Assessing the interplay of shape and physical parameters by nonlinear dimensionality reduction methods

The paper presents an exploratory study on the application to ship hydrodynamics of nonlinear design-space dimensionality reduction methods, assessing the interaction of shape and physical parameters. Nonlinear extensions of the principal component analysis (PCA) are applied, namely local and kernel PCA. An artificial neural network approach, specifically a deep autoencoder (DAE) method is also applied and compared to PCA-based approaches. The data set under investigation is formed by the results of 9,000 potential flow simulations coming from an extensive exploration of a 27-dimensional design space, associated to a shapeoptimization problem of the DTMB 5415 model in calm water at 18kn (Froude number, Fr = 0.25). Data include three heterogeneous distributed and suitably discretized parameters (shape modification vector, pressure distribution on the hull, and wave elevation pattern) and one lumped parameter (wave resistance coefficient), for a total of 5, 101 × 9, 000 elements. The reduceddimensionality representation of shape and physical parameters is set to provide a normalized mean squared error smaller than 5%. The standard PCA meets the requirement using 18 principal components/parameters. LPCA provides the most promising compression capability with 14 parameters required by the reduceddimensionality parametrization. Kernel PCA and DAE achieve the same error with 15 components, indicating significant nonlinear interactions in the data structure of shape and physical parameters. Although the focus of the current work is on design-space dimensionality reduction, the formulation goes beyond shape optimization and can be applied to large sets of heterogeneous physical data from simulations, experiments, and real operation measurements.