A shape optimization design method based on PCA geometric dimensionality reduction and Kriging inverse mapping for a blended-wing-body underwater glider

• A geometric dimensionality reduction-based optimization approach to perform to shape optimization of BWB underwater glider. • The traditional geometric parameters are sampled using the Design of Experiments (DOE) to form the shape data set. • PCA is applied to reduce the dimensionality of the shape data set. • A Kriging model is created to establish a relationship between the traditional and dimension-reduced variables. • The effectiveness and efficiency of the proposed approach is demonstrated by optimizing a blended-wing-body underwater glider. In the shape optimization of underwater gliders, conventional geometric parameterization methods usually require a large number of design variables to ensure sufficient shape representation capability, which in turn leads to excessive optimization iterations, high CFD computational cost, and low optimization efficiency. To address this “high-dimensional and high-cost” issue, this paper proposes a shape optimization design method based on principal component analysis (PCA) geometric dimensionality reduction and Kriging inverse mapping for a blended-wing-body underwater glider (BWBUG). In this method, firstly, PCA is employed to the conventional geometric parameterization variables, significantly reducing the dimensionality of the design variables while preserving the principal shape variation features. Subsequently, a Kriging inverse mapping model is constructed between the reduced-dimensional variables and the original parameterization variables, enabling reversible reconstruction from the low-dimensional feature space to the original parameter space. On this basis, a shape optimization design framework based on geometric parameterization dimensionality reduction for a BWBUG is established, which effectively reduces computational cost and significantly improves optimization efficiency. To validate the effectiveness and efficiency of the proposed method, a shape optimization case study is conducted on a BWBUG. The results show that, by reducing 12 geometric parameters to 4 principal components, 98.36% of the shape deformation information is retained, while the number of CFD evaluations during the optimization process is reduced by 64, and the lift-to-drag ratio ( L / D ) is effectively improved.