An Efficient Adaptive Sequential Methodology for Expensive Response Surface Optimization

The preset response surface methodology (RSM) designs are commonly used in a wide range of process and design optimization applications. Although they offer ease of implementation and good performance, they are not sufficiently adaptive to reduce the required number of experiments and thus are not cost effective for applications with high cost of experimentation. We propose an efficient adaptive sequential methodology based on optimal design and experiments ranking for response surface optimization (O‐ASRSM) for industrial experiments with high experimentation cost, limited experimental resources, and requiring high design optimization performance. The proposed approach combines the concepts from optimal design of experiments, nonlinear optimization, and RSM. By using the information gained from the previous experiments, O‐ASRSM designs the subsequent experiment by simultaneously reducing the region of interest and by identifying factor combinations for new experiments. Given a given response target, O‐ASRSM identifies the input factor combination in less number of experiments than the classical single‐shot RSM designs. We conducted extensive simulated experiments involving quadratic and nonlinear response functions. The results show that the O‐ASRSM method outperforms the popular central composite design, the Box–Behnken design, and the optimal designs and is competitive with other sequential response surface methods in the literature. Furthermore, results indicate that O‐ASRSM's performance is robust with respect to the increasing number of factors. Copyright © 2012 John Wiley & Sons, Ltd.     

A Robust Framework for Multi‐Response Surface Optimization Methodology

A robust multi‐response optimization framework is proposed for simultaneously optimizing multiple conflicting quality characteristics. Unlike prior methods, the proposed approach is insensitive to subjective inputs like target specifications and improves optimization process for correlated responses. The effectiveness of the proposed approach is demonstrated and compared with existing methods considering two examples from the literature. The proposed method yields similar results consistently for different assigned target values demonstrating repeatability of the model, hence demonstrating insensitivity to assigned subjective target values. Furthermore, the study also considers multiple correlated design characteristics issue to achieve better trade‐off during design optimization. Copyright © 2013 John Wiley & Sons, Ltd.     

Use of Orthogonal Array Composite Designs to Study Lipid Accumulation in a Cell‐Free System

The development of clean, sustainable alternative energy sources is increasingly important. One promising alternative to depleting fuel reserves is algae‐based biodiesel fuel, which is both non‐toxic and renewable. Despite the tremendous potential of algae‐based biodiesel fuel, it has not yet been profitable because of the high cost per unit area of large cultivation. We present a novel application of Orthogonal Array Composite Designs (OACDs) to optimize lipid production of a cell‐free system for algae. An OACD consists of a two‐level fractional factorial design and a three‐level orthogonal array. We start with an initial screening experiment based on six chemicals using an OACD with 50 runs. Based on this experiment, two chemical compounds were removed and a follow‐up 25‐run OACD with four chemicals was performed. Our analysis shows that only three chemicals – nitrogen, magnesium, and phosphate – are essential for lipid accumulation, and a range of optimum combinations of these three chemicals is identified. The lipid accumulation for these three chemical combinations is substantially higher in comparison to the commercial medium, which contains 16 chemicals and soil water. This leads to a reduced cost of the chemical medium and increased efficiency of biodiesel production from the algal‐based cell‐free system, which can be used to significantly expand the use of biodiesel as a viable alternative to fossil fuels. Copyright © 2015 John Wiley & Sons, Ltd.     

Use of Fractional Factorial Designs in Antiviral Drug Studies

Experimental design and analysis is an effective and commonly used tool in scientific investigations and industrial applications. Many successful applications have been reported in engineering domains, such as chemical engineering, electrical engineering, and mechanical engineering. However, few cases have been reported in biological research, particularly in virology study. Antiviral drug combinations are increasingly used to reduce possible drug‐resistant viral mutant and reduce cytotoxicity. Drug combinations have often been reported to have higher efficacy and lower individual drug dosage. However, the combined antiviral drug effect is generally hard to assess. One important reason is due to the complex interactions between biological systems and drug molecules. We report a study using fractional factorial designs to investigate a biological system with Herpes simplex virus type 1 and five antiviral drugs. The experiment uses a novel composite design that consists of a 16‐run fractional factorial design and an 18‐run orthogonal array. The results indicate that two chemical drugs, Ribavirin and Acyclovir, are more effective than three Interferon drugs. Furthermore, significant interactions exist within the Interferon drug group and within the Ribavirin‐Acyclovir chemical drug group, but the interactions between the Interferon group and the chemical group are not significant. These observations have major implications in the understanding of antiviral drug mechanism towards better design of combinatorial antiviral drug therapy. Copyright © 2012 John Wiley & Sons, Ltd.     

响应曲面建模的稳健M-回归方法

响应曲面方法是生产过程改进和优化的一种非常有效的方法。在传统的响应曲面模型的建立过程中,通常假定随机误差服从正态分布且相互独立具有相同的方差。但是实际生产中随机误差的方差并不是完全相同,观测值中会存在异常点,这就需要稳健的估计方法来抑制异常点对模型估计的影响。为了降低异常点对响应曲面模型最优值的影响,针对响应曲面方法中的中心复合设计,〖JP2〗充分考虑到不同实验设计位置上可能出现异常点的情况,对稳健M 回归方法：Huber 估计、Tukey 估计和Welsch 估计进行了理论比较研究。研究结果表明Welsch和Tukey 估计能有效改善异常点对响应曲面模型最优值的影响,消弱异常点对中心复合设计的干扰。通过一个来自化工方面的案例,计算了中心复合设计不同位置存在异常点与不存在异常点时,响应曲面模型的最优值,对比分析得出当异常点与响应均值的偏离程度较大时（10倍标准差）,稳健M 估计尤其是Welsch和Tukey 估计显著提高响应曲面建模的稳健性。     

ASRSM: A Sequential Experimental Design for Response Surface Optimization

Most preset response surface methodology (RSM) designs offer ease of implementation and good performance over a wide range of process and design optimization applications. These designs often lack the ability to adapt the design on the basis of the characteristics of application and experimental space so as to reduce the number of experiments necessary. Hence, they are not cost‐effective for applications where the cost of experimentation is high or when the experimentation resources are limited. In this paper, we present an adaptive sequential response surface methodology (ASRSM) for industrial experiments with high experimentation cost, limited experimental resources, and high design optimization performance requirement. The proposed approach is a sequential adaptive experimentation approach that combines concepts from nonlinear optimization, design of experiments, and response surface optimization. The ASRSM uses the information gained from the previous experiments to design the subsequent experiment by simultaneously reducing the region of interest and identifying factor combinations for new experiments. Its major advantage is the experimentation efficiency such that for a given response target, it identifies the input factor combination (or containing region) in less number of experiments than the classical single‐shot RSM designs. Through extensive simulated experiments and real‐world case studies, we show that the proposed ASRSM method outperforms the popular central composite design method and compares favorably with optimal designs. Copyright © 2012 John Wiley & Sons, Ltd.     

Stu Hunter's Contributions to Experimental Design and Quality Engineering

ABSTRACT

Professor J. Stuart Hunter has long been one of the leaders of our field. He has made many pioneering contributions to experimental design and the general field of quality engineering, including response surface methodology, fractional factorial designs, and the use of experimental design in product and process design including the robust design problem. This article highlights some of his key technical contributions and identifies some additional work that has been inspired by his research.     

A note on the Bayesian analysis of experiments with correlated multiple responses using a matrix‐logarithmic covariance model

In the literature, analysis of multiple responses from experiments with replicates has modeled the covariance matrix directly as linear models of the transformed variances and correlations, ie, covariance modeling. This article considers models based on the matrix‐logarithm of the covariance matrix. This so‐called log‐covariance modeling is illustrated with data from actual experiments and compared with the traditional covariance modeling.     

A method of steepest ascent for multiresponse surface optimization using a desirability function method

Multiresponse problems are common in product or process development. A conventional approach for optimizing multiple responses is to use a response surface methodology (RSM), and this approach is called multiresponse surface optimization (MRSO). In RSM, the method of steepest ascent is widely used for searching for an optimum region where a response is improved. In MRSO, it is difficult to directly apply the method of steepest ascent because MRSO includes several responses to be considered. This paper suggests a new method of steepest ascent for MRSO, which accounts for tradeoffs between multiple responses. It provides several candidate paths of steepest ascent and allows a decision maker to select the most preferred path. This generation and selection procedure is helpful to better understand the tradeoffs between the multiple responses, and ultimately, it moves the experimental region to a good region where a satisfactory compromise solution exists. A hypothetical example is employed for illustrating the proposed procedure. The results of this case study show that the proposed method searches the region containing an optimum where a satisfactory compromise solution exists.     

混合动力汽车快速控制原型系统仿真平台开发

为加快混合动力汽车控制策略的开发进度,缩短产品开发周期,设计与开发了基于飞思卡尔MC9S12DG256控制器、驾驶员模拟器、控制器自动代码生成编译工具包及Freemaster实时数据监测软件构成的混合动力汽车控制策略快速控制原型系统半实物仿真平台,将底层驱动与上层控制策略模型一键下载到MC9S12DG256控制器,实现模型到代码的自动下载,并能与AVL CRUISE中车辆信息进行实时的串口通信。针对一款并联式混合动力客车进行仿真实验,结果能较好地模拟实车特性,验证了该仿真平台的有效性,其开发成本低廉,易在高校中推广。     

Investigations on Factors Affecting Chitosan for Dissolution Enhancement of Oxcarbazepine by Spray Dried Microcrystal Formulation With an Experimental Design Approach

In the present work effect of chitosan on microcrystal formulation for dissolution enhancement of oxcarbazepine using controlled crystallization technique coupled with spray drying was explored. The work was extended for exploration of simplified approach for stable particle size reduction. The study was performed with an experimental design approach i. e. a fractional factorial design of resolution 5 (with all 2 factor interaction) for the screening of predefined independent variables drug concentration, chitosan concentration, feed rate, inlet temperature and percent aspiration for spray drying. Whereas percent drug dissolved, wettability time, flowability in terms of angle of repose and particle size were designated as response variables. Resultant models were analyzed using multiple linear regression analysis, which generated equation to plot response surface curves along with desirability function. Results showed that chitosan concentration had significant effect on dissolution enhancement of oxcarbazepine at a level of 2% w/v. Increase in drug concentration showed decreased dissolution rate however on particle size it did not show statistically significant effect. Topographical characterization was carried out by SEM which showed that feed rate, percent aspiration and inlet temperature had significant effect on particle morphology. For deriving optimized formulation results were analyzed using desirability function for the maximum percent drug dissolved and least drug polymer matrix particle size. DSC studies showed that drug was molecularly associated with chitosan matrix or particles.     

基于响应面方法的支架结构模型修正研究

为减小有限元建模中不可避免的误差,以支架结构模型为研究对象,选取结构不同部件的三个弹性模量和三个密度参数作为设计变量。根据中心复合设计,建立试验样本空间,利用样本参数的显著性分析结果筛选修正参数。结合线性回归方法,建立支架模态频率与修正参数的二阶多项式。以试验模态分析结果为依据,完成支架结构模型修正。响应面方法修正后的模态频率与试验模态频率具有一致性,且避免重复调用有限元模型,大大提高修正效率,具有修正响应快速性和工程实用性。     

Ensemble of Surrogates for Dual Response Surface Modeling in Robust Parameter Design

The robust parameter design of industrial processes and products on the basis of the concept of building quality into a design has attracted much attention from researchers and practitioners for many years, and several methods have been studied in the research community. Dual response surface methodology is one of the most commonly used approaches for simultaneously optimizing the mean and the variance of response in quality engineering. Nevertheless, when the relationship between influential input factors and output quality characteristics of a process is very complex (e.g. highly nonlinear and noisy), traditional approaches have their limitations. In this article, we introduced support vector regression, kriging model, and radial basis function, which are commonly used in computer experiments, into robust parameter design, and especially introduced a new strategy that builds the dual response surface using the ensemble of surrogates, which can provide a more robust approximation model. We demonstrated the advantages of kriging, support vector regression, radial basis function, and the ensemble of surrogates by reinvestigating the dual response approach on the basis of parametric, nonparametric, and semiparametric approaches, and a simulation experiment is studied. The results show that our presented models can achieve more desirable results than parametric, nonparametric, and semiparametric approaches in terms of fitting and predictive accuracy, and the optimal operating conditions recommended by our presented models are similar to those recommended in literature, which indicates the validation of our presented models. Copyright © 2012 John Wiley & Sons, Ltd.     

A desirability function method for optimizing mean and variability of multiple responses using a posterior preference articulation approach

A desirability function approach has been widely used in multi‐response optimization due to its simplicity. Most of the existing desirability function‐based methods assume that the variability of the response variables is stable; thus, they focus mainly on the optimization of the mean of multiple responses. However, this stable variability assumption often does not apply in practical situations; thus, the quality of the product or process can be severely degraded due to the high variability of multiple responses. In this regard, we propose a new desirability function method to simultaneously optimize both the mean and variability of multiple responses. In particular, the proposed method uses a posterior preference articulation approach, which has an advantage in investigating tradeoffs between the mean and variability of multiple responses. It is expected that process engineers can use this method to better understand the tradeoffs, thereby obtaining a satisfactory compromise solution.     

Media milling process optimization for manufacture of drug nanoparticles using design of experiments (DOE)

Design of experiments (DOE), a component of Quality by Design (QbD), is systematic and simultaneous evaluation of process variables to develop a product with predetermined quality attributes. This article presents a case study to understand the effects of process variables in a bead milling process used for manufacture of drug nanoparticles. Experiments were designed and results were computed according to a 3-factor, 3-level face-centered central composite design (CCD). The factors investigated were motor speed, pump speed and bead volume. Responses analyzed for evaluating these effects and interactions were milling time, particle size and process yield. Process validation batches were executed using the optimum process conditions obtained from software Design-Expert® to evaluate both the repeatability and reproducibility of bead milling technique. Milling time was optimized to <5?h to obtain the desired particle size (d90?相似文献   

New gentle-wing high-shear granulator: impact of processing variables on granules and tablets characteristics of high-drug loading formulation using design of experiment approach

The aim of this work was to study the application of design of experiment (DoE) approach in defining design space for granulation and tableting processes using a novel gentle-wing high-shear granulator. According to quality-by-design (QbD) prospective, critical attributes of granules, and tablets should be ensured by manufacturing process design. A face-centered central composite design has been employed in order to investigate the effect of water amount (X₁), impeller speed (X₂), wet massing time (X₃), and water addition rate (X₄) as independent process variables on granules and tablets characteristics. Acetaminophen was used as a model drug and granulation experiments were carried out using dry addition of povidone k30. The dried granules have been analyzed for their size distribution, density, and flow pattern. Additionally, the produced tablets have been investigated for; weight uniformity, breaking force, friability and percent capping, disintegration time, and drug dissolution. Results of regression analysis showed that water amount, impeller speed and wet massing time have significant (p?相似文献   

Formulation of Insulin-Loaded Polymeric Nanoparticles Using Response Surface Methodology

The objective of this work was to formulate new oral insulin-loaded nanoparticules using the response surface methodology. The insulin nanoparticles were prepared by a water-in-oil-in-water emulsification and evaporation method. The polymers used for the encapsulation were blends of biodegradable poly-epsilon-caprolactone (PCL) and of positively-charged, nonbiodegradable polymer (Eudragis RS®). A central composite design has been built to investigate the effects of three controlled variables: ratio of polymers (PCL/RS ratio), volume, and pH of the aqueous solution of polyvinyl alcohol. The nanoparticles were characterized by measuring the amount of entrapped insulin, the particle size, the polydispersity of the obtained particles, the zeta potential, and the amount of insulin released after 7 hours. A second-order model was evaluated by multiple regression and was statistically tested for each of the studied controlled variable. The obtained polynomials proved efficient to localize an optimal operating area highlighted by the use of three-dimensional response surfaces and their corresponding isoresponse curves. An interesting formulation given by the models was selected, prepared, and evaluated. The corresponding quantity of entrapped insulin was 25 IU per 100 mg of polymer, and the particle size was 350 nm with a polydispersity of 0.21. The quantity of released insulin was 4.8 IU per 100 mg of polymer after 7 hours and the zeta potential was + 44 mV. All these collected values were in perfect accordance with values estimated by the models. Finally, the results suggested that PCL/RS 50/50 nanoparticles might represent a promising formulation for oral delivery of insulin.     

采用响应曲面分析的声屏障优化设计

采用响应曲面法和Box-Behnken设计优化声屏障设计参数。以声屏障设计高度、长度、起点桩号为考察自变量,以声屏障对敏感区域内三处受声点理论插入损失、工程造价为考察因变量,构建多元二次回归模型考察因变量与自变量间的函数关系。设定以敏感区域内声环境质量达标、工程造价最低为优化目标,利用Minitab软件优化分析得到声屏障最优设计参数。     

Multiresponse optimization of a multistage manufacturing process using a patient rule induction method

Most manufacturing industries produce products through a series of sequential stages, known as a multistage process. In a multistage process, each stage affects the stage that follows, and the process often has multiple response variables. In this paper, we suggest a new procedure for optimizing a multistage process with multiple response variables. Our method searches for an optimal setting of input variables directly from operational data according to a patient rule induction method (PRIM) to maximize a desirability function, to which multiple response variables are converted. The proposed method is explained by a step-by-step procedure using a steel manufacturing process as an example. The results of the steel manufacturing process optimization show that the proposed method finds the optimal settings of input variables and outperforms the other PRIM-based methods.     

基于Deform和响应曲面法的钢丝拉拔工艺优化

目的对钢丝拉拔过程的成形质量和拉拔力同时进行优化。方法通过Deform-3D软件建立钢丝拉拔第一道次的有限元分析模型,并验证其可靠性。结合建立的有限元模型,采用正交试验设计,寻找钢丝拉拔过程的显著性影响因素,再以显著性因素为变量,以成形质量指标(文中定义为不均匀系数N)和拉拔力P为响应,建立响应曲面模型,对工艺参数进行优化。结果通过正交试验设计分析发现,模具半锥角和压缩率既是不均匀系数N的显著性影响因素,又是拉拔力P的显著性影响因素;通过分析建立的响应曲面模型发现,单独优化一个指标时,会劣化另一个指标,综合考虑两个指标,得到的较优的工艺参数为模具半锥角5°,压缩率17.65%,此时不均匀系数N为0.247,拉拔力P为2593.77N。结论经过验证,建立的有限元模型和响应曲面模型均具有可靠性,可用于钢丝拉拔工艺的研究和优化。