Non-linear Creep Factor for Iterative Process Convergence
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Solution Overview
Problem
Existing systems for process optimization in refinery and petrochemical plants face convergence issues due to uncertain initial estimates, leading to poor robustness and unsatisfactory results, particularly in nonlinear optimization problems.
Innovation Solution
The implementation of a non-linear correction factor, known as 'creep', which is applied to iterative processes to improve robustness by adjusting initial estimates and guiding the solver towards convergence, using a processor-based system that defines and applies non-linear correction factors to variables in iterative processes.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If fixed creep or linear creep is used to improve robustness with uncertain initial estimates, then convergence reliability improves, but the correction approach remains insufficient for complex nonlinear problems
Solution Approach 1:
The patent applies dynamics by transitioning from fixed or linear creep factors to a dynamic non-linear creep factor that adapts during iteration. The creep factor is updated based on the ratio of successive iteration changes (||x^(k+1)-x^(k)||/||x^(k)-x^(k-1)||), allowing the correction mechanism to respond to the actual convergence behavior of the iterative process, thereby improving both reliability and adaptability to nonlinear problems.
Solution Approach 2:
The patent implements parameter changes by modifying the creep factor parameter from constant or linear values to non-linear values that change based on iteration characteristics. The non-linear creep factor is calculated as c_k = c_{k-1} * (||x^(k+1)-x^(k)||/||x^(k)-x^(k-1)||), where the parameter adapts to the local convergence properties of each iteration step, enabling better handling of uncertain initial estimates in nonlinear optimization.
2Reliability
If non-linear correction factor is applied to guide solver towards convergence, then robustness with uncertain initial estimates improves, but computational complexity increases
Solution Approach 1:
The patent applies self-service by making the non-linear creep factor automatically adjust based on the iterative process's own convergence behavior. The system uses the actual changes observed in successive iterations (||x^(k+1)-x^(k)||/||x^(k)-x^(k-1)||) to determine the appropriate creep factor, eliminating the need for external manual adjustment or complex pre-computation, thereby improving robustness without proportionally increasing computational complexity.
Solution Approach 2:
The patent implements feedback by using the convergence behavior of the iterative process to inform the creep factor selection. The non-linear creep factor is updated based on feedback from the ratio of successive iteration changes, creating a closed-loop control mechanism that automatically adjusts the correction strength based on actual solver performance, improving robustness while keeping computational overhead manageable.
Data Source
AI summary
A processor connected to a process module executes processor executable instructions stored on the process module according to process input data received by a process definition interface, according to variables input data received by a variables interface. A non-linear correction factor as defined by a non-linear correction factor module is applied to provide a solution to an iterative process. A processor implemented process solves a process problem and comprises processor executable instructions stored on a tangible storage device.