Yizhong Ma

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

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

A new Bayesian approach to multi-response surface optimization integrating loss function with posterior probability

Multi-response surface (MRS) optimization in quality design often involves some problems such as correlation among multiple responses, robustness measurement of multivariate process, confliction among multiple goals, prediction performance of the process model and the reliability assessment for optimization results. In this paper, a new Bayesian approach is proposed to address the aforementioned multi-response optimization problems. The proposed approach not only measures the reliability of an acceptable optimization result, but also incorporates expected loss (i.e., bias and robustness) into a uniform framework of Bayesian modeling and optimization. The advantages of this approach are illustrated by one example. The results show that the proposed approach can give more reasonable solutions than the existing approaches when both quality loss and the reliability of optimization results are important issues.

An Integrative Loss Function Approach to Multi-Response Optimization

Loss function approach is effective for multi-response optimization. However, previous loss function approaches ignore thedispersion performance of squared error loss and model uncertainty. In this paper, a weighted loss function is proposed tosimultaneously consider the location and dispersion performances of squared error loss to optimize correlated multipleresponseswith model uncertainty. We proposean approach tominimize the weighted loss function underthe constraint thatthe confidence intervals of future predictions for the multiple responses should be contained in specification limits of theresponses. An example is illustrated to verify the effectiveness of the proposed method. The results show that the proposedmethod can achieve reliable optimal operating condition under model uncertainty. Copyright

Robust optimisation of Nd: YLF laser beam micro-drilling process using Bayesian probabilistic approach

Nd: YLF laser beam machining (LBM) process has a great potential to manufacture intricate shaped microproducts with its unique characteristics. Continuous improvement (CI) effort for LBM process is usually realised by response surface methodology, which is an important tool in Design of Six Sigma. However, when determining the optimal machining parameters in CI for LBM process, model parameter uncertainty is typically neglected. Performing worst case analysis in CI, this paper presents a new loss function method that takes model parameter uncertainty into account via Bayesian credible region. Unlike existing CI methods in LBM process, the proposed Bayesian probabilistic approach is based on seemingly unrelated regression which can produce more precise estimations of the model parameters than ordinary least squares in correlated multiple responses problems. An Nd: YLF laser beam micro-drilling process is used to demonstrate the effectiveness of the proposed approach. The comparison results show that micro-holes produced by the proposed approach have better quality than those of existing approaches in terms of robustness and process capability.

An interval approach to robust design with parameter uncertainty

In robust design, it is common to estimate empirical models that relate an output response variable to controllable input variables and uncontrollable noise variables from experimental data. However, when determining the optimal input settings that minimise output variability, parameter uncertainties in noise factors and response models are typically neglected. This article presents an interval robust design approach that takes parameter uncertainties into account through the confidence regions for these unknown parameters. To avoid obtaining an overly conservative design, the worst and best cases of mean squared error are both adopted to build an optimisation approach. The midpoint and radius of the interval are used to measure the location and dispersion performances, respectively. Meanwhile, a data-driven method is applied to obtain the relative weights of the location and dispersion performances in the optimisation approach. A simulation example and a case study using automobile manufacturing data from the dimensional tolerance design process are used to demonstrate the effectiveness of the proposed approach. The proposed approach of considering both uncertainties is shown to perform better than other approaches.

Extended Gaussian Kriging for computer experiments in engineering design

Metamodeling or surrogate modeling is becoming increasingly popular for product design optimization in manufacture industries. In this paper, an extended Gaussian Kriging method is proposed to improve the prediction performance of widely used ordinary Kriging in engineering design. Unlike the forgoing approaches, the proposed method places a variance-varying Gaussian prior on the unknown regression coefficients in the mean model of Kriging and makes prediction at untried design points based on the principle of Bayesian maximum a posterior. The achieved regression mean model is adaptive, therefore capable of capturing more effectively the overall trend of computer responses and leading to a more accurate metamodel. Particularly, the regression coefficients in the mean model are estimated by a fast numerical algorithm, making extended Gaussian Kriging implemented roughly as efficient as ordinary Kriging. Experiment results on several examples are presented, showing remarkable improvement in prediction using extended Gaussian Kriging over ordinary Kriging and several other metamodeling methods.

Bayesian Metamodeling for Computer Experiments Using the Gaussian Kriging Models

In the past two decades, more and more quality and reliability activities have been moving into the design of product and process. The design and analysis of computer experiments, as a new frontier of the design of experiments, has become increasingly popular among modern companies for optimizing product and process conditions and producing high-quality yet low-cost products and processes. This article mainly focuses on the issue of constructing cheap metamodels as alternatives to the expensive computer simulators and proposes a new metamodeling method on the basis of the Gaussian stochastic process model or Gaussian Kriging. Rather than a constant mean as in ordinary Kriging or a fixed mean function as in universal Kriging, the new method captures the overall trend of the performance characteristics of products and processes through a more accurate mean, by efficiently incorporating a scheme of sparseness prior–based Bayesian inference into Kriging. Meanwhile, the mean model is able to adaptively exclude the unimportant effects that deteriorate the prediction performance. The results of an experiment on empirical applications demonstrate that, compared with several benchmark methods in the literature, the proposed Bayesian method is not only much more effective in approximation but also very efficient in implementation, hence more appropriate than the widely used ordinary Kriging to empirical applications in the real world. Copyright

A new loss function for multi-response optimization with model parameter uncertainty and implementation errors

Response surface-based design optimization has been commonly used to seek the optimal input settings in process or product design problems. Yet in most of the existing researches, there is no model parameter uncertainty in the modeling process and the optimal settings can be implemented at the precise values. These two assumptions are far from the reality. Consequently, the optimal settings often turn out to be suboptimal in some manner. This paper proposes a new loss function method to deal with model parameter uncertainty and implementation errors (MPUIE). An interpretable expression for the new optimization strategy is derived, which provides insights into the impact of MPUIE on the determination of the optimal settings. A random simulation example and a real-life case study are used to demonstrate the effectiveness of the proposed approach. The approach gives the optimal settings that are the result of making tradeoffs among different directions from the center of the experimental design region or, more generally, in a manner that mitigates the adverse effects of MPUIE.

An interval programming model for continuous improvement in micro-manufacturing

ABSTRACT Continuous quality improvement in micro-manufacturing processes relies on optimization strategies that relate an output performance to a set of machining parameters. However, when determining the optimal machining parameters in a micro-manufacturing process, the economics of continuous quality improvement and decision makers’ preference information are typically neglected. This article proposes an economic continuous improvement strategy based on an interval programming model. The proposed strategy differs from previous studies in two ways. First, an interval programming model is proposed to measure the quality level, where decision makers’ preference information is considered in order to determine the weight of location and dispersion effects. Second, the proposed strategy is a more flexible approach since it considers the trade-off between the quality level and the associated costs, and leaves engineers a larger decision space through adjusting the quality level. The proposed strategy is compared with its conventional counterparts using an Nd:YLF laser beam micro-drilling process.

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