Hybrid multi-response optimization of friction stir spot welds: failure load,effective bonded size and flash volume as responses

Friction stir spot welding (FSSW) is a multi-input multi-response process. Effective multi-response optimization of welds is desirable to create welds with a balance of quality responses. In order to eliminate the subjectivity (uncertainty and engineering judgment) with the existing multi-response Taguchi-based Grey relational analysis, principal component analysis (PCA) was integrated into it. The PCA helps in determining the effective optimal weighting values required for the estimation of Grey relational grade (GRG). As a result, tool rotational speed, plunge depth and dwell time were employed as input parameters while failure load (FL), expelled flash volume (EFV) and effective bonded size (EBS) of conical pin friction stir spot-welded joint of AA2219-O alloy were the chosen output responses. EFV was minimized while FL and EBS of the joints were maximized using this hybrid multi-response approach. From the analysis of variance of GRG and its response graphs, the significant parameters and their levels were obtained. Experimental results confirmed the effectiveness and robustness of this method. In addition, three critical zones were observed on the fracture surfaces of joints, namely, tool impelled unbonded zone, partially bonded zone and effective bonded/nugget zone. The weld nugget failed by circumferential nugget shear mode.     

The use of a grey-based Taguchi method for optimizing multi-response simulation problems

Simulation modelling is a widely accepted tool in system design and analysis, particularly when the system or environment has stochastic and nonlinear behaviour. However, it does not provide a method for optimization. In general, problems contain more than one response, which are often in conflict with each other. This article proposes a grey-based Taguchi method to solve the multi-response simulation problem. The grey-based Taguchi method is based on the optimizing procedure of the Taguchi method, and adopts grey relational analysis (GRA) to transfer multi-response problems into single-response problems. A practical case study from an integrated-circuit packaging company illustrates that differences in performance of the proposed grey-based Taguchi method and other methods found in the literature were not significant. The grey-based Taguchi method thus provides a new option when solving a multi-response simulation-optimization problem.     

Improving the electroforming process in optical recordable media manufacturing via an integrated procedure

In optical recordable media manufacturing, an electroforming process uses glass masters to produce metal shells which then act as stampers to replicate thousands of copies of a disc. The physical characteristics of stampers influence their life time significantly and, moreover, significantly affect the quality performance of the finished optical recordable media. Traditionally, engineers sought the optimal parameter settings in the electroforming process through trial and error, and thus serious losses were experienced owing to the low yield of stampers. This study proposes an integrated procedure for optimizing parameter settings in electroforming to improve stamper quality performance. The proposed procedure combines neural networks, desirability functions and tabu search to solve multi-response parameter design problems. The proposed procedure was applied at a Taiwanese optical recordable media manufacturer, and the implementation results demonstrated its feasibility and effectiveness. Through this work, the average defect rate of stampers can be expected to decline to approximately 4.76%, from over 10% previously. The annual savings through applying the proposed procedure are estimated at US$750,000, easily exceeding the US$80,000 expended on the experiment.     

Novel orthogonal simulated annealing with fractional factorial analysis to solve global optimization problems

A classical simulated annealing (SA) method is a generic probabilistic and heuristic approach to solving global optimization problems. It uses a stochastic process based on probability, rather than a deterministic procedure, to seek the minima or maxima in the solution space. Although the classical SA method can find the optimal solution to most linear and nonlinear optimization problems, the algorithm always requires numerous numerical iterations to yield a good solution. The method also usually fails to achieve optimal solutions to large parameter optimization problems. This study incorporates well-known fractional factorial analysis, which involves several factorial experiments based on orthogonal tables to extract intelligently the best combination of factors, with the classical SA to enhance the numerical convergence and optimal solution. The novel combination of the classical SA and fractional factorial analysis is termed the orthogonal SA herein. This study also introduces a dynamic penalty function to handle constrained optimization problems. The performance of the proposed orthogonal SA method is evaluated by computing several representative global optimization problems such as multi-modal functions, noise-corrupted data fitting, nonlinear dynamic control, and large parameter optimization problems. The numerical results show that the proposed orthogonal SA method markedly outperforms the classical SA in solving global optimization problems with linear or nonlinear objective functions. Additionally, this study addressed two widely used nonlinear functions, proposed by Keane and Himmelblau to examine the effectiveness of the orthogonal SA method and the presented penalty function when applied to the constrained problems. Moreover, the orthogonal SA method is applied to two engineering optimization design problems, including the designs of a welded beam and a coil compression spring, to evaluate the capacity of the method for practical engineering design. The computational results show that the proposed orthogonal SA method is effective in determining the optimal design variables and the value of objective function.     

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.     

Optimization of process parameters of friction welding of UNS S31803 duplex stainless steels joints

This article presents an approach based on Taguchi method and Grey relational analysis to optimize process parameters of friction welding of UNS31803 duplex stainless steel. The main objective is to maximize mechanical properties like tensile strength, hardness and impact toughness and to minimize corrosion rate. Heating pressure, heating time, upsetting pressure and upsetting time were the four process parameters taken each at three levels. According to Taguchi quality design concept, an L9 orthogonal array was selected for experiments. The best combination of process parameters was found by both Taguchi method and Grey relational analysis. The influence of the process parameters on overall quality characteristics of the friction welding process was evaluated by the analysis of variance (ANOVA) method. The confirmation test results with optimal parameters confirmed the effectiveness of the proposed method in this study. Later, comparison was done between Taguchi method and Grey relational analysis on the basis of improvement in multiresponse signal to noise (S/N) ratio over initial process parameters. Grey relational analysis was proved to be a better technique than Taguchi method for optimization of multiple responses.     

Application of semi-definite programming to the design of multi-response experiments

The need to be able to design experiments with multiple responses is becoming apparent in many real-world applications. The generation of an optimal design to estimate the parameters of a multi-response model is a challenging problem. Currently available algorithms require the solution of many optimization problems in order to generate an optimal design. In this paper, the problem of multi-response D-optimal design is formulated as a semi-definite programming model and a relaxed form of it is solved using interior-point solvers. The main advantage of the proposed method lies in the amount of computation time taken to generate a D-optimal design for multi-response models. The proposed method is tested on several test problems and is shown to be very efficient with optimal designs being found very quickly in all cases. The robustness of the generated designs with respect to the variance-covariance matrix is also assessed for the test problems in order to show how a sensitivity analysis can be performed. The characteristics of the proposed method are also compared with those of other existing methods.     

Optimization of Plasma Arc Welding Parameters by Using the Taguchi Method with the Grey Relational Analysis

The optimal parameters process of plasma arc welding (PAW) by the Taguchi method with Grey relational analysis is studied. The Grey relational grade is used to find optimal PAW parameters with multiple response performance characteristics. The welding parameters (welding current, welding speed, plasma gas flow rate, and torch stand-off) are optimized with consideration of the multiple response performance characteristics (the penetration of root, the weld groove width, and the weld pool undercut). As a result, the improvement percentage of the Grey relational grade with the multiple performance characteristics is 31.8%. It is shown that the multiple response performance characteristics are greatly improved through this study.     

Electrical and optical studies of Ga-doped ZnO thin films

Nanostructure Ga-doped zinc oxide (GZO) thin films with highly (0 0 2) preferred orientation were fabricated on glass substrates, using radio frequency magnetron sputtering with an GZO ceramic target (The Ga₂O₃ contents was about 3 wt%) and different deposition conditions. The structural features, surface morphology and electrical and optical properties of the GZO thin films were studied, in terms of the deposition parameters. A Grey-based Taguchi method was used to determine the optimal deposition parameters for GZO thin films by considering multiple performance characteristics. The response graph and table for each level of the deposition parameters forms the Grey relational grade and the optimal levels of the deposition parameters were chosen. The experimental results show that the process pressure and the thickness make the most significant contribution to the overall performance. In the confirmation runs, Grey relational analysis showed that the improvement in deposition rate is 14.2 %, the improvement in electrical resistivity 38.1 % and the improvement in optical transmittance is 1.2 %. Annealing in a vacuum further improved the crystalline quality and optoelectronic performances of the GZO thin films.     

The incorporation of the Taguchi and the VIKOR methods to optimize multi-response problems in intuitionistic fuzzy environments

The Taguchi method is a powerful method of solving quality problems in various fields of engineering. However, this method was developed to optimize single-response processes. In many multi-response optimization problems, the important response is determined subjectively, based on knowledge or experience. However, using only exact numbers to represent this importance is problematic, because there is uncertainty and vagueness. The concept of intuitionistic fuzzy sets (IFSs) is a powerful method for characterization, using a membership function and a non-membership function. This paper proposes an efficient VIKOR method that optimizes multi-response problems in intuitionistic fuzzy environments. The importance weights of various responses are evaluated in terms of IFSs. In the proposed method, the similarity measure between IFSs is used to determine the crisp weights of the responses. This scheme eliminates the need for complicated intuitionistic fuzzy arithmetic operations and increases efficiency in solving multi-response optimization problems in intuitionistic fuzzy environments. Two case studies: plasma-enhanced chemical vapor deposition and a double-sided surface mount technology electronic assembly operation are used to demonstrate the effectiveness of the proposed method.     

Grey-fuzzy algorithm to optimise machining parameters in drilling of hybrid metal matrix composites

Metal matrix composites (MMCs) are difficult to machine due to their abrasive properties. With the projected widespread application of MMCs, it is necessary to develop an appropriate technology for their effective machining. The present investigation focuses on finding the optimal machining parameters setting in drilling of hybrid aluminium metal matrix composites using the grey-fuzzy algorithm. This proposed algorithm, coupling the grey relational analysis with the fuzzy logic, obtains a grey-fuzzy reasoning grade to evaluate the multiple performance characteristics according to the grey relational coefficient of each performance characteristics. The Taguchi method of experimental design is a widely accepted technique used for producing high quality products at low cost, therefore a L₂₇ 3-level orthogonal array is used for the experiments. The optimisation of multiple responses in complex processes is common; therefore, to reduce the degree of uncertainty during the decision making, fuzzy rule-based reasoning is integrated with the Taguchi’s method. The response table, response graph and analysis of variance (ANOVA) are used to find the optimal setting and the influence of machining parameters on the multiple performance characteristics. Experimental results have shown that the required performance characteristics in the drilling process are improved by using this approach.     

Penalty adapting ant algorithm: application to pipe network optimization

A penalty adapting ant algorithm is presented in an attempt to eliminate the dependency of ant algorithms on the penalty parameter used for the solution of constrained optimization problems. The method uses an adapting mechanism for determination of the penalty parameter leading to elimination of the costly process of penalty parameter tuning. The method is devised on the basis of observation that for large penalty parameters, infeasible solutions will have a higher total cost than feasible solutions and vice versa. The method therefore uses the best feasible and infeasible solution costs of the iteration to adaptively adjust the penalty parameter to be used in the next iteration. The pheromone updating procedure of the max–min ant system is also modified to keep ants on and around the boundary of the feasible search space where quality solutions can be found. The sensitivity of the proposed method to the initial value of the penalty parameter is investigated and indicates that the method converges to optimal or near-optimal solutions irrespective of the initial starting value of the penalty parameter. This is significant as it eliminates the need for sensitivity analysis of the method with respect to the penalty factor, thus adding to the computational efficiency of ant algorithms. Furthermore, it is shown that the success rate of the search algorithm in locating an optimal solution is increased when a self-adapting mechanism is used. The presented method is applied to a benchmark pipe network optimization problem in the literature and the results are presented and compared with those of existing algorithms.     

Machining parameters optimization for satisfying the multiple objectives in machining of MMCs

The metal matrix composites (MMCs) have gained acceptance in an extensive range of applications owing to their high strength to mass ratio. Machining of such complex MMCs is often challenging. It is essential to optimize the controllable machining parameters to simultaneously attain manifold objectives. In the current work, response surface design is created for experiments, and Genetic algorithm (GA) combined with Principal Components Analysis (PCA) coupled Grey Relational Analysis (GRA) is employed to improve the straight turning process of MMCs. The procedure is demonstrated by machining aluminum-based MMC with 25% SiC particulates. The procedure aims at identifying optimal combination of machining parameters to obtain high surface quality at lower cutting force without increasing the specific power consumption. PCA is helpful in providing the individual uncorrelated quality characteristics called as quality indices that do not have any influence on other responses. Individual quality indices have been utilized to obtain the grey relational grade through GRA. GRA has been used to alter manifold quality indices into singular column of grey relational grade as a means to change the manifold objective problem into a sole objective problem. Then, GA has been used to get the optimal parameters combination. The novelty present in this work is the avoidance of correlation existing among the quality characteristics and combining of the GRA and GA. This is an endeavor to augment the performance and accuracy of GA to solve the optimization problem associated with the turning operation.     

A mathematical model for selecting mixed models with due dates

The performance of a sequencing procedure to smooth out the fluctuating workload (and part utilization) on a paced assembly line relies heavily on the average load of the model mixes chosen from the order-bank. Meanwhile, the due-dates of orders may conflict with this production-centred goal. This study proposes a mathematical model to select a fixed number of jobs while minimizing the total cost of producing them at the next period and satisfying capacity (RHS) limits at stations. A branch-and-bound procedure, which employs some dominance criteria, is proposed to provide optimal solutions. Pairwise interchange heuristics are developed to improve the initial solution, which is optimum but not feasible. Computational results show that optimal solutions can be obtained very efficiently for 100-job and 10-station problems. A three-factor experiment indicates that the RHS limit is the only significant parameter on the performance of the procedures. For over 1000-job problems, the best heuristic finds the optimal solution most of the time and, in the worst case, yields a solution that is 7.38% from optimality.     

基于全局灵敏度分析的某自动装填机构轻量化设计

针对某自动装填机构轻量化设计中出现参数多、模型计算量大等问题,提出将全局灵敏度分析与代理模型技术相结合的优化策略。通过基于Morris轨迹的全局灵敏度分析从32个系统参数中确定14个关键参数,基于拉丁超立方采样技术及径向基函数神经网络技术(Radial basis function neural networks, RBF NN)建立系统响应关于关键参数的代理模型,用多岛遗传算法对系统参数进行优化求解,致机构重量下降21.8%。数值检验结果表明仅含关键参数的代理模型预测精度较高,证明该方法在多参数复杂系统结构轻量化设计中的有效性。     

Robust design with dynamic characteristics using stochastic sequential quadratic programming

Robust design with dynamic characteristics is an important off-line quality engineering technique for improving product quality over a range of input conditions by reducing variations caused by uncontrolled factors. Since several studies have indicated that there are important limitations to Taguchi's S/N ratio analysis, the solution procedure for dynamic systems deserves further investigation. This paper proposes a stochastic optimization modeling procedure to overcome the difficulty in Taguchi's method to accommodate dynamic characteristics. The main idea underlying the proposed method is to minimize the total variations on quality characteristics while attaining the target performance over a range of input conditions. Due to the nonlinear nature of the stochastic optimization model, two stochastic versions of sequential quadratic programming respectively embedded with a Monte Carlo simulation and numerical approximations are devised to solve the problem. In the robust design of a temperature control circuit often discussed in dynamic problems, the proposed method performs efficiently and effectively. Compared with the Taguchi method, the design solved in this paper has smaller variations, indicating that the proposed method is a promising technique for dynamic-characteristic robust design.     

A deep learning approach for the dynamic dispatching of unreliable machines in re-entrant production systems

This research combines deep neural network (DNN) and Markov decision processes (MDP) for the dynamic dispatching of re-entrant production systems. In re-entrant production systems, jobs enter the same workstation multiple times and dynamic dispatching oftentimes aims to dynamically assign different priorities to various job groups to minimise weighted cycle time or maximise throughput. MDP is an effective tool for dynamic production control, but it suffers from two major challenges in dynamic control problems. First, the curse of dimensionality limits the computational performance of solving large MDP problems. Second, a different model should be built and solved after system configuration is changed. DNN is used to overcome both challenges by learning directly from optimal dispatching policies generated by MDP. Results suggest that a properly trained DNN model can instantly generate near-optimal dynamic control policies for large problems. The quality of the DNN solution is compared with the optimal dynamic control policies through the standard K-fold cross-validation test and discrete event simulation. On average, the performance of the DNN policy is within 2% of optimal in both tests. The proposed artificial intelligence algorithm illustrates the potential of machine learning methods in manufacturing applications.     

Boundary element methods for optimization of distributed parameter systems

A numerical method of solution is proposed for optimization problems of distributed parameter systems. Two model problems from continuum mechanics are investigated by means of constructing the problems as the steady-state optimal control problems governed by elliptic partial differential equations. The basis of the suggested method of solution lies in the space discretization of the necessary conditions for optimality by the boundary element method, and the minimization of the performance indices by the conjugate gradient method of optimization.     

Compromise design of stochastic dynamical systems: A reliability-based approach

This paper presents a procedure for obtaining compromise designs of structural systems under stochastic excitation. In particular, an effective strategy for determining specific Pareto optimal solutions is implemented. The design goals are defined in terms of deterministic performance functions and/or performance functions involving reliability measures. The associated reliability problems are characterized by means of a large number of uncertain parameters (hundreds or thousands). The designs are obtained by formulating a compromise programming problem which is solved by a first-order interior point algorithm. The sensitivity information required by the proposed solution strategy is estimated by an approach that combines an advanced simulation technique with local approximations of some of the quantities associated with structural performance. An efficient Pareto sensitivity analysis with respect to the design variables becomes possible with the proposed formulation. Such information is used for decision making and tradeoff analysis. Numerical validations show that only a moderate number of stochastic analyses (reliability estimations) has to be performed in order to find compromise designs. Two example problems are presented to illustrate the effectiveness of the proposed approach.     

Optimization of weld bead geometry of laser welded ANSI 304 austenitic stainless steel using grey-based Taguchi method

This paper investigates the quality characteristics of the welding geometry of the laser welding process for the ANSI 304 austenitic stainless steel, with the use of a pulsed Nd:YAG laser welding system. Laser welding of 2 mm thick ANSI 304 stainless steel is performed at three different levels of three factors, i. e., peak power, welding speed and pulse duration. In this study, a multi-response optimization problem is developed to achieve weld bead geometry with full penetration as well as a narrow bead width and minimum crater. Grey relational analysis based on Taguchi orthogonal array is used to present an effective approach for the optimization of laser welding process parameters. Regression equations between the welding parameters and the bead dimensions for laser welded austenitic stainless steels are developed, which are used in predicting the penetration, width and crater. Finally, the equations are tested for values different from the levels of the parameters in the orthogonal array. It will be beneficial to engineers for continuous improvement in laser welded product quality.