Data-driven parallel Koopman subsystem modeling and distributed moving horizon state estimation for large-scale nonlinear processes

TL;DR

This work considers a state estimation problem for large-scale nonlinear processes in the absence of first-principles process models, and proposes a parallel subsystem modeling approach that provides accurate estimates of the process states without requiring a first-principles process model.

Abstract

In this work, we consider a state estimation problem for large-scale nonlinear processes in the absence of first-principles process models. By exploiting process operation data, both process modeling and state estimation design are addressed within a distributed framework. By leveraging the Koopman operator concept, a parallel subsystem modeling approach is proposed to establish interactive linear subsystem process models in higher-dimensional subspaces, each of which correlates with the original nonlinear subspace of the corresponding process subsystem via a nonlinear mapping. The data-driven linear subsystem models can be used to collaboratively characterize and predict the dynamical behaviors of the entire nonlinear process. Based on the established subsystem models, local state estimators that can explicitly handle process operation constraints are designed using moving horizon estimation. The local estimators are integrated via information exchange to form a distributed estimation scheme, which provides estimates of the unmeasured/unmeasurable state variables of the original nonlinear process in a linear manner. The proposed framework is applied to a chemical process and an agro-hydrological process to illustrate its effectiveness and applicability. Good open-loop predictability of the linear subsystem models is confirmed, and accurate estimates of the process states are obtained without requiring a first-principles process model.

Figures (12)

• Figure 1: An illustrative diagram depicting the connection between the subsystem modeling and local estimator design of the proposed distributed estimation framework.
• Figure 2: A schematic of the distributed state estimation scheme developed using Koopman subsystem models.
• Figure 3: A schematic of the four-CSTR process.
• Figure 4: Cross-validation of the Koopman subsystem models for the four-CSTR process.
• Figure 5: Trajectories of the actual system states and state estimates for four vessel CSTRs.

Theorems & Definitions (7)

• Remark 1
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• Remark 7