accurate real-time sensing of thermoelastic displacement fields in such structures is essential for ensuring dimensional stability. However, existing shapesensing techniques are primarily designed for mechanically induced displacements and often fail when thermal loads dominate. To fill this gap, this paper proposes a dedicated sensing approach for structural thermoelastic displacement fields by cooperatively fusing prior knowledge with limited measurement data. First, starting with finite element modeling, the superposition principle of structural thermal responses is theoretically derived. Then, an estimator based on thermal mode superposition is presented to simultaneously recover the temperature, thermoelastic displacement, and thermal strain fields from limited sensor data. Finally, a cooperative measurement strategy based on hybrid modes is proposed, enabling multiple sensors to work together in field reconstruction. Simulation and experimental case studies on cantilever plates validated the underlying principles, demonstrating that the proposed estimator not only replicates the accuracy of finite element analysis but also achieves a fourfold improvement in computational efficiency. Moreover, its results show good agreement with measured data. Additionally, the paper compares the performance of different thermal mode construction methods, offering new insights with significant guiding value for engineering applications.