Towards simultaneous reduction of both input and output spaces for interactive simulation-based structural design

Abstract

International audienceEngineering design problems generally involve a high-dimensional input space of design variables yielding an output space by means of costly high-fidelity evaluations. In order to decrease the overall cost, reduced-order models for the output space such as Proper Orthogonal Decomposition (POD) and Proper Generalized Decomposition (PGD) are an active area of research. However, little research has been conducted into alleviating the problems associated with a high-dimensional input space. In addition to higher dimensionality being an impediment to efficient design by itself, complex shapes involve a high number of explicit/implicit constraints restricting the design space. Geometric parameterization methods in traditional CAD present difficulties in expressing these constraints leading to a high failure rate and the generation of inadmissible shapes. In this paper, we propose a simultaneous meta-modeling protocol for both input and output spaces. We perform a reparametrization of the input space using constrained shape interpolation by introducing the concept of an alpha-manifold of admissible meshed shapes. The output space is reduced using constrained Proper Orthogonal Decomposition. By simultaneously using metamodeling for both spaces, we facilitate interactive design space exploration for the purpose of design. The proposed approach is applied to the industrial problem of designing a car engine intake port

Identification of material properties using indentation test and shape manifold learning approach

“…This, then, is an additional argument in favor of solely using the imprint shape in place of the indentation curve. In the present work, we propose a novel material parameter identification protocol based only on the imprint shape of the indentation test using Proper Orthogonal Decomposition [33,34] and manifold learning [35][36][37]. Following [38,39], originally applied to the numerical assessment of spring back for the deep drawing process, we build a "shape space" [40] and we apply the concept of shape manifold to describe all the imprint shapes admissible for a postulated constitutive law.…”

A manifold learning-based reduced order model for springback shape characterization and optimization in sheet metal forming

“…In the field of metal forming, [29] presented an approach for displacement field approximation using the Proper Orthogonal Decomposition (POD) combined with kriging interpolation of projection coefficients. The authors have presented shape space meta-models for a variety of industrial problems [30,31,13] ending finally in the α-manifold [14]. Around the same time, [32,33] developed similar ideas of "slow manifolds" for the reduction of the output space of a problem in elastodynamics.…”

“…In order to numerically evaluate the springback and to be able to characterize complex shapes, we need a universal and case-independent technique to find the smallest number of parameters needed to fully describe the final shape obtained regardless of complexity, and easily compare it with the desired geometry. The first effort was made by the authors in [12] using their previously introduced "shape manifold" concept [13,14] for the simple NUMISHEET 93 benchmark problem of 2-D draw bending. Here, the concept of an "admissible shape" for a forming process was introduced for the first time to distinguish beween realizable/attainable post-springback shapes and idealized shapes for a given drawing process, and the notion of interpolation between admissible shapes was introduced.…”

Orthogonal decomposition as a design tool: With application to a mixing impeller

“…In the past ROMs have been used to predict limited geometry changes of designs that could be defined by a single variable (Hay et al 2010, McCorkle andBryden 2011) or an equation to describe a curve (Suram, McCorkle, Bryden 2008, Raghavan et al 2013), but the geometries in this research were too complicated to be defined by either method. Zonal models have been used in concert with reduced order models that improved the accuracy of results for cases of shape optimization (Iuliano and Quagliarella 2013).…”