Constrained Empirical Modeling for Reliable Extrapolation Control
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Solution Overview
Problem
Empirical models used in control systems, predictive systems, and optimization systems often fail to accurately extrapolate beyond their training data range, leading to inaccurate results and issues like zero model gains and gain inversion, which can result in inappropriate control actions.
Innovation Solution
Incorporating asymptotic behavior information into the empirical modeling process by selecting basis/kernel functions that emulate the desired asymptotic behavior of the system, ensuring the model's extrapolation properties align with the actual system's behavior, and using general constrained training to enforce global constraints.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If traditional empirical modeling is used with training data, then the model fits the training data well, but the model fails to accurately extrapolate beyond the training range
Solution Approach 1:
The patent transforms the empirical model parameters by applying a change of variables that incorporates asymptotic behavior constraints. Specifically, it uses a transformation where the model parameters are redefined in terms of new parameters that inherently satisfy the desired asymptotic behavior, thereby improving extrapolation accuracy while maintaining training data fit quality.
Solution Approach 2:
The patent applies preliminary action by pre-defining the asymptotic behavior constraints before the actual modeling process. The desired asymptotic behavior is specified in advance, and the model structure is designed to automatically satisfy these constraints, ensuring reliable extrapolation from the outset rather than attempting to correct extrapolation issues after model training.
2Measurement precision
If the empirical model is trained to fit training data accurately, then the model quality within training range is high, but the model may produce zero model gains or gain inversion outside training range
Solution Approach 1:
The patent changes the parameterization of the empirical model by introducing transformed parameters that are constrained to maintain proper gain behavior. The transformation ensures that the model gains remain positive and bounded, preventing zero model gains and gain inversion that would otherwise occur when extrapolating beyond the training range.
Solution Approach 2:
The patent incorporates feedback mechanisms by using the desired asymptotic behavior as a constraint that continuously guides the model behavior. The model structure includes built-in feedback through the asymptotic constraints, ensuring that the model responds appropriately to inputs outside the training range by maintaining gains that reflect the expected system behavior.
3Device complexity
If standard empirical modeling approaches are used, then the modeling process is simple, but the model cannot enforce global constraints relating to first-principles information
Solution Approach 1:
The patent applies parameter changes by transforming the model parameters into a form that naturally incorporates first-principles constraints. By redefining the parameters through a mathematical transformation, the model automatically satisfies global constraints related to physical principles without requiring complex additional computational steps or iterative optimization procedures.
Data Source
AI summary
In certain embodiments, a method includes formulating an optimization problem to determine a plurality of model parameters of a system to be modeled. The method also includes solving the optimization problem to define an empirical model of the system. The method further includes training the empirical model using training data. The empirical model is constrained via general constraints relating to first-principles information and process knowledge of the system.