Dynamic Hybrid Modeling: Incremental Identification and Model Predictive Control

TL;DR

This work tackles the identification of dynamic hybrid models that couple mechanistic DAEs with data-driven corrections by proposing an incremental identification framework. The method decouples the process into four steps: regularized dynamic parameter estimation to obtain time profiles $p(t)$, correlation analysis to select relevant inputs, data-driven model identification to map selected inputs to $p(t)$ via neural networks, and hybrid model integration that replaces $p(t)$ with the learned $ML(\cdot)$ within the DAE. The authors demonstrate robustness and efficiency through three case studies—a chemical reactor, a bioreactor, and a real research plant integrated with MPC—showing the approach can operate under limited data and complex mechanistic cores. The work provides a practical, diagnosable pathway to building accurate, deployable hybrid models with MPC-ready capabilities, while highlighting the importance of regularization and careful input selection for reliable data-driven components.

Abstract

Mathematical models are crucial for optimizing and controlling chemical processes, yet they often face significant limitations in terms of computational time, algorithm complexity, and development costs. Hybrid models, which combine mechanistic models with data-driven models (i.e. models derived via the application of machine learning to experimental data), have emerged as a promising solution to these challenges. However, the identification of dynamic hybrid models remains difficult due to the need to integrate data-driven models within mechanistic model structures. We present an incremental identification approach for dynamic hybrid models that decouples the mechanistic and data-driven components to overcome computational and conceptual difficulties. Our methodology comprises four key steps: (1) regularized dynamic parameter estimation to determine optimal time profiles for flux variables, (2) correlation analysis to evaluate relationships between variables, (3) data-driven model identification using advanced machine learning techniques, and (4) hybrid model integration to combine the mechanistic and data-driven components. This approach facilitates early evaluation of model structure suitability, accelerates the development of hybrid models, and allows for independent identification of data-driven components. Three case studies are presented to illustrate the robustness, reliability, and efficiency of our incremental approach in handling complex systems and scenarios with limited data.

Figures (11)

• Figure 1: Overview of incremental hybrid model identification approach.
• Figure 2: Results of dynamic parameter estimation problem (Step 1) for chemical reactor case study. Blue dots: Noisy pseudo-experimental measurement data. Red, solid lines: optimal profiles, i.e., solution of the parameter optimization problem. Black, dashed lines: mechanistic model predictions for parameters $p_1$, $p_2$, $p_3$. For ease of presentation, each figure represents the concatenation of 8 separate experiments, each of 2.5 h duration but with different initial conditions and MV input profiles. (a) Height $h$. (b) Parameter $p_1$. (c) Concentration $c$. (d) Parameter $p_2$. (e) Temperature $T$. (f) Parameter $p_3$.
• Figure 3: Pearson correlation matrix (Step 2) for chemical reactor case study.
• Figure 4: Simulation results with hybrid model compared to simulation results with mechanistic model for chemical reactor case study. Red, solid lines: simulation results with hybrid model. Black, dashed lines: simulation results with mechanistic model. (a) Concentration profiles. (b) Parameter $p_2$ profiles. (c) Temperature profiles. (d) Parameter $p_3$ profiles.
• Figure 5: Solution of dynamic parameter estimation (step 1) with the regularization term (blue, dash-dotted lines) and without the regularization term (brown, dashed lines) in the objective function \ref{['eq:parameter_estimation:obj']}. The measurement samples used for parameter estimation are illustrated by black dots. (a) Height profile. The correct profiles (determined via simulation of the original model) are illustrated by black, solid lines. (b) Parameter $p_1$ profile. (c) Concentration profile. (d) Parameter $p_2$ profile. (e) Temperature profile. (f) Parameter $p_3$ profile.