CONSTRUCTING UNIFORM DESIGNS WITH TWO- OR THREE-LEVEL

When the number of runs is large, to search for uniform designs in the sense of low-discrepancy is an NP hard problem. The number of runs of most of the available uniform designs is small （≤50）. In this article, the authors employ a kind of the so-called Hamming distance method to construct uniform designs with two- or three-level such that some resulting uniform designs have a large number of runs. Several infinite classes for the existence of uniform designs with the same Hamming distances between any distinct rows are also obtained simultaneously. Two measures of uniformity, the centered L2-discrepancy （CD, for short） and wrap-around L2-discrepancy （WD, for short）, are employed.

An Adjusted Gray Map Technique for Constructing Large Four-Level Uniform Designs

A uniform experimental design(UED)is an extremely used powerful and efficient methodology for designing experiments with high-dimensional inputs,limited resources and unknown underlying models.A UED enjoys the following two significant advantages:(i)It is a robust design,since it does not require to specify a model before experimenters conduct their experiments;and(ii)it provides uniformly scatter design points in the experimental domain,thus it gives a good representation of this domain with fewer experimental trials(runs).Many real-life experiments involve hundreds or thousands of active factors and thus large UEDs are needed.Constructing large UEDs using the existing techniques is an NP-hard problem,an extremely time-consuming heuristic search process and a satisfactory result is not guaranteed.This paper presents a new effective and easy technique,adjusted Gray map technique(AGMT),for constructing(nearly)UEDs with large numbers of four-level factors and runs by converting designs with s two-level factors and n runs to(nearly)UEDs with 2^(t−1)s four-level factors and 2tn runs for any t≥0 using two simple transformation functions.Theoretical justifications for the uniformity of the resulting four-level designs are given,which provide some necessary and/or sufficient conditions for obtaining(nearly)uniform four-level designs.The results show that the AGMT is much easier and better than the existing widely used techniques and it can be effectively used to simply generate new recommended large(nearly)UEDs with four-level factors.

Research on the design method for uniform wear of shield cutters in sand-pebble strata

During shield tunneling in highly abrasive formations such as sand–pebble strata,nonuniform wear of shield cutters is inevitable due to the different cutting distances.Frequent downtimes and cutter replacements have become major obstacles to long-distance shield driving in sand–pebble strata.Based on the cutter wear characteristics in sand–pebble strata in Beijing,a design methodology for the cutterhead and cutters was established in this study to achieve uniform wear of all cutters by the principle of frictional wear.The applicability of the design method was verified through three-dimensional simulations using the engineering discrete element method.The results show that uniform wear of all cutters on the cutterhead could be achieved by installing different numbers of cutters on each trajectory radius and designing a curved spoke with a certain arch height according to the shield diameter.Under the uniform wear scheme,the cutter wear coefficient is greatly reduced,and the largest shield driving distance is increased by approximately 47%over the engineering scheme.The research results indicate that the problem of nonuniform cutter wear in shield excavation could be overcome,thereby providing guiding significance for theoretical innovation and construction of long-distance shield excavation in highly abrasive strata.

Optimization of Callus Induction Medium for Schisandga chinensis Baill via Uniform Design

[Objective]This study was to optimize callus induction medium for Schisandga chinensis Baill.[Method]Using callus induction rate as an indicator,uniform design was employed to optimize hormone combination at poly-factors and poly-levels for callus induction from Schisandga chinensis Baill.[Results]Optimal hormone combinations depended on different explants：optimum medium for both tender leaf and petiole was MS ＋3 mg/L 6-BA,for stem segment was MS ＋3 mg/L 6-BA ＋0.6 mg/L NAA.[Conclusion]Uniform design is a time-saving and convenient method for the optimum medium for callus and yields a higher callus induction rate.

Optimizing Yanbian Cow Oocytes Mature in vitro and Cleavage System after Nuclear Transfer Based on Uniform Design

[Objective] The aim was to optimize Yanbian cow oocytes mature in vitro and cleavage system after nuclear transfer based on uniform design. [Method] Oocytes were recovered by aspiration method, and oocytes were matured in vitro （IVM） with different conditions, and then carried out nucleus transfer, fusion, activation and in vitro culture （IVC） of embryo. Effects of ovary storage temperature, maturation time and follicular diameter size on in vitro maturation and cleavage rates of cow oocytes were compared. [ Result] The best conditions of IVM of Yanbian cow oocytes was that： the oocytes of 8 mm diameter were matured in vitro for 24 hours when the ovaries were stored at 26℃ or 31 ℃. The best cleave conditions after nucleus transfer of oocytes was that： the oocytes of 6 mm or 8 mm diameter were cultured in vitro for 24 hours when the ovaries were stored at 26℃. [ Conclusion] The result has some reference to Yanbian cow and other cow breeding and population expanding propagation.

Uniformity of Asymmetric Augmented Designs

Follow-up experimental designs are widely applied to explore the relationship between factors and responses step by step in various fields such as science and engineering.When some additional resources or information become available after the initial design of experiment is carried out,some additional runs and/or factors may be added in the follow-up stage.In this paper,the issue of the uniform row augmented designs and column augmented designs with mixed two-,three-and four-level is investigated.The uniformity of augmented designs is discussed under the wrap-around L_(2)-discrepancy.Some lower bounds of wrap-around L_(2)-discrepancy for the augmented designs are obtained,which can be used to assess uniformity of augmented design.Numerical results show that augmented designs have high efficiency,which have low discrepancy and close to the proposed lower bounds.

Optimizing Efficient Micropropagation System of Rhododendron Brachycarpum D. Don by Uniform Design Method

[Objective] The study was conducted to establish a high efficient micropropagation system for Rhododendron Brachycarpum D. Don and realize the high efficiency in vitro micropropagation of R. brachycarpum. [ Method ] Young stems of R. brachycarpum were used as explants, suitable medium compositions for axillary bud growing and rooting were screened through uniform design exPeriments. [ Result] MS （modified） ＋ IAA 0,15 mg/ L ＋ IBA 0.30 mg/L ＋ GA3 3.00 mg/L was the most suitable medium with the regeneration rate of 92%. Stems each with one node were cut from regenerated shoots and cultured for propagation, the proliferative multiple was over 45 within one culture period of 35 d. [ Conclusion] High efficient micropropagation system of R. brachycarpum has been successfully established, which provides some basis for development and utilization and industrial seedling growth of the alpine rhododendron in Changbai Mountain northeast China.

Optimization of tensile strength for new type acetone-urea-formaldehyde furan resin using uniform design

In this study,the 24 h tensile strength of new type acetone-urea-formaldehyde furan resin (nitrogen content 3%) was investigated by uniform design optimization.Four independent variables such as acetone:formaldehyde molar ratio (mol/mol),solution pH value,reaction temperature (℃) and reaction time (min) were considered in the experiments.U13(134) uniform design was employed and the equation of 24 h tensile strength model was obtained after 13 experimentations.The 24 h tensile strength was optimized by applying single factor experiments and stepwise non-linear regression analysis.Minitab (Minitab 15 trial version) and MATLAB (R2010a trial version) were used for data analysis.The t-value and p-value indicate that the major impact factors include the interaction effect of solution pH value and reaction temperature (X2X3),the linear terms of acetone:formaldehyde molar ratio (X1),reaction time (X4) followed by the square effects of acetone/formaldehyde molar ratio (X1X1).The optimized results were achieved with the acetone:formaldehyde molar ratio (mol/mol) at 3:1,solution pH value at 6.0,reaction temperature at 70℃,and reaction time at 140 min,respectively.This method can not only significantly reduce the number and cost of the tests,but also provide a good experimental design strategy for the development of furan resin.The investigation shows that the predicted results of 24 h tensile strength are consistent well with the experimental ones.

Optimization of Culture Conditions and Medium Composition for the Marine Algicidal Bacterium Alteromonas sp. DH46 by Uniform Design

Harmful algal blooms(HABs) have led to extensive ecological and environmental issues and huge economic losses.Various HAB control techniques have been developed,and biological methods have been paid more attention.Algicidal bacteria is a general designation for bacteria which inhibit algal growth in a direct or indirect manner,and kill or damage the algal cells.A metabolite which is strongly toxic to the dinoflagellate Alexandrium tamarense was produced by strain DH46 of the alga-lysing bacterium Alteromonas sp.The culture conditions were optimized using a single-factor test method.Factors including carbon source,nitrogen source,temperature,initial pH value,rotational speed and salinity were studied.The results showed that the cultivation of the bacteria at 28℃ and 180 r min-1with initial pH 7 and 30 salt contcentration favored both the cell growth and the lysing effect of strain DH46.The optimal medium composition for strain DH46 was determined by means of uniform design experimentation,and the most important components influencing the cell density were tryptone,yeast extract,soluble starch,NaNO3 and MgSO4.When the following culture medium was used(tryptone 14.0g,yeast extract 1.63g,soluble starch 5.0 g,NaNO3 1.6 g,MgSO4 2.3 g in 1L),the largest bacterial dry weight(7.36 g L-1) was obtained,which was an enhancement of 107% compared to the initial medium;and the algal lysis rate was as high as 98.4% which increased nearly 10% after optimization.

The height-width ratio limited value for rubber bearing isolated structure computed by uniform design method

Rubber isolation is the most mature control technology in practical application, and is widely used by short rigid buildings. However, many high isolation buildings have been built around the world in recent years, which do not follow the existing criterions and codes. Many researchers began to research the special problems caused by larger height-width ratio isolation structures. The overturning effect of high height-width ratio structures with rubber bearing is firstly studied. Considering the main factors, such as the height-width ratio of structures, type of site, the designed basic acceleration of ground motion and the decouple factor in horizon, computing experiment is defined with the Uniform Design Method, which is also known as designing isolation structure. The forces of the bearing under edge of structures based on the position of the rubber bearing are calculated. The result indicates that the rubber bearings will lose its functionality under very high tension and compressing force of earthquake motion in horizon and vertical, when the height-width ratio is over a certain value. Thus, based on the calculation result of isolation structures defined in the uniform design method, regression analysis is conducted, and also the rubber edge force regression formula are gotten, which has higher correlation and smaller standard deviation. This formula can be used to roughly calculate whether the pull force occurs at the edge of the building. By the edge bearings of isolation structure minimum force formula, the height-width ratio limited value of the isolation structure is deducted when rubber bearing has minimum force of zero.

APPLICATION OF UNIFORM PRECRIPTION DESIGN IN STUDYING OF WEARREISTANT COATING IN PLASMA SPRAYING

Plasma spraying technics, a method of strengthening surfaces, shows advantages in wear-resistant, reducing friction, bearing corrosion and enduring higher temperature. While for the coating material, it is important to improve the ability of the functional coating. In this paper, a coating material of wear-resistant, bearing corrosion and enduring higher temperature in middle and low speed diesel is studied quantificationally with a uniform prescription design method, which reduced the test period as the test points distribute uniformly. An optimized combination is put forward of each part in the coating and a method to develop a new coating material is supplied.

Integration of uniform design and quantum-behaved particle swarm optimization to the robust design for a railway vehicle suspension system under different wheel conicities and wheel rolling radii

This paper proposes a systematic method, integrating the uniform design (UD) of experiments and quantum-behaved particle swarm optimization (QPSO), to solve the problem of a robust design for a railway vehicle suspension system. Based on the new nonlinear creep model derived from combining Hertz contact theory, Kalker's linear theory and a heuristic nonlinear creep model, the modeling and dynamic analysis of a 24 degree-of-freedom railway vehicle system were investigated. The Lyapunov indirect method was used to examine the effects of suspension parameters, wheel conicities and wheel rolling radii on critical hunting speeds. Generally, the critical hunting speeds of a vehicle system resulting from worn wheels with different wheel rolling radii are lower than those of a vehicle system having original wheels without different wheel rolling radii. Because of worn wheels, the critical hunting speed of a running railway vehicle substantially declines over the long term. For safety reasons, it is necessary to design the suspension system parameters to increase the robustness of the system and decrease the sensitive of wheel noises. By applying UD and QPSO, the nominal-the-best signal-to-noise ratio of the system was increased from -48.17 to -34.05 dB. The rate of improvement was 29.31%. This study has demonstrated that the integration of UD and QPSO can successfully reveal the optimal solution of suspension parameters for solving the robust design problem of a railway vehicle suspension system.

A CASE STUDY IN THE APPLICATION OF SUPERSATURATED DESIGNS TO COMPUTER EXPERIMENTS

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.

The Complex System Modeling Method Based on Uniform Design and Neural Network

In this paper, the method based on uniform design and neural network is proposed to model the complex system. In order to express the system characteristics all round, uniform design method is used to choose the modeling samples and obtain the overall information of the system;for the purpose of modeling the system or its characteristics, the artificial neural network is used to construct the model. Experiment indicates that this method can model the complex system effectively.

Extraction optimization of coumarins from radix angelicae pubescentis by HPLC-DAD coupled with uniform design

Uniform design was used to optimize extraction condition of direct refluence extraction of coumarins from the Chinese traditional medicine of radix angelicae pubescentis(Duhuo); the sum peak area of coumarins separated with high performance liquid chromatography(HPLC) at detection wavelength of 320nm was considered as detection index, two factors of solvent concentration and extraction time were mainly studied at extraction temperature of 85℃ and a volume ratio of solvent to sample of 10∶1. Optimal subclass, quadric polynomial step by step aggression and neural network method were applied to process the experimental results. The results show that the first and second methods give the same factors combination (concentration of ethanol: 95%, extraction time: 3.6 h) and the second method is much better than the first one. The extraction model is consequently developed.

Process parameter optimization for local post-weld heat treatment.of turbine rotor based on uniform design

During the process of local post-weld heat treatment （ PWHT） , the temperature difference inside the weld overlay is a very influential factor on relieving residual stress. In this paper, a commercial program （ABAQUS） was used to simulate the temperature field in turbine rotor, and the influence of heat treatment parameters on temperature was investigated by finite element method. Weight analysis shows that the holding temperature and heating rate are the main factors affecting on temperature, especially the holding temperature. Besides, two regression equations that reflect the relationship between temperature and heat treatment parameters were fitted with uniform design method. Both the correlation coefficients of the regression equations are up to O. 999 2, and the maximum residual error is only O. 7. The agreement between simulation results and regression results is shown to be excellent. At the end, local heat treatment parameters were optimized using the simplex method.

Simulation and uniform design-based automatic generation of risk scenarios

This paper presents a methodology for automatically generating risk scenarios for dynamic reliability applications in which some dynamic characteristics(e.g.,the order,timing and magnitude of events,the value of relevant process parameters and initial conditions) have a significant influence on the evolution of the system.The main idea of the methodology is:(i) making the system model "express itself" through simulation by having the model driven by an elaborated simulation engine;(ii) exploiting uniform design to pick out a small subset of representative design points from the space of relevant dynamic characteristics;(iii) for each selected design point,employing a depth-first systematic exploration strategy to cover all possible scenario branches at each branch point.A highly dynamic example adapted from the literature(a chemical batch reactor) is studied to test the effectiveness of the proposed methodology.

Orthogonal Array-based Uniform Latin Hypercube Design and Its Construction

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 constructed by using our method.

A study of arc stability of basic electrode in view of uniform design method

In order to develop a basic electrode with low fume and good usability, a uew slag system has been designed after analyzing several basic electrode slag systems. Then in view of uniform design method, arranging the experiment points by it, the influenced laws of the uew system coating compouents on the arc stability had been searched. In the formula, niue coating compouents were taken as independent variables and they were divided into six levels in all twenty-four experiments. The arc stability was taken as function and taken down the data when welding and then put them into the computer to be processed statistically. The analysis results give the mathematical model and trend diagrams between independent variables and the function. They indicate that the effects of many coating compouents on the arc stability are in the mutual form. The mutual effects between CaCO3 and BaF2, BaF2 and BaCO3 , increases the arc stability separately. While the mutual effects between CaF2 and iron powder, the square item of iron powder itself decreases the arc stability separately.

Investigation of paeonol-geniposide on acute alcoholic liver injury based on uniform design method

Objective:To explore the optimal ratio and compatibility effect of paeonol-geniposide combination on acute alcoholic liver injury by uniform design.Methods:Lieber-DeCarli alcoholic liquid feed was used to induce acute alcoholic liver injury in mice.Uniform design was used to select the best dosage combination of paeonol and geniposide,and the related indexes of liver injury and oxidative stress were detected by kit.Serum inflammatory factors were detected by ELISA,and the expressions of p38 MAPK,JNK and NF-κB P65 related proteins in liver were detected by Western-blot.Results:The regression equation suggested that paeonol:geniposide=220:20 was the best ratio of paeonol and geniposide to resist alcoholic liver injury.Compared with the model group,the liver injury indexes and oxidation products of the paeonol+geniposide group decreased significantly,the antioxidant activity of liver tissue increased significantly,and the expression levels of p-p38 MAPK,p-JNK and NF-κB P65 protein decreased significantly.Conclusion:The optimal dosage of paeonolgeniposide was effectively optimized by uniform design and pharmacodynamic analysis.The combination of the two drugs could reduce the alcoholic liver injury by reducing the oxidative stress injury and inflammatory response in the liver tissue of mice,and its effect might be related to the targeting of p38 MAPK/JNK/NF-κB channel.