Gray-Box Model Estimation for Tractable Process Control Tuning
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Solution Overview
Problem
Gray-box modeling for advanced controllers faces challenges in efficiently estimating nonlinear model parameters due to the complexity of the optimization task, which is often non-convex and computationally demanding, especially when dealing with dynamic systems that require precise control across varying operating conditions.
Innovation Solution
A method is introduced that involves a two-step parameter estimation approach, starting with a nonlinear steady-state model estimation using static data, followed by tuning the parameters to fit a dynamic model using transient data, leveraging local linear approximations and sensitivity evaluations to simplify the optimization problem and reduce computational intensity.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If gray-box model parameter estimation is performed using traditional optimization methods, then model accuracy is improved, but computational complexity and time consumption increase significantly
Solution Approach 1:
The patent segments the complex gray-box model parameter estimation into two distinct phases: (1) steady-state parameter estimation using static data, and (2) dynamic parameter estimation using transient data. This segmentation transforms a single complex non-convex optimization problem into two simpler, more tractable sub-problems that can be solved more efficiently while maintaining overall model accuracy.
Solution Approach 2:
The patent performs preliminary estimation of steady-state parameters before proceeding to dynamic parameter estimation. By first determining parameters that govern steady-state behavior using static data, the method establishes a foundation that simplifies the subsequent dynamic parameter identification, reducing the overall computational burden.
2Measurement precision
If comprehensive experimental data is collected to improve model identification, then model accuracy is improved, but measurement cost and time requirements increase
Solution Approach 1:
The patent divides data collection into two separate campaigns: (1) static data collection for steady-state parameter estimation, and (2) transient data collection for dynamic parameter estimation. This segmentation allows each phase to use tailored experimental procedures optimized for its specific purpose, reducing overall time requirements compared to collecting comprehensive data for both purposes simultaneously.
Solution Approach 2:
The patent uses partial data sets appropriate for each estimation phase rather than requiring complete comprehensive data. Static data suffices for steady-state parameters, and transient data suffices for dynamic parameters, eliminating the need to collect excessive data that would be redundant for each specific estimation objective.
3Reliability
If gray-box models are used to capture first-principle knowledge, then model robustness is improved, but parameter estimation difficulty increases
Solution Approach 1:
The patent separates parameter estimation into steady-state and dynamic components, allowing first-principle knowledge to be leveraged more effectively in each phase. The steady-state estimation can utilize thermodynamic and mass balance relationships more directly, while dynamic estimation focuses on kinetic parameters, making the overall estimation process more tractable despite maintaining model robustness.
Solution Approach 2:
The patent introduces steady-state parameters as intermediate variables that bridge first-principle knowledge and dynamic behavior. By first estimating steady-state parameters that embody fundamental physical relationships, the method creates an intermediary foundation that simplifies subsequent dynamic parameter estimation while preserving the robustness provided by first-principle modeling.
Data Source
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AI summary
A method includes using first principles and engineering knowledge to define a continuous time nonlinear gray-box model of a system performing a process, defining a numerically tractable optimization problem for parameter estimation of the nonlinear gray-box model, tuning a vector of parameters of a static model of the nonlinear gray-box model, and extending the vector of parameters of the static model to a dynamic model by fitting measured transient data from the process.