Technologic parameter optimization of gas quenching process using response surface method

A step function model with time is presented in the paper, and an axisymmetric component is regarded as the study objective in this model. The heat transfer coefficient during the gas quenching process is described as a function of time in this model, and five design variables are selected to do the design of Box–Behnken experiment with five factors and three levels. The levels of design variables that attain from the result of Box–Behnken experiment design are regard as the technical parameters of gas quenching to simulate the gas quenching process using the FEM software developed in the paper. Some mathematical models of response surface are gained by the mixed regression method and response surface method. These mathematical models show the dependencies of distortion, surface average equivalent residual stress, standard deviation of equivalent residual stress, average surface hardness and standard deviation of surface hardness with respect to the design variables. The optimization model is presented with the distortion as the optimization objective, and the model is optimized with an upper limit, a lower limit and the constraint function by the non-linear method and the Lagrange multiplier method.     

Variable-complexity optimization applied to airfoil design

Variable-complexity methods are applied to aerodynamic shape design problems with the objective of reducing the total computational cost of the optimization process. Two main strategies are employed: the use of different levels of fidelity in the analysis models (variable fidelity) and the use of different sets of design variables (variable parameterization). Variable-fidelity methods with three different types of corrections are implemented and applied to a set of two-dimensional airfoil optimization problems that use computational fluid dynamics for the analysis. Variable parameterization is also used to solve the same problems. Both strategies are shown to reduce the computational cost of the optimization.     

Simultaneous partial topology and size optimization of a wing structure using ant colony and gradient based methods

This article presents a methodology and process for a combined wing configuration partial topology and structure size optimization. It is aimed at achieving a minimum structural weight by optimizing the structure layout and structural component size simultaneously. This design optimization process contains two types of design variables and hence was divided into two sub-problems. One is structure layout topology to obtain an optimal number and location of spars with discrete integer design variables. Another is component size optimization with continuous design variables in the structure FE model. A multi city-layer ant colony optimization (MCLACO) method is proposed and applied to the topology sub-problem. A gradient based optimization method (GBOM) built in the MSC.NASTRAN SOL-200 module was employed in the component size optimization sub-problem. For each selected layout of the wing structure, a size optimization process is performed to obtain the optimum result and feedback to the layout topology process. The numerical example shows that the proposed MCLACO method and a combination with the GBOM are effective for solving such a wing structure optimization problem. The results also indicate that significant structural weight saving can be achieved.     

Integration of design systems for energy related applications

An EPSRC funded Engineering Design Centre (EDC) has been established at The Queen's University of Belfast to develop integrated design software for energy related applications. Software is being developed for the design of two-stroke engines, power station controllers and wave power stations. These ‘real’ design problems are highly complex with a large number of interrelated variables resulting in a wide range of design permutations. Although at an early state of application, the advantages of using object orientated design/programming methodologies is being demonstrated in the development of ‘structured’ design software. It is concluded that a balance must be struck between the complexity and the accuracy of the analytic models describing the interrelationship between the variables. This depends on the stage of the design optimization process. It is argued that complex optimization routines can only be justified when the process is well-defined and accurately modelled. Modelling of many systems includes approximations which have a more significant effect on the design optimization process than some of the variables.     

Optimization of Welding Process Parameters for 9Cr-1Mo Steel Using RSM and GA

Optimization of A-TIG welding process parameters for 9Cr-1Mo steel has been carried out using response surface methodology (RSM) and genetic algorithm (GA). RSM has been used to obtain the design matrix for generating data on the influence of process parameters on the response variables. A second-order response surface model was developed for predicting the response for the set of given input variables. Then, numerical and graphical optimization was performed using RSM to obtain the target depth of penetration (DOP) and heat-affected zone (HAZ) width using desirability approach. Multiple regression models were developed based on the generated data, and then the models were used in GA to determine the optimum process parameters for achieving the target DOP and HAZ width. GA-based models employed two different selection processes. Both the RSM- and GA-based models suggested a number of solutions in terms of process parameters, and the identified solutions were validated by experiments. GA-based model employing tournament selection has been found to be a more accurate method for determining the optimum A-TIG welding process parameters.     

ADAPTIVE RESPONSE SURFACE METHOD - A GLOBAL OPTIMIZATION SCHEME FOR APPROXIMATION-BASED DESIGN PROBLEMS

For design problems involving computation-intensive analysis or simulation processes, approximation models are usually introduced to reduce computation lime. Most approximation-based optimization methods make step-by-step improvements to the approximation model by adjusting the limits of the design variables. In this work, a new approximation-based optimization method for computation-intensive design problems - the adaptive response surface method(ARSM), is presented. The ARSM creates quadratic approximation models for the computation-intensive design objective function in a gradually reduced design space. The ARSM was designed to avoid being trapped by local optima and to identify the global design optimum with a modest number of objective function evaluations. Extensive tests on the ARSM as a global optimization scheme using benchmark problems, as well as an industrial design application of the method, are presented. Advantages and limitations of the approach are also discussed     

Developing a fuzzy proportional–derivative controller optimization engine for engineering design optimization problems

In real world engineering design problems, decisions for design modifications are often based on engineering heuristics and knowledge. However, when solving an engineering design optimization problem using a numerical optimization algorithm, the engineering problem is basically viewed as purely mathematical. Design modifications in the iterative optimization process rely on numerical information. Engineering heuristics and knowledge are not utilized at all. In this article, the optimization process is analogous to a closed-loop control system, and a fuzzy proportional–derivative (PD) controller optimization engine is developed for engineering design optimization problems with monotonicity and implicit constraints. Monotonicity between design variables and the objective and constraint functions prevails in engineering design optimization problems. In this research, monotonicity of the design variables and activities of the constraints determined by the theory of monotonicity analysis are modelled in the fuzzy PD controller optimization engine using generic fuzzy rules. The designer only needs to define the initial values and move limits of the design variables to determine the parameters in the fuzzy PD controller optimization engine. In the optimization process using the fuzzy PD controller optimization engine, the function value of each constraint is evaluated once in each iteration. No sensitivity information is required. The fuzzy PD controller optimization engine appears to be robust in the various design examples tested.     

Process-oriented tolerancing for multi-station assembly systems

In multi-station manufacturing systems, the quality of final products is significantly affected by both product design as well as process variables. Historically, however, tolerance research has primarily focused on allocating tolerances based on the product design characteristics of each component. Currently, there are no analytical approaches to optimally allocate tolerances to integrate product and process variables in multi-station manufacturing processes at minimum costs. The concept of process-oriented tolerancing expands the current tolerancing practices, which bound errors related to product variables, to explicitly include process variables. The resulting methodology extends the concept of “part interchangeability” into “process interchangeability,” which is critical due to increasing requirements related to the selection of suppliers and benchmarking. The proposed methodology is based on the development and integration of three models: (i) the tolerance-variation relation; (ii) variation propagation; and (iii) process degradation. The tolerance-variation model is based on a pin-hole fixture mechanism in multi-station assembly processes. The variation propagation model utilizes a state space representation but uses a station index instead of a time index. Dynamic process effects such as tool wear are also incorporated into the framework of process-oriented tolerancing, which provides the capability to design tolerances for the whole life-cycle of a production system. The tolerances of process variables are optimally allocated through solving a nonlinear constrained optimization problem. An industry case study is used to illustrate the proposed approach.     

EQ6111LH客车整车扭转刚度的分析与优化

以EQ6111LH客车为例,采用有限元法分析了整车扭转刚度和模态.通过灵敏度分析,了解了车身骨架不同构件的质量变化对整车性能的影响.根据灵敏度分析结果,选择有效的设计变量进行了整车扭转刚度优化.并且为了符合工程实际,优化过程中采用了离散的设计变量.     

A Prediction Region‐based Approach to Model Uncertainty for Multi‐response Optimization

Multi‐response optimization methods rely on empirical process models based on the estimates of model parameters that relate response variables to a set of design variables. However, in determining the optimal conditions for the design variables, model uncertainty is typically neglected, resulting in an unstable optimal solution. This paper proposes a new optimization strategy that takes model uncertainty into account via the prediction region for multiple responses. To avoid obtaining an overly conservative design, the location and dispersion performances are constructed based on the best‐case strategy and the worst‐case strategy of expected loss. We reveal that the traditional loss function and the minimax/maximin strategy are both special cases of the proposed approach. An example is illustrated to present the procedure and the effectiveness of the proposed loss function. The results show that the proposed approach can give reasonable results when both the location and dispersion performances are important issues. Copyright © 2015 John Wiley & Sons, Ltd.     

Application of multiple objective optimization theory to a preliminary missile design study

In this large-scale project, the design tasks were divided into two parts which allowed for increased efficiency. The modelling and generation of optimal candiatte missile designs were separated from the preference-laden design selection process. A set of performance indices including range, cost, trajectory error, system susceptibility, and reliability were established as the system measures with which all the subsystems were subsequently optimized. A team of technical designers used computer-based submodels in the areas of propulsion, lifecycle cost, and system susceptibility along with analytical models in the areas of trajectory analysis and system reliability to construct a statespace model. The system statespace included a set of established constants, and it mathematically linked the various subsystems to the performance measures. This model was then nested inside a vector optimization algorithm on a digital computer. The output of this interactive computer program is a set of efficient or nondominated missile designs. Each design is defined by its set of state variables, and accompanied by a set of performance index scores and control variables which define its particular trajectory. These nondominated designs show explicitly the tradeoffs among the performance indices for the missile systems as one moves along the efficient frontier of designs. Additional sensitivity analysis is provided by the optimization software for each efficient design. The second phase of the design process consisted of identifying one missile design from the efficient set for further development. This identification process results from ranking of the efficient designs according to a scalar scoring function which relies on the decision maker's preferences.     

反渗透膜系统查表法广谱优化设计

通过反渗透膜系统设计内涵的分析,建立了膜系统优化设计的原始数学模型;通过设计依据转换、独立变量分解等数学处理,导出了系统设计的经典数学模型与分解数学模型;进而提出了基于设计产水量、设计透盐率、极限回收率三维转换设计依据,借用现行系统设计软件的膜系统查表法广谱优化设计模式;而相应表格的设计为反渗透膜系统提供了一个概念全新又便捷有效的优化设计方法．     

A hybrid of back propagation neural network and genetic algorithm for optimization of injection molding process parameters

This paper presents a hybrid optimization method for optimizing the process parameters during plastic injection molding (PIM). This proposed method combines a back propagation (BP) neural network method with an intelligence global optimization algorithm, i.e. genetic algorithm (GA). A multi-objective optimization model is established to optimize the process parameters during PIM on the basis of the finite element simulation software Moldflow, Orthogonal experiment method, BP neural network as well as Genetic algorithm. Optimization goals and design variables (process parameters during PIM) are specified by the requirement of manufacture. A BP artificial neural network model is developed to obtain the mathematical relationship between the optimization goals and process parameters. Genetic algorithm is applied to optimize the process parameters that would result in optimal solution of the optimization goals. A case study of a plastic article is presented. Warpage as well as clamp force during PIM are investigated as the optimization objectives. Mold temperature, melt temperature, packing pressure, packing time and cooling time are considered to be the design variables. The case study demonstrates that the proposed optimization method can adjust the process parameters accurately and effectively to satisfy the demand of real manufacture.     

基于密度分布曲线法的复合材料变刚度铺层优化

基于梯度的优化方法对复合材料层合板进行了变刚度铺层优化设计。在优化过程中需确定铺层中各单元的密度以及角度。为了使优化结果具有可制造性,优化结果需满足制造工艺约束并且铺层角度需从预定角度中选取。为了避免在优化问题中引入过多的约束并减少设计变量的数目,提出密度分布曲线法(DDCM)对层合板中各单元的密度进行参数化。根据各单元的密度以及角度设计变量并基于Bi-value Coding Parameterization(BCP)方法中的插值公式确定各单元的弹性矩阵。优化过程中以结构柔顺度作为优化目标,结构体积作为约束,优化算法采用凸规划对偶算法。对碳纤维复合材料的算例结果表明:采用DDCM可得到较理想的优化结果,并且收敛速率较快。     

Optimal design of multi-response experiments using semi-definite programming

Optimal design of multi-response experiments for estimating the parameters of multi-response linear models is a challenging problem. The main drawback of the existing algorithms is that they require the solution of many optimization problems in the process of generating an optimal design that involve cumbersome manual operations. Furthermore, all the existing methods generate approximate design and no method for multi-response n-exact design has been cited in the literature. This paper presents a unified formulation for multi-response optimal design problem using Semi-Definite Programming (SDP) that can generate D-, A- and E-optimal designs. The proposed method alleviates the difficulties associated with the existing methods. It solves a one-shot optimization model whose solution selects the optimal design points among all possible points in the design space. We generate both approximate and n-exact designs for multi-response models by solving SDP models with integer variables. Another advantage of the proposed method lies in the amount of computation time taken to generate an optimal design for multi-response models. Several test problems have been solved using an existing interior-point based SDP solver. Numerical results show the potentials and efficiency of the proposed formulation as compared with those of other existing methods. The robustness of the generated designs with respect to the variance-covariance matrix is also investigated.     

Bayesian design of experiments for generalized linear models and dimensional analysis with industrial and scientific application

ABSTRACT

The design of an experiment can always be considered at least implicitly Bayesian, with prior knowledge used informally to aid decisions such as the variables to be studied and the choice of a plausible relationship between the explanatory variables and measured responses. Bayesian methods allow uncertainty in these decisions to be incorporated into design selection through prior distributions that encapsulate information available from scientific knowledge or previous experimentation. Further, a design may be explicitly tailored to the aim of the experiment through a decision-theoretic approach using an appropriate loss function. We review the area of decision-theoretic Bayesian design, with particular emphasis on recent advances in computational methods. For many problems arising in industry and science, experiments result in a discrete response that is well described by a member of the class of generalized linear models. Bayesian design for such nonlinear models is often seen as impractical as the expected loss is analytically intractable and numerical approximations are usually computationally expensive. We describe how Gaussian process emulation, commonly used in computer experiments, can play an important role in facilitating Bayesian design for realistic problems. A main focus is the combination of Gaussian process regression to approximate the expected loss with cyclic descent (coordinate exchange) optimization algorithms to allow optimal designs to be found for previously infeasible problems. We also present the first optimal design results for statistical models formed from dimensional analysis, a methodology widely employed in the engineering and physical sciences to produce parsimonious and interpretable models. Using the famous paper helicopter experiment, we show the potential for the combination of Bayesian design, generalized linear models, and dimensional analysis to produce small but informative experiments.     

Accelerated Life Testing (ALT) Design Based on Computational Reliability Analysis

Accelerated life testing (ALT) design is usually performed based on assumptions of life distributions, stress–life relationship, and empirical reliability models. Time‐dependent reliability analysis on the other hand seeks to predict product and system life distribution based on physics‐informed simulation models. This paper proposes an ALT design framework that takes advantages of both types of analyses. For a given testing plan, the corresponding life distributions under different stress levels are estimated based on time‐dependent reliability analysis. Because both aleatory and epistemic uncertainty sources are involved in the reliability analysis, ALT data is used in this paper to update the epistemic uncertainty using Bayesian statistics. The variance of reliability estimation at the nominal stress level is then estimated based on the updated time‐dependent reliability analysis model. A design optimization model is formulated to minimize the overall expected testing cost with constraint on confidence of variance of the reliability estimate. Computational effort for solving the optimization model is minimized in three directions: (i) efficient time‐dependent reliability analysis method; (ii) a surrogate model is constructed for time‐dependent reliability under different stress levels; and (iii) the ALT design optimization model is decoupled into a deterministic design optimization model and a probabilistic analysis model. A cantilever beam and a helicopter rotor hub are used to demonstrate the proposed method. The results show the effectiveness of the proposed ALT design optimization model. Copyright © 2015 John Wiley & Sons, Ltd.     

Design of manufacturing systems by a hybrid approach with neural network metamodelling and stochastic local search

Metamodels are models of simulation models. Metamodels are able to estimate the simulation responses corresponding to a given combination of input variables. A simulation metamodel is easier to manage and provides more insights than simulation alone. Traditionally, the multiple regression analysis is utilized to develop the metamodel from a set of simulation experiments. Simulation can consequentially benefit from the metamodelling in post-simulation analysis. A backpropagation (BP) neural network is a proven tool in providing excellent response predictions in many application areas and it outperforms regression analysis for a wide array of applications. In this paper, a BP neural network is used to generate metamodels for simulated manufacturing systems. For the purpose of optimal manufacturing systems design, mathematical models can be formulated by using the mapping functions generated from the neural network metamodels. The optimization model is then solved by a stochastic local search approach, simulated annealing (SA), to obtain an optimal configuration with respect to the objective of the systems design. Instead of triggering the detailed simulation programs, the SA-based optimization procedure evaluates the simulation outputs by the neural network metamodels. By using the SA-based optimization algorithm, the solution space of the studied problem is extensively exploited to escape the entrapment of local optima while the number of time consuming simulation runs is reduced. The proposed methodology is illustrated to be both effective and efficient in solving a manufacturing systems design problem through an example.     

Fault-tolerant embedded system design and optimization considering reliability estimation uncertainty

In this paper, we model embedded system design and optimization, considering component redundancy and uncertainty in the component reliability estimates. The systems being studied consist of software embedded in associated hardware components. Very often, component reliability values are not known exactly. Therefore, for reliability analysis studies and system optimization, it is meaningful to consider component reliability estimates as random variables with associated estimation uncertainty. In this new research, the system design process is formulated as a multiple-objective optimization problem to maximize an estimate of system reliability, and also, to minimize the variance of the reliability estimate. The two objectives are combined by penalizing the variance for prospective solutions. The two most common fault-tolerant embedded system architectures, N-Version Programming and Recovery Block, are considered as strategies to improve system reliability by providing system redundancy. Four distinct models are presented to demonstrate the proposed optimization techniques with or without redundancy. For many design problems, multiple functionally equivalent software versions have failure correlation even if they have been independently developed. The failure correlation may result from faults in the software specification, faults from a voting algorithm, and/or related faults from any two software versions. Our approach considers this correlation in formulating practical optimization models. Genetic algorithms with a dynamic penalty function are applied in solving this optimization problem, and reasonable and interesting results are obtained and discussed.     

A new optimization framework using genetic algorithm and artificial neural network to reduce uncertainties in petroleum reservoir models

In this article, a new optimization framework to reduce uncertainties in petroleum reservoir attributes using artificial intelligence techniques (neural network and genetic algorithm) is proposed. Instead of using the deterministic values of the reservoir properties, as in a conventional process, the parameters of the probability density function of each uncertain attribute are set as design variables in an optimization process using a genetic algorithm. The objective function (OF) is based on the misfit of a set of models, sampled from the probability density function, and a symmetry factor (which represents the distribution of curves around the history) is used as weight in the OF. Artificial neural networks are trained to represent the production curves of each well and the proxy models generated are used to evaluate the OF in the optimization process. The proposed method was applied to a reservoir with 16 uncertain attributes and promising results were obtained.