Response Surface Method Optimization Research Articles

An experimental methodology for response surface optimization methods

Response surface methods, and global optimization techniques in general, are typically evaluated using a small number of standard synthetic test problems, in the hope that these are a good surrogate for real-world problems. We introduce a new, more rigorous methodology for evaluating global optimization techniques that is based on generating thousands of test functions and then evaluating algorithm performance on each one. The test functions are generated by sampling from a Gaussian process, which allows us to create a set of test functions that are interesting and diverse. They will have different numbers of modes, different maxima, etc., and yet they will be similar to each other in overall structure and level of difficulty. This approach allows for a much richer empirical evaluation of methods that is capable of revealing insights that would not be gained using a small set of test functions. To facilitate the development of large empirical studies for evaluating response surface methods, we introduce a dimension-independent measure of average test problem difficulty, and we introduce acquisition criteria that are invariant to vertical shifting and scaling of the objective function. We also use our experimental methodology to conduct a large empirical study of response surface methods. We investigate the influence of three properties--parameter estimation, exploration level, and gradient information--on the performance of response surface methods.

Weighted Centroid Modified Simplex and Linear Constrained Response Surface Optimization Methods for the Xbar-R Chart Variable Determination

Problem statement: Although economic Xbar-R chart designs do guarantee the minimal operating cost, they typically have poor levels of statistical performance measures. The obvious limitation of the economic design is that the Type I error rate seems to be very high for many situations and will cause a large number of false alarms. This situation leads to an investigation of appropriate levels of control chart variables which consist of a sample size, an interval between samples or sampling frequency and the control chart limits. Approach: Evolutionary operations via the weighed centroid modified simplex, WCMSM and linear constrained response surface optimization, LCRSOM, methods are applied to optimize the Xbar-R chart variables in the analytical model called as the operating cost function. WCMSM allows the simplex to converge more rapidly towards an optimum via the weighted centroid of the hyperface by expansion and multiple ways of simplex contraction along the line of conventional reflection in order to speed up the convergence. LCRSOM is a combination of the principles of experimental designs, least squares and related mathematical programming models to approach the optimum. Results: The computational results for economic Xbar-R charts via both methods reveal that the process quality level affects the total cost more than relevant errors from selecting and inspecting samples including identifying assignable causes. However, total costs obtained from the LCRSOM seem to be better for all process scenarios. Conclusions: On Xbar-R charts, if a process is at the high quality level the total cost is better than a process with a low quality level without a consideration of errors from selecting/inspecting samples and identifying assignable causes.

Learning Physical Parameters of Capsid Assembly Systems from Indirect Measures of Assembly Progress

Theoretical models and simulation methods have played important roles in understanding virus capsid assembly, providing key insights into possible modes and pathways of assembly, the physical mechanisms by which these are controlled, and potential sources of off-pathway assembly and the means by which they may be avoided. These theoretical and simulation studies have, however, traditionally been limited in their ability to draw conclusions about specific capsid assembly systems, largely because the theoretical models are controlled by physical parameters (e.g., binding rates), that cannot be analytically determined from any available experimental data source. Much of the seminal work on theoretical models of capsid assembly has therefore been confined either to looking at highly simplified models of generic icosahedral capsid assembly or to studies of ranges of possibilities found over broad parameter domains. We describe work intended to help bridge this gap between theoretical models of capsid assembly in general and experimental work on specific model systems by using computational parameter estimation to learn rate parameters for stochastic simulations of capsid assembly from available experimental data. Our method combines ideas from gradient-based and response-surface optimization methods with a heuristic global search strategy to find parameter fits that approximately reproduce experimental measures of overall assembly progress. We demonstrate the approach through application to light scattering data tracking assembly progress of several in vitro capsid assembly systems. The results provide insight into possible mechanisms and pathways of assembly for specific capsid systems in vitro. They further provide a basis for future studies attempting to computationally project how behavior of these systems would be altered in conditions more closely approximating those expected at sites of capsid assembly in vivo.

High Efficiency of Optimization of Response Surface Method for Structure Dynamic Characteristics by Using Perturbation Method with Complementary Term

In this paper, a new perturbation method is proposed, and is shown that the correction vector can be calculated shorter than ever. And, the computing efficiency of the response surface optimization method could improve greatly by applying perturbation method with complementary term to example analysis in the optimization of vibration characteristics by the response surface methodology and by finishing eigenvalue analysis which takes most computing time just once. Moreover, the validity and effectiveness is examined by examples by inducing approximately estimated formula of the vibration response value based on orthogonal polynomial. Lastly, it is shown that the computing time is shorten greatly compared with former method by applying this method to analysis of optimization problem of vibration characteristics.

The research on extracting oil from watermelon seeds by aqueous enzymatic extraction method

Watermelon kernels were used as raw materials in this study and treated with ultrasound. The effects of different factors on oil extraction from watermelon kernel were studied during the experiments. The optimum parameters obtained form single-factor experiments and response surface method optimization were as follows: enzyme additive amount 2.63%, hydrolysis temperature 47.13°C, hydrolysis time 4.29h, materials to water rate 1:4.35 and pH 7.89. The optimum oil extraction under the above optimum condition was 97.92%.

Constrained Response Surface Optimization for a Laser Beam Welding Process

Problem statement: On a current operating condition of a laser beam welding process in the hard disk drive industry, it has been found that shear strength of the head support and suspension assembly is slightly higher than customers' specification. This situation leads to an inspection with a large sample size and a high frequency. Shear strength is not only one quality characteristic for this assembly, but other critical physical specifications of welding diameter and depth need to be also considered. Approach: A hybridization strategy, based on linear and nonlinear Constrained Response Surface Optimization Methods (CRSOM), has been developed for this process refinement. The hybridization is having a provision to include both explicit constraints of influential process variables as well as implicit constraints of physical specifications. Results: The proposed levels of influential process variables have been successfully implemented in terms of shear strength and satisfied both welding diameter and depth specifications. Conclusion: The advantage of the hybridization compared with individually CRSOM is that all the data from the experiment is collected together to make a final decision. When engineering problems are large and complicated, an effective finite sequence of instructions from the hybridization can be very useful and practical in setting industrial processes such as semiconductor or automotive manufacturing systems.

Improving an Electrostatic Powder Coating Process via Signal to Noise Response Surface

Problem statement: In a coating process, the master plate referenced brightness or color shade was critical to the exterior appearance on aluminum alloy wheels. The quality measures of interest are the metallic paint thickness values on four areas. Because of these lower quality levels, the manufacturer has spent more on the cost of restudy or scrap as well as the longer production time. Approach: An expert system revealed seven process variables affecting those quality characteristics. Taguchi signal to noise ratio or SN of paint thickness values on the outboard spoke area was determined as a process response whereas SN on the remaining areas of window outboard, window between spoke and inboard spoke became merely process constraints. A constrained response surface optimization method and a modified complex method were performed to move the current operating condition towards the optimum. Results: The new settings improved the paint thickness values in terms of both the average and the standard deviation on all critical areas except the window between spoke. Conclusion: As expected, the implementation brings the reduction of the metallic paint consumption and the mismatch level of color shade.

RSM optimization of the operating parameters for a butanol distillation column

AbstractComprehensive optimization of distillation column operating parameters is very important in chemical production. Response surface methodology (RSM) was used in combination with process simulation for complex optimization of operating parameters on the butanol distillation column in solvent fermentation process. The single‐parameter effect of theoretical number of plates, feed positions, flow rate, and reflux rate on the content of water and butanol in the overhead distillate were investigated using the chemical process simulation software PRO/II. Then, according to the results of single‐parameter simulation, comprehensive optimization was done using the response surface optimization method—central composite design (CCD), with the minimization of water content in the overhead distillate as the objective. The best optimized mathematical model was established and the result was verified by industrial production process. It was that satisfactory results can be obtained when RSM is combined with process simulation. This can produce more optimal conditions than those obtained by single‐factor optimization in multivariate optimization problems. The optimal operating conditions are as follows: number of theoretical plates = 47, feed positions at the 7th and 12th theoretical plates (from top to bottom), overhead distillate flow rate = 441 kg/h, and reflux rate = 1860 kg/h. The water and butanol contents in the overhead distillate under these conditions are 0.5093 and 0.001%, respectively. This process was a reference point for the optimization of operating parameters of a distillation system. Copyright © 2010 Curtin University of Technology and John Wiley & Sons, Ltd.

Application of the Response Surface Method for Optimization of Headspace Liquid Phase Microextraction of Trihalomethanes in Drinking Water

AbstractAn optimized analysis method based on headspace liquid phase microextraction (HS‐LPME) and gas chromatography coupled with mass spectrometry was proposed for the determination of trihalomethanes (THMs) in drinking water. The response surface method (RSM) was used to optimize the extraction of THMs for analysis by HS‐LPME. The temperature, extraction time and NaCl concentration were found to be important extraction parameters. The coefficient of determination (R2) for the model was 94.97%. A high probability value (P < 0.0001) for the regression indicated that the model had a high level of significance. The optimum conditions were seen to be: temperature 42.0°C, NaCl concentration 0.30 g/mL, and extraction time 28 min. The response variable was the summation of the THMs chromatography peak areas and the reproducibility of this was investigated in five replicate experiments under the optimized conditions. The relative standard deviations (RSD%) of the THMs ranged from 8.0–11.6%. The limits of detection (LODs), based on a signal‐to‐noise ratio (S/N) of three ranged from 0.42–0.78 μg/L, and were lower than the maximum limits for THMs in drinking water established by the WHO.

Response Ant Colony Optimization of End Milling Surface Roughness

Metal cutting processes are important due to increased consumer demands for quality metal cutting related products (more precise tolerances and better product surface roughness) that has driven the metal cutting industry to continuously improve quality control of metal cutting processes. This paper presents optimum surface roughness by using milling mould aluminium alloys (AA6061-T6) with Response Ant Colony Optimization (RACO). The approach is based on Response Surface Method (RSM) and Ant Colony Optimization (ACO). The main objectives to find the optimized parameters and the most dominant variables (cutting speed, feedrate, axial depth and radial depth). The first order model indicates that the feedrate is the most significant factor affecting surface roughness.

Multi-objective optimization of the tooth surface in helical gears using design of experiment and the response surface method

The design of tooth surface for low gear noise under various load conditions is very important, and gear noise is highly related to transmission error. Optimal tooth surface for reduction of transmission error is very difficult to analytically determine due to nonlinearity of transmission error and the need to satisfy multiple load conditions. Satisfying design variables in multiple load conditions leads to the Pareto optimum of multi-objective optimization. There, the method to determine optimal lead curve and robust tooth surface design is proposed, using the response surface method and multi-objective optimization. The effect of transmission error on the candidate design variables by a screening experiment has been investigated using analysis of variance. Design variables are likewise selected. The fitted regression model of transmission error is built with the statistic validation of the representation. The model with constraints is solved to obtain optimum lead curve design and robust design for the tooth surface under multiple loads.

A Computationally Efficient Formal Optimization of Regional Myocardial Contractility in a Sheep With Left Ventricular Aneurysm

A non-invasive method for estimating regional myocardial contractility in vivo would be of great value in the design and evaluation of new surgical and medical strategies to treat and/or prevent infarction-induced heart failure. As a first step towards developing such a method, an explicit finite element (FE) model-based formal optimization of regional myocardial contractility in a sheep with left ventricular (LV) aneurysm was performed using tagged magnetic resonance (MR) images and cardiac catheterization pressures. From the tagged MR images, 3-dimensional (3D) myocardial strains, LV volumes and geometry for the animal-specific 3D FE model of the LV were calculated, while the LV pressures provided physiological loading conditions. Active material parameters (T(max_B) and T(max_R)) in the non-infarcted myocardium adjacent to the aneurysm (borderzone) and in myocardium remote from the aneurysm were estimated by minimizing the errors between FE model-predicted and measured systolic strains and LV volumes using the successive response surface method for optimization. The significant depression in optimized T(max_B) relative to T(max_R) was confirmed by direct ex vivo force measurements from skinned fiber preparations. The optimized values of T(max_B) and T(max_R) were not overly sensitive to the passive material parameters specified. The computation time of less than 5 hours associated with our proposed method for estimating regional myocardial contractility in vivo makes it a potentially very useful clinical tool.

Development of an adaptive response surface method for optimization of computation-intensive models

In general, optimization techniques involve numerous repeated objective function evaluations. As a consequence, optimization times can become very large depending on the complexity of the model to be optimized. This manuscript describes the development of an adaptive response surface method for optimization of computation-intensive models, capable of reducing optimization times. The response model to be optimized is not built from a pre-defined number of design experiments but is adapted and refined during the optimization routine. Different approximation models are applicable in combination with the developed optimization technique. The proposed optimization technique is evaluated on a standard test problem as well as a finite element model design optimization with multiple parameters.

Application of response surface method for optimization of dispersive liquid–liquid microextraction of water-soluble components of Rosa damascena Mill. essential oil

Dispersive liquid–liquid microextraction (DLLME) coupled with gas chromatography–mass spectrometry (GC–MS) was applied for the determination of Rose water constituents. The effective parameters such as volume of extraction and disperser solvents, temperature, and salt effect were inspected by a full factorial design to identify important parameters and their interactions. It showed that salt addition had no effect on the efficiency. Next, a central composite design was applied to obtain optimum point of the important parameters. The optimal condition was obtained as 37.0 μL for extractor, 0.42 mL for disperser and temperature for 48 °C. The main components that were extracted at the optimum point were benzeneethanol (24.87%), geraniol (23.07%), beta-citronellol (22.38%), nerol (8.48%), eugenol (5.98%) and linalool (5.62%).

등가하중법을 이용한 비선형 반응 구조최적설계 사례연구

Nonlinear response structural optimization is performed using equivalent loads (NROEL). Nonlinear response optimization is extremely cost because many nonlinear analyses are required. In NROEL, the external loads are transformed to the equivalent loads (EL) for linear static analysis and linear response optimization is carried out based on the EL in a cyclic manner until the convergence criteria are satisfied. EL is the load set which generates the same response field of linear analysis as that of nonlinear analysis. The primitive form of theory has been published. In this research, the theory is investigated with large scale example problems. Four examples are solved by using NROEL. Conventional optimization with sensitivity analysis using the finite difference method (FDM) is also applied to the same examples. Moreover, response surface optimization method is applied to the last two examples. The results of the optimizations are compared. In nonlinear response optimization of large scale problems, hundreds (or even thousands) of nonlinear analyses are expected to satisfy the convergence criteria. However, in nonlinear response optimization using equivalent loads, only tens of nonlinear analyses are required. The results are discussed and the usefulness of NROEL is presented.

형상 최적화를 통한 축류송풍기의 설계

This paper presents the response surface optimization method using three-dimensional Wavier-Stokes analysis to optimize the blade shape of an axial flow fan. Reynolds-averaged Wavier-Stokes equations with turbulence model are discretized with finite volume approximations using the unstructured grid. Regression analysis is used for generating response surface, and it is validated by ANOVA and t-statistics. Four geometric variables, i.e., sweep and lean angles at mean and tip respectively were employed to improve the efficiency. The computational results are compared with experimental data and the comparisons show generally good agreements. As a main result of the optimization, the total efficiency was successfully improved. Also, detailed effects of sweep and lean on the axial flow fan are discussed.

Response Surface Method Optimization of Uniform and Axially Segmented Duct Acoustics Liners

An extensive duct acoustics propagation study is presented that has been conducted to assess the design of a liner for an aeroengine inlet duct. The aim is to predict how different liner configuarations, at various flight conditions affect the attenuation of sound in an inlet. Two different noise source models are used: single mode and multimode. These represent the two principal fan noise sources: tonal and broadband noise. The two noise source models are then combined to predict the overall attenuation. An optimization procedure based on a response surface model is presented, to investigate a uniform and an axially segmented acoustic liner. The objective function used in the optimization is based on an approximate calculation of the perceived noise level. The aim is to utilize and axially segmented liner to increase, compared to a unifrom liner, the overall sound attenuation that is predicted. The main feature that emerges is that it is possible to increase the attenuation with an axially segmented liner only when a limited number of propagating modes are present.

NEURAL NETWORK RESPONSE SURFACE OPTIMIZATION DESIGN FOR COMPOSITE STIFFENED STRUCTURES

To avoid drawbacks of conventional structural op- timization approaches,a neural network(NN)response surface optimization method is proposed for the design of composite stiffened structures.Such NN-based structural analysis re- sponse surfaces can reflect the global mapping relationship between design inputs and structural response outputs.By using the orthotropic experiment method to select the appropriate structural finite element analysis samples,neural network re- sponse surfaces can be trained with reasonable accuracies.The constructed response surfaces can be either used as objective function or constraints or both.Together with other conven- tional constraints,an revised optimization design model can be formed which can be solved by using genetic algorithm(GA). Taking a hat-stiffened composite panel of blended wing-body aircraft as example,the structural weight response surface is developed as objective function,and strength and buckling factor response surfaces as constraints.All these neural net- works are trained by finite element samples computed through PATRAN/NASTRAN software.The optimization results illus- trate that it can significantly reduce the cycles of finite element model analysis and achieve highly accurate response approxi- marion results.Eventually,the approach can greatly save the com- putation time and raise the efficiency of optimization process.

Application of Numerical Optimization Technique to Design of Forward-Curved Blades Centrifugal Fan

This paper presents the response surface optimization method using three-dimensional Navier-Stokes analysis to optimize the shape of a forward-curved blades centrifugal fan. For numerical analysis, Reynolds-averaged Navier-Stokes equations with k-e turbulence model are discretized with finite volume approximations. In order to reduce huge computing time due to a large number of blades in forward-curved blades centrifugal fan, the flow inside of the fan is regarded as steady flow by introducing the impeller force models. Three geometric variables, i.e., location of cut off, radius of cut off, and width of impeller, and one operating variable, i.e., flow rate, were selected as design variables. As a main result of the optimization, the efficiency was successfully improved. And, optimum design flow rate was found by using flow rate as one of design variables. It was found that the optimization process provides reliable design of this kind of fans with reasonable computing time.

설계유량을 변수로 한 원심다익송풍기의 최적설계

This paper presents the response surface optimization method using three-dimensional Navier-Stokes analysis to optimize the shape of a forward-curved blades centrifugal fan For numerical analysis, Reynolds-averaged Navier-Stokes equations with k-ε turbulence model are discretized with finite volume approximations In order to reduce huge computing time due to a large number of blades ill forward-curved blades centrifugal fan, the flow inside of the fan is regarded as steady flow by introducing the Impeller force models Three geometric variables, ie, location of cut off, rooms of cut off, and width of Impeller, and one operating variable, i.e, flow rate, were selected as design variables As a main result of the optimization, the efficiency was successfully improved And, optimum design flow rate was found by using flow rate as one of design variables It was found that the optimization process provides reliable design of this kind of fans with reasonable computing time.