![]() Sort(s4) = Īll samples (25) are located at the edges of (24) evenly divided subregions: such as,. Meanwhile, the results from four times sampling are same except their orders before sorting. (sort(s4))' = Īll samples are located at the centers of 25 evenly divided subregions: such as,. S4 = QuasiMonteCarlo.sample(25,, , LatinHypercubeSample()) S3 = QuasiMonteCarlo.sample(25,, , LatinHypercubeSample()) S2 = QuasiMonteCarlo.sample(25,, , LatinHypercubeSample()) S1 = QuasiMonteCarlo.sample(25,, , … LatinHypercubeSample()) S1 = QuasiMonteCarlo.sample(25,, , LatinHypercubeSample()) It can be demonstrated in the following simplified one-dimensional case: The two packages would show same behavior if one chooses the left boundary for LatinHypercubeSampling.jl considering the above difference. This paper addresses several aspects of the analysis of uncertainty in the output of computer models arising from uncertainty in inputs (parameters). ![]() Both packages only choose samples from these edges, their behaviors are different from R package “lhs”, which draws samples not only at the edges of subregions, but also in the subregions. LatinHypercubeSampling.jl divides the region into N-1 subregions with N edges at (a, a+(b-a)/(N-1), a+(b-a)/(N-1)*2, a+(b-a)/(N-1)*3, …, b) and uses all edges for sampling. For a N-sample case from a region, QuasiMonteCarlo.jl divides the region into N subregions with N+1 edges at (a, a+(b-a)/(N), a+(b-a)/(N)*2, a+(b-a)/(N)*3, …, b), but the package ignores the very left edge during sampling. Two packages handle the boundaries of a closed region differently. 15 references, 4 figures, 9 tables.The cause was found. Other techniques for sensitivity/uncertainty analysis, e.g., kriging followed by conditional simulation, will be used also. For example, the adjoint method may be used to reduce the scope to a size that can be readily handled by a technique such as LHS. The Office of Nuclear Waste Isolation will use the technique most appropriate for an individual situation. Design and analysis of computer experiments, Latin hypercube sampling, space-filling designs, Computer models are often used in sensitivity analysis, reliability assessment, design optimization and a number of other studies which tend to require many function evaluations. This unlimited number of parameters capability can be extremely useful for finite element or finite difference codes with a large number of grid blocks. The adjoint method is recommended when there are a limited number of performance measures and an unlimited number of parameters. To use, simply do:: > import lhsmdu > k lhsmdu.sample(2, 20) Latin Hypercube Sampling with multi-dimensional uniformity This will generate a nested list with 2 variables, with 20 samples each. Of deterministic techniques, the more » direct method is preferred when there are many performance measures of interest and a moderate number of parameters. This is a package for generating latin hypercube samples with multi-dimensional uniformity. ![]() The LHS technique is easy to apply and should work well for codes with a moderate number of parameters. One approach, based on Latin Hypercube Sampling (LHS), is a statistical sampling method, whereas, the second approach is based on the deterministic evaluation of sensitivities. On the other hand, although Rosenblueth’s 2 K + 1 point-estimate method is much simpler, it is not capable of capturing the important attributes of the distribution of either input or output variables. Two different approaches to sensitivity/uncertainty analysis were used on this code. The simulations show that the Latin hypercube method is an efficient alternative to the computationally intensive Monte Carlo technique. This study focused on steady-state flow as the performance measure of interest. Design and analysis of simulation experiments. It provides a flexible, powerful and intuitive tool for the analysis of complicated processes 1 Kleijnen JPC. The model consists of three coupled equations with only eight parameters and three dependent variables. With the advantages of being economic, safe and repeatable, simulation has been widely used in many fields, such as military, medical, education and manufacturing. A computer code was used to study steady-state flow for a hypothetical borehole scenario. ![]()
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