A trust region-based approach to optimize triple response systems

This article presents a new computing procedure for the global optimization of the triple response system (TRS) where the response functions are non-convex quadratics and the input factors satisfy a radial constrained region of interest. The TRS arising from response surface modelling can be approximated using a nonlinear mathematical program that considers one primary objective function and two secondary constraint functions. An optimization algorithm named the triple response surface algorithm (TRSALG) is proposed to determine the global optimum for the non-degenerate TRS. In TRSALG, the Lagrange multipliers of the secondary functions are determined using the Hooke–Jeeves search method and the Lagrange multiplier of the radial constraint is located using the trust region method within the global optimality space. The proposed algorithm is illustrated in terms of three examples appearing in the quality-control literature. The results of TRSALG compared to a gradient-based method are also presented.     

Multiresponse optimization using multivariate process capability index

Robust design is an efficient method for product and process improvement which combines experimentation with optimization to create a system that is less sensitive to uncontrollable variation. In this article, a simple and integrated modeling methodology for robust design is proposed. This methodology achieves the robustness objective function and input variables constraints simultaneously. The objective function is written in terms of the multivariate process capability vector (MC_pm) of several competing features of the system under study. The proposed methodology is applicable to general functions of the system performance with random variables. The effectiveness of the methodology is verified using two real‐world examples which are compared with those of other robust design methods. Copyright © 2010 John Wiley & Sons, Ltd.     

Thermal optimization in transient thermoelasticity using response surface approximations

Response surface methodology is used to construct approximations to temperature and stress in transient thermoelastic analysis of non-linear systems. The analysis forms the core component of a heating/cooling rate maximization problem in which the ordinates of the ambient temperature at equally spaced time intervals are chosen as the design variables. Polynomials or cubic splines are fitted through the ordinates to describe the ambient temperature profile required for the convective heat transfer analysis. An experimental design method based on D-optimality and a genetic algorithm was used to select the design points used to create the approximations. Linear response surfaces were found to be sufficiently accurate, thereby minimizing the number of finite element analyses. Two examples of which one is a thick-walled pressure vessel are used to illustrate the methodology. © 1998 John Wiley & Sons, Ltd.     

Trust regions in Kriging-based optimization with expected improvement

The Kriging-based Efficient Global Optimization (EGO) method works well on many expensive black-box optimization problems. However, it does not seem to perform well on problems with steep and narrow global minimum basins and on high-dimensional problems. This article develops a new Kriging-based optimization method called TRIKE (Trust Region Implementation in Kriging-based optimization with Expected improvement) that implements a trust-region-like approach where each iterate is obtained by maximizing an Expected Improvement (EI) function within some trust region. This trust region is adjusted depending on the ratio of the actual improvement to the EI. This article also develops the Kriging-based CYCLONE (CYClic Local search in OptimizatioN using Expected improvement) method that uses a cyclic pattern to determine the search regions where the EI is maximized. TRIKE and CYCLONE are compared with EGO on 28 test problems with up to 32 dimensions and on a 36-dimensional groundwater bioremediation application in appendices supplied as an online supplement available at http://dx.doi.org/10.1080/0305215X.2015.1082350. The results show that both algorithms yield substantial improvements over EGO and they are competitive with a radial basis function method.     

Die shape design optimization of sheet metal stamping process using meshfree method

A die shape design sensitivity analysis (DSA) and optimization for a sheet metal stamping process is proposed based on a Lagrangian formulation. A hyperelasticity‐based elastoplastic material model is used for the constitutive relation that includes a large deformation effect. The contact condition between a workpiece and a rigid die is imposed through the penalty method with a modified Coulomb friction model. The domain of the workpiece is discretized by a meshfree method. A continuum‐based DSA with respect to the rigid die shape parameter is formulated using a design velocity concept. The die shape perturbation has an effect on structural performance through the contact variational form. The effect of the deformation‐dependent pressure load to the design sensitivity is discussed. It is shown that the design sensitivity equation uses the same tangent stiffness matrix as the response analysis. The linear design sensitivity equation is solved at each converged load step without the need of iteration, which is quite efficient in computation. The accuracy of sensitivity information is compared to that of the finite difference method with an excellent agreement. A die shape design optimization problem is solved to obtain the desired shape of the workpiece to minimize spring‐back effect and to show the feasibility of the proposed method. Copyright © 2001 John Wiley & Sons, Ltd.     

Automatic vision-based grain optimization and analysis of multi-crystalline solar wafers using hierarchical region growing

Solar power has become an attractive alternative source of energy. The multi-crystalline solar cell has been widely accepted in the market because it has a relatively low manufacturing cost. Multi-crystalline solar wafers with larger grain sizes and fewer grain boundaries are higher quality and convert energy more efficiently than mono-crystalline solar cells. In this article, a new image processing method is proposed for assessing the wafer quality. An adaptive segmentation algorithm based on region growing is developed to separate the closed regions of individual grains. Using the proposed method, the shape and size of each grain in the wafer image can be precisely evaluated. Two measures of average grain size are taken from the literature and modified to estimate the average grain size. The resulting average grain size estimate dictates the quality of the crystalline solar wafers and can be considered a viable quantitative indicator of conversion efficiency.     

Antecedents of trust in using social media for E-government services: An empirical study in Pakistan

Trust is a major concern that develops citizens' willingness to use social media as a technology platform for e-government services. However, despite its importance, there is lack of prior investigation about the factors that can generate citizens' trust to use such services, particularly in a developing country like Pakistan. To address this research gap, this study aims to develop a model that identifies antecedents of citizens' trust to use social media for e-government services. A total of 615 responses were collected from Pakistani citizens having familiarity with e-government and social media services. Partial least squares (PLS-SEM) method was employed to test the proposed relationships in the model. The findings show a significant relationship of trust with citizens intention to use government social media services. Information quality, structural assurances, perceived security, perceived privacy and perceived ease of use are identified as antecedents of trust. The proposed model of this study explains 56.4% of the variance in trust. The implications, limitations and suggestions for future research have also been discussed. These findings can assist government organizations and policy makers in making decisions to increase citizens participation by facilitating their trust on social media-based services of e-government.     

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   

Modelling the Pareto-optimal set using B-spline basis functions for continuous multi-objective optimization problems

In the past few years, multi-objective optimization algorithms have been extensively applied in several fields including engineering design problems. A major reason is the advancement of evolutionary multi-objective optimization (EMO) algorithms that are able to find a set of non-dominated points spread on the respective Pareto-optimal front in a single simulation. Besides just finding a set of Pareto-optimal solutions, one is often interested in capturing knowledge about the variation of variable values over the Pareto-optimal front. Recent innovization approaches for knowledge discovery from Pareto-optimal solutions remain as a major activity in this direction. In this article, a different data-fitting approach for continuous parameterization of the Pareto-optimal front is presented. Cubic B-spline basis functions are used for fitting the data returned by an EMO procedure in a continuous variable space. No prior knowledge about the order in the data is assumed. An automatic procedure for detecting gaps in the Pareto-optimal front is also implemented. The algorithm takes points returned by the EMO as input and returns the control points of the B-spline manifold representing the Pareto-optimal set. Results for several standard and engineering, bi-objective and tri-objective optimization problems demonstrate the usefulness of the proposed procedure.     

Uncertainty quantification using evidence theory in multidisciplinary design optimization

Advances in computational performance have led to the development of large-scale simulation tools for design. Systems generated using such simulation tools can fail in service if the uncertainty of the simulation tool's performance predictions is not accounted for. In this research an investigation of how uncertainty can be quantified in multidisciplinary systems analysis subject to epistemic uncertainty associated with the disciplinary design tools and input parameters is undertaken. Evidence theory is used to quantify uncertainty in terms of the uncertain measures of belief and plausibility. To illustrate the methodology, multidisciplinary analysis problems are introduced as an extension to the epistemic uncertainty challenge problems identified by Sandia National Laboratories.After uncertainty has been characterized mathematically the designer seeks the optimum design under uncertainty. The measures of uncertainty provided by evidence theory are discontinuous functions. Such non-smooth functions cannot be used in traditional gradient-based optimizers because the sensitivities of the uncertain measures are not properly defined. In this research surrogate models are used to represent the uncertain measures as continuous functions. A sequential approximate optimization approach is used to drive the optimization process. The methodology is illustrated in application to multidisciplinary example problems.     

Surrogate modelling and optimization using shape-preserving response prediction: A review

Computer simulation models are ubiquitous in modern engineering design. In many cases, they are the only way to evaluate a given design with sufficient fidelity. Unfortunately, an added computational expense is associated with higher fidelity models. Moreover, the systems being considered are often highly nonlinear and may feature a large number of designable parameters. Therefore, it may be impractical to solve the design problem with conventional optimization algorithms. A promising approach to alleviate these difficulties is surrogate-based optimization (SBO). Among proven SBO techniques, the methods utilizing surrogates constructed from corrected physics-based low-fidelity models are, in many cases, the most efficient. This article reviews a particular technique of this type, namely, shape-preserving response prediction (SPRP), which works on the level of the model responses to correct the underlying low-fidelity models. The formulation and limitations of SPRP are discussed. Applications to several engineering design problems are provided.     

Simultaneous optimization of the microextraction of coffee volatiles using response surface methodology and principal component analysis

It is well known that no single experimental condition can be found under which the extraction of all the volatile compounds in a gas chromatographic analysis of roasted coffee beans by headspace-solid phase microextraction (HS-SPME) is maximized. This is due to the large number of peaks recorded. In this work, the scores vector of the first principal component obtained from PCA on chromatographic peak areas was used as the response to find the optimal conditions for simultaneous optimization of coffee volatiles extraction via response surface methodology (RSM). This strategy consists in compressing several highly correlated peak areas into a single response variable for a central composite design (CCD). RSM was used to identify an optimal factor combination that reflects a compromise between the partially conflicting behavior of the volatiles groups. This simultaneous optimization approach was compared with the desirability function method. The versatility of the PCA-RSM methodology allows it to be used in other chromatographic applications, resulting in an interpretable procedure to solve new analytical problems.     

Model-based process optimization in the presence of parameter uncertainty

In model-based process optimization one uses a mathematical model to optimize a certain criterion, for example the product yield of a chemical process. Models often contain parameters that have to be estimated from data. Typically, a point estimate (e.g. the least squares estimate) is used to fix the model for the optimization stage. However, parameter estimates are uncertain due to incomplete and noisy data. In this article, it is shown how parameter uncertainty can be taken into account in process optimization. To quantify the uncertainty, Markov Chain Monte Carlo (MCMC) sampling, an emerging standard approach in Bayesian estimation, is used. In the Bayesian approach, the solution to the parameter estimation problem is given as a distribution, and the optimization criteria are functions of that distribution. The formulation and implementation of the optimization is studied, and numerical examples are used to show that parameter uncertainty can have a large effect in optimization results.     

Optimization of process parameters for transalkylation of toluene to xylene using response surface methodology

ABSTRACT

H-beta zeolite was modified by the ion exchange method to replace its H⁺ ions with Ce⁴⁺ ions. The catalytic performance of this cerium exchanged beta zeolite was evaluated for vapor phase transalkylation of 1,2,4 TMB (1,2,4 trimethylbenzene) with toluene for the production of xylene in a fixed bed, down-flow reactor. The modified zeolite was found to be highly active for this transalkylation reaction. The response surface methodology (RSM) is used for designing the experiments. The effect of three important reaction parameters viz. temperature, reactant ratio, and space time on response variables (toluene conversion and xylene selectivity) is studied and discussed. All the three selected reaction parameters were found to be significant for the toluene conversion; whereas, xylene selectivity was not much influenced by the temperature. The optimum values of the reaction parameters predicted by the model (temperature: 409.7°C, reactant ratio: 2.024, and space time: 4.451) were validated by an experimental run. The results of the experimental run were in close agreement with the model predicted results.     

Characterization of sequential optimization strategies in concurrent product and process design: A dual-team approach

In team-based design optimization, one type of workflow is relevant to sequential design decision-making; that is, one team's design decision goes after another team's in an alternate fashion. However, the strategies in use for sequential optimization significantly affect the final design solutions. Conventionally, the over-the-wall strategy and the Stackelberg solution strategy from game theory are extensively used for sequential optimization. In this paper, these strategies are extended to cover more design case scenarios in sequential optimization. A dual-team approach is presented to model, in particular, concurrent product and process design (CPPD) using a bi-objective optimization formalism in which a team acts as a decision maker towards a design objective. By differentiating the role of a team in sequential optimization, a set of sequential optimization strategies is provided for CPPD applications. Four CPPD models are accordingly derived to account for four case scenarios in CPPD. The implementation-related algorithms are also presented, along with an example illustration, to support computational design executions.     

Shape optimization of the initial blank in the sheet metal forming process using equivalent static loads

In the sheet metal forming process, forming the final desired shape is difficult to obtain due to wrinkling, tearing, failure of material, etc. Various conditions of the forming process should be controlled for the desired shape. These conditions are the velocity of the punch, the friction factor, the blank holding force, the initial shape of the blank and others. Many researchers have conducted studies to predetermine the initial blank shape. The structural optimization technique is one of them. Non‐linear response structural optimization is required because non‐linearities are involved in the analysis of the metal forming process. When the conventional method is utilized, the cost is extremely high due to repeated non‐linear analysis for function and sensitivity calculation. In this paper, the equivalent static loads (ESLs) method is used to determine the blank shape which leads to the final desired shape and reduced wrinkling. The ESLs method is a structural optimization method where non‐linear dynamic loads are transformed into ESLs, and these ESLs are utilized as external loads in linear response optimization. The design is updated in linear response optimization. Non‐linear analysis is performed with the updated design and the process proceeds in a cyclic manner. An optimization formulation is defined for the examples, the formulated problems are solved to verify the proposed method and the results are discussed. Non‐linear analysis is performed using the commercial software LS‐DYNA, NASTRAN is used for calculating the ESLs and linear response optimization, and an interface program for LS‐DYNA and NASTRAN is developed. Copyright © 2010 John Wiley & Sons, Ltd.     

基于响应面全局优化技术的蜂窝板材料性能参数修正

蜂窝夹层板结构广泛应用于航空航天行业中,建立准确的蜂窝夹芯板有限元模型是分析和优化航天器微振动的必要前提。基于蜂窝芯的力学等效参数模型,建立了蜂窝板的动力学有限元模型。使用正交数值实验设计筛选出对蜂窝板动力学性能影响最大的蜂窝芯等效材料参数,并利用基于响应面模型自适应采样技术的全局优化方法快速地完成了蜂窝芯关键材料参数的优化修正。修正后的蜂窝板有限元模型前六阶模态频率与实验结果的平均误差小于1%。     

Topology optimization of compliant mechanisms using the homogenization method

A procedure to obtain a topology of an optimal structure considering flexibility is presented. The methodology is based on a mutual energy concept for formulation of flexibility and the homogenization method. A multi-objective optimization problem is formulated as an application of compliant mechanism design. Some examples of the design of compliant mechanisms for plane structures are presented. © 1998 John Wiley & Sons, Ltd.     

Beneficiation of low-grade iron ore fines by multi-gravity separator (MGS) using optimization studies

There is an urgent need for development of environmental friendly processes through which iron ore fines can be beneficiated and utilized effectively. For processing of low-grade iron ores, ground to finer size necessitates the use of centrifugal force. This is because the settling rate of the particles in centrifugal force is 500–600 times more than that noticed for the nominal gravitational force. Multi-gravity separator (MGS) is the one such unit used for recovering hematitic fines without addition of chemicals. In the present article, an approach has been made to beneficiate low-grade hematitic iron ore of Jilling mine, Odisha, India, using MGS. The effect of three important variables was studied and their influences were analyzed through statistical approach to optimize grade, recovery, and separation efficiency. Use of response surface methodology (RSM) based on Box–Behnken design has also been adopted for analysis purpose. The results obtained indicate that it is possible to beneficiate low-grade hematitic iron ore from a feed of 50.74% Fe to 65.11% Fe with an acceptable recovery of 71.88%. Optimization of process variables was done for each response, optimized independently irrespective of other responses. Further optimization of the variables was carried out with a multi-objective target.     

Multiobjective robust optimization method for drawbead design in sheet metal forming

It is recognized that fracture and wrinkling in sheet metal forming can be eliminated via an appropriate drawbead design. Although deterministic multiobjective optimization algorithms and finite element analysis (FEA) have been applied in this respect to improve formability and shorten design cycle, the design could become less meaningful or even unacceptable when considering practical variation in design variables and noises of system parameters. To tackle this problem, we present a multiobjective robust optimization methodology to address the effects of parametric uncertainties on drawbead design, where the six sigma principle is adopted to measure the variations, a dual response surface method is used to construct surrogate model and a multiobjective particle swarm optimization is developed to generate robust Pareto solutions. In this paper, the procedure of drawbead design is divided into two stages: firstly, equivalent drawbead restraining forces (DBRF) are obtained by developing a multiobjective robust particle swarm optimization, and secondly the DBRF model is integrated into a single-objective particle swarm optimization (PSO) to optimize geometric parameters of drawbead. The optimal design showed a good agreement with the physical drawbead geometry and remarkably improve the formability and robust. Thus, the presented method provides an effective solution to geometric design of drawbead for improving product quality.