Hybrid Nonlinear Process Modeling for Real-Time Predictive Control
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Solution Overview
Problem
Existing predictive modeling techniques for complex systems face challenges in accurately representing nonlinear dynamics and optimizing processes due to incomplete first-principles information, computational inefficiencies, and the need for additional experimental data, especially when first-principles models are incomplete or empirical models are insufficient.
Innovation Solution
The Parametric Universal Nonlinear Dynamics Approximator (PUNDA) model combines a nonlinear approximator, such as a neural network, with a dynamic parameterized model to systematically utilize empirical and first-principles knowledge, allowing for real-time optimization and control by formulating the training of neural network parameters as a constrained nonlinear programming problem with derivative constraints.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If a first-principles model is used to represent the system, then the model is based on physical laws and general process behavior, but the model accuracy is insufficient when first-principles information is incomplete
Solution Approach 1:
The patent combines a first-principles model with a neural network model into a hybrid architecture. The neural network compensates for the incomplete first-principles information by learning from empirical data, while the first-principles model provides the physical law foundation. This merging resolves the contradiction by integrating both approaches to achieve higher accuracy despite incomplete theoretical knowledge.
Solution Approach 2:
The hybrid model functions as a composite modeling approach, combining the strengths of physics-based modeling (generality and interpretability) with data-driven modeling (accuracy for specific systems). The composite structure allows the model to leverage both theoretical knowledge and empirical observations to overcome the limitations of incomplete first-principles information.
2Measurement precision
If an empirical model is used to improve accuracy, then the model can capture specific system behavior, but additional experimental data is required
Solution Approach 1:
The hybrid model merges empirical data-driven components with first-principles components. The neural network portion learns from empirical data to capture specific system behaviors, while the first-principles portion reduces the need for extensive experimentation by providing physics-based constraints and relationships. This combination achieves high accuracy while reducing experimental data requirements compared to purely empirical approaches.
3Reliability
If a complex predictive model is used to accurately represent nonlinear dynamics, then the model fidelity improves, but computational efficiency decreases
Solution Approach 1:
The hybrid model segments the modeling task into two parts: the first-principles model handles the general physical relationships and provides a computationally efficient framework, while the neural network handles the specific nonlinear dynamics that are difficult to model theoretically. This segmentation allows the system to achieve high fidelity in representing nonlinear dynamics while maintaining computational efficiency through the use of simplified physics-based equations for the bulk of the computation.
4Adaptability or versatility
If a purely data-driven model is used to capture complex system behavior, then the model can adapt to specific systems, but the model lacks interpretability and physical consistency
Solution Approach 1:
The hybrid model merges data-driven neural network components with physics-based first-principles components. The neural network adapts to system-specific behaviors by learning from data, while the first-principles component preserves physical knowledge and ensures physical consistency. This merging resolves the contradiction by maintaining both adaptability to specific systems and fidelity to physical laws simultaneously.
Data Source
AI summary
System and method for modeling a nonlinear process. A combined model for predictive optimization or control of a nonlinear process includes a nonlinear approximator, coupled to a parameterized dynamic or static model, operable to model the nonlinear process. The nonlinear approximator receives process inputs, and generates parameters for the parameterized dynamic model. The parameterized dynamic model receives the parameters and process inputs, and generates predicted process outputs based on the parameters and process inputs, where the predicted process outputs are useable to analyze and/or control the nonlinear process. The combined model may be trained in an integrated manner, e.g., substantially concurrently, by identifying process inputs and outputs (I/O), collecting data for process I/O, determining constraints on model behavior from prior knowledge, formulating an optimization problem, executing an optimization algorithm to determine model parameters subject to the determined constraints, and verifying the compliance of the model with the constraints.