Latin hypercube designs for selecting experimental designs are highlighted. A second design type called a bridge design is also evaluated, which further integrates the disparate design types. This paper aims at providing a short overview of the research in latin hypercube design of experiments with few hypotheses to explain its extensive use. Because of the use of lhd, historical design experiments can be inherited in later i terations. Constructing nearly orthogonal latin hypercubes for any.
Spacefilling designs can be used to specify the points so that as much of the design space is sampled as. Introduction in this paper, we deal with the topic of estimation of statistics of a function gx. The aim of this paper is to present the construction of the optimal design for computer simulated experiments cse based on three different classes of latin hypercube design lhd, random latin hypercube design rlhd, symmetric latin hypercube design slhd, and orthogonal arraybased latin hypercube design oalhd, respectively. Sanchez adepartment of industrial engineering and management science, northwestern university, evanston, il 60208 bdepartment of operations research, naval postgraduate school.
Many kinds of latin hypercube designs with good spacefilling properties have been proposed for designing the initial computer experiments. This in contrast to periodic designs, for which the modulooperator insures. Things you wanted to know about the latin hypercube design. Formulation of the optimal latin hypercube design of.
Optimizing latin hypercube design for sequential sampling. In the example cases of this paper, 28 responses were estimated from 39 input. The choice of location of the evaluation points is important in response surface generation, especially when the evaluations are expensive. This example shows how to improve the performance of an engine cooling fan through a design for six sigma approach using define, measure, analyze, improve, and control dmaic. An algorithm for fast optimal latin hypercube design of experiments article in international journal for numerical methods in engineering 822.
The variables found to be active from the experiment. Latin hypercube sampling, including cascading latin hypercubes, selecting from the class of all latin hypercubes of size n the one with some additional optimal property, orthogonal arrays generalize latin hypercubes to designs with uniform. Lucas, and matthew carlyle,united states naval postgraduate school we present a new method for constructing nearly orthogonal latin hypercubes that greatly expands their availability to experimenters. In this paper, optimal latinhypercube designs minimizing imse or maximizing entropy are considered. The discussion starts with the early developments in optimization of the point selection and goes all the way to the pitfalls of the indiscriminate use of latin hypercube designs.
Extension of sample size in latin hypercube sampling with. Its mission is to contribute to the development and use of statistical methods in the physical, chemical, and engineering sciences as well as information sciences and technology. An example for lhs design with two input factors and four intervals. Even so, our recent case study was typical in referencing the latin hypercube designofexperiments method. We introduce a new class of designs, called marginally coupled designs, for computer experiments with both qualitative and quantitative variables. Design for sequential followup experiments in computer.
Hybrid spacefilling designs, generated as latin hypercubes augmented with i optimal points, are compared to designs of each contributing component. This paper provides a tutorial on latin hypercube design of experiments, highlighting potential reasons of its widespread use. For given n, the structure of the lattice will, however, not always lead to a latin hypercube design with a su cient number of points. The basic idea is to take into account the irregularity in the design construction so that the design can still maintain the onedimensional balance. Comparing and generating latin hypercube designs in kriging. We propose an approach to constructing nested latin hypercube designs.
Figure 3a illustrates the case of a latin hypercube design with d3 dimensions and p15 points. Therefore, solving this problem requires an optimization technique to search the design space. The design points for quantitative factors forms a latin hypercube design. In this work, latin hypercube design lhd is utilized to generate saturated design experiments. Technometrics is copublished by the asq and the american statistical association asa. Spacefilling latin hypercube designs for computer experiments. These designs are obtained by a quantile transformation of the onedimensional. Audzeeglais uniform latin hypercube design of experiments. Adaptive response surface method using inherited latin. The procedure requires minimal computational effort with results. The method that i am going to use is the latin hypercube, but i do not not what the sample size should be for a valid experiment. We prove that when used for integration, the sampling scheme with oabased latin hypercubes offers a substantial improvement over latin hypercube sampling. Sliced full factorialbased latin hypercube designs as a. For example, orthogonal arrays organize the design matrix x in p.
Things you wanted to know about the latin hypercube design and. Competitive comparison of optimal designs of experiments for. An nrun slhd is a special type of lhd that can be partitioned into t slices blocks, each of which is also an lhd containing. For example, orthogonal arrays organize the design. The method is based on the following physical analogy. Construction of latin hypercube designs with nested and. In this paper, a new type of experimental design called block latin hypercube design blhd has been proposed to locate the sampling experimental points for variable fidelity metamodeling. Space filling designs, which satisfy a uniformity property, are widely used in computer experiments. Latin hypercube samples, response surface designs for quantitative variables package doe. For given n, the structure of the lattice will, however, not always lead to a latin hypercube design with a sufficient number of points. Pdf an algorithm for fast optimal latin hypercube design. Introduction to design of experiments and anova youtube. Download citation a tutorial on latin hypercube design of experiments the. That happens because latin hypercube samples are noncollapsing.
The proposed design maintains an economic run size with attractive spacefilling properties. However, the task of obtaining an optimal latin hypercube design is di. In order to construct a latin hypercube design of p n points from a seed design of s n points, the. However, its generation is nontrivial, time consuming and is but for the simplest problems infeasible to carry out by enumeration. Some of the variables have 2 and others have 3 levels. In the present paper, the performance of nonuniform experimental designs, which locate more points in a neighborhood of the boundary of the design space, is investigated. Bridge designs are the re sult of a latin hypercube undergoing. These designs turn out to be well spread over the design region without replicated coordinate values, often symmetric, and nearly optimal among all latinhypercube designs. However, little work based on latin hypercubes has focused on the. Making design exploration software speak the language of engineers and not mathematicians has been a focus of development since the industrys inception. A tutorial on latin hypercube design of experiments wiley online.
An alternative criterion was introduced by audze, eglais 1977 and is based on the analogy of minimizing forces between charged. Abstractsequential experiments composed of initial experiments and followup experiments are widely adopted for economical computer emulations. Pdf formulation of the optimal latin hypercube design of. A tutorial on latin hypercube design of experiments. Latin hypercubes provide more suitable designs for computer experiments and numerical integration than do general latin hypercubes. Pdf exploratory optimal latin hypercube designs for. The optimal latin hypercube design augments the latin hypercube design by requiring that the sample points be distributed as uniformly as possible through out the design space. The main difference is that lattices are infinite sets of points, which may collapse, and, hence, to construct a finite latin hypercube design a proper subset of noncollapsing lattice points should be chosen. When the points are released from an initial state, they move. This paper presents the translational propagation algorithm, a new method for obtaining optimal or near optimal latin hypercube designs lhds without using formal optimization. Keywords computer experiment nested latin hypercube design sliced latin hypercube design structural vectormatrix 1 introduction in many engineering and scienti. Viana 1 university of florida, gainesville, fl 32611, usa gerhard venter 2 stellenbosch university, matieland, stellenbosch 7602, south africa. Classical comparative experiments two groups of observations, independant or not, the natural extension to the case of k means to be compared oneway anova, various ways of blocking randomized blocks, latin squares and derived, the factorial in particular.
As the problem is discrete, it is ideally suited to the use of. Select a latin hypercube sample lhs of n points in x. Sliced full factorialbased latin hypercube designs as a framework for a batch sequential design algorithm weitao duan a, bruce e. Bridging the gap between spacefilling and optimal designs. Nested latin hypercube designs biometrika oxford academic. In particular, we consider the arcsine distribution and the generalized latin hypercube designs derived from this transfor. Pdf design for computer experiments with qualitative and. Formulation of the audzeeglais uniform latin hypercube. This video will give the audience a high level overview of different statistical design of experiments and how to analyze the data. Probability density function for any inputoutput variable. Optimal latinhypercube designs for computer experiments.
Constructing nearly orthogonal latin hypercubes for any nonsaturated runvariable combination alejandro s. Optimizing latin hypercube design for sequential sampling of computer experiments article in engineering optimization 418. Design of experiment is used here to test paper airplane flight distance. An algorithm for fast optimal latin hypercube design of. This matlab function returns an nbyp matrix, x, containing a latin hypercube sample of n values on each of p variables. A nested latin hypercube design with two layers is defined to be a special latin hypercube design that contains a smaller latin hypercube design as a subset. The purpose of this example is to show that each column factor is assigned each level only once, and each column is a different permutation of the levels. An algorithm for fast optimal latin hypercube design of experiments. A tutorial on latin hypercube design of experiments researchgate. Computer experiments, latin hypercube, mean square prediction. However, its generation is nontrivial, time consuming and is but. Such designs are useful for conducting multiple computer experiments with different levels of accuracy. Generalized latin hypercube design for computer experiments.
Factor settings and design diagnostics results appear similar to those in figure 21. Doptimal design from candidate set using row exchanges. Formulation of the optimal latin hypercube design of experiments. Initially screening experiments are used to reduce the number of. One important area where computer simulation is used a lot is engineering. For example, if p 120 and n 5 then 480 design variables are used. As a result, arsm only requires a limited number of design experiments even for high dimensional design problems.
In addition, for each level of any qualitative factor of a. A latin hypercube design, which maximizes pl in the class of all lhd, is called a maximin latin hypercube design mlhd. For computer experiments with both continuous and categorical inputs, qian 2012proposedgeneratingasliced latin hypercube design slhd for the p continuous factors. Given that latin hypercube designs can create samples that poorly cover. How to determine the sample size of a latin hypercube.
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