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In robust parameter design (RPD), estimating the response surface model from the noisy experimental data is critical for parameter optimization. The multivariate Gaussian process (MGP) model has become a popular tool for response surface modelling. However, most existing MGP models may not effectively evaluate the uncertainty of noisy data. This article proposes a stochastic MGP for efficient emulation and robust optimization by considering uncertainty. Firstly, the hierarchical modelling technique is adopted to estimate the relationship model with noisy data. Secondly, the hyperparameters are estimated by the Gibbs technique, and the Bayesian averaging method is used to measure the parameter uncertainty. Finally, a novel optimization model integrated with the Bayesian averaging and quality loss function is developed to find the optimal solution. Two case studies are used to illustrate the effectiveness of the proposed method. The results show that the proposed approach obtains smaller quality loss than the existing ones. [ABSTRACT FROM AUTHOR]

Traditional robust parameter design methods mainly focus on the optimization of quantitative quality characteristics. However, computer experiments involving qualitative and quantitative mixed input and output occur frequently in the manufacturing industry, which prompted the authors to develop an effective meta-modeling and optimization technique for such experiments. This article combines the latent variable Gaussian process (LVGP) model and fuzzy set theory to create a mixed multi-response LVGP (MMR-LVGP) model involving qualitative and quantitative mixed input and output. Then, the optimization scheme is established by comprehensively weighing the location and dispersion effects of each quality characteristic to find the joint optimal solution of qualitative and quantitative factors. Numerical and industrial cases are used to illustrate the validity of the proposed method in the modeling and optimization of experimental data with qualitative and quantitative mixed input and output or spatio-temporal structure. The comparison results indicate that the proposed method is preferred over existing methods. [ABSTRACT FROM AUTHOR]

In robust parameter design, it is common to use computer models to simulate the relationships between input variables and output responses. However, for the contaminated experimental data, the model uncertainty between computer models and actual physical systems will seriously impair the robustness of the optimal input settings. In this paper, we propose a new weighted robust design approach concerning the model uncertainty from outliers based on the robust Gaussian process model with a Student-t likelihood (StGP). Firstly, to reduce the impact of outliers on the output means and variances, the StGP modelling technique is adopted to estimate the relationship models for contaminated data. Secondly, the Gibbs sampling technique is employed to estimate model parameters for better mixing and convergence. Finally, an optimisation scheme integrating the quality loss function and confidence interval analysis approach is built to find the feasible optimisation solution. Meanwhile, the hypersphere decomposition method and data-driven method are applied to determine the relative weights of objective functions. Two examples are used to demonstrate the effectiveness of the proposed approach. The comparison results show that the proposed approach can achieve better performance than other approaches by considering the model uncertainty from outliers. [ABSTRACT FROM AUTHOR]

Robust parameter design (RPD), an important method for quality improvement, can effectively mitigate the negative impact of fluctuations on product quality. Traditional RPD adopts offline design, that is, the optimal level of parameter combination is fixed by one-time modeling throughout the production process. This strategy is obviously unreasonable. Online RPD breaks through the limitation of traditional offline design, which can update the optimal setting by utilizing the new sample when the current optimal setting of controllable factors is not suitable. However, there are still some problems in the current version of online RPD, such as poor data fitting ability of response surface model and low efficiency of parameter design. In this paper, a new online RPD method based on Gaussian process (GP) is proposed. The GP model is used to construct the response surface, which has the capacity of dealing with high-dimensional nonlinear data. But traditional GP method adopts batch learning, it cannot update the model online with new samples. So this paper proposes an incremental Gaussian process model (IGP), which can update the response surface in real-time. In the proposed IGP based online robust parameter design method (IGP-RPD), an effective optimization strategy is used to find the optimal setting of controllable factors, and a reasonable selection criterion is used to determine the noise factor setting for the next stage. The optimal setting of the controllable factor in the previous stage and the currently observed noise factor are used as input, and the corresponding quality characteristic is taken as the output. The input and output form a new sample to update the response surface model. In this way, the RPD process can be redone continuously until the desirable optimal setting of the controllable factor is found. Three cases are used to verify the IGP-RPD method and compare it with the existing methods. The experiments manifest that the IGP-RPD method has better performance in both accuracy and efficiency. [ABSTRACT FROM AUTHOR]

To address the problem of robust parameter design for high-dimensional experimental data, the parallel partial Gaussian process (PPGP) model is adopted to construct the response surfaces between the test factors and the multivariate quality characteristics under the modeling framework of Gaussian process (GP). On this basis, the multivariate quality loss function is used as an optimization index to obtain the optimal parameter design values of the controllable factors. A classic simulation examples and two actual cases are used to verify the effectiveness and advantages of the proposed method. The research results show that compared with the independent modeling of the univariate GP model or the Kriging model, the proposed method can not only deal with the modeling and parameter optimization problems of high-dimensional experimental data effectively, but also obtain more robust optimization results and higher operational efficiency. [ABSTRACT FROM AUTHOR]

Parameter design and tolerance design are commonly used methods in continuous quality improvement. However, it is difficult to use univariate Gaussian process models to perform the parameter and tolerance design for multi-response physics experiments. In this article, an integrated parameter and tolerance design (IPTD) method is proposed based on a multivariate Gaussian process (MGP) model. MGP models are used to estimate the relationship models for physical experiments with input uncertainty, and a covariance structure with the input noise distribution is constructed. Then an optimization scheme integrating the quality loss function and tolerance cost function is built to find the compromise solutions. The optimal solution is selected from the Pareto set by using grey relation analysis (GRA) technique. Two examples are used to illustrate the effectiveness of the proposed approach. The results show that the proposed approach can obtain optimal settings that minimize quality loss and tolerance cost simultaneously. [ABSTRACT FROM AUTHOR]