Sliced Latin Hypercube Designs Research Articles

Construction of orthogonal general sliced Latin hypercube designs

Construction of orthogonal general sliced Latin hypercube designs

Orthogonal designs with branching and nested factors

Computer experiments with branching and nested factors are a common class of computer experiments, but it is challenging to construct designs for this type of experiments. In this paper, we define a special type of design called branching orthogonal Latin hypercube design (BOLHD). Such a design has an appealing structure, that is, no matter at each level of a branching factor or the level‐combination of branching factors, the corresponding design points of nested factors form an orthogonal Latin hypercube design (OLHD). This structure makes it a good choice for designing computer experiments with branching and nested factors. We propose several deterministic construction methods when branching factors have the same number of levels. Based on sliced Latin hypercube designs (SLHDs), the proposed methods are easy to operate. Some construction results are tabulated for practical use.

Sequential approximate optimization on projectile disturbances of the moving tank based on BP neural network

For the firing accuracy problem of the moving tank with different speed and different road level, the modelling and optimization method of the projectile disturbances of the moving tank under the general driving conditions were studied. A high-dimensional multi-objective optimization method for the projectile disturbances of the moving tank considering the different driving conditions was proposed based on the sequential approximate optimization method. Therein, a projectile disturbance multi-disciplinary simulation model of the moving tank considering multiple nonlinear factors was built and the sliced Latin hypercube design method was introduced to apply the experimental design. On the basis, the BP neural network surrogate model of the projectile disturbances at muzzle-exit of the moving tank under the general driving conditions was established. With the genetic algorithm and the potential optimal criterion, the sample points were updated to improve the accuracy of the surrogate model during the optimization. The optimization results show that the projectile disturbances at muzzle-exit of the moving tank under the general driving conditions were reduced effectively, and the comprehensive firing accuracy of the moving tank was improved. The research can provide a reference for realizing the reasonable match between firing accuracy and mobility of the tank.

Dark Quest. I. Fast and Accurate Emulation of Halo Clustering Statistics and Its Application to Galaxy Clustering

Abstract We perform an ensemble of N-body simulations with 20483 particles for 101 flat wCDM cosmological models sampled based on a maximin distance sliced Latin hypercube design. By using the halo catalogs extracted at multiple redshifts in the range of z = [0,1.48], we develop Dark Emulator, which enables fast and accurate computations of the halo mass function, halo–matter cross-correlation, and halo autocorrelation as a function of halo masses, redshift, separations, and cosmological models based on principal component analysis and Gaussian process regression for the large-dimensional input and output data vector. We assess the performance of the emulator using a validation set of N-body simulations that are not used in training the emulator. We show that, for typical halos hosting CMASS galaxies in the Sloan Digital Sky Survey, the emulator predicts the halo–matter cross-correlation, relevant for galaxy–galaxy weak lensing, with an accuracy better than 2% and the halo autocorrelation, relevant for galaxy clustering correlation, with an accuracy better than 4%. We give several demonstrations of the emulator. It can be used to study properties of halo mass density profiles such as the concentration–mass relation and splashback radius for different cosmologies. The emulator outputs can be combined with an analytical prescription of halo–galaxy connection, such as the halo occupation distribution at the equation level, instead of using the mock catalogs to make accurate predictions of galaxy clustering statistics, such as galaxy–galaxy weak lensing and the projected correlation function for any model within the wCDM cosmologies, in a few CPU seconds.

Optimal Sliced Latin Hypercube Designs with Slices of Arbitrary Run Sizes

Sliced Latin hypercube designs (SLHDs) are widely used in computer experiments with both quantitative and qualitative factors and in batches. Optimal SLHDs achieve better space-filling property on the whole experimental region. However, most existing methods for constructing optimal SLHDs have restriction on the run sizes. In this paper, we propose a new method for constructing SLHDs with arbitrary run sizes, and a new combined space-filling measurement describing the space-filling property for both the whole design and its slices. Furthermore, we develop general algorithms to search for the optimal SLHD with arbitrary run sizes under the proposed measurement. Examples are presented to illustrate that effectiveness of the proposed methods.

Flexible sliced Latin hypercube designs with slices of different sizes

Sliced Latin hypercube designs (SLHDs) are widely used in various computer experiments. Literatures concerning the construction of SLHDs are all about constructing SLHDs with slices of the same size. However, in some cases, e.g. when an experiment with multiple computer models having different complexities or a sequential experiment with varying costs in different periods is considered, SLHDs with slices of different sizes are preferable. In this paper, we propose a new class of SLHD, named the flexible SLHD, in which the whole design is a Latin hypercube design (LHD), and each slice is also an LHD when its levels being properly collapsed, the difference lies in that its slices may have different run sizes. Several methods for constructing such designs are developed. Theoretical results on the constructed designs are derived, and discussion on the slice sizes of the constructed flexible SLHDs is provided. Furthermore, an optimization algorithm is developed to improve the space-filling property of the constructed SLHDs. The newly proposed flexible SLHD is also a special nested LHD (Qian in Biometrika 96:957–970, 2009), each of its slice can be viewed as a small LHD nested in the whole design.

A flexible construction for sliced Latin hypercube designs

Sliced Latin hypercube design is useful for computer experiments in batches or with quantitative factors. However, some constructions require the run size of each slice to be same. In this paper, we propose a method to construct a flexible sliced Latin hypercube design (FSLHD) with unequal run size for each slice. The whole design and each slice of FSLHD can achieve projective uniformity in one dimension. The FSLHD method is illustrated by some examples. The simulation indicates that, compared with some other sampling methods, the FSLHD method performs well.

Sliced Latin hypercube designs with both branching and nested factors

One special kind of sliced Latin hypercube designs (SLHDs) for computer experiments with branching and nested factors is proposed here, where not only the whole design is an SLHD, but all its slices are also SLHDs. In addition, the SLHD in the first layer has a flexible number of slices, and the slice numbers of the SLHDs in the second layer can be flexible (either the same or different). The construction method is easy to implement, and the resulting designs are orthogonal under some mild conditions. Based on the centered L2-discrepancy, uniform SLHDs with branching and nested factors are further constructed.

Sliced Latin Hypercube Designs for Computer Experiments With Unequal Batch Sizes

Latin hypercube designs are frequently used in estimating the mean output value of computer simulations given random environmental factors. Sliced Latin hypercube designs are designs that can be partitioned into a number of batches so that both the whole design and the batches achieve optimal univariate uniformity. Such designs are useful for computer simulations that are carried out in batches, come from multiple resources, or have categorical variables. All existing sliced Latin hypercube designs have equal batch sizes. In this paper, we propose a new type of sliced Latin hypercube design that has unequal batch sizes and show their advantages theoretically and numerically.

Controlling Correlations in Sliced Latin Hypercube Designs

Controlling Correlations in Sliced Latin Hypercube Designs

Construction of Latin hypercube designs with nested and sliced structures

Recently, the construction of nested or sliced Latin hypercube designs (LHDs) has received notable interest for planning computer experiments with special combinational structures. In this paper, we propose an approach to constructing nested and/or sliced LHDs by using small LHDs and structural vectors/matrices. This method is easy to implement, and can generate nested and sliced LHDs through a unified algorithm. Moreover, an algorithm for improving the space-filling properties of the resulting designs is developed, and under some control the orthogonality of the constructed designs are attainable. Some examples are provided for illustrating the proposed algorithms.

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.

Construction of (nearly) orthogonal sliced Latin hypercube designs

Sliced Latin hypercube designs have found a wide range of applications. Such a design is a special Latin hypercube design that can be partitioned into slices which are still LHDs when the levels of each slices are collapsed properly. In this paper we propose a method for constructing sliced Latin hypercube designs with second-order orthogonality. The resulting designs are further augmented to be nearly orthogonal sliced Latin hypercube designs which have much more columns. Also, two methods of generating nearly orthogonal sliced Latin hypercube designs are proposed. The methods are convenient, efficient and capable of accommodating any number of slices.

Computer Experiments With Both Qualitative and Quantitative Variables

Computer experiments have received a great deal of attention in many fields of science and technology. Most literature assumes that all the input variables are quantitative. However, researchers often encounter computer experiments involving both qualitative and quantitative variables (BQQV). In this article, a new interface on design and analysis for computer experiments with BQQV is proposed. The new designs are one kind of sliced Latin hypercube designs with points clustered in the design region and possess good uniformity for each slice. For computer experiments with BQQV, such designs help to measure the similarities among responses of different level-combinations in the qualitative variables. An adaptive analysis strategy intended for the proposed designs is developed. The proposed strategy allows us to automatically extract information from useful auxiliary responses to increase the precision of prediction for the target response. The interface between the proposed design and the analysis strategy is demonstrated to be effective via simulation and a real-life example from the food engineering literature. Supplementary materials for this article are available online.

Uniform sliced Latin hypercube designs

Sliced Latin hypercube designs (SLHDs) achieve maximum stratification in each dimension, but neither the full designs nor their slices can guarantee a good uniformity over the experimental region. Although the uniformity of the full SLHD and that of its slices are related, there is no one‐to‐one correspondence between them. In this paper, we propose a new uniformity measure for SLHDs by combining the two kinds of uniformity. Based on such a combined uniformity measure, the obtained uniform SLHDs have the design points evenly spread over the experimental region not only for the whole designs but also for their slices. Numerical simulation shows the effectiveness of the proposed uniform SLHDs for computer experiments with both quantitative and qualitative factors. Copyright © 2016 John Wiley & Sons, Ltd.

A central limit theorem for nested or sliced Latin hypercube designs

A central limit theorem for nested or sliced Latin hypercube designs

Bi-directional Sliced Latin Hypercube Designs

Bi-directional Sliced Latin Hypercube Designs

Optimal Sliced Latin Hypercube Designs

Sliced Latin hypercube designs (SLHDs) have important applications in designing computer experiments with continuous and categorical factors. However, a randomly generated SLHD can be poor in terms of space-filling, and based on the existing construction method that generates the SLHD column by column using sliced permutation matrices, it is also difficult to search for the optimal SLHD. In this article, we develop a new construction approach that first generates the small Latin hypercube design in each slice and then arranges them together to form the SLHD. The new approach is intuitive and can be easily adapted to generate orthogonal SLHDs and orthogonal array-based SLHDs. More importantly, it enables us to develop general algorithms that can search for the optimal SLHD efficiently.

Construction of second-order orthogonal sliced Latin hypercube designs

Sliced Latin hypercube designs are useful for computer experiments with qualitative and quantitative factors, model calibration, cross validation, multi-level function estimation, stochastic optimization and data pooling. Orthogonality and second-order orthogonality are crucial in identifying important inputs. Besides orthogonality, good space-filling properties are also necessary for Latin hypercube designs. In this paper, a construction method for second-order orthogonal sliced Latin hypercube designs is proposed. The constructed designs are further optimized to achieve better space-filling properties. Furthermore, the method is extended to construct nearly orthogonal sliced Latin hypercube designs. The numbers of slices and columns as well as the levels of the resulting designs are more flexible than those obtained by existing methods.

Resolvable orthogonal array-based uniform sliced Latin hypercube designs

Sliced Latin hypercube designs, introduced by Qian (2012), are widely used for computer experiments with qualitative and quantitative factors, multiple experiments, cross-validation and stochastic optimization. In this paper, we propose a new class of sliced Latin hypercube design, called the resolvable orthogonal array-based uniform sliced Latin hypercube design. Such designs are constructed via both symmetric and asymmetric resolvable orthogonal arrays, and measured by the centered L2 discrepancy criterion. When the construction is based on a resolvable orthogonal array with strength w+1, the resulting design not only possesses stratification in any w-dimensional projection for each slice, but also achieves stratification in any (w+1)-dimensional projection for the whole design. Furthermore, the uniformity of the resulting design is also highly improved with respect to the centered L2 discrepancy criterion.