Supersaturated design is essentially a fractional factorial design in which the number of potential effects is greater than the number of runs. In this article, the supersaturated design is applied to a computer exper...Supersaturated design is essentially a fractional factorial design in which the number of potential effects is greater than the number of runs. In this article, the supersaturated design is applied to a computer experiment through an example of steady current circuit model problem. A uniform mixed-level supersaturated design and the centered quadratic regression model are used. This example shows that supersaturated design and quadratic regression modeling method are very effective for screening effects and building the predictor. They are not only useful in computer experiments but also in industrial and other scientific experiments.展开更多
Latin hypercube design and uniform design are two kinds of most popular space-filling designs for computer experiments. The fact that the run size equals the number of factor levels in a Latin hypercube design makes i...Latin hypercube design and uniform design are two kinds of most popular space-filling designs for computer experiments. The fact that the run size equals the number of factor levels in a Latin hypercube design makes it difficult to be orthogonal. While for a uniform design, it usually has good space-filling properties, but does not necessarily have small or zero correlations between factors. In this paper, we construct a class of column-orthogonal and nearly column-orthogonal designs for computer experiments by rotating groups of factors of orthogonal arrays, which supplement the designs for computer experiments in terms of various run sizes and numbers of factor levels and are flexible in accommodating various combinations of factors with different numbers of levels. The resulting column-orthogonal designs not only have uniformly spaced levels for each factor but also have uncorrelated estimates of the linear effects in first order models. Further, they are 3-orthogonal if the corresponding orthogonal arrays have strength equal to or greater than three. Along with a large factor-to-run ratio, these newly constructed designs are economical and suitable for screening factors for physical experiments.展开更多
In this paper,we propose a new method,called the level-collapsing method,to construct branching Latin hypercube designs(BLHDs).The obtained design has a sliced structure in the third part,that is,the part for the shar...In this paper,we propose a new method,called the level-collapsing method,to construct branching Latin hypercube designs(BLHDs).The obtained design has a sliced structure in the third part,that is,the part for the shared factors,which is desirable for the qualitative branching factors.The construction method is easy to implement,and(near)orthogonality can be achieved in the obtained BLHDs.A simulation example is provided to illustrate the effectiveness of the new designs.展开更多
Computer experiments require space-filling designs with good low-dimensional projection properties.Strong orthogonal arrays are a type of space-filling design that provides better stratifications in low dimensions tha...Computer experiments require space-filling designs with good low-dimensional projection properties.Strong orthogonal arrays are a type of space-filling design that provides better stratifications in low dimensions than ordinary orthogonal arrays.In this paper,we address the problem of constructing strong orthogonal arrays and column-orthogonal strong orthogonal arrays of strength two plus.Existing methods typically rely on regular designs or specific nonregular designs as base orthogonal arrays,limiting the sizes of the final designs.Instead,we propose two general methods that are easy to implement and applicable to a wide range of base orthogonal arrays.These methods produce space-filling designs that can accommodate a large number of factors,provide significant flexibility in terms of run sizes,and possess appealing low-dimensional projection properties.Therefore,these designs are ideal for computer experiments.展开更多
Space-filling designs are popular for computer experiments.Therein space-filling designs with good two-dimensional projection are preferred as two-factor interactions are more likely to be important than three-or high...Space-filling designs are popular for computer experiments.Therein space-filling designs with good two-dimensional projection are preferred as two-factor interactions are more likely to be important than three-or higher-order interactions in practice.Considering two-dimensional projection,the authors propose a new class of designs called group strong orthogonal arrays.A group strong orthogonal array enjoys attractive two-dimensional space-filling property in the sense that it can be partitioned into groups,where any two columns can achieve stratifications on s^(u_(1))×s^(u_(2))grids for any positive integers u_(1),u_(2) with u_(1)+u_(2)=3,and any two columns from different groups can achieve stratifications on s^(v_(1))×s^(v_(2))grids for any positive integers v_(1),v_(2) with v_(1)+v_(2)=4.Few existing designs enjoy such a.ppealing two-dimensional stratification property in the literature.And the level numbers of the obtained designs can be s^(3)or s^(4).In addition to the attractive stratification property,the proposed designs perform very well under orthogonality and uniform projection criteria,and are flexible in run sizes,rendering them highly suitable for computer experiments.展开更多
Strong orthogonal arrays(SOAs) were recently introduced and studied as a class of spacefilling designs for computer experiments. To surely realize better space-filling properties, SOAs of strength three or higher are ...Strong orthogonal arrays(SOAs) were recently introduced and studied as a class of spacefilling designs for computer experiments. To surely realize better space-filling properties, SOAs of strength three or higher are desirable. In addition, orthogonality is also an important property for designs of computer experiments, because it guarantees that the estimates of the main effects are uncorrelated. This paper first provides a systematic study on the construction of(nearly) orthogonal strength-three SOAs with better space-filling properties. The newly proposed strength-three SOAs enjoy almost the same space-filling properties of strength-four SOAs, and can accommodate much more columns than the latter. Moreover, they are(nearly) orthogonal and flexible in run sizes. The construction methods are straightforward to implement, and their theoretical supports are well established. In addition to the theoretical results, many designs are tabulated for practical needs.展开更多
Latin hypercube designs(LHDs)are very popular in designing computer experiments.In addition,orthogonality is a desirable property for LHDs,as it allows the estimates of the main effects in linear models to be uncorrel...Latin hypercube designs(LHDs)are very popular in designing computer experiments.In addition,orthogonality is a desirable property for LHDs,as it allows the estimates of the main effects in linear models to be uncorrelated with each other,and is a stepping stone to the space-filling property for fitting Gaussian process models.Among the available methods for constructing orthogonal Latin hypercube designs(OLHDs),the rotation method is particularly attractive due to its theoretical elegance as well as its contribution to spacefilling properties in low-dimensional projections.This paper proposes a new rotation method for constructing OLHDs and nearly OLHDs with flexible run sizes that cannot be obtained by existing methods.Furthermore,the resulting OLHDs are improved in terms of the maximin distance criterion and the alias matrices and a new kind of orthogonal designs are constructed.Theoretical properties as well as construction algorithms are provided.展开更多
基金Research supported by the National Natural Science Foundation of China (10301015)the Science and Technology Innovation Fund of Nankai University, the Visiting Scholar Program at Chern Institute of Mathematicsa Hong Kong Research Grants Council Grant (RGC/HKBU 200804)
文摘Supersaturated design is essentially a fractional factorial design in which the number of potential effects is greater than the number of runs. In this article, the supersaturated design is applied to a computer experiment through an example of steady current circuit model problem. A uniform mixed-level supersaturated design and the centered quadratic regression model are used. This example shows that supersaturated design and quadratic regression modeling method are very effective for screening effects and building the predictor. They are not only useful in computer experiments but also in industrial and other scientific experiments.
基金supported by the Program for New Century Excellent Talents in Universityof China (Grant No. NCET-07-0454)National Natural Science Foundation of China (Grant No. 10971107)the Fundamental Research Funds for the Central Universities (Grant No. 10QNJJ003)
文摘Latin hypercube design and uniform design are two kinds of most popular space-filling designs for computer experiments. The fact that the run size equals the number of factor levels in a Latin hypercube design makes it difficult to be orthogonal. While for a uniform design, it usually has good space-filling properties, but does not necessarily have small or zero correlations between factors. In this paper, we construct a class of column-orthogonal and nearly column-orthogonal designs for computer experiments by rotating groups of factors of orthogonal arrays, which supplement the designs for computer experiments in terms of various run sizes and numbers of factor levels and are flexible in accommodating various combinations of factors with different numbers of levels. The resulting column-orthogonal designs not only have uniformly spaced levels for each factor but also have uncorrelated estimates of the linear effects in first order models. Further, they are 3-orthogonal if the corresponding orthogonal arrays have strength equal to or greater than three. Along with a large factor-to-run ratio, these newly constructed designs are economical and suitable for screening factors for physical experiments.
基金supported by the National Natural Science Foundation of China (11601367,11771219 and 11771220)National Ten Thousand Talents Program+1 种基金Tianjin Development Program for Innovation and EntrepreneurshipTianjin "131" Talents Program
文摘In this paper,we propose a new method,called the level-collapsing method,to construct branching Latin hypercube designs(BLHDs).The obtained design has a sliced structure in the third part,that is,the part for the shared factors,which is desirable for the qualitative branching factors.The construction method is easy to implement,and(near)orthogonality can be achieved in the obtained BLHDs.A simulation example is provided to illustrate the effectiveness of the new designs.
基金supported by the Fundamental Research Funds for the Central Universities(Grant Nos.2023JBMC010 and 2412023YQ003)National Natural Science Foundation of China(Grant Nos.12001036,12271166,11901199 and 12371259)。
文摘Computer experiments require space-filling designs with good low-dimensional projection properties.Strong orthogonal arrays are a type of space-filling design that provides better stratifications in low dimensions than ordinary orthogonal arrays.In this paper,we address the problem of constructing strong orthogonal arrays and column-orthogonal strong orthogonal arrays of strength two plus.Existing methods typically rely on regular designs or specific nonregular designs as base orthogonal arrays,limiting the sizes of the final designs.Instead,we propose two general methods that are easy to implement and applicable to a wide range of base orthogonal arrays.These methods produce space-filling designs that can accommodate a large number of factors,provide significant flexibility in terms of run sizes,and possess appealing low-dimensional projection properties.Therefore,these designs are ideal for computer experiments.
基金supported by the National Natural Science Foundation of China under Grant Nos.12301323,12261011,and 12131001the MOE Project of Key Research Institute of Humanities and Social Sciences under Grant No.22JJD110001。
文摘Space-filling designs are popular for computer experiments.Therein space-filling designs with good two-dimensional projection are preferred as two-factor interactions are more likely to be important than three-or higher-order interactions in practice.Considering two-dimensional projection,the authors propose a new class of designs called group strong orthogonal arrays.A group strong orthogonal array enjoys attractive two-dimensional space-filling property in the sense that it can be partitioned into groups,where any two columns can achieve stratifications on s^(u_(1))×s^(u_(2))grids for any positive integers u_(1),u_(2) with u_(1)+u_(2)=3,and any two columns from different groups can achieve stratifications on s^(v_(1))×s^(v_(2))grids for any positive integers v_(1),v_(2) with v_(1)+v_(2)=4.Few existing designs enjoy such a.ppealing two-dimensional stratification property in the literature.And the level numbers of the obtained designs can be s^(3)or s^(4).In addition to the attractive stratification property,the proposed designs perform very well under orthogonality and uniform projection criteria,and are flexible in run sizes,rendering them highly suitable for computer experiments.
基金supported by the National Natural Science Foundation of China under Grant Nos. 12131001and 12226343the MOE Project of Key Research Institute of Humanities and Social Sciences under Grant No.22JJD110001the National Ten Thousand Talents Program of China。
文摘Strong orthogonal arrays(SOAs) were recently introduced and studied as a class of spacefilling designs for computer experiments. To surely realize better space-filling properties, SOAs of strength three or higher are desirable. In addition, orthogonality is also an important property for designs of computer experiments, because it guarantees that the estimates of the main effects are uncorrelated. This paper first provides a systematic study on the construction of(nearly) orthogonal strength-three SOAs with better space-filling properties. The newly proposed strength-three SOAs enjoy almost the same space-filling properties of strength-four SOAs, and can accommodate much more columns than the latter. Moreover, they are(nearly) orthogonal and flexible in run sizes. The construction methods are straightforward to implement, and their theoretical supports are well established. In addition to the theoretical results, many designs are tabulated for practical needs.
基金supported by National Natural Science Foundation of China(Grant Nos.12131001 and 11871288)National Ten Thousand Talents Program and the 111 Project B20016。
文摘Latin hypercube designs(LHDs)are very popular in designing computer experiments.In addition,orthogonality is a desirable property for LHDs,as it allows the estimates of the main effects in linear models to be uncorrelated with each other,and is a stepping stone to the space-filling property for fitting Gaussian process models.Among the available methods for constructing orthogonal Latin hypercube designs(OLHDs),the rotation method is particularly attractive due to its theoretical elegance as well as its contribution to spacefilling properties in low-dimensional projections.This paper proposes a new rotation method for constructing OLHDs and nearly OLHDs with flexible run sizes that cannot be obtained by existing methods.Furthermore,the resulting OLHDs are improved in terms of the maximin distance criterion and the alias matrices and a new kind of orthogonal designs are constructed.Theoretical properties as well as construction algorithms are provided.
