To enable multi-query analyses, such as optimisations of large-scale crashworthiness problems, a numerically efficient model is crucial for the development process. Therefore, data-driven Model Order Reduction (MOR) aims at generating low-fidelity models that approximate the solution while strongly reducing the computational cost. MOR methods for crashworthiness became only available in recent years; a detailed and comparative assessment of their potential is still lacking. Hence, this work evaluates the advantages and drawbacks of intrusive and non-intrusive projection based MOR methods in the framework of non-linear structural transient analysis. Both schemes rely on the collection of full-order training simulations and a subsequent subspace construction via Singular Value Decomposition. The intrusive MOR is based on a Galerkin projection and a consecutive hyper-reduction step. In this work, its inter-and extrapolation abilities are compared to the non-intrusive technique, which combines the subspace approach with machine learning methods. Moreover, an optimisation analysis incorporating the MOR methods is proposed and discussed for a crashworthiness example.

Multidisciplinary design optimization has great potential to support the turbomachinery development process by improving designs at reduced time and cost. As part of the industrial compressor design process, we seek for a rotor blade geometry that minimizes stresses without impairing the aerodynamic performance. However, the presence of structural mechanics, aerodynamics, and their interdisciplinary coupling poses challenges concerning computational effort and organizational integration. In order to reduce both computation times and the required exchange between disciplinary design teams, we propose an inter- instead of multidisciplinary design optimization approach tailored to the studied optimization problem. This involves a distinction between main and side discipline. The main discipline, structural mechanics, is computed by accurate high-fidelity finite element models. The side discipline, aerodynamics, is represented by efficient low-fidelity models, using Kriging and proper-orthogonal decomposition to approximate constraints and the gas load field as coupling variable. The proposed approach is shown to yield a valid blade design with reasonable computational effort for training the aerodynamic low-fidelity models and significantly reduced optimization times compared to a high-fidelity multidisciplinary design optimization. Especially for expensive side disciplines like aerodynamics, the multi-fidelity interdisciplinary design optimization has the potential to consider the effects of all involved disciplines at little additional cost and organizational complexity, while keeping the focus on the main discipline.

Multi-fidelity optimization schemes enriching expensive high-fidelity functions with cheap-to-evaluate low-fidelity functions have gained popularity in recent years. In the present work, an optimization scheme based on a hierarchical kriging is proposed for large-scale and highly non-linear crashworthiness problems. After comparison to other multi-fidelity techniques an infill criterion called variable-fidelity expected improvement is applied and evaluated. This is complemented by two innovative techniques, a new approach regarding initial sampling and a novel way to generate the low-fidelity model for crash problems are suggested. For the former, a modified Latin hypercube sampling, pushing samples more towards design space boundaries, increases the quality of sampling selection. For the latter, a projection-based non-intrusive model order reduction technique accelerates and simplifies the low-fidelity model evaluation. The proposed techniques are investigated with two application problems from the field of automotive crashworthiness—a size optimization problem for lateral impact and a shape optimization problem for frontal impact. The use of a multi-fidelity scheme compared to baseline single-fidelity optimization saves computational effort while keeping an acceptable level of accuracy. Both suggested modifications, independently and especially combined, increase computational performance and result quality in the presented examples.

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