Geometric Moment-Dependent Global Sensitivity Analysis without Simulation Data: Application to Ship Hull Form Optimisation

In this work, we propose and test a method to expedite Global Sensitivity Analysis (GSA) in the context of shape optimisation of free-form shapes. To leverage the computational burden that is likely to occur in engineering problems, we construct a Shape-Signature-Vector (SSV) and propose to use it as a substitute for physics. SSV is composed of shapes' integral properties, in our case geometric moments and their invariants of varying order, and is used as quantity-of-interest (QoI) for prior estimation of parametric sensitivities. Opting for geometric moments is motivated by the fact that they are intrinsic properties of shapes' underlying geometry, and their evaluation is essential in many physical computations as they act as a medium for interoperability between geometry and physics. The proposed approach has been validated in the area of computer-aided ship design with regard to the capability of global- and composite-SSV to reveal parametric sensitivities of different ship hulls for the wave-making resistance coefficient (Cw), which is a critical QoI towards improving ship's efficiency and thus decreasing emissions. More importantly, the longitudinal distribution of the volume below the ship's floating waterline, which is measurable via geometric moments, has an impact on Cw. Through extensive experimentation, we show a strong correlation between the sensitive parameters obtained with respect to SSV and those based on Cw. Consequently, we can estimate parameters' sensitivity with considerably reduced computational cost compared to when sensitivity analysis is performed with respect to Cw. Finally, two design spaces are constructed with sensitive parameters evaluated from SSV and Cw, and spaces' quality and richness are analysed in terms of their capability to provide an optimised solution. (c) 2022 The Author(s). Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).