Supporting Expensive Physical Models With Geometric Moment Invariants to Accelerate Sensitivity Analysis for Shape Optimisation

In this work, we proposed a computationally inexpensive Parametric Sensitivity Analysis (PSA), which, to evaluate the parameters' sensitivity, substitutes design's physical quantities by the geometric ones, such as geometric moments and their invariants. Physical quantities rely strongly on design's geometry, and the evaluation of geometric properties is computationally inexpensive; therefore, our approach utilises these quantities to aid users in making informed decisions on parametric sensitivities. The feasibility of the proposed method is tested on a ship hull parameterised with 27 parameters. The sensitives of these 27 parameters are assessed with a global variance-based PSA first with respect to wave resistance coefficient (c ), which is a crucial physical quantity for ship design, and then with respect to the second-order geometric moment invariants (M ). The parametric sensitives obtained with two quantities showed a good correlation, i.e., the four most sensitive parameters to c are also sensitive to M . Finally, two design spaces are constructed with only the sensitive parameters evaluated from the two quantities and shape optimisation is performed in both design spaces to optimise the hull shape for c . The c values of optimised shapes obtained from the two spaces showed only 2.5589% of difference. Moreover, the computational cost to perform PSA and shape optimisation with c and M is approximately 375 and 9.5 hours, respectively. These results indicate that PSA performed with moments can reasonably estimate parameters' sensitivity to the design's physics with considerably reduced computational cost.