Near-real-time online process control using grey-box models

Abstract

Near-real time control of dynamical processes is very beneficial as it enables detection and timely intervention in case of diminishing quality or necessary parameter adjustment. This can improve quality and reliability, thus extending the overall lifetime, increasing the safety and reducing maintenance and/or production costs. The manufacturing process is one area, in which the application of machine-based control is especially valuable and has great advantage over user-based monitoring and control as it can provide more reliable, fast and cost-efficient results. To perform robust process control, a model that can continuously evaluate and update itself and its future predictions with high reliability is of utmost importance.

A methodology to create a reliable and self-improving digital twin for near-real-time process monitoring of dynamical processes is proposed. A digital twin not only mirrors the physical entity under consideration of aleatory and epistemic uncertainty, but also performs analysis based on the current process state, taking its parameter drift into account. The latter, caused by e.g., the wear and tear of the material, is unpredictable and uncontrollable. So, while it is necessary to consider, it is also rather challenging to do.

The proposed method is a grey-box model, which consists of a numerical model and a roughly calibrated surrogate model, the physics informed white-box and the data-driven black-box respectively. The numerical model has a high precision but is too slow to evaluate in a near-real-time context. The surrogate model, which is considerably faster to evaluate, is however also subjected to modelling error, introducing additional epistemic uncertainties. For the surrogate model, an adaptive Kriging scheme is used. In this context, two set of input variables are considered. The first set contains the process parameters that are affected by process drift. As such, they are time dependent, uncontrollable and generally difficult to predict. The other set contains the controllable input parameter, which are used to adapt to the process drift. The goal of this methodology is to both improve the calibration of the surrogate and simultaneously control the input parameters iteratively to minimise the probability of failure. The general concept of learning functions used in adaptive Kriging is applied to the specific needs of the proposed method. Finally, validation is performed on a non-linear but controlled dynamical example under uncertainty.