Column-orthogonal designs with multi-dimensional stratifications

The orthogonal Latin hypercube design and its relaxation, and column-orthogonal design, are two kinds of orthogonal designs for computer experiments. However, they usually do not achieve maximum stratifications in multi-dimensional margins. In this paper, we propose some methods to construct column-orthogonal designs with multi-dimensional stratifications by rotating symmetric and asymmetric orthogonal arrays. The newly constructed column-orthogonal designs ensure that the estimates of all linear effects are uncorrelated with each other and even uncorrelated with the estimates of all second-order effects(quadratic effects and bilinear effects) when the rotated orthogonal arrays have strength larger than two. Besides orthogonality, the resulting designs also preserve better space-filling properties than those constructed by using the existing methods. In addition, we provide a method to construct a new class of orthogonal Latin hypercube designs with multi-dimensional stratifications by rotating regular factorial designs. Some newly constructed orthogonal Latin hypercube designs are tabulated for practical use.     

基于正交表的均匀Latin Hypercube设计及其构造

Orthogonal array-based uniform Latin hypercube design(uniform OALHD) is a class of orthogonal array-based Latin hypercube designs to have the best uniformity. In this paper, we provide a less computational algorithm to construct uniform OALHD in 2-dimensional space from Bundschuh and Zhu(1993). And some uniform OALHDs are con- structed by using our method.     

投影均匀分片拉丁超立方体设计

空间填充设计是有效的计算机试验设计,比如均匀设计、最大最小距离拉丁超立方体设计等.虽然这些设计在整个试验空间中有较好的均匀性,但其低维投影均匀性可能并不理想.对于因子是定量的计算机试验,已有文献构造了诸如最大投影设计、均匀投影设计等相适应的设计;而对于同时含有定性因子和定量因子的计算机试验,尚未有投影均匀设计的相关文献.文章提出了综合投影均匀准则,利用门限接受算法构造了投影均匀的分片拉丁超立方体设计.在新构造设计中,整体设计与每一片设计均具有良好的投影均匀性.模拟结果显示,与随机分片拉丁超立方体设计相比,利用新构造设计进行试验而拟合的高斯过程模型具有更小的均方根预测误差.     

A Note on the Construction of Orthogonal Latin Hypercube Designs

Latin hypercube designs have been found very useful for designing computer experiments. In recent years, several methods of constructing orthogonal Latin hypercube designs have been proposed in the literature. In this article, we report some more results on the construction of orthogonal Latin hypercubes which result in several new designs.     

低偏差OALHD的构造

本文给出了利用均匀设计和正交表构造低偏差OALH设计的方法，该方法构造的设计既有优良的均匀性具有正交设计的均衡性，一个更重要的优点是可以构造较大样本容量的设计点集，本文同时给出了某些参数的均匀设计表，这些设计优于现有的均匀设计，具有实用价值。     

Construction of sliced (nearly) orthogonal Latin hypercube designs

Sliced Latin hypercube designs are very useful for running a computer model in batches, ensembles of multiple computer models, computer experiments with qualitative and quantitative factors, cross-validation and data pooling. However, the presence of highly correlated columns makes the data analysis intractable. In this paper, a construction method for sliced (nearly) orthogonal Latin hypercube designs is developed. The resulting designs have flexible sizes and most are new. With the orthogonality or near orthogonality being guaranteed, the space-filling property of the resulting designs is also improved. Examples are provided for illustrating the proposed method.     

一类正交空间填充设计的构造

空间填充设计在计算机试验中应用十分广泛,当拟合回归模型时,正交的空间填充设计保证了因子效应估计的独立性.基于广义正交设计,文章给出了构造二阶正交拉丁超立方体设计和列正交设计的方法,新构造的设计不仅满足任意两列之间相互正交,还能保证每一列与任一列元素平方组成的列以及任两列元素相乘组成的列都正交.当某些正交的空间填充设计不存在时,具有较小相关系数的近似正交设计可作为替代设计使用.设计构造的灵活性为计算机试验在实践中的广泛应用提供了必要的支持.     

Flexible sliced designs for computer experiments

Sliced Latin hypercube designs are popularly adopted for computer experiments with qualitative factors. Previous constructions require the sizes of different slices to be identical. Here we construct sliced designs with flexible sizes of slices. Besides achieving desirable one-dimensional uniformity, flexible sliced designs (FSDs) constructed in this paper accommodate arbitrary sizes for different slices and cover ordinary sliced Latin hypercube designs as special cases. The sampling properties of FSDs are derived and a central limit theorem is established. It shows that any linear combination of the sample means from different models on slices follows an asymptotic normal distribution. Some simulations compare FSDs with other sliced designs in collective evaluations of multiple computer models.     

正交平衡区组设计统计分析模型参数估计的矩阵表达

正交平衡区组设计(或者广义正交表)是一种类似于正交拉丁方(或者正交表)的新设计,但试验次数大幅减少.定义了一种基于正交相遇平衡区组设计(或者广义正交表)的统计分析模型,根据这个模型,给出了参数的最小二乘估计的矩阵形式.     

Optimization of a large-scale water reservoir network by stochastic dynamic programming with efficient state space discretization

A numerical solution to a 30-dimensional water reservoir network optimization problem, based on stochastic dynamic programming, is presented. In such problems the amount of water to be released from each reservoir is chosen to minimize a nonlinear cost (or maximize benefit) function while satisfying proper constraints. Experimental results show how dimensionality issues, given by the large number of basins and realistic modeling of the stochastic inflows, can be mitigated by employing neural approximators for the value functions, and efficient discretizations of the state space, such as orthogonal arrays, Latin hypercube designs and low-discrepancy sequences.     

正交平衡区组设计统计分析模型参数估计的分布特征研究

正交平衡区组设计(或者广义正交表)是一种类似于正交拉丁方(或者正交表)的新设计,但试验次数大幅减少.通过对正交平衡区组设计统计分析模型参数估计的分布特征进行了深入研究.研究发现,在试验数据正态性的情况下,各种参数估计也服从正态分布,并且各种参数的最小二乘估计都是无偏的,得到了各种参数估计的方差和独立性性质.     

正交平衡区组设计统计模型中的方差分析

正交平衡区组设计(或广义正交表)的数据分析类似于正交拉丁方(或正交表)的数据分析.利用类似于正交表数据分析中的投影矩阵的正交分解技术,研究正交平衡区组设计的统计分析模型,给出了方差分析中的二次型以及各因子的二次型的分布性质,从而给出正交平衡区组设计统计模型中的方差分析方法.     

基于计算机试验设计的遗传算法参数配置

遗传算法作为一种随机化优化搜索方法,已经在很多领域得到了成功应用,但其存在控制参数多且配置困难的问题.本文采用一类最新试验设计方法-计算机试验设计,对遗传算法的参数配置进行优化.结果表明,基于正交拉丁超立方设计的参数配置,其算法的计算精度和速度表现最佳.模拟结果进一步讨论了不同试验设计方案在遗传算法中的差别.     

Generalized latin matrix and construction of orthogonal arrays

In this paper, generalized Latin matrix and orthogonal generalized Latin matrices are proposed. By using the property of orthogonal array, some methods for checking orthogonal generalized Latin matrices are presented. We study the relation between orthogonal array and orthogonal generalized Latin matrices and obtain some useful theorems for their construction. An example is given to illustrate applications of main theorems and a new class of mixed orthogonal arrays are obtained.     

正交平衡区组设计统计分析模型的参数估计

正交平衡区组设计(或者广义正交表)的数据分析类似于正交拉丁方(或者正交表)的数据分析,但试验次数大幅减少.引入了相遇平衡区组设计矩阵象的概念,定义了一种基于正交相遇平衡区组设计(或者广义正交表)的统计分析模型,根据这个模型,推导得到了参数的最小二乘估计.     

Centered -discrepancy of random sampling and Latin hypercube design, and construction of uniform designs

In this paper properties and construction of designs under a centered version of the -discrepancy are analyzed. The theoretic expectation and variance of this discrepancy are derived for random designs and Latin hypercube designs. The expectation and variance of Latin hypercube designs are significantly lower than that of random designs. While in dimension one the unique uniform design is also a set of equidistant points, low-discrepancy designs in higher dimension have to be generated by explicit optimization. Optimization is performed using the threshold accepting heuristic which produces low discrepancy designs compared to theoretic expectation and variance.

     

Metamodeling: Radial basis functions,versus polynomials

For many years, metamodels have been used in simulation to provide approximations to the input–output functions provided by a simulation model. In this paper, metamodels based on radial basis functions are applied to approximate test functions known from the literature. These tests were conducted to gain insights into the behavior of these metamodels, their ease of computation and their ability to capture the shape and minima of the test functions. These metamodels are compared against polynomial metamodels by using surface and contour graphs of the error function (difference between metamodel and the given function) and by evaluating the numerical stability of the required computations. Full factorial and Latin hypercube designs were used to fit the metamodels. Graphical and statistical methods were used to analyze the test results. Factorial designs were generally more successful for fitting the test functions as compared to Latin hypercube designs. Radial basis function metamodels using factorial and Latin hypercube designs provided better fit than polynomial metamodels using full factorial designs.     

A Family of Asymmetrical Orthogonal Arrays with Run Sizes 4p^2

Nowadays orthogonal arrays play important roles in statistics, computer science, coding theory and cryptography. The usual difference matrices are essential for the construction of many mixed orthogonal arrays. But there are also many orthogonal arrays, especially mixed-level or asymmetrical which can not be obtained by the usual difference matrices. In order to construct these asymmetrical orthogonal arrays, a class of special matrices, so-called generalized difference matrices, were discovered by Zhang（1989, 1990, 1993） by the orthogonal decompositions of projective matrices. In this article, an interesting equivalent relationship between the orthogonal arrays and the generalized difference matrices is presented. As an application, a family of orthogonal arrays of run sizes 4p2, such as L36（6^13^42^10）, are constructed.     

Two-dimensional minimax Latin hypercube designs

We investigate minimax Latin hypercube designs in two dimensions for several distance measures. For the ?^∞-distance we are able to construct minimax Latin hypercube designs of n points, and to determine the minimal covering radius, for all n. For the ?¹-distance we have a lower bound for the covering radius, and a construction of minimax Latin hypercube designs for (infinitely) many values of n. We conjecture that the obtained lower bound is attained, except for a few small (known) values of n. For the ?²-distance we have generated minimax solutions up to n=27 by an exhaustive search method. The latter Latin hypercube designs are included in the website www.spacefillingdesigns.nl.     

一类试验次数为4p2的非对称正交表的构造

Nowadays orthogonal arrays play important roles in statistics,computer science, coding theory and cryptography.The usual difference matrices are essential for the con- struction of many mixed orthogonal arrays.But there are also many orthogonal arrays, especially mixed-level or asymmetrical which can not be obtained by the usual difference matrices.In order to construct these asymmetrical orthogonal arrays,a class of special matrices,so-called generalized difference matrices,were discovered by Zhang(1989,1990, 1993) by the orthogonal decompositions of projective matrices.In this article,an interesting equivalent relationship between the orthogonal arrays and the generalized difference matri- ces is presented.As an application,a family of orthogonal arrays of run sizes 4p~2,such as L_(36)(6~13~42~(10)),are constructed.