Laser dimpling process parameters selection and optimization using surrogate-driven process capability space

Remote laser welding technology offers opportunities for high production throughput at a competitive cost. However, the remote laser welding process of zinc-coated sheet metal parts in lap joint configuration poses a challenge due to the difference between the melting temperature of the steel (∼1500 C) and the vaporizing temperature of the zinc (~907 C). In fact, the zinc layer at the faying surface is vaporized and the vapour might be trapped within the melting pool leading to weld defects. Various solutions have been proposed to overcome this problem over the years. Among them, laser dimpling has been adopted by manufacturers because of its flexibility and effectiveness along with its cost advantages. In essence, the dimple works as a spacer between the two sheets in lap joint and allows the zinc vapour escape during welding process, thereby preventing weld defects. However, there is a lack of comprehensive characterization of dimpling process for effective implementation in real manufacturing system taking into consideration inherent changes in variability of process parameters. This paper introduces a methodology to develop (i) surrogate model for dimpling process characterization considering multiple–inputs (i.e. key control characteristics) and multiple–outputs (i.e. key performance indicators) system by conducting physical experimentation and using multivariate adaptive regression splines; (ii) process capability space (Cp–Space) based on the developed surrogate model that allows the estimation of a desired process fallout rate in the case of violation of process requirements in the presence of stochastic variation; and, (iii) selection and optimization of the process parameters based on the process capability space. The proposed methodology provides a unique capability to: (i) simulate the effect of process variation as generated by manufacturing process; (ii) model quality requirements with multiple and coupled quality requirements; and (iii) optimize process parameters under competing quality requirements such as maximizing the dimple height while minimizing the dimple lower surface area

Student-t Processes as Alternatives to Gaussian Processes

We investigate the Student-t process as an alternative to the Gaussian process as a nonparametric prior over functions. We derive closed form expressions for the marginal likelihood and predictive distribution of a Student-t process, by integrating away an inverse Wishart process prior over the covariance kernel of a Gaussian process model. We show surprising equivalences between different hierarchical Gaussian process models leading to Student-t processes, and derive a new sampling scheme for the inverse Wishart process, which helps elucidate these equivalences. Overall, we show that a Student-t process can retain the attractive properties of a Gaussian process -- a nonparametric representation, analytic marginal and predictive distributions, and easy model selection through covariance kernels -- but has enhanced flexibility, and predictive covariances that, unlike a Gaussian process, explicitly depend on the values of training observations. We verify empirically that a Student-t process is especially useful in situations where there are changes in covariance structure, or in applications like Bayesian optimization, where accurate predictive covariances are critical for good performance. These advantages come at no additional computational cost over Gaussian processes.Comment: 13 pages, 6 figures, 1 table. To appear in "The Seventeenth International Conference on Artificial Intelligence and Statistics (AISTATS), 2014.

A Robust Multi Response Surface Approach for Optimization of Multistage Processes

Purpose: In a multistage process, the final quality in the last stage not only depends on the quality of the task performed in that stage but also is dependent on the quality of the products and services in intermediate stages as well as the design parameters in each stage. One of the most efficient statistical approaches used to model the multistage problems is the response surface method (RSM). However, it is necessary to optimize each response in all stages so to achieve the best solution for the whole problem. Robust optimization can produce very accurate solutions in this case. Design/methodology/approach: In order to model a multistage problem, the RSM is often used by the researchers. A classical approach to estimate response surfaces is the ordinary least squares (OLS) method. However, this method is very sensitive to outliers. To overcome this drawback, some robust estimation methods have been presented in the literature. In optimization phase, the global criterion (GC) method is used to optimize the response surfaces estimated by the robust approach in a multistage problem. Findings: The results of a numerical study show that our proposed robust optimization approach, considering both the sum of square error (SSE) index in model estimation and also global criterion (GC) index in optimization phase, will perform better than the classical full information maximum likelihood (FIML) estimation method. Originality/value: To the best of the authors’ knowledge, there are few papers focusing on quality oriented designs in the multistage problem by means of RSM. Development of robust approaches for the response surface estimation and also optimization of the estimated response surfaces are the main novelties in this study. The proposed approach will produce more robust and accurate solutions for multistage problems rather than classical approaches