Bridging AI and Control: Surrogate Models for Dynamic Process Optimization
- Introduction
- What Is a Surrogate Model?
- Why Use Surrogate Models Instead of Informer or Transformer Models?
- The Limitations of Conventional Monitoring
- Working Principle
- Working Architecture
- Applications of Surrogate Models
- Importance of Surrogate Models in Process Optimization
- Case Study: Three-Tank Coupled Process System
- References
Introduction
In modern industrial systems, such as furnaces, blowers, gas cleaning & handling equipment, separators, conveyor belts, compressors, reactors, and distillation columns-processes are becoming increasingly dynamic and data-rich. Complex & computationally expensive time-series deep learning, like Informer, Transformer, and Temporal Convolutional Networks (TCN)or CFD simulation, have emerged as powerful tools to forecast and optimize these systems. However, their complexity and computational demands often limit their practical use in real-time industrial control.
To address this, Surrogate Models are gaining attention as lightweight, interpretable, and computationally efficient alternatives for control and optimization. These models emulate the behavior of complex neural networks or real processes, enabling rapid predictions and decision-making without heavy computation.
What Is a Surrogate Model?
A Surrogate Model is a simplified representation of a complex system that approximates its input–output behavior. Instead of running time-consuming simulations or deep learning models, the surrogate model provides fast predictions, making it ideal for Model Predictive Control (MPC), optimization, and digital twin applications.
Surrogate models are especially effective when the original process is:
- Highly nonlinear or dynamic
- Computationally expensive to simulate
- Governed by multiple correlated inputs and outputs
Why Use Surrogate Models Instead of Informer or Transformer Models?
| Challenge | Informer/Transformer Models | Surrogate Model |
|
Computational Load |
High GPU requirement |
Lightweight, fast |
|
Interpretability |
Complex attention layers |
Transparent regression basis |
|
Control Integration |
Hard to embed in MPC |
Easily integrable |
|
Real-Time Feasibility |
Limited |
Excellent |
|
Retraining Frequency |
Frequent |
Retraining Frequency |
While Informer or Transformer networks excel at long-term dependency learning in multivariate time series, surrogate models allow these insights to be translated into practical, real-time control applications
Types of Algorithms Used for Surrogate Modeling
|
Algorithm Type |
Examples |
Use Case |
|
Regression-Based Models |
Polynomial Regression, Ridge/Lasso Regression |
Smooth, low-noise processes |
|
Machine Learning Models |
Random Forest, XGBoost, Gaussian Process Regression |
Nonlinear relationships with noise |
|
Kriging / Gaussian Process Models |
Ordinary Kriging, Dynamic Kriging, Co-Kriging |
Spatial-temporal modeling |
|
Neural Network Simplifications |
Shallow NNs, Autoencoders, MLPs |
Capturing nonlinear patterns |
|
Hybrid Models |
PLS + Kriging, PCA + RF |
Dimensionality reduction + accuracy |
|
Dynamic Surrogate Models |
Recurrent Surrogates, ARX with ML extensions |
Time-dependent industrial systems |
Working Principle
The surrogate model mimics the mapping between process inputs (manipulated variables) and outputs (controlled variables). During real-time operation:
- The process controller queries the surrogate model to predict system behavior for a range of future control actions.
- An optimization algorithm selects the control action that minimizes a cost function (e.g., fuel use, emissions, temperature error).
- The surrogate’s fast prediction enables rapid optimization without expensive simulation or deep learning inference.
Working Architecture
Applications of Surrogate Models
1. Reheating Furnaces: Predict billet temperature and optimize burner operation for fuel efficiency.
2. Compressor Systems: Estimate emission parameters (CO₂, NOx, CH₄) under variable load conditions.
3. Distillation Columns: Replace rigorous thermodynamic models with fast surrogates for optimal reflux control.
4. Batch Reactors: Optimize reaction temperature and catalyst dosage using dynamic surrogate models.
5. Energy Systems: Model turbine performance and predict power output in hybrid renewable grids.
6. Digital Twins: Serve as real-time engines for virtual plant simulations, enabling predictive maintenance and optimization.
Importance of Surrogate Models in Process Optimisation
- Real-Time Optimization: Enables on-the-fly decision-making in MPC frameworks.
- Energy Efficiency: Reduces fuel and power consumption through optimal control.
- Reduced Simulation Cost: Minimizes computational demand versus deep learning.
- Enhanced Interpretability: Easier to explain model decisions to operators.
- Digital Twin Integration: Acts as the “brain” of the digital twin for predictive control.
Case Study: Three-Tank Coupled Process System
Objective: To demonstrate surrogate model effectiveness in capturing nonlinear and dynamic interactions of a three-tank coupled water flow system, where each tank influences the others through interconnections and gravity-driven discharge
System Description: The three-tank process system consists of three vertically aligned tanks connected through valves and pipelines. The inflow to the first tank is controlled, and the liquid flows sequentially to the second and third tanks, with outlets at each stage. The system exhibits nonlinear flow dynamics due to gravitational effects and valve-controlled interactions.
Methodology for Developing a Surrogate Model
To demonstrate, consider a three-tank process system. Each tank interacts dynamically, with liquid flows between tanks and exits through outlets influenced by gravity and control valves.
We simulate this process using differential equations (ODEs) that describe tank heights based on input flow rates Q1 and Q2. This generates the “ideal” (true) dynamic data used for training the surrogate.
The surrogate model (Kriging) is then trained on:
Inputs: [h1, h2, h3, Q1, Q2]
Outputs: [h1_next, h2_next, h3_next]
to learn how the system evolves over time.
Results and Discussion
After training, the Kriging surrogate was recursively used to predict tank heights over 600 time steps. The predicted outputs were compared with the “ideal” simulated heights.
Tank-wise RMSE values:
- Tank 1: 0.0021
- Tank 2: 0.0018
- Tank 3: 0.0023
The surrogate model effectively replicates the dynamic behavior of the system, as shown in the following plots.
Figure 1. Tank heights (outputs) prediction by surrogate model.
Figure 2. Validation: Actual vs Prediction of tank 1 height.
Figure 3. Validation: Actual vs Prediction of tank 2 height.
Figure 4. Validation: Actual vs Prediction of tank 3 height.
References
- Rasmussen, C.E., & Williams, C.K.I. Gaussian Processes for Machine Learning.
- Forrester, A.I.J., Sobester, A., & Keane, A.J. Engineering Design via Surrogate Modelling.
- Qin, S.J., Badgwell, T.A. “A survey of industrial model predictive control technology.” Control Engineering Practice, 2003.
- Vaswani, A. et al., Attention Is All You Need, 2017.
