Confidence regions for the stationary point of a quadratic response surface based on the asymptotic distribution of its MLE

2010 ◽  
Vol 22 (3) ◽  
pp. 739-751 ◽  
Author(s):  
Valeria Sambucini
Keyword(s):  
Response Surface ◽  
Asymptotic Distribution ◽  
Stationary Point ◽  
Confidence Regions ◽  
Quadratic Response Surface ◽  
Quadratic Response

A Large-Sample Confidence Region Useful in Characterizing the Stationary Point of a Quadratic Response Surface

Technometrics ◽  
1990 ◽  
Vol 32 (4) ◽  
pp. 425-435 ◽  
Author(s):  
Waiter H. Carter ◽  
Vernon M. Chinchilli ◽  
Eleanor D. Campbell
Keyword(s):  
Response Surface ◽  
Stationary Point ◽  
Confidence Region ◽  
Large Sample ◽  
Quadratic Response Surface ◽  
Quadratic Response

An asymptotic confidence interval for the response at the stationary point of a quadratic response surface

1991 ◽  
Vol 1 (2) ◽  
pp. 287-301 ◽  
Author(s):  
Vernon M. Chinchilli ◽  
Walter H. Carter ◽  
Timothy J. Breen ◽  
Eleanor D. Campbell
Keyword(s):  
Confidence Interval ◽  
Response Surface ◽  
Stationary Point ◽  
Asymptotic Confidence Interval ◽  
Quadratic Response Surface ◽  
Quadratic Response

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 .

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