基于双响应曲面法的稳健参数设计

针对焊膏印刷过程中,设计变量与输出质量特性间非线性关系难以获得的情况,提出了基于双响应曲面法的参数优化方法。以焊膏厚度均值及其方差作为优化目标,首先建立焊膏厚度均值及其方差与设计变量之间的响应曲面模型;其次,考虑焊膏厚度的波动,提出以置信度概念缩小设计区间,以提高设计结果的稳健性。最后,求解最优化模型,其最优解即为最佳参数组合。试验结果表明,采用所提出的方法,工序能力指数Cp从1.01提高到了1.52。     

A comparative study of the scalability of alternative metamodelling techniques

Metamodels, also known as surrogate models, can be used in place of computationally expensive simulation models to increase computational efficiency for the purposes of design optimization or design space exploration. The accuracy of these metamodels varies with the scale and complexity of the underlying model. In this article, three metamodelling methods are evaluated with respect to their capabilities for modelling high-dimensional, nonlinear, multimodal functions. Methods analyzed include kriging, radial basis functions, and support vector regression. Each metamodelling technique is used to model a set of single output functions with dimensionality ranging from fifteen to fifty independent variables and modality ranging from one to ten local maxima. The number of points used to train the models is increased until a predetermined error threshold is met. Results show that kriging metamodels perform most consistently across a variety of functions, although radial basis functions and support vector regression are very competitive for highly multimodal functions and functions with large local gradients, respectively. Support vector regression metamodels consistently offer the shortest build and prediction times when applied to large scale multimodal problems.     

Robust Parameter Design for Profile Quality Control

In certain manufacturing processes, product quality is characterized by spatial profiles, and such profiles are expected to meet specific shape requirements. As profile shapes are affected by process conditions, properly adjusted process variables are expected to help improve profile quality. This work aims to achieve desired shapes of profiles that are sensitive to the variation of noise factors through optimizing settings of controllable factors. A hierarchical model is first built to characterize the spatial correlation of measurement points on a profile and link quality metrics with process variables. The process is then optimized using the robust parameter design technique. The performance of the proposed method is studied using a motivating example from nanomanufacturing. Copyright © 2015 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。     

ESVR算法及支撑向量机算法中参数的确定

支撑向量机是基于有限数据的机器学习算法,主要研究如何从一些给定的观测数据获得目前尚不能通过原理分析得出的规律,利用这些规律去分析客观现象并对无法观测的数据进行预测。本文在已有的支撑向量机算法的基础上,提出了一种新的算法——ESVR算法,它是基于支撑向量回归机的改进算法,利用原有用于回归问题的SVM算法消除了孤立点对已知问题的影响。针对支撑向量机算法中核参数取值对推广性的影响较明显的特点,本文给出了一种核函数中参数的确定方法——渐进搜索法,它可以得到支撑向量机算法中核参数的取值范围,并具有推广误差较小的特点。数值实验表明它们具有较好的效果。     

Robust Parameter Design of an EDM Process

The paper details a robust parameter design of an electrical discharge machining process. The influence of capacitance, pulse off‐time, pulse on‐time and pulse current on both the average and variability of surface roughness and material removal rate of a titanium alloy was investigated. The analysis revealed that to attain robustness against the impact of noise parameters, no capacitance should be applied. Furthermore, increasing pulse on‐time and its current increased the average of both the surface roughness and material removal rate. Two approaches were suggested to deal with the trade‐off between minimizing the former and maximizing the latter. The study confirmed empirically the inferiority of Taguchi's S/N ratios to a robust design method involving the use of log(s) together with a simple graphical tool for determining the appropriate data transformation called lambda plot. In fact, it was revealed that the employed S/N ratios were driven mainly by the average and involved unaided, unexplained and unjustified transformations. The log(s), on the other hand, provided an independent means of quantifying the variability and, when integrated with lambda plot, rendered not only a simplified analysis but also a better process understanding. The study is the first to report the use of this powerful approach in the context of electrical discharge machining parameter design. Copyright © 2012 John Wiley & Sons, Ltd.     

Use of Design Sensitivity Information in Response Surface and Kriging Metamodels

Metamodels based on responses from designed (numerical) experiments may form efficient approximations to functions in structural analysis. They can improve the efficiency of Engineering Optimization substantially by uncoupling computationally expensive analysis models and (iterative) optimization procedures. In this paper we focus on two strategies for building metamodels, namely Response Surface Methods (RSM) and kriging. We discuss key-concepts for both approaches, present strategies for model training and indicate ways to enhance these metamodeling approaches by including design sensitivity data. The latter may be advantageous in situations where information on design sensitivities is readily available, as is the case with e.g. Finite Element Models. Furthermore, we illustrate the use of RSM and kriging in a numerical model study and conclude with some remarks on their practical value.     

Studies on the Effects of Estimator Selection in Robust Parameter Design under Asymmetric Conditions

The primary goal of robust parameter design (RPD) is to determine the optimum operating conditions that achieve process performance targets while minimizing variability in the results. To achieve this goal, typical approaches to RPD problems use ordinary least squares methods to obtain response functions for the mean and variance by assuming that the experimental data follow a normal distribution and are relatively free of contaminants or outliers. Consequently, the most common estimators used in the initial tier of estimation are the sample mean and sample variance, as they are very good estimators when these assumptions hold. However, it is often the case that such assumed conditions do not exist in practice; notably, that inherent asymmetry pervades system outputs. If unaccounted for, such conditions can affect results tremendously by causing the quality of the estimates obtained using the sample mean and standard deviation to deteriorate. Focusing on asymmetric conditions, this paper examines several highly efficient estimators as alternatives to the sample mean and standard deviation. We then incorporate these estimators into RPD modeling and optimization approaches to ascertain which estimators tend to yield better solutions when skewness exists. Monte Carlo simulation and numerical studies are used to substantiate and compare the performance of the proposed methods with the traditional approach. Copyright © 2012 John Wiley & Sons, Ltd.     

Simultaneous Optimization of Robust Parameter and Tolerance Design Based on Generalized Linear Models

Robust parameter design (RPD) and tolerance design (TD) are two important stages in design process for quality improvement. Simultaneous optimization of RPD and TD is well established on the basis of linear models with constant variance assumption. However, little attention has been paid to RPD and TD with non‐constant variance of residuals or non‐normal responses. In order to obtain further quality improvement and cost reduction, a hybrid approach for simultaneous optimization of RPD and TD with non‐constant variance or non‐normal responses is proposed from generalized linear models (GLMs). First, the mathematical relationship among the process mean, process variance and control factors, noise factors and tolerances is derived from a dual‐response approach based on GLMs, and the quality loss function integrating with tolerance is developed. Second, the total cost model for RPD‐TD concurrent optimization based on GLMs is proposed to determine the best control factors settings and the optimal tolerance values synchronously, which is solved by genetic algorithm in detail. Finally, the proposed approach is applied into an example of electronic circuit design with non‐constant variance, and the results show that the proposed approach performs better on quality improvement and cost reduction. Copyright © 2012 John Wiley & Sons, Ltd.     

An Optimized Ensemble Model for Prediction the Bandwidth of Metamaterial Antenna

Metamaterial Antenna is a special class of antennas that uses metamaterial to enhance their performance. Antenna size affects the quality factor and the radiation loss of the antenna. Metamaterial antennas can overcome the limitation of bandwidth for small antennas. Machine learning (ML) model is recently applied to predict antenna parameters. ML can be used as an alternative approach to the trial-and-error process of finding proper parameters of the simulated antenna. The accuracy of the prediction depends mainly on the selected model. Ensemble models combine two or more base models to produce a better-enhanced model. In this paper, a weighted average ensemble model is proposed to predict the bandwidth of the Metamaterial Antenna. Two base models are used namely: Multilayer Perceptron (MLP) and Support Vector Machines (SVM). To calculate the weights for each model, an optimization algorithm is used to find the optimal weights of the ensemble. Dynamic Group-Based Cooperative Optimizer (DGCO) is employed to search for optimal weight for the base models. The proposed model is compared with three based models and the average ensemble model. The results show that the proposed model is better than other models and can predict antenna bandwidth efficiently.     

An efficient ensemble of radial basis functions method based on quadratic programming

Radial basis function (RBF) surrogate models have been widely applied in engineering design optimization problems to approximate computationally expensive simulations. Ensemble of radial basis functions (ERBF) using the weighted sum of stand-alone RBFs improves the approximation performance. To achieve a good trade-off between the accuracy and efficiency of the modelling process, this article presents a novel efficient ERBF method to determine the weights through solving a quadratic programming subproblem, denoted ERBF-QP. Several numerical benchmark functions are utilized to test the performance of the proposed ERBF-QP method. The results show that ERBF-QP can significantly improve the modelling efficiency compared with several existing ERBF methods. Moreover, ERBF-QP also provides satisfactory performance in terms of approximation accuracy. Finally, the ERBF-QP method is applied to a satellite multidisciplinary design optimization problem to illustrate its practicality and effectiveness for real-world engineering applications.     

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.     

Gaussian Process Modeling and Optimization of Profile Response Experiments

Experiments where the response of interest is a curve or ‘profile’ arise in a variety of applications in engineering practice. In a recent paper (Journal of Quality Technology, 44, 2, pp. 117–135, 2012), a mixed‐effects Bayesian approach was proposed for the Bayesian optimization of profile response systems, where a particular shape of the profile response defines desired properties of the product or process. This paper proposes an alternative spatio‐temporal Gaussian random function process model for such profile response systems, which is more flexible with respect to the types of desired profile shapes that can be modeled and allows us to model profile‐to‐profile correlation, if this exists. The method is illustrated with real examples taken from the literature, and practical aspects related to model building and diagnostics are discussed. Copyright © 2013 John Wiley & Sons, Ltd.     

纸浆模塑缓冲包装结构参数的稳健性分析

针对纸浆模塑缓冲包装结构参数对缓冲性能的影响程度,引入基于实验设计的稳健性实验设计方法,探讨了纸浆模塑缓冲包装结构的厚度、斜度、缓冲高度和接触边长对缓冲性能的影响程度.此研究结果为缓冲包装结构的设计提供一定参考.     

噪声因子存在下的多响应参数设计的优化

采用多元损失函数法,对噪声因子存在下的多响应稳健性参数设计进行了优化.该方法考虑了噪声因子的影响,结合响应期望值和响应方差,其中响应方差结合了噪声因子产生的方差和拟合模型的预测方差,给出了综合方差的无偏估计,使解决方案对噪声因子和参数估计的不确定性都具有稳健性,避免了方差出现非正定的可能性.采用该方法对实例进行分析,得到较好的优化结果.     

Solving the Multidisciplinary Robust Parameter Design Problem for Mixed Type Quality Characteristics under Asymmetric Conditions

Quality practitioners often identify robust parameter design (RPD) as one of the most important and effective methods for process and quality improvement. Within this framework, identifying the optimal factor settings that achieve desired process targets with minimum variance is critical and can translate to significant reductions in product waste and processing costs. In solving this problem, most traditional RPD models consider only a single quality characteristic of interest. However, products are often judged by multiple quality characteristics, which often have conflicting objectives. Conventional RPD models that address the multi‐response problem typically only examine like‐type cases, and those that consider mixed types of quality characteristics often overlook any asymmetry that is likely to exist in certain types. In contrast, this article proposes a multidisciplinary RPD methodology that provides an enhanced approach for modeling multiple, mixed type quality characteristics; uses the skew normal distribution to allow for a fuller and more accurate representation of asymmetric system properties and to facilitate simultaneous modeling of both symmetric and asymmetric conditions; and implements a priority‐based optimization scheme that affords engineers' and decision makers' flexibility in establishing and modifying optimization priorities. A numerical example is used to demonstrate the proposed methodology, and the results are compared traditional approaches to illustrate potential improvements. Copyright © 2013 John Wiley & Sons, Ltd.     

Automatic detection of brain tumor in magnetic resonance images using multi‐texton histogram and support vector machine

Segmentation is the process of labeling objects in image data. It is a decisive phase in several medical imaging processing tasks for operation planning, radio therapy or diagnostics, and widely useful for studying the differences of healthy persons and persons with tumor. Magnetic Resonance Imaging brain tumor segmentation is a complicated task due to the variance and intricacy of tumors. In this article, a tumor segmentation scheme is presented, which focuses on the structural analysis on both tumorous and normal tissues. Our proposed method hits the target with the aid of the following major steps: (i) Tumor Region Location, (ii) Feature Extraction using Multi‐texton Technique, and (iii) Final Classification using support vector machine (SVM). The results for the tumor detection are validated through evaluation metrics such as, sensitivity, specificity, and accuracy. The comparative analysis is carried out by Radial Basis Function neural network and Feed Forward Neural Network. The obtained results depict that the proposed Multi‐texton histogram and support vector machine based brain tumor detection approach is more robust than the other classifiers in terms of sensitivity, specificity, and accuracy. © 2013 Wiley Periodicals, Inc. Int J Imaging Syst Technol, 23, 97–103, 2013     

An Affordable Approach for Robust Design of Thick Laminated Composite Structure

A systematic and affordable approach is proposed for the robust design of thick laminated composite structures. Our approach integrates the principles of the Robust Concept Exploration Method (RCEM) for designing complex engineering systems and the hierarchical multi-level optimization procedure for managing the complexity of composite structure optimization. Foundational to the proposed approach is the use of Design of Experiments (DOE) techniques and the Response Surface Methodology (RSM) for improving computational efficiency in using high fidelity design simulations; and the use of the robust design method for improving the quality of a product that is insensitive to potential variations of design parameters. Our approach is illustrated through the design of a laminated composite femoral component for hip joint arthroplasty. The solution yields the robust design of a composite hip implant, which is applicable for a range of bone stiffness, thereby eliminating the need to design specifically for an individual.     

一种自适应抽样的代理模型构建及其在复材结构优化中的应用

提出了基于一种自适应抽样和增强径向基插值的自适应代理模型方法,这种自适应抽样方法以确定适量的样本点数量和提高代理模型自适应能力为目的,使新增样本点位于设计空间的稀疏区域并确保所有的样本点均匀分布于设计空间以提高代理模型精度。标准误差用来判断代理模型的精度大小并决定是否对代理模型进行更新。一种条件随机抽样被用来对比本文的自适应抽样方法。经过对比验证发现,采用自适应抽样方法的代理模型精度比条件随机抽样方法的代理模型精度高。这种自适应代理模型结合多岛遗传算法被用来优化旋翼臂的碳纤维增强环氧树脂复合材料铺层角度使得旋翼臂的一阶模态频率最大。优化结果表明,不同的碳纤维增强环氧树脂复合材料铺层角度对旋翼臂的一阶模态频率值影响较大,优化结果获取了最优铺层角度,旋翼臂的一阶模态频率值被提高以远离激励频率而避免旋翼飞机的共振。     

Development of a Rapid Prototyping System using Response Surface Methodology

This case study presents an investigation of the relationships between eight process operating variables (factors) and five part performance measures (responses) in a rapid prototyping system. The use of fractional factorial, single‐factor foldover, and central composite designs is demonstrated. Polynomial regression models are constructed for each response, followed by a desirability function model. Canonical and ridge analyses are used to identify a group of factor settings that simultaneously produce improved performance for all responses. Copyright © 2006 John Wiley & Sons, Ltd.