Empirical Model Constraints 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 provide accurate results when extrapolating beyond the range of their training data, leading to 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 only, then the model fits the training data well, but the model produces inaccurate results when extrapolating beyond the training data range
Solution Approach 1:
The patent applies preliminary action by incorporating asymptotic behavior constraints into the empirical model formulation before training. By pre-defining the desired asymptotic behavior that the model should exhibit at extreme values, the model is prepared in advance to handle extrapolation scenarios correctly, rather than learning this behavior from limited training data alone.
Solution Approach 2:
The patent changes parameters by modifying the model formulation to include asymptotic behavior constraints. This involves transforming the standard empirical model into a constrained optimization problem where the model parameters must satisfy both the training data fit and the prescribed asymptotic behavior conditions, thereby improving extrapolation reliability.
2Ease of manufacture
If the empirical model is trained only on available data without additional constraints, then the modeling process is simple, but the model may produce invalid control actions such as infinite or inverted controller gains
Solution Approach 1:
The patent applies preliminary anti-action by proactively preventing invalid control actions through asymptotic behavior constraints. By specifying the desired asymptotic behavior in advance, the model is constrained to produce valid controller gains even at extreme operating conditions, thereby preventing issues like infinite or inverted gains before they occur.
Solution Approach 2:
The patent incorporates feedback by using the asymptotic behavior constraints to guide the model training process. The constraints provide continuous feedback during model formulation and training, ensuring that the model parameters adjust to satisfy both the training data fit and the asymptotic behavior requirements, thereby maintaining control action validity.
3Adaptability or versatility
If basis functions are selected without considering asymptotic behavior, then the model structure is flexible and easy to implement, but the model cannot accurately represent system behavior outside the training range
Solution Approach 1:
The patent applies local quality by making different parts of the model serve different functions. The basis functions maintain flexibility for fitting training data within the operating range, while the asymptotic behavior constraints ensure accurate representation of system behavior at extreme values. This division of functional responsibilities resolves the contradiction between flexibility and extrapolation accuracy.
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.