scholarly journals Construction of twenty-six points specific optimum second order rotatable designs in three dimensions with a practical example

2020 ◽  
Vol 8 (1) ◽  
pp. 1
Author(s):  
Tum Isaac Kipkosgei
Keyword(s):  
Response Surface ◽  
Second Order ◽  
Three Dimensions ◽  
Predictor Variables ◽  
Scarce Resources ◽  
Quadratic Response Surface ◽  
Quadratic Response ◽  
Free Parameters ◽  
Economic Use ◽  
Rotatable Design

This quadratic response surface methodology focuses on finding the levels of some (coded) predictor variables x = (x1u, x2u, x3u)' that optimize the expected value of a response variable yu from natural levels. The experiment starts from some best guess or “control” combination of the predictor variables (usually coded to x = 0 for this case x1u=30, x2u=25 and x3u =40) and experiment is performed varying them in a region around this center point.We go further to construct a specific optimum second order rotatable design of three factors in twenty-six points. The achievement of this is done with estimation of the free parameters using calculus in an existing second order rotatable design of twenty-six points. Such a design permits a response surface to be fitted easily and provides spherical information contours besides the realizations of optimum combination of ingredients in Agriculture, horticulture and allied sciences which results in economic use of scarce resources in relevant production processes. The expected second order rotatable design model in three dimensions is available where the responses would then facilitate the estimation of the linear and quadratic coefficients. An example involving Phosphate (x1u), Nitrogen (x2u) and Potassium (x3u) is used to represent the three factors in the coded level and converted into natural levels.  

scholarly journals Modeling of rose coco beans using twenty four points optimum second order rotatable design

2017 ◽  
Vol 5 (2) ◽  
pp. 96
Author(s):  
Isaac Tum ◽  
John Mutiso ◽  
Joseph Koske
Keyword(s):  
Response Surface ◽  
Maximum Yield ◽  
Second Order ◽  
Three Dimensions ◽  
Coefficient Of Determination ◽  
Yield Response ◽  
Efficient Production ◽  
Phosphorus And Potassium ◽  
Nitrogen Phosphorus ◽  
Rotatable Design

The response surface methodology (RSM) is a collection of mathematical and statistical techniques useful for the modeling and analysis of problems in which a response of interest is influenced by several variables, and the objective is to optimize the response. The objective of the study was to model the rose coco beans (Phaseolus vulgaris) through an existing A-optimum and D-efficient second order rotatable design of twenty four points in three dimensions in a greenhouse setting using three inorganic fertilizers, namely, nitrogen, phosphorus and potassium. Thus, the objective of the study was accomplished using the calculus optimum value of the free/letter parameter f=1.1072569. This was done by estimating the parameters via least square's techniques, by making available for the yield response of rose coco beans at calculus optimum value design for the first time. The results showed that, the three factors: nitrogen, phosphorus, and potassium contributed significantly on the yield of rose coco beans (p<0.05). In GP3G, the second-order model was adequate for 1% level of significance with p value of 0.0034. The analysis of variance (ANOVA) of response surface for rose coco yield showed that this design was adequate due to satisfactory level of a coefficient of determination, R2, 0.8066 and coefficient variation, CV was 10.30. This study demonstrated the importance of statistical methods in the optimal and efficient production of rose coco beans. We do recommend a randomize screening of all the fertilizer components with which it has influence on rose coco beans be done to ascertain the right initial amount of each fertilizer that could achieve maximum yield than this study realized.

scholarly journals Optimal and efficient production of rose coco beans through the twenty-four points second order rotatable design

2017 ◽  
Vol 6 (1) ◽  
pp. 1
Author(s):  
Isaac Tum ◽  
Joseph Koske ◽  
John Mutiso
Keyword(s):  
Response Surface ◽  
Maximum Yield ◽  
Response Surfaces ◽  
Second Order ◽  
Three Dimensions ◽  
Coefficient Of Determination ◽  
Efficient Production ◽  
Phosphorus And Potassium ◽  
Nitrogen Phosphorus ◽  
Rotatable Design

The yield results of the twenty four points response surface methodology (RSM) design permitted a response surface to be fitted easily and provided spherical information contours besides the realizations of an optimum combination of the fertilizers in rose coco beans, which resulted in economic use of scarce resources for optimal production of rose coco beans. In this study an existing A-optimum and D-efficient second order rotatable design in three dimensions was used to produce rose coco beans optimally and efficiently. The general objective of the study was to produce rose coco beans (Phaseolus vulgaris) optimally and efficiently using an existing A-optimum and D-efficient twenty four points second order rotatable design in three dimensions in a greenhouse setting using three inorganic fertilizers, namely, nitrogen, phosphorus and potassium. Thus the study was accomplished using the calculus optimum value of the free/letter parameter f=1.1072569. The specific objectives were to estimate the linear parameters, thereby making available for the yield response of rose coco beans at calculus optimum value design for the first time, fitted and tested the model adequacy via lack of fit test, and then found the setting of the experimental factors that produces optimal response using contour plots to assist visualizes the response surfaces. This study demonstrated the importance of statistical methods in the optimal and efficient production of rose coco beans. The results showed that the three factors: nitrogen, phosphorus, and potassium contributed significantly on the yield of rose coco beans (p<0.05). The regression coefficients were determined by employing least square's techniques to predict quadratic polynomial model for group 3 greenhouse (GP3G) for the three fertilizer combinations. In GP3G, the second-order model was adequate at 1% level of significance with a p-value of 0.0034. The analysis of variance (ANOVA) of response surface for rose coco yield showed that this design was adequate due to satisfactory level of a coefficient of determination, R2, 0.8066 (GP3G) and coefficient variation, CV was 10.30. The canonical analysis showed that there was the saddle point for GP3G, meaning there was no unique optimum; therefore, ridge analysis was used to overcome the saddle problem. The result from ridge analysis provided the maximum yield of 70.25grams for the three fertilizer combinations at radii of one. We, therefore, recommend the use of GP3G design since it gave the required coefficient of determination (R2=80.66) and the maximum yield (70. 25grams) was achieved.

A New Adaptive Higher Order Response Surface Method

2011 ◽  
Vol 243-249 ◽  
pp. 5946-5954 ◽  
Author(s):  
Feng Han ◽  
Zheng Liang Li ◽  
Wen Liang Fan
Keyword(s):  
Response Surface ◽  
Response Surface Method ◽  
Univariate Analysis ◽  
Higher Order ◽  
Ultimate State ◽  
Strongly Nonlinear ◽  
Surface Method ◽  
Quadratic Response Surface ◽  
Undetermined Coefficient ◽  
Quadratic Response

Response surface method has won numerous concerns in the reliability analysis of structure due to its simplicity and practicability, especially quadratic response surface taking no account of cross terms is most widely used. However, for the complex ultimate state curved surface corresponding to strongly nonlinear, the approximate accuracy of quadratic response surface is apparently not enough, causing a biggish error in estimation of reliability. Although, theoretically, higher order response surface method can resolve this problem, the sharp increase of undetermined coefficient reduces calculation efficiency, and even, cannot achieve. Therefore, on the basis of univariate analysis of multivariable function, an algorithm which can reasonably determine higher order response surface form is presented in this article, able to effectively reduce the number of undetermined coefficients in response surface, so as to reduce computational difficulties and put forward improving measures for possible problems; In addition, based on the tactics of number-theoretic setpoint, a type of scheme of number-theoretic selecting point applicable to response surface method has been developed. Finally, through the analysis of examples, the suggested algorithm was validated, with the result showing that the algorithm has good accuracy and efficiency.

scholarly journals Optimization for maximum specific energy density of a lithium-ion battery using progressive quadratic response surface method and design of experiments

2020 ◽  
Vol 10 (1) ◽  
Author(s):  
Ji-San Kim ◽  
Dong-Chan Lee ◽  
Jeong-Joo Lee ◽  
Chang-Wan Kim
Keyword(s):  
Energy Density ◽  
Design Of Experiments ◽  
Response Surface ◽  
Specific Energy ◽  
Lithium Ion ◽  
Specific Energy Density ◽  
Surface Method ◽  
Quadratic Response Surface ◽  
Quadratic Response ◽  
Electrochemical Model

Abstract The demand for high-capacity lithium-ion batteries (LIB) in electric vehicles has increased. In this study, optimization to maximize the specific energy density of a cell is conducted using the LIB electrochemical model and sequential approximate optimization (SAO). First, the design of experiments is performed to analyze the sensitivity of design factors important to the specific energy density, such as electrode and separator thicknesses, porosity, and particle size. Then, the design variables of the cell are optimized for maximum specific energy density using the progressive quadratic response surface method (PQRSM), which is one of the SAO techniques. As a result of optimization, the thickness ratio of the electrode was optimized and the porosity was reduced to keep the specific energy density high, while still maintaining the specific power density performance. This led to an increase in the specific energy density of 56.8% and a reduction in the polarization phenomenon of 11.5%. The specific energy density effectively improved through minimum computation despite the nonlinearity of the electrochemical model in PQRSM optimization.

Multi-Objective Optimization of Multistage Centrifugal Pump Based on Surrogate Model

2019 ◽  
Vol 142 (1) ◽  
Author(s):  
Tong Shuiguang ◽  
Zhao Hang ◽  
Liu Huiqin ◽  
Yu Yue ◽  
Li Jinfu ◽  
...  
Keyword(s):  
Response Surface ◽  
Centrifugal Pump ◽  
Calculation Method ◽  
Cfd Simulation ◽  
Surrogate Models ◽  
Hydraulic Loss ◽  
Loss Model ◽  
Design Variables ◽  
Quadratic Response Surface ◽  
Quadratic Response

Abstract In this paper, the hydraulic efficiency optimization calculation method of a ten-stage centrifugal pump is researched. According to the hydraulic loss model, a multi-objective optimization calculation method based on surrogate models is proposed. In order to study the highly nonlinear relationship between key design variables and centrifugal pump external characteristic values, this paper builds the quadratic response surface, the radial basis Gaussian response surface, and Kriging three surrogate models using computer fluid dynamics (CFD) simulation analysis. Two types of calculation models (hydraulic loss model and three surrogate models) combined NSGA-Π genetic algorithm are applied to optimize the key design variables and to find the optimal solution of each model. The accuracy and effectiveness of the efficiency optimization methods based on the two types of calculation models are compared and analyzed. The results show that the calculation method of hydraulic loss model based on the semitheoretical and semi-empirical formula is less time-consuming but inaccurate. In contrast, the optimization method based on surrogate models using CFD simulation is accurate. What's more, comparing the surrogate models, the results based on the complete quadratic response surface model which make the efficiency of the first stage centrifugal pump reach 77.26% are more accurate.

High-Order RSM for Dynamic Reliability of UHV Transmission Tower

2015 ◽  
Vol 799-800 ◽  
pp. 1295-1298
Author(s):  
Li Qin ◽  
Wei Lin Peng ◽  
Wei Han
Keyword(s):  
Response Surface ◽  
Estimation Error ◽  
Univariate Analysis ◽  
High Order ◽  
Reliability Estimation ◽  
Transmission Tower ◽  
Dynamic Reliability ◽  
Large Span ◽  
Quadratic Response Surface ◽  
Quadratic Response

As transmission tower system has the characteristics of large-span and spatial truss structure, the study of the reliability is also developed on the basis of space truss research and large-span structure system. As simple and suitable, RSM (response surface method), in particular, quadratic response surface without considering the cross term is often used in reliability calculation. However, strong nonlinear limit that corresponding to a complex surface, the accuracy of quadratic response surface is inadequate, causing greater reliability estimation error. High-order response surface solves it well. To this end, based on univariate analysis of multivariate function, a reasonable algorithm as to assure that the form of higher-order response surface is proposed; on the algorithm is verified by given examples, the result shows better accuracy and efficiency .

Sign in / Sign up

Export Citation Format

Share Document