• Structural Engineering and Mechanics
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• 제34권6호
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• pp.779-799
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• 2010

In order to consider high-order effects on the actual limit state function, a new response surface method is proposed for structural reliability analysis by the use of high-order approximation concept in this study. Hermite polynomials are used to determine the highest orders of input random variables, and the sampling points for the determination of highest orders are located on Gaussian points of Gauss-Hermite integration. The cross terms between two random variables, only in case that their corresponding percent contributions to the total variation of limit state function are significant, will be added to the response surface function to improve the approximation accuracy. As a result, significant reduction in computational cost is achieved with this strategy. Due to the addition of cross terms, the additional sampling points, laid on two-dimensional Gaussian points off axis on the plane of two significant variables, are required to determine the coefficients of the approximated limit state function. All available sampling points are employed to construct the final response surface function. Then, Monte Carlo Simulation is carried out on the final approximation response surface function to estimate the failure probability. Due to the use of high order polynomial, the proposed method is more accurate than the traditional second-order or linear response surface method. It also provides much more efficient solutions than the available high-order response surface method with less loss in accuracy. The efficiency and the accuracy of the proposed method compared with those of various response surface methods available are illustrated by five numerical examples.

• Structural Engineering and Mechanics
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• 제76권6호
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• pp.675-685
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• 2020

As the classical response surface method (RSM), the polynomial RSM is so easy-to-apply that it is widely used in reliability analysis. However, the trade-off of accuracy and efficiency is still a challenge and the "curse of dimension" usually confines RSM to low dimension systems. In this paper, based on the univariate decomposition, the polynomial RSM is executed in a new mode, called as DPRSM. The general form of DPRSM is given and its implementation is designed referring to the classical RSM firstly. Then, in order to balance the accuracy and efficiency of DPRSM, its adaptive order revision around the most probable point (MPP) is proposed by introducing the univariate polynomial order analysis, noted as RDPRSM, which can analyze the exact nonlinearity of the limit state surface in the region around MPP. For testing the proposed techniques, several numerical examples are studied in detail, and the results indicate that DPRSM with low order can obtain similar results to the classical RSM, DPRSM with high order can obtain more precision with a large efficiency loss; RDPRSM can perform a good balance between accuracy and efficiency and preserve the good robustness property meanwhile, especially for those problems with high nonlinearity and complex problems; the proposed methods can also give a good performance in the high-dimensional cases.

• The Journal of Asian Finance, Economics and Business
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• 제2권2호
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• pp.13-18
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• 2015

In this paper the DRC model is presented for solving multi objective problem. The proposed model is a combination of data envelopment analysis, Cuckoo algorithm and the response surface method. Due to reasons like costs, time and irreversible damages, it is not possible to analyze each and every one of the proposed models in practice, so the simulation is used. Since the number of experiments for simulation process is high then the optimization has gone to practice and directs the simulation process. The response surface method is used as one of the approaches of simulation optimization. Furthermore, data envelopment analysis is used to consider several response surfaces as efficiency response surface. Then this efficiency response surface is solved by Cuckoo algorithms. The main advantage of DRC model is to make one efficiency response surface function instate of multi surface function for every output and also using the advantages of Cuckoo algorithms. In order to demonstrate the effectiveness of the proposed approach, the branches of Refah bank in Mashhad is analyzed and the results are presented.

• 항공우주시스템공학회지
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• 제7권3호
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• pp.1-6
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• 2013

Numerical optimization of two dimensional high lift configuration was performed with flow solver and optimization method based on RSM(Response Surface Model). Navier-Stokes solver with Spalart-Allmaras turbulence model was selected for the simulation of highly complex and separated flows on the flap. For the simultaneous optimization of both flap shape and setting (gap/overlap), 10 design variables (eight variables for flap shape variation and two variables for flap setting) were chosen. In order to generate the response surface model, 128 experimental points were selected for 10 design variables. The objective function considering maximum lift coefficient, lift to drag ratio and lift coefficient at specific angle of attack was selected to reduce flow separation on the flap surface. The present method was applied to two dimensional fowler flap in landing configuration. After applying the present method, it was shown that the optimized high lift configuration had less flow separation on the flap surface and lift to drag ratio was suppressed over entire angle of attack range.

• 한국생산제조학회지
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• 제9권2호
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• pp.52-58
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• 2000

the quality of a TV is closely connected with the high quality surface of Braun tube. To get high quality surface an improved grinding system is needed. It has three main parts : the housing part of supporting frame the outershaft part rotat-ed by motor and the innershaft part having eccentricity from the rotation axis of the outershaft. the housing part and the outershaft part are connected by outerbearings, The outershaft part and the innershaft part are connected by innerbearings. Although the outershaft part is rotated at high-speed the innershaft part is not rotated by offset coupling. The high quality grinding surface can be obtained by this mechanism of panel surface grinder, Because the innershaft is unbalanced by eccentricity from rotation axis of outershaft the unbalancing vibration is resulted In this rotor system with high-speed rota-tion the unbalancing vibration makes the opertion unstable. In this research the transfer function is obtained bythe frequency response analysis of finite element model. The simu-lation result is proved by comparing with the experimental result measured by signal analyzer Then the results are corre-lated. in order to improve the design an optimization method is used instead of two-planes balancing method The parts of the 3-dimensional panel surface grinder satisfy the each constraint, The result shows that the design of the panel surface grinder can be optimized.

• 대한기계학회:학술대회논문집
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• 대한기계학회 2004년도 춘계학술대회
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• pp.1023-1028
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• 2004

A micro-pressure wave is generated by the high-speed train which enters a tunnel, and it causes explosive noise and vibration at the exit. It is known that train speed, train-tunnel area ratio, nose slenderness and nose shape mainly influence on generating micro-pressure wave. So it is required to minimize it by searching optimal values of such train shape factors and tunnel condition. In this study, response surface model, one of approximation models, is used to perform optimization effectively and analyze sensitivity of design variables. Owen's randomized orthogonal array and D-optimal Design are used to construct response surface model. In order to increase accuracy of model, stepwise regression is selected. Finally SQP(Sequential Quadratic Programming) optimization algorithm is used to minimize the maximum micro-pressure wave by using built approximation model.

• 한국기계가공학회지
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• 제15권3호
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• pp.44-51
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• 2016

This paper presents the characteristics of the energy absorption in an expansion tube type impact absorber that is applied to a high weight drop tester and the use of a response surface methodology to predict the impact energy absorption. In order to identify the characteristics of the energy absorption, a set of finite element analysis was conducted with Abaqus Explicit. Moreover, the ISCD-II sampling method and a first order polynomial were used to build a response surface. As a result, we demonstrated that the impact energy could be controlled by four main design variables, namely an expansion pipe's thickness, inner radius, pressing die's expansion angle and expansion ratio. Additionally, we observed the relationship between the four main design variables and the impact energy absorbing time, displacement, and maximum impact force.

• 대한산업공학회지
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• 제38권1호
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• pp.25-30
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• 2012

Desirability approaches have been proposed to find an optimum of multiple response problem. The existing desirability approaches use either of mean or min of individual desirability in aggregation of multiple responses. However, in order to find an optimum having high mean and low dispersion among individual desirability, the dispersion needs to be simultaneously considered with its mean. This study proposes bias and variance (BV) method which aggregates bias (ideal target-mean) and variance of individual desirability in multiple response optimization. The proposed BV method was applied to an example to evaluate its usefulness by comparing with existing methods. Evaluation results showed that the solution of BV method was a fairly good compared with DS (Derringer and Suich, 1980) and KL (Kim and Lin, 2000) methods. The BV method can be utilized to multiple response surface problems when decision makers want to find an optimum having high mean and low variance among responses.

• 한국안전학회지
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• 제30권1호
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• pp.8-13
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• 2015

The experimental design methodology was applied in the drop tube furnace (DTF) to predict the various combustion properties according to the operating conditions and to assess the coal plant safety. Response surface method (RSM) was introduced as a design of experiment, and the database for RSM was set with the numerical simulation of DTF. The dependent variables such as burnout ratios (BOR) of coal and $CO/CO_2$ ratios were mathematically described as a function of three independent variables (coal particle size, carrier gas flow rate, wall temperature) being modeled by the use of the central composite design (CCD), and evaluated using a second-order polynomial multiple regression model. The prediction of BOR showed a high coefficient of determination (R2) value, thus ensuring a satisfactory adjustment of the second-order polynomial multiple regression model with the simulation data. However, $CO/CO_2$ ratio had a big difference between calculated values and predicted values using conventional RSM, which might be mainly due to the dependent variable increses or decrease very steeply, and hence the second order polynomial cannot follow the rates. To relax the increasing rate of dependent variable, $CO/CO_2$ ratio was taken as common logarithms and worked again with RSM. The application of logarithms in the transformation of dependent variables showed that the accuracy was highly enhanced and predicted the simulation data well.

• 한국환경과학회지
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• 제26권6호
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• pp.719-728
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• 2017

In order to investigate the adsorption characteristics for Sr ion using the Na-X zeolite synthesized from coal fly ash, batch tests and response surface analyses were carried out. The adsorption kinetic data for Sr ions, using Na-X zeolite, fitted well with the pseudo-second-order model. The uptake of Sr ions followed the Langmuir isotherm model, with a maximum adsorption capacity of 196.46 mg/g. Thermodynamic studies were conducted at different reaction temperatures, with the results indicating that Sr ion adsorption by Na-X zeolite was an endothermic (${\Delta}H^o$>0) and spontaneous (${\Delta}G^o$<0) process. Using the response surface methodology of the Box-Behnken method, initial Sr ion concentration ($X_1$), initial temperature ($X_2$), and initial pH ($X_3$) were selected as the independent variables, while the adsorption of Sr ions by Na-X zeolite was selected as the dependent variable. The experimental data fitted well with a second-order polynomial equation by multiple regression analysis. The value of the determination coefficient ($R^2=0.9937$) and the adjusted determination coefficient (adjusted $R^2=0.9823$) was close to 1, indicating high significance of the model. Statistical results showed the order of Sr removal based on experimental factors to be initial pH > initial concentration > temperature.