Identifying Key Parameters for Design Improvement in High-Dimensional Systems With Uncertainty

Abstract

Key parameters may be used to turn a bad design into a good design with comparatively little effort. The proposed method identifies key parameters in high-dimensional nonlinear systems that are subject to uncertainty. A numerical optimization algorithm seeks a solution space on which all designs are good, that is, they satisfy a specified design criterion. The solution space is box-shaped and provides target intervals for each parameter. A bad design may be turned into a good design by moving its key parameters into their target intervals. The solution space is computed so as to minimize the effort for design work: its shape is controlled by particular constraints such that it can be reached by changing only a small number of key parameters. Wide target intervals provide tolerance against uncertainty, which is naturally present in a design process, when design parameters are unknown or cannot be controlled exactly. In a simple two-dimensional example problem, the accuracy of the algorithm is demonstrated. In a high-dimensional vehicle crash design problem, an underperforming vehicle front structure is improved by identifying and appropriately changing a relevant key parameter.

Set‐based design: The state‐of‐practice and research opportunities

“…US research generally focuses on SBD methodology development, as well as general defense and maritime applications, with an eye toward defense acquisition 8 . In addition to research applying SBD to manufacturing and construction processes, we observe similar SBD research and application areas in papers originating from other countries 45,48,49 . We present these statistics, for Groups A & B, in Table 5.…”

“…From this set, we identified and collected only refereed journal articles and conference papers, reducing the set to the 64 SBD specific documents considered in the final review. We refer to this set of documents as Group A throughout the remainder of this paper 2–65 . We provide the complete listing for all Group A documents in Table 1.…”

From Prescriptive to Predictive: an Interdisciplinary Perspective on the Future of Computational Chemistry

“…Global or correlated sensitivity analysis takes the entire design space into account to assess how the variability of the output parameters is effected by the variability in each input parameter. 182 A way of dealing with parametric and measurement uncertainties is to propagate some uncertainties of the input variables through the studied system, 183 e.g., with stochastic collocation methods as in peridynamics for crack propagation. 184 Global sensitivity analysis of ordinary differential equations can also be performed with error-controlled PDEs describing the evolution of the probability density function associated with the input uncertainty.…”

“…188 Further measures in global sensitivity analysis are regression coefficients, Pearson correlation coefficients, Spearman correlation coefficients, Sobol indices, or Morris' elementary effects method for multidimensional functions as in finite element simulations. 182,189 In micro-kinetic models of chemical systems, the uncertainty in kinetic parameters refers to pre-exponentials, bond indices, 190 or energies to determine reaction rates. 191 They are all prone to carry errors from previous calculations of parameters into the newly designed model which can be measured through the concept of 'degree of rate control'.…”

A portable triaxial cell for beamline imaging of rocks under triaxial state of stress

“…Often, such multidisciplinary project teams comprise participants less familiar with the design philosophy wherein the identification of information sources and their appropriate use is critical to the success of the designed product [18]. An effective design should always be based on the key parameters that could clearly distinguish a good design from a bad one [19]. There are three key design parameters of the triaxial cell for imaging:…”