A novel shape sensing method based on principal component analysis: formulation and validation on a composite grid structure under thermal loads

This work presents the principal component analysis-based method, a novel approach for shape sensing in complex structures. Shape sensing is the process of reconstructing a structure’s deformed shape from discrete strain measurements. This challenge has been addressed with various algorithms over the past three decades, each with its advantages and disadvantages. The principal component analysis-based method derives its structure from the modal method, a traditional approach, replacing the normal modes with bases obtained through a four-step process: (1) defining representative base loads (whatever their physical origin may be, whether mechanical, thermal or otherwise), (2) computing corresponding displacement fields via finite element analysis, (3) applying principal component analysis to these fields to derive an ordered set of new displacement bases, and (4) calculating the associated strain fields through further finite element simulations. The method’s effectiveness is demonstrated by reconstructing the shape of a composite grid-like structure under non-uniform thermal loads with limited sensor availability. Thermal deformations are particularly relevant to the aerospace community and are largely absent from the shape-sensing literature. The principal component analysis-based method outperforms the modal method by providing an accurate solution for a complex case in which the normal modes are not valid bases for reconstructing the deformed shape.