scholarly journals A Sequential Third Order Rotatable Design of Eighty Points in Four Dimensions with an Hypothetical Case Study

2019 ◽  
pp. 1-9
Author(s):  
Nyakundi Omwando Cornelious ◽  
Matunde Nambilo Cruyff
Keyword(s):  
Response Surface ◽  
Continuous Cultivation ◽  
Mineral Elements ◽  
Hypothetical Case ◽  
Third Order ◽  
Four Dimensions ◽  
Design Variables ◽  
Controllable Factors ◽  
Rotatable Design

In research, experiments must be performed at pre determined levels of the controllable factors, meaning that an experimental design must be selected before the experiment takes place. Once an experimenter has chosen a polynomial model of suitable order, the problem arises on how best to choose the settings for the independent variables over which he has control. A particular selection of settings or factor levels at which observations are to be taken is called a design. A design may become inappropriate under special circumstances requiring an increase in factors or levels to make it more desirable. In agriculture for instance, continuous cultivation of crops may exhaust the previously available mineral elements necessitating a sequential appendage of the mineral elements which become deficient in the soil over time. In current study, an eighty  points four  dimensional  third order rotatable design is constructed by combining two, four dimensional second order rotatable  designs and a practical hypothetical case study is given by converting coded levels to natural levels. We present an illustration on how to obtain the mathematical parameters of the coded values and its corresponding natural levels for a third order rotatable design in four dimensions by utilizing response surface methodology to approximate the functional relationship between the performance characteristics and the design variables.  This design permits a response surface to be fitted easily and provides spherical information contours besides the economic use of scarce resources in relevant production processes.

scholarly journals A Sequential Third Order Rotatable Design in Four Dimensions

2019 ◽  
pp. 1-7 ◽  
Author(s):  
Nyakundi O. Cornelious
Keyword(s):  
Continuous Cultivation ◽  
Mineral Elements ◽  
Third Order ◽  
Four Dimensions ◽  
Scarce Resources ◽  
Controllable Factors ◽  
Special Circumstances ◽  
Economic Use ◽  
Selection Of ◽  
Rotatable Design

In research, experiments must be performed at pre-determined levels of the controllable factors, meaning that an experimental design must be selected prior to experimentation. Once an experimenter has chosen a polynomial model of suitable order, the problem arises on how best to choose the settings for the independent variables over which he has control. A particular selection of settings or factor levels at which observations are to be taken is called a design. A design may become inappropriate under special circumstances requiring an increase in factors or levels to make it more desirable. In agriculture for instance, continuous cultivation of crops may exhaust previously available mineral elements necessitating a sequential appendage of the mineral elements which become deficient in the soil over time. In this study, a fifty six points third order rotatable design is constructed by adding a set of factors to a second order  rotatable design in four dimensions and a practical hypothetical example is given by converting coded level to natural levels.  This design permits a response surface to be fitted easily and provide spherical information contours besides the economic use of scarce resources in relevant production processes.

scholarly journals A note on Variance-Sum Third Order Slope Rotatable Designs

2021 ◽  
Vol 9 (10) ◽  
pp. 760-766
Author(s):  
R. Md. Mastan Shareef
Keyword(s):  
Response Surface Methodology ◽  
Response Surface ◽  
Interesting Property ◽  
Response Surfaces ◽  
Statistical Techniques ◽  
Third Order ◽  
Controllable Factors ◽  
Four Levels ◽  
Rotatable Design

Abstract: Response Surface Methodology (RSM) is a collection of mathematical and statistical techniques useful for analyzing experiments where the yield is believed to be influenced by one or more controllable factors. Box and Hunter (1957) introduced rotatable designs in order to explore the response surfaces. The analogue of Box-Hunter rotatability criterion is a requirement that the variance of i yˆ(x)/ x be constant on circles (v=2), spheres (v=3) or hyperspheres (v 4) at the design origin. These estimates of the derivatives would then be equally reliable for all points (x , x ,...,x ) 1 2 v equidistant from the design origin. This property is called as slope rotatability (Hader and Park (1978)).Anjaneyulu et al (1995 &2000) introduced Third Order Slope Rotatable Designs. Anjaneyulu et al(2004) introduced and established that TOSRD(OAD) has the additional interesting property that the sum of the variance of estimates of slopes in all axial directions at any point is a function of the distance of the point from the design origin. In this paper we made an attempt to construct Variance-Sum Third Order Slope Rotatable in four levels. Keywords: Response Surface Methodology. Third Order Slope Rotatable Design; TOSRD (OAD), Variance-Sum Third Order Slope Rotatable Design.

scholarly journals Group Divisible Variance – Sum Third Order Rotatable Design through Balanced Incomplete Block Designs in Four Dimensions

2018 ◽  
pp. 1-9
Author(s):  
N. Chebet ◽  
M. Kosgei ◽  
G. Kerich
Keyword(s):  
Block Design ◽  
Block Designs ◽  
Incomplete Block ◽  
Third Order ◽  
Four Dimensions ◽  
Dimensional Group ◽  
Group Divisible ◽  
Origin Group ◽  
Balanced Incomplete Block ◽  
Rotatable Design

In the study of rotatable designs, the variance of the estimated response at a point is a function of the distance of that point from a particular origin. Group divisible Rotatable Designs have been evolved by imposing conditions on the levels of factors in a rotatable design. In Group Divisible Third Order Rotatable Designs (GDTORD), the v-factors are split into two groups of p and (v-p) factors such that the variance of a response estimated at a point equidistant from the centre of the designs is a function of the distances  and from a suitable origin for each group respectively. Where  and   denotes the distances of the projection of the points in each of the group from a suitable origin respectively. In this paper, a four dimensional Group Divisible Variance-Sum Third Order Rotatable Design is constructed using a balanced incomplete block design.  

scholarly journals Hybrid Seven-bar Press Mechanism

2018 ◽  
Vol 12 (3) ◽  
pp. 181-187
Author(s):  
M. Erkan Kütük ◽  
L. Canan Dülger
Keyword(s):  
Genetic Algorithm ◽  
Objective Function ◽  
Design Optimization ◽  
Hybrid System ◽  
Degrees Of Freedom ◽  
Dimensional Synthesis ◽  
Design Variables ◽  
Optimization Study ◽  
Metal Stamping

An optimization study with kinetostatic analysis is performed on hybrid seven-bar press mechanism. This study is based on previous studies performed on planar hybrid seven-bar linkage. Dimensional synthesis is performed, and optimum link lengths for the mechanism are found. Optimization study is performed by using genetic algorithm (GA). Genetic Algorithm Toolbox is used with Optimization Toolbox in MATLAB®. The design variables and the constraints are used during design optimization. The objective function is determined and eight precision points are used. A seven-bar linkage system with two degrees of freedom is chosen as an example. Metal stamping operation with a dwell is taken as the case study. Having completed optimization, the kinetostatic analysis is performed. All forces on the links and the crank torques are calculated on the hybrid system with the optimized link lengths

scholarly journals Parametric Analysis on Landing Gear Strut Friction of Light Aircraft for Touchdown Performance

2021 ◽  
Vol 11 (12) ◽  
pp. 5445
Author(s):  
Shengyong Gan ◽  
Xingbo Fang ◽  
Xiaohui Wei
Keyword(s):  
Response Surface ◽  
Energy Absorption ◽  
Landing Gear ◽  
Surface Model ◽  
Absorption Properties ◽  
Surface Method ◽  
Design Variables ◽  
Landing Impact ◽  
Landing Response ◽  
Parametric Studies

The aim of this paper is to obtain the strut friction–touchdown performance relation for designing the parameters involving the strut friction of the landing gear in a light aircraft. The numerical model of the landing gear is validated by drop test of single half-axle landing gear, which is used to obtain the energy absorption properties of strut friction in the landing process. Parametric studies are conducted using the response surface method. Based on the design of the experiment results and response surface functions, the sensitivity analysis of the design variables is implemented. Furthermore, a multi-objective optimization is carried out for good touchdown performance. The results show that the proportion of energy absorption of friction load accounts for more than 35% of the total landing impact energy. The response surface model characterizes well for the landing response, with a minimum fitting accuracy of 99.52%. The most sensitive variables for the four landing responses are the lower bearing width and the wheel moment of inertia. Moreover, the max overloading of sprung mass in LC-1 decreases by 4.84% after design optimization, which illustrates that the method of analysis and optimization on the strut friction of landing gear is efficient for improving the aircraft touchdown performance.

Optimization Design of Pressure Shell in Underwater Vehicle Based on Response Surface Model

2009 ◽  
Vol 419-420 ◽  
pp. 89-92
Author(s):  
Zhuo Yi Yang ◽  
Yong Jie Pang ◽  
Zai Bai Qin
Keyword(s):  
Finite Element ◽  
Response Surface ◽  
Optimization Design ◽  
Engineering Application ◽  
Element Model ◽  
Response Surface Model ◽  
Design Stage ◽  
Surface Model ◽  
Design Variables ◽  
Structure Strength

Cylinder shell stiffened by rings is used commonly in submersibles, and structure strength should be verified in the initial design stage considering the thickness of the shell, the number of rings, the shape of ring section and so on. Based on the statistical techniques, a strategy for optimization design of pressure hull is proposed in this paper. Its central idea is that: firstly the design variables are chosen by referring criterion for structure strength, then the samples for analysis are created in the design space; secondly finite element models corresponding to the samples are built and analyzed; thirdly the approximations of these analysis are constructed using these samples and responses obtained by finite element model; finally optimization design result is obtained using response surface model. The result shows that this method that can improve the efficiency and achieve optimal intention has valuable reference information for engineering application.

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