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

Engineering 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 α-manifold of admissible meshed shapes. The output space is reduced using constrained Proper Orthogonal Decomposition. By simultaneously using meta-modeling 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.