Abstract

A large-scale production of carbon nanotubes has been of great interest due to their practical needs, which is limited by the difficulty of producing them with controlled structures and properties. We seek for a surrogate modeling to predict the process yield for a given process configuration under control uncertainties. The predictive power can be used to optimize the process configuration in a closed-loop production system. A challenge in the surrogate modeling is that some process conditions are controlled by other manipulating factors, and the control precision is not high. Therefore, the process conditions vary significantly even under the same setting of the manipulating factors. Due to this variation, the surrogate modeling that directly relates the manipulating factors to the process outcome does not provide a great predictive power on the outcome. At the same time, the model relating the process conditions to the outcome is not appropriate for the prediction purpose because the process conditions cannot be accurately set as planned due to the control uncertainties for a future process run. Motivated by the example, we propose a two-tiered Gaussian process (GP) model, where the bottom tier relates the manipulating factors to the process conditions with control variation, and the top tier relates the process conditions to the outcome. It explicitly models the propagation of the control uncertainty to the outcome through the two modeling tiers. The benefits of the approach over the standard GP approach are illustrated with multiple simulated scenarios and carbon nanotube production processes.

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