From regional sensitivity to intra-sensitivity for parametric analysis of free-form shapes: Application to ship design. (August 2021) - Khan, Shahroz; Kaklis, Panagiotis
Abstract: Robust Parametric Sensitivity Analysis (PSA) is a prerequisite for efficient shape optimisation via parametric modelling. A major challenge PSA has to handle is related to the fact that a parameter can be sensitive in certain local areas of the design space but become insensitive in others. Therefore, setting an applicable space for this analysis becomes a difficult task. In this paper, we introduce the concept of intra-sensitivity to identify parameters whose perturbation has a major impact on the sensitivity index of the remaining parameters. For this purpose, we firstly appeal to Active Subspace Method (ASM) and develop an ASM-based regional sensitivity analysis, which investigates parametric sensitivity in local regions of the design space and aids conducing to parameters' intra-sensitivity. This regional analysis is applied in conjunction with a Dynamic Propagation Sampling approach, for tackling the computational complexity arising when high-dimensional problems are concerned. Once sensitive and intra-sensitive parameters are identified, then free-form features, correlated to these parameters, are evaluated using a feature saliency map built with the aid of Hausdorff distance. The so resulting methodology has been validated in the area of computer-aided ship design using two parametric modellers: the first one is a Procedural Deformation (PD) modeller which is based on T-splines and involves 24 parameters while the second one is based on Free-Form Deformation (FFD) and involves 104 parameters. The corresponding design spaces have been generated using a parent hull close to the KCS container ship and are analysed against hull's volume of displacement and total resistance. Finally, the convergence performance of the various components of this approach is compared with state-of-the-art techniques. Highlights: Sensitivity and intra-sensitivity indices are evaluated within active subspace. Sensitivity ranking of sensitive parameters is stable compare to insensitive ones. Highly sensitive parameters follow a monotonic behaviour as their range shrinks. Regional behaviour of sensitivity is visualised with variational sensitivity plots. Change in the range of an intra-sensitive parameter highly affects the sensitivity of the remaining parameters.