Precise and robust shape sensing considering sensor placement and measurement uncertainties

Shape sensing, which involves reconstructing the displacement field of a structure from discrete strain measurements, is widely utilized in aerospace, marine, civil engineering, and other domains. Since macroscopic deformations are evaluated based on measured local strains by limited sensors, the sensor placements play a significant role in ensuring precise and robust shape sensing. In practical applications, inevitable and indistinguishable measurement uncertainties can lead to deviations in measured strain and subsequently result in significant errors or even mistakes during reconstruction. Therefore, it is essential to determine suitable sensor placements that are insensitive to measurement deviations for robust shape sensing. This paper proposes an optimal methodology for sensor placement considering measurement uncertainty with the aim of enhancing accuracy and robustness in shape sensing. We establish a mapping relationship between sensor placement and reconstruction accuracy to develop a sensor placement scheme for precise shape sensing. Additionally, a novel technique is presented for the quantification of multiple uncertainties, such as sensor installation errors and signal noise, based on Sparse Grid Numerical Integration (SGNI). Consequently, analytical equations for reconstruction effectively considering measurement uncertainties are derived. Based on the work mentioned above, the optimization of sensor locations can be performed by considering the influences of multiple measurement uncertainties on reconstruction accuracy and robustness. The effectiveness of all proposed methods is verified through experiments, and the applicability of the proposed method to composite structures is confirmed via a deformation reconstruction simulation of a representative composite material.