Metamodel-Based Numerical Techniques for Self-Optimizing Control

Abstract

Self-optimizing control technologies are a well-known study field of control structure design, having a robust mathematical background. With the aid of commercial process simulators and numerical packages, process modeling became an easier task. However, dealing with extremely large and complex systems still is a tedious task, and sometimes not feasible, even with these innovative tools. Surrogate models, also called metamodels, can be used to substitute partially or totally the original mathematical models for prediction and optimization purposes, reducing the complexity of evaluating large-scale and highly nonlinear processes. This work aims at applying recent self-optimizing control techniques to surface responses of processes using the Kriging method as a reduced model builder. A procedure to apply self-optimizing control to surrogate responses was described in detail, together with how the optimization can be done. Well-known case studies had their surface responses successfully built and analyzed to generate using the techniques cited, the optimal selection of controlled variables that minimizes the worst-case loss, and the same results were found when compared with the implementation in the original models from previous authors. The results indicate the effectiveness of the reduced models when applied to design self-optimizing control structures, simplifying the task.

An inverse mapping approach for process systems engineering using automatic differentiation and the implicit function theorem

“…For example, there are applications in PSE that have successfully used machine learning models as surrogates for process simulation platforms. [18][19][20][21] In this work, both case studies are first-principles models implemented using JAX and its respective NumPy implementation.…”

“…Despite the fact that JAX has its own syntax that the model implementation must follow, it fully supports loops, control statements and typical numerical methods such as numerical integration, for instance.Note that if the process model is originally developed in a platform that impedes the use of JAX's capabilities directly (e.g., process simulation platforms with closed source‐code in which automatic differentiation cannot be made directly), a machine‐learning model can be easily built for such applications using a JAX‐compatible package, such as GPJax 17 which is a JAX‐based Gaussian Process Regression package, for instance. For example, there are applications in PSE that have successfully used machine learning models as surrogates for process simulation platforms 18–21 . In this work, both case studies are first‐principles models implemented using JAX and its respective NumPy implementation. Output space region definition : At this step the output space region has to be defined.…”