How to obtain an effective design is a major concern of scientific research. This topic always involves high-dimensional inputs with limited resources. The foldover is a quick and useful technique in construction of f...How to obtain an effective design is a major concern of scientific research. This topic always involves high-dimensional inputs with limited resources. The foldover is a quick and useful technique in construction of fractional designs, which typically releases aliased factors or interactions.This paper takes the wrap-around L_2-discrepancy as the optimality measure to assess the optimal three-level combined designs. New and efficient analytical expressions and lower bounds of the wraparound L_2-discrepancy for three-level combined designs are obtained. The new lower bound is useful and sharper than the existing lower bound. Using the new analytical expression and lower bound as the benchmarks, the authors may implement an effective algorithm for constructing optimal three-level combined designs.展开更多
Configuration design is an essential, creative and decision-making step m parallel manipulator design process, in which modeling and assembly are iterative and trivial. Combined approach with automatic parametric mode...Configuration design is an essential, creative and decision-making step m parallel manipulator design process, in which modeling and assembly are iterative and trivial. Combined approach with automatic parametric modeling and automatic assembly is proposed for parallel manipulator configuration design. The design process and key techniques, such as configuration design, configuration verification, poses calculation of all parts in parallel manipulator, virtual assembly and etc., are discussed and demonstrated by an example. A software package is developed for parallel manipulator configuration design based on the proposed method with Visual C＋＋ and UG/OPEN on Unigraphics.展开更多
By means of the quadratic regression combination design process, the regression equations of nugget diameter and tensile shear load of spot welded joint were established. Effects of welding parameters on the nugget di...By means of the quadratic regression combination design process, the regression equations of nugget diameter and tensile shear load of spot welded joint were established. Effects of welding parameters on the nugget diameter and the tensile shear load were investigated. The results show that effect of welding current on nugget diameter is the most evident. And higher welding current will result in bigger nugget diameter. Besides, interaction effect of electrode force and welding current on tensile shear load is the most evident compared with others. The optimum welding parameters corresponding to the maximum of tensile shear load have been obtained by programming using Matlab software, which is 4, 7 kN electrode force, 28 kA welding current and 4 cycle welding time. Under the condition of the optimum welding parameters, the joint having no visible defects can be obtained, nugget diameter and tensile shear load being 6. 8 mm and 3 256 N, respectively.展开更多
A direct digital design method （DDDM） of worm-gear drive is proposed. It is directly based on the simulation of manufacturing process and completely different from the conventional modeling method. The loaded tooth ...A direct digital design method （DDDM） of worm-gear drive is proposed. It is directly based on the simulation of manufacturing process and completely different from the conventional modeling method. The loaded tooth contact analysis （LTCA） method is analyzed, in which the advanced surface to surface searching technique is included. The influence of misalignment errors and contact deformations on contact zone and transmission error （TE） is discussed. Combined modification approach on worm tooth surface is presented. By means of DDDM and LTCA, it is very conven- ient to verify the effect of worm-gear drive＇s modification approach. The analysis results show that, the modification in profile direction reduces the sensitivity of worm-gear drive to misalignment errors and the modification in longitudinal direction decreases the TE. Thus the optimization design of worm-gear drive can be achieved prior to the actual manufacturing process.展开更多
A method of designing an E-plane power combiner composed of two quarter-arc bent rectangular waveguides is proposed for sub-THz and THz waves. The quarter-arc bent-waveguide power combiner has a simple geometry which ...A method of designing an E-plane power combiner composed of two quarter-arc bent rectangular waveguides is proposed for sub-THz and THz waves. The quarter-arc bent-waveguide power combiner has a simple geometry which is easy to design and fabricate. By HFSS codes, the physical mechanism and performance of the power combiner are analyzed, and the relationship between the output characteristics and the structure/operating parameters is given. Simulation results show that our power combiner is suitable for the combining of two equalpower and reversed-phase signals, the bandwidth of the combiner is wide and can be adjusted by the radius of the quarter-arc, and the isolation performance of the combiner can be improved by adding thin film resistive septa at the junction of two quarter-arc bent waveguides. Meanwhile, an approximate method based on the analytic geometrical analysis is given to design this power combiner for different frequency bands.展开更多
[Objective] This study aimed to investigate the combined effects of sowing date, plant density, nitrogenous fertilizer, phosphorus fertilizer and potassium fertilizer on quality parameters of high grade hybrid rapesee...[Objective] This study aimed to investigate the combined effects of sowing date, plant density, nitrogenous fertilizer, phosphorus fertilizer and potassium fertilizer on quality parameters of high grade hybrid rapeseed. [Method] By using Youyan 599 and Sanbei 98 as experimental materials, quadratic orthogonal rotation combination with five factors was designed for this study. [Result] Erucic acid content was nega- tively correlated with sowing date and nitrogen fertilizer, positively correlated with plant density. Glucosinolate content was negatively correlated with sowing date, positively correlated with potash fertilizer amount. Oil content was negatively correlated with sowing date and nitrogen fertilizer amount, positively correlated with plant density and potash fertilizer amount. Protein content was positively correlated with sowing date and nitrogen fertilizer amount, negatively correlated with plant density and potash fer- tilizer amount. Oleic acid content was negatively correlated with phosphate fertilizer amount, positively correlated with nitrogen fertilizer amount. Palmitic acid was nega- tively correlated with potash fertilizer amount, positively correlated with sowing date, plant density, nitrogen fertilizer amount and phosphate fertilizer amount in Youyan 599, but negatively correlated with sowing date, plant density, nitrogen fertilizer amount and phosphate fertilizer amount in Sanbei 98. Stearic acid content was posi- tively correlated with sowing date, plant density, nitrogen fertilizer amount and phos- phate fertilizer amount. Linoleic acid was positively correlated with density and nitroge- nous fertilizer, but negatively correlated with potash fertilizer amount. Linolenic acid was positively correlated with nitrogen fertilizer amount and potash fertilizer amount. Eicosenoic acid was negatively correlated with sowing date. There were positive cor- relations and negative correlations among cultivation conditions and quality parame- ters, and the positive correlations and negative correlations could counteract each other. Expression of quality parameters for each treatment was the combined effect. Among the 50 pairs of simple correlations of five cultivation factors and ten quality parameters, 26 pairs were consistent between two varieties, 24 pairs of simple corre- lation were not. Sowing date, plant density, nitrogen fertilizer amount and phosphate fertilizer amount showed significant influence on erucic acid of two varieties, but small effect on palmitic acid. [Conclusion] The combined effect of the five cultivation factors could not fundamentally improve the quality traits of high grade hybrid rapeseed.展开更多
Background:Blood stasis syndrome is one of the major syndromes in the development of chronic conditions in traditional Chinese medicine.Blood stasis syndrome is closely related to microcirculation dysfunction and thro...Background:Blood stasis syndrome is one of the major syndromes in the development of chronic conditions in traditional Chinese medicine.Blood stasis syndrome is closely related to microcirculation dysfunction and thrombosis.Trigonaceae,as a representative traditional Chinese medicine for promoting blood circulation and removing blood stasis,there are many studies on its anticoagulant,antiplatelet aggregation and antithrombotic effects.Methods:Optimization of sparganin compounds,comprising sparganin A,sparganin B,and sparganin C for the characterization of drug pair effects against blood stasis syndrome was carried out.Ternary quadratic regression orthogonal combination design was carried out in a mouse model of blood stasis syndrome.The concentrations of thromboxane B2,plasminogen activator inhibitor 1,fibrinogen,and endothelin 1 were evaluated by enzyme linked immunosorbent assay.Thymus,hepatic,and spleen indices were also assessed.The outcomes of the evaluations aided in identifying optimum parameter values for the most favorable precipitation against blood stasis syndrome.Subsequently,Cytoscape 3.7.1 was used for network pharmacology to predict the key targets of sparganins and disease.Results:After sparganin A,sparganin B,and sparganin C treatment,hepatic had a downward trend,while spleen indices and thymus had an upward trend.Compared with the model group,thromboxane B2,endothelin 1,plasminogen activator inhibitor 1,and fibrinogen were decreased(P<0.05).The blood stasis syndrome model regression equation was extremely significant,and the correlation coefficient of R was 0.939,indicating that sparganin A,sparganin B and sparganin C were positively correlated at all levels.According to the dosage of these three factors and test results,the equation was fitted and the maximum values of the three sparganin in the corresponding dose range were obtained as follows:A=0.2982 mg/10g,B=0.1438 mg/10g,C=0.0417 mg/10g.Thus,the optimum parameters were found to be 0.298:0.144:0.042 for synergistic drug combinations of sparganin compounds sparganin A,sparganin B,and sparganin C in blood stasis syndrome.The possible key targets of sparganins included matrix metalloproteinase 9,plasminogen,proto-oncogene tyrosine-protein kinase src,and akt serine/threonine kinase 1 in blood stasis syndrome.Conclusion:Our study for the first time found two novel cyclic peptide compounds sparganin B and sparganin C have an anti-blood stasis effect,and speculated sparganins key targets included matrix metalloproteinase 9,plasminogen,proto-oncogene tyrosine-protein kinase src,and akt serine/threonine kinase 1 in blood stasis syndrome.展开更多
Understanding the structure-property relationships in polycyclic conjugated hydrocarbons(PCHs)is crucial in controlling their electronic properties and developing new optically functional materials.Aromaticity is a fu...Understanding the structure-property relationships in polycyclic conjugated hydrocarbons(PCHs)is crucial in controlling their electronic properties and developing new optically functional materials.Aromaticity is a fundamentally important and intriguing property of numerous organic chemical structures and has stimulated a myriad of experimental and theoretical investigations.Exploiting aromaticity rules for the rational design of optoelectronic materials with the desired photophysical characteristics is a challenging yet fascinating task.Herein we present an in-depth computational and spectroscopic study on the structure-property relationships of dinaphthopentalenes(DNPs).Results highlight that the different fusion patterns between 4nπand 4n+2πunits endow these PCHs with the tunable aromaticity in the ground state/excited state,which leads to the diverse electronic structures and consequently the distinctive excited state photophysics.Accordingly,we propose a combined aromaticity design strategy for rationally modulating and tailoring electronic and optical properties of PCH skeletons.These outcomes not only present a full picture of the excited state dynamics of the DNP system and afford a new class of efficient singlet fission-active materials but also provide some basic guidelines for exploiting aromaticity rules to design and develop new optical function materials.展开更多
Effects of Mg^2＋, NTPs and Taq DNA polymerase in pear SSR-PCR system were analyzed by quadratic regressive orthogonal rotational combinational design. Results showed： absolute IOD （Integrated OD of each band） valu...Effects of Mg^2＋, NTPs and Taq DNA polymerase in pear SSR-PCR system were analyzed by quadratic regressive orthogonal rotational combinational design. Results showed： absolute IOD （Integrated OD of each band） value of target band reduced with concentration rising of Mg^2＋ and Taq DNA polymerase, but heightened with concentration rising of dNTPs. The decay rate of absolute IOD value increased progressively with rising Mg^2＋ concentration, decreased gradually with rising Taq DNA polymerase concentration; the rising speed would be slower than the dNTPs increase. Absolute IOD value would reduce with concentration rising of dNTPs at a low level of Mg^2＋ concentration. Conversely it would rise with the increase of dNTPs while high Mg^2＋ concentration. Absolute IOD value would generally rise with concentration rising of Taq DNA polymerase while low Mg^2＋ concentration. On the contrary it would reduce with concentration rising of Taq DNA polymerase while high Mg^2＋ concentration.展开更多
Abstract The objective of this paper is to study the issue of employing the uniformity criterion measured by the wrap-around L2-discrepancy to assess the optimal foldover plans for three-level designs.For three-level ...Abstract The objective of this paper is to study the issue of employing the uniformity criterion measured by the wrap-around L2-discrepancy to assess the optimal foldover plans for three-level designs.For three-level fractional factorials as the original designs,the general foldover plan and combined design under a foldover plan are defined,some theoretical properties of the defined foldover plans are obtained,a tight lower bound of the wrap-around L2-discrepancy of combined designs under a general foldover plan is also obtained,which can be used as a benchmark for searching optimal foldover plans.For illustration of the usage of our theoretical results,a catalog of optimal foldover plans for uniform initial designs with s three-level factors is tabulated,where 2≤ s ≤11.展开更多
The foldover is a quick and useful technique in construction of fractional factorial designs, which typically releases aliased factors or interactions. The issue of employing the uniformity criterion measured by the c...The foldover is a quick and useful technique in construction of fractional factorial designs, which typically releases aliased factors or interactions. The issue of employing the uniformity criterion measured by the centered L2-discrepancy to assess the optimal foldover plans was studied for four-level design. A new analytical expression and a new lower bound of the centered L2-discrepancy for fourlevel combined design under a general foldover plan are respectively obtained. A necessary condition for the existence of an optimal foldover plan meeting this lower bound was described. An algorithm for searching the optimal four-level foldover plans is also developed. Illustrative examples are provided, where numerical studies lend further support to our theoretical results. These results may help to provide some powerful and efficient Mgorithms for searching the optimal four-level foldover plans.展开更多
基金supported by the National Natural Science Foundation of China under Grant Nos.11271147,11471135,11471136the UIC Grant R201409+1 种基金the Zhuhai Premier Discipline Grantthe Self-Determined Research Funds of CCNU from the Colleges Basic Research and Operation of MOE under Grant Nos.CCNU14A05041,CCNU16A02012
文摘How to obtain an effective design is a major concern of scientific research. This topic always involves high-dimensional inputs with limited resources. The foldover is a quick and useful technique in construction of fractional designs, which typically releases aliased factors or interactions.This paper takes the wrap-around L_2-discrepancy as the optimality measure to assess the optimal three-level combined designs. New and efficient analytical expressions and lower bounds of the wraparound L_2-discrepancy for three-level combined designs are obtained. The new lower bound is useful and sharper than the existing lower bound. Using the new analytical expression and lower bound as the benchmarks, the authors may implement an effective algorithm for constructing optimal three-level combined designs.
文摘Configuration design is an essential, creative and decision-making step m parallel manipulator design process, in which modeling and assembly are iterative and trivial. Combined approach with automatic parametric modeling and automatic assembly is proposed for parallel manipulator configuration design. The design process and key techniques, such as configuration design, configuration verification, poses calculation of all parts in parallel manipulator, virtual assembly and etc., are discussed and demonstrated by an example. A software package is developed for parallel manipulator configuration design based on the proposed method with Visual C＋＋ and UG/OPEN on Unigraphics.
文摘By means of the quadratic regression combination design process, the regression equations of nugget diameter and tensile shear load of spot welded joint were established. Effects of welding parameters on the nugget diameter and the tensile shear load were investigated. The results show that effect of welding current on nugget diameter is the most evident. And higher welding current will result in bigger nugget diameter. Besides, interaction effect of electrode force and welding current on tensile shear load is the most evident compared with others. The optimum welding parameters corresponding to the maximum of tensile shear load have been obtained by programming using Matlab software, which is 4, 7 kN electrode force, 28 kA welding current and 4 cycle welding time. Under the condition of the optimum welding parameters, the joint having no visible defects can be obtained, nugget diameter and tensile shear load being 6. 8 mm and 3 256 N, respectively.
基金This project is supported by National Natural Science Foundation of China (No.E50575234).
文摘A direct digital design method （DDDM） of worm-gear drive is proposed. It is directly based on the simulation of manufacturing process and completely different from the conventional modeling method. The loaded tooth contact analysis （LTCA） method is analyzed, in which the advanced surface to surface searching technique is included. The influence of misalignment errors and contact deformations on contact zone and transmission error （TE） is discussed. Combined modification approach on worm tooth surface is presented. By means of DDDM and LTCA, it is very conven- ient to verify the effect of worm-gear drive＇s modification approach. The analysis results show that, the modification in profile direction reduces the sensitivity of worm-gear drive to misalignment errors and the modification in longitudinal direction decreases the TE. Thus the optimization design of worm-gear drive can be achieved prior to the actual manufacturing process.
基金Supported by the National Natural Science Foundation of China under Grant No 11075032the Fundamental Research Funds for the Central Universities under Grant No ZYGX2014J033
文摘A method of designing an E-plane power combiner composed of two quarter-arc bent rectangular waveguides is proposed for sub-THz and THz waves. The quarter-arc bent-waveguide power combiner has a simple geometry which is easy to design and fabricate. By HFSS codes, the physical mechanism and performance of the power combiner are analyzed, and the relationship between the output characteristics and the structure/operating parameters is given. Simulation results show that our power combiner is suitable for the combining of two equalpower and reversed-phase signals, the bandwidth of the combiner is wide and can be adjusted by the radius of the quarter-arc, and the isolation performance of the combiner can be improved by adding thin film resistive septa at the junction of two quarter-arc bent waveguides. Meanwhile, an approximate method based on the analytic geometrical analysis is given to design this power combiner for different frequency bands.
基金Supported by Earmarked Fund for Modern Rapeseed Research System of China(nycytx-00563)High-oil Hybrid Brassica napus Rapeseed Cultivation Technology Research Program of Guizhou Academy of Agricultural Sciences [ZX (2007)015]+2 种基金New High-yield Rapeseed Cultivar Yoyan 599 Cultivation and Promotion Program of Agriculture department of Guizhou Province [(2009)007]Hybrid Rapeseed Culitivar Youyan 599 Promotion Test Program of Guizhou Academy of Agricultural Sciences[(2009)030]New High-oil Rapeseed Cultivar Sanbei 98 Cultivation and Promotion Program of Agriculture Department of Guizhou Province [(2010)3087]~~
文摘[Objective] This study aimed to investigate the combined effects of sowing date, plant density, nitrogenous fertilizer, phosphorus fertilizer and potassium fertilizer on quality parameters of high grade hybrid rapeseed. [Method] By using Youyan 599 and Sanbei 98 as experimental materials, quadratic orthogonal rotation combination with five factors was designed for this study. [Result] Erucic acid content was nega- tively correlated with sowing date and nitrogen fertilizer, positively correlated with plant density. Glucosinolate content was negatively correlated with sowing date, positively correlated with potash fertilizer amount. Oil content was negatively correlated with sowing date and nitrogen fertilizer amount, positively correlated with plant density and potash fertilizer amount. Protein content was positively correlated with sowing date and nitrogen fertilizer amount, negatively correlated with plant density and potash fer- tilizer amount. Oleic acid content was negatively correlated with phosphate fertilizer amount, positively correlated with nitrogen fertilizer amount. Palmitic acid was nega- tively correlated with potash fertilizer amount, positively correlated with sowing date, plant density, nitrogen fertilizer amount and phosphate fertilizer amount in Youyan 599, but negatively correlated with sowing date, plant density, nitrogen fertilizer amount and phosphate fertilizer amount in Sanbei 98. Stearic acid content was posi- tively correlated with sowing date, plant density, nitrogen fertilizer amount and phos- phate fertilizer amount. Linoleic acid was positively correlated with density and nitroge- nous fertilizer, but negatively correlated with potash fertilizer amount. Linolenic acid was positively correlated with nitrogen fertilizer amount and potash fertilizer amount. Eicosenoic acid was negatively correlated with sowing date. There were positive cor- relations and negative correlations among cultivation conditions and quality parame- ters, and the positive correlations and negative correlations could counteract each other. Expression of quality parameters for each treatment was the combined effect. Among the 50 pairs of simple correlations of five cultivation factors and ten quality parameters, 26 pairs were consistent between two varieties, 24 pairs of simple corre- lation were not. Sowing date, plant density, nitrogen fertilizer amount and phosphate fertilizer amount showed significant influence on erucic acid of two varieties, but small effect on palmitic acid. [Conclusion] The combined effect of the five cultivation factors could not fundamentally improve the quality traits of high grade hybrid rapeseed.
基金This work was supported by the National Natural Science Foundation of China(No.81773884,81473413,81274060)the National Science and Technology Major Project(No.2017ZX09301077)+1 种基金Guangzhou Science and Technology Project(No.201803010115)Technology Funds were obtained from the Key Unit of Chinese Medicine Digitalization Quality Evaluation of State Administration of Traditional Chinese Medicine.
文摘Background:Blood stasis syndrome is one of the major syndromes in the development of chronic conditions in traditional Chinese medicine.Blood stasis syndrome is closely related to microcirculation dysfunction and thrombosis.Trigonaceae,as a representative traditional Chinese medicine for promoting blood circulation and removing blood stasis,there are many studies on its anticoagulant,antiplatelet aggregation and antithrombotic effects.Methods:Optimization of sparganin compounds,comprising sparganin A,sparganin B,and sparganin C for the characterization of drug pair effects against blood stasis syndrome was carried out.Ternary quadratic regression orthogonal combination design was carried out in a mouse model of blood stasis syndrome.The concentrations of thromboxane B2,plasminogen activator inhibitor 1,fibrinogen,and endothelin 1 were evaluated by enzyme linked immunosorbent assay.Thymus,hepatic,and spleen indices were also assessed.The outcomes of the evaluations aided in identifying optimum parameter values for the most favorable precipitation against blood stasis syndrome.Subsequently,Cytoscape 3.7.1 was used for network pharmacology to predict the key targets of sparganins and disease.Results:After sparganin A,sparganin B,and sparganin C treatment,hepatic had a downward trend,while spleen indices and thymus had an upward trend.Compared with the model group,thromboxane B2,endothelin 1,plasminogen activator inhibitor 1,and fibrinogen were decreased(P<0.05).The blood stasis syndrome model regression equation was extremely significant,and the correlation coefficient of R was 0.939,indicating that sparganin A,sparganin B and sparganin C were positively correlated at all levels.According to the dosage of these three factors and test results,the equation was fitted and the maximum values of the three sparganin in the corresponding dose range were obtained as follows:A=0.2982 mg/10g,B=0.1438 mg/10g,C=0.0417 mg/10g.Thus,the optimum parameters were found to be 0.298:0.144:0.042 for synergistic drug combinations of sparganin compounds sparganin A,sparganin B,and sparganin C in blood stasis syndrome.The possible key targets of sparganins included matrix metalloproteinase 9,plasminogen,proto-oncogene tyrosine-protein kinase src,and akt serine/threonine kinase 1 in blood stasis syndrome.Conclusion:Our study for the first time found two novel cyclic peptide compounds sparganin B and sparganin C have an anti-blood stasis effect,and speculated sparganins key targets included matrix metalloproteinase 9,plasminogen,proto-oncogene tyrosine-protein kinase src,and akt serine/threonine kinase 1 in blood stasis syndrome.
基金supported by the National Natural Science Foundation of China(grant nos.22005210,21833005,and 22231009).
文摘Understanding the structure-property relationships in polycyclic conjugated hydrocarbons(PCHs)is crucial in controlling their electronic properties and developing new optically functional materials.Aromaticity is a fundamentally important and intriguing property of numerous organic chemical structures and has stimulated a myriad of experimental and theoretical investigations.Exploiting aromaticity rules for the rational design of optoelectronic materials with the desired photophysical characteristics is a challenging yet fascinating task.Herein we present an in-depth computational and spectroscopic study on the structure-property relationships of dinaphthopentalenes(DNPs).Results highlight that the different fusion patterns between 4nπand 4n+2πunits endow these PCHs with the tunable aromaticity in the ground state/excited state,which leads to the diverse electronic structures and consequently the distinctive excited state photophysics.Accordingly,we propose a combined aromaticity design strategy for rationally modulating and tailoring electronic and optical properties of PCH skeletons.These outcomes not only present a full picture of the excited state dynamics of the DNP system and afford a new class of efficient singlet fission-active materials but also provide some basic guidelines for exploiting aromaticity rules to design and develop new optical function materials.
文摘Effects of Mg^2＋, NTPs and Taq DNA polymerase in pear SSR-PCR system were analyzed by quadratic regressive orthogonal rotational combinational design. Results showed： absolute IOD （Integrated OD of each band） value of target band reduced with concentration rising of Mg^2＋ and Taq DNA polymerase, but heightened with concentration rising of dNTPs. The decay rate of absolute IOD value increased progressively with rising Mg^2＋ concentration, decreased gradually with rising Taq DNA polymerase concentration; the rising speed would be slower than the dNTPs increase. Absolute IOD value would reduce with concentration rising of dNTPs at a low level of Mg^2＋ concentration. Conversely it would rise with the increase of dNTPs while high Mg^2＋ concentration. Absolute IOD value would generally rise with concentration rising of Taq DNA polymerase while low Mg^2＋ concentration. On the contrary it would reduce with concentration rising of Taq DNA polymerase while high Mg^2＋ concentration.
基金supported by National Natural Science Foundation of China(Grant Nos.11201177 and 11271147)China Postdoctoral Science Foundation(Grant No.2013M531716)+2 种基金Scientific Research Plan Item of Hunan Provincial Department of Education(Grant No.12C0287)Jishou University Doctor Science Foundation(Grant No.jsdxxcfxbskyxm201113)Scientific Research Plan Item of Jishou University(Grant No.13JDY041)
文摘Abstract The objective of this paper is to study the issue of employing the uniformity criterion measured by the wrap-around L2-discrepancy to assess the optimal foldover plans for three-level designs.For three-level fractional factorials as the original designs,the general foldover plan and combined design under a foldover plan are defined,some theoretical properties of the defined foldover plans are obtained,a tight lower bound of the wrap-around L2-discrepancy of combined designs under a general foldover plan is also obtained,which can be used as a benchmark for searching optimal foldover plans.For illustration of the usage of our theoretical results,a catalog of optimal foldover plans for uniform initial designs with s three-level factors is tabulated,where 2≤ s ≤11.
基金Supported by National Natural Science Foundation of China(Grant Nos.11271147,11471135 and 11471136)
文摘The foldover is a quick and useful technique in construction of fractional factorial designs, which typically releases aliased factors or interactions. The issue of employing the uniformity criterion measured by the centered L2-discrepancy to assess the optimal foldover plans was studied for four-level design. A new analytical expression and a new lower bound of the centered L2-discrepancy for fourlevel combined design under a general foldover plan are respectively obtained. A necessary condition for the existence of an optimal foldover plan meeting this lower bound was described. An algorithm for searching the optimal four-level foldover plans is also developed. Illustrative examples are provided, where numerical studies lend further support to our theoretical results. These results may help to provide some powerful and efficient Mgorithms for searching the optimal four-level foldover plans.
