Dynamic Property Approximation for Faster Process Simulation
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Solution Overview
Problem
Dynamic process simulation in industrial processes is computationally intensive due to the need for second-order Taylor series expansions, which are time-consuming and inefficient.
Innovation Solution
A method using a super-linear approximation based on first-order derivatives of a dynamic equation, automatically updated and refined with rigorous values when errors exceed a predetermined threshold, allowing for faster and more efficient calculation of dynamic properties.
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 mathematical parameters of the approximation method from second-order derivatives to first-order derivatives combined with super-linear terms. This parameter change maintains sufficient accuracy for dynamic property approximation while dramatically reducing the computational complexity and calculation time required
Solution Approach 2:
The patent segments the approximation calculation into distinct components: first-order derivative terms and super-linear correction terms. This segmentation allows for more efficient computation by calculating each component separately and combining them, avoiding the need for computationally intensive second-order derivative calculations
2Manufacturing precision
If second-order Taylor series expansion is used, then manufacturing precision is improved, but loss of time increases
Solution Approach 1:
The patent changes the mathematical parameters from second-order to first-order derivatives with super-linear terms, achieving a better time-precision tradeoff suitable for real-time process control applications where both accuracy and speed are critical
3Device complexity
If existing approximation methods are used, then device complexity is reduced, but adaptability deteriorates due to limited range representation
Solution Approach 1:
The patent introduces dynamic adaptation by automatically adjusting the approximation range based on process conditions. The super-linear approximation method can adapt to varying operating conditions and maintain accuracy over a wider range of dynamic properties compared to fixed second-order Taylor series expansions
Solution Approach 2:
The patent extends the approximation capability by adding super-linear terms that capture higher-order behavior without requiring full second-order derivative calculations. This dimensional extension in the mathematical approach enables representation of a broader range of dynamic properties while maintaining computational efficiency
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.