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Estimates of the coverage of parameter space by Latin Hypercube and Orthogonal sampling: connections between Populations of Models and Experimental Designs

Donovan, Diane; Burrage, Kevin; Burrage, Pamela; McCourt, Thomas A; Thompson, Harold Bevan; Yazici, Emine Sule
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 12/10/2015 Português
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In this paper we use counting arguments to prove that the expected percentage coverage of a $d$ dimensional parameter space of size $n$ when performing $k$ trials with either Latin Hypercube sampling or Orthogonal sampling (when $n=p^d$) is the same. We then extend these results to an experimental design setting by projecting onto a 2 dimensional subspace. In this case the coverage is equivalent to the Orthogonal sampling setting when the dimension of the parameter space is two. These results are confirmed by simulations. The ideas presented here have particular relevance when attempting to perform uncertainty quantification or when building populations of models.; Comment: 15 pages, 2 figures. arXiv admin note: text overlap with arXiv:1502.06559

On Robustness Criteria and Robust Topology Optimization with Uncertain Loads

Kocvara, Michal
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 29/07/2013 Português
Relevância na Pesquisa
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We propose a new algorithm for the solution of the robust multiple-load topology optimization problem. The algorithm can be applied to any type of problem, e.g., truss topology, variable thickness sheet or free material optimization. We assume that the given loads are uncertain and can be subject to small random perturbations. Furthermore, we define a rigorous measure of robustness of the given design with respect to these perturbations. To implement the algorithm, the users only need software to solve their standard multiple-load problem. Additionally, they have to solve a few small-dimensional eigenvalue problems. Numerical examples demonstrate the efficiency of our approach.