Shape Optimization under Stochastic Conditions by Design-space Augmented Dimensionality Reduction

Abstract

The rapidly evolving field of engineering design of functional surfaces necessitates sophisticated tools to manage the inherent complexity of high-dimensional design spaces. This review delves into the field of design-space dimensionality reduction techniques tailored for shape optimization, bridging traditional methods and cutting-edge technologies. Dissecting the spectrum of these techniques, from classical linear approaches like principal component analysis to more nuanced nonlinear methods such as autoencoders, the discussion extends to innovative physics-informed methods that integrate physical data into the dimensionality reduction process, enhancing the predictive accuracy and relevance of reduced models. By integrating these methods into optimization frameworks, it is shown how they significantly mitigate the curse of dimensionality, streamline computational processes, and refine the exploration and optimization of complex functional surfaces. The survey provides a classification of method and highlights the transformative impact of these techniques in simplifying design challenges, thereby fostering more efficient and effective engineering solutions.

Stochastic Shape Optimization via Design-Space Augmented Dimensionality Reduction and RANS Computations

“…Combining design modifications and performance improves the effectiveness of the design space dimensionality reduction for the subsequent design optimization by high-fidelity solvers (Fig. 1), has shown in [2,3].…”

“…Calm water performace are assessed by the linear potential flow solver WARP [26], whereas seakeeping performance are assessed by SMP. Details can be found in [3]. Figure 8 shows the geometry and multi-physics based variability associated with the design space.…”

“…Lately, Diez et al [12] have extended (augmented) the DR based on KLE, combining geometry modification vectors with associated physics-based vectors by an offline variable-fidelity formulation of the design-space DR problem. The design-space augmented dimensionality reduction (ADR) was applied to deterministic [1], robust [2], and reliability-based robust [3] shape optimization, but limited to low fidelity solvers.…”

“…The objective of the present work is to show how design-space ADR can lead to an efficient and accurate shape optimization procedure, by application of high-fidelity computational fluid dynamics (CFD) solvers. The current work is an extension of earlier research by the authors [1][2][3] where only low-fidelity solvers were used. This paper shows the RANS (Reynolds-averaged Navier-Stokes) based optimization of a naval destroyer, namely the DTMB 5415 model, for improved resistance in calm water and waves and seakeeping under stochastic environmental and operating conditions including variable speed, sea state, and heading.…”

Physics-Informed Feature-to-Feature Learning for Design-Space Dimensionality Reduction in Shape Optimisation

“…However, subspace containing only geometric variability may not be the most efficient for creating the surrogate model and running the optimisation. This is because the impact of geometric variability on design's physics might not be the same [15,16], therefore, it is essential, especially in the context of surrogate modelling, that during the feature extraction the information about QoI should be present so the latent space includes both geometric and functional variability. To tackle this problem, a physics-informed feature learning technique called Active Subspace Method (ASM) was proposed by Lukaczyk et al [17] and Constantine [18], which learns a lower-dimensional subspace while capturing maximum variance in QoI.…”