Relaxing high-dimensional constraints in the direct solution space method for early phase development

Lange, Volker; Fender, Johannes; Duddeck, Fabian

doi:10.1007/s11081-018-9381-x

Cited by 3 publications

(1 citation statement)

References 21 publications

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“…Notice that the subspace is convex, as explained in [2,11]. The solution to the problem of Equation ( 3) is computed with the interior point methods available in [16].…”

Section: Direct Methods For Solution Spacementioning

confidence: 99%

Increasing design flexibility by manually adapting the solution space for crashworthiness

Ascia,

Lange,

Duddeck

2023

J.Math.Industry

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The solution space methodology, as presented in 2013, was meant to guide developers at the very beginning of the development process of a new mechanically crashworthy car. Several attempts were already made to use this methodology at later development stages. However, they all encountered problems related to its very strict and demanding corridors, thus constricting the design parameters. To allow more flexibility, two different approaches were proposed to relax the initial strict conditions. The first introduced temporal dependencies to widen the corridors. The second locally changed the corridors to adapt to the needs of the development, introducing dependencies between components. We, on the contrary, propose a new method to increase flexibility without introducing any kind of dependencies. We manage this by computing the intervals of solution space under user-defined conditions, hence selecting a custom set of independent corridors that fits the data gathered during development; i.e.: force-deformation curves that can be measured during a drop-tower test simulation. This new methodology of the adaptive solution space allows designers to edit the corridors, in order to have more flexibility for fulfilling high-level requirements when independently designing new components.

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“…Notice that the subspace is convex, as explained in [2,11]. The solution to the problem of Equation ( 3) is computed with the interior point methods available in [16].…”

Section: Direct Methods For Solution Spacementioning

confidence: 99%

Increasing design flexibility by manually adapting the solution space for crashworthiness

Ascia,

Lange,

Duddeck

2023

J.Math.Industry

Self Cite

View full text Add to dashboard Cite

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Isovolumetric adaptations to space-filling design of experiments

2022

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A brief review of methods in design of experiments and criteria to determine space-filling properties of a set of samples is given. Subsequently, the so-called curse of dimensionality in sampling is reviewed and used as motivation for the proposal of an adaptation to the strata creation process in Latin hypercube sampling based on the idea of nested same-sized hypervolumes. The proposed approach places samples closer to design space boundaries, where in higher dimensions the majority of the design space volume is located. The same idea is introduced for Monte Carlo considering an affordable number of samples as an a-posteriori transformation. Both ideas are studied on different algorithms and compared using different distance-based space-filling criteria. The proposed new sampling approach then enables more efficient sampling for optimization especially for high-dimensional problems, i.e. for problems with a high number of design variables.

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Structural properties of superior design solutions of steel buildings associated with BRBs

2021

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Relaxing high-dimensional constraints in the direct solution space method for early phase development

Cited by 3 publications

References 21 publications

Increasing design flexibility by manually adapting the solution space for crashworthiness

Increasing design flexibility by manually adapting the solution space for crashworthiness

Isovolumetric adaptations to space-filling design of experiments

Structural properties of superior design solutions of steel buildings associated with BRBs

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