Gaussian Process Dynamical Models for Designing Multi-Stage Manufacturing Processes
Performance driven design of manufacturing processes requires multiple evaluations of computationally expensive solvers. We present a method to enable robust design optimizations through significant reduction in model evaluation time by replacing the expensive models with stochastic data-driven dynamical models of substrate undergoing manufacturing. Dynamic modeling of each manufacturing stage with substrate properties as a state allows direct optimization of apparatus parameters. Optimization of multi stage manufacturing processes like drawing, rolling and extrusion can benefit even more due to their repetitive nature. The computation time reduction and uncertainty bounds on objectives allows robust design optimizations. The challenge in creating such dynamical models appears from high dimensionality of state space variables; caused by modeling across different length scales for material property simulations. To enable computationally affordable robust design process, we have developed Gaussian process based surrogate models to obtain distributions of system objective predictions. Specifically, we achieve the following using a high fidelity wire drawing solver: a) dynamic modeling of manufacturing apparatus with substrate as a system, b) finding a feasible low dimensional representation of the substrate features via principal components analysis, c) recursive gaussian process based mapping in low dimensional space with cross-validation, d) optimization of substrate properties with quantified uncertainties. The methodology presented here is applicable to other multi-stage processes such as rolling and extrusion, where obtaining a low dimensional representation is as feasible as wire drawing.
Panchal, Purdue University.
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