Dynamic Metamodeling for Predictive Analytics in Advanced Manufacturing

Metamodeling has been widely used in engineering for simplifying predictions of behavior in complex systems. The kriging method (Gaussian Process Regression) could be considered as a metamodeling technique that uses spatial correlations of sampling points to predict outcomes in complex and random processes. However, for large and nonideal data sets typical to those found in complex manufacturing scenarios, the kriging method is susceptible to losing its predictability and efficiency. To address these potential vulnerabilities, this article introduces a novel, dynamic metamodeling method that adapts kriging covariance matrices to improve predictability in contextualized, nonideal data sets. A key highlight of this approach is the optimal linking process, based on the location of prospective points, to alter the conventional stationary covariance matrices. This process reduces the size of resulting dynamic covariance matrices by retaining only the most critical elements necessary to maintain accuracy and reliability of new-point predictability. To further improve model fidelity, both the Gaussian parameters and design space attributes are optimized holistically within a problem space. Case studies with a representative test function show that the resulting Dynamic Variance-Covariance Matrix (DVCM) method is highly efficient without compromising accuracy. A second case study representative of an advanced manufacturing setting demonstrates the applicability and advantages of the DVCM method, including significantly increased model robustness.