Super-Linear Dynamic Property Approximation in Process Control
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Solution Overview
Problem
Dynamic process simulation in industrial settings is computationally intensive due to the need for second-order Taylor series expansions, which are time-consuming and inefficient.
Innovation Solution
A method using super-linear approximation based on first-order derivatives of dynamic equations, automatically updated and refined with rigorous values when errors exceed predetermined thresholds, allowing for wider representation of dynamic properties without requiring second-order derivatives.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If second-order Taylor series expansion is used for dynamic property approximation, then measurement precision is improved, but productivity deteriorates due to computational intensity
Solution Approach 1:
The patent changes the order of the Taylor series expansion from second-order to first-order, fundamentally altering the computational parameters. This parameter change reduces the calculation complexity from O(n²) to O(n), significantly improving simulation speed while maintaining acceptable accuracy through adaptive refinement mechanisms
Solution Approach 2:
The patent applies partial action by using first-order derivatives only when sufficient, and selectively applying more rigorous second-order calculations only when error thresholds are exceeded. This selective approach avoids the constant computational overhead of full second-order expansions while maintaining precision where needed
2Measurement precision
If second-order derivatives are calculated for accurate dynamic property representation, then measurement precision is improved, but device complexity increases
Solution Approach 1:
The patent simplifies the computational algorithm by changing the derivative order parameter from 2 to 1 in the Taylor series expansion. This parameter change reduces the number of calculations required, simplifying the computational structure and reducing algorithmic complexity while maintaining practical accuracy through error-controlled refinement
3Productivity
If first-order Taylor series expansion is used, then productivity is improved through reduced computational burden, but measurement precision deteriorates
Solution Approach 1:
The patent implements feedback control by continuously monitoring the error between first-order approximation results and actual dynamic property values. When the error exceeds a predetermined threshold, the system automatically triggers a refinement step using more rigorous calculation methods, ensuring precision is maintained dynamically throughout the simulation process
Solution Approach 2:
The patent applies excessive action selectively by using first-order expansion as the base method for most calculations, and only applying the more computationally intensive second-order or rigorous methods when and where the error threshold is exceeded. This selective excessive action maintains precision only where necessary, optimizing the balance between speed and accuracy
Data Source
AI summary
Simulation of process control environments, including dynamic properties, with a modified first-order Taylor series expansion. By using more linear calculations, a physical dynamic property is approximated in less time and with fewer computing resources. By adjusting the approximation to introduce curvature, a physical dynamic property is represented over a wider range than with basic linear series expansions. A comparison to a basic linear first-order series expansion identifies conditions when a rigorous update of a dynamic property is needed.