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A computer model can be used for predicting an output only after specifying the values of some unknown physical constants known as calibration parameters. The unknown calibration parameters can be estimated from real data by conducting physical experiments. This paper presents an approach to optimally design such a physical experiment. The problem of optimally designing physical experiment, using a computer model, is similar to the problem of finding optimal design for fitting nonlinear models. However, the problem is more challenging than the existing work on nonlinear optimal design because of the possibility of model discrepancy, that is, the computer model may not be an accurate representation of the true underlying model. Therefore, we propose an optimal design approach that is robust to potential model discrepancies. We show that our designs are better than the commonly used physical experimental designs that do not make use of the information contained in the computer model and other nonlinear optimal designs that ignore potential model discrepancies. We illustrate our approach using a toy example and a real example from industry., 25 pages, 10 figures

A manufacturing system collects big and heterogeneous data for tasks such as product quality modeling and data-driven decision-making. However, as the size of data grows, timely and effective data utilization becomes challenging. We propose an unsupervised data filtering method to reduce manufacturing big data sets with multi-variate continuous variables into informative small data sets. Furthermore, to determine the appropriate proportion of data to be filtered, we propose a filtering information criterion (FIC) to balance the tradeoff between the filtered data size and the information preserved. The case study of a babycare manufacturing and a simulation study have shown the effectiveness of the proposed method.

Computer experiments may involve not only continuous input factors but also nominal factors, discrete numeric factors, and ordinal factors. Most existing literature in designing computer experiment...

In multistage manufacturing systems, modeling multiple quality indices based on the process sensing variables is important. However, the classic modeling technique predicts each quality variable one at a time, which fails to consider the correlation within or between stages. We propose a deep multistage multi-task learning framework to jointly predict all output sensing variables in a unified end-to-end learning framework according to the sequential system architecture in the MMS. Our numerical studies and real case study have shown that the new model has a superior performance compared to many benchmark methods as well as great interpretability through developed variable selection techniques., Comment: Accepted by Journal of Quality Technology

To identify the robust settings of the control factors, it is very important to understand how they interact with the noise factors. In this article, we propose space-filling designs for computer experiments that are more capable of accurately estimating the control-by-noise interactions. Moreover, the existing space-filling designs focus on uniformly distributing the points in the design space, which are not suitable for noise factors because they usually follow non-uniform distributions such as normal distribution. This would suggest placing more points in the regions with high probability mass. However, noise factors also tend to have a smooth relationship with the response and therefore, placing more points towards the tails of the distribution is also useful for accurately estimating the relationship. These two opposing effects make the experimental design methodology a challenging problem. We propose optimal and computationally efficient solutions to this problem and demonstrate their advantages using simulated examples and a real industry example involving a manufacturing packing line.

The purpose of model calibration is to make the model predictions closer to reality. The classical Kennedy-O'Hagan approach is widely used for model calibration, which can account for the inadequacy of the computer model while simultaneously estimating the unknown calibration parameters. In many applications, the phenomenon of censoring occurs when the exact outcome of the physical experiment is not observed, but is only known to fall within a certain region. In such cases, the Kennedy-O'Hagan approach cannot be used directly, and we propose a method to incorporate the censoring information when performing model calibration. The method is applied to study the compression phenomenon of liquid inside a bottle. The results show significant improvement over the traditional calibration methods, especially when the number of censored observations is large.

Problem: The prediction of cutting forces is very important in designing mechanical micromachining to ensure geometrical accuracy of the machined feature and avoid tool breakage. These predictions can be done either via analytical models or finite-element models. The finite-element models are precise but usually time consuming to run. Analytical models, on the other hand, are less accurate but computationally much cheaper. The problem here is to integrate these two types of physics-based models and obtain an easy-to-evaluate statistical model that can approximate the machining forces. Approach: We propose performing a sensitivity analysis using the computationally cheap analytical models prior to conducting the computationally intensive finite-element simulations. With the elicited prior knowledge from the sensitivity analysis, a two-stage strategy is presented for designing the finite-element simulations in which customized number of levels can be assigned for each input factor. The finite-element simulation data can then be integrated with the analytical models in developing the final metamodel. Results: We show that the initial sensitivity analysis can reveal critical information about the underlying system and guide us to more efficiently extract information from the finite-element models. The proposed design for the finite-element simulations is comprised of two subarrays and overall can achieve desirable orthogonality and space-filling properties. Compared with using n different levels for all input factors, as in the traditional space-filling design, the new design is more capable for estimating factor interactions while still maintaining the ability to capture necessary nonlinear effects. By using fewer levels, it can also improve the efficiency of estimating the effects when the simulation is subject to stochastic noise. In model validation, our numerical results indicate that the fitted integrated metamodel can more precisely approximate the machining forces than either using the analytical models or the traditional metamodel based on the finite-element simulations alone.