Optimization Layer Interface Stabilization via Conditioned Constraints
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Solution Overview
Problem
The stability of the interface between optimization layers in processing environments, such as refineries and chemical plants, is compromised due to discrepancies between higher and lower layers, leading to instability and large swings in process operations when faced with changes or disturbances.
Innovation Solution
A method is introduced to improve stability by determining additional variables for constraint based on condition numbers, converting non-square sub-matrices into square ones, and modifying process control variables to ensure consistency and reduced condition numbers, thereby stabilizing the optimization solutions across layers.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Adaptability or versatility
If multiple layers of optimization are used in a hierarchical manner with different execution frequencies, then comprehensive optimization coverage is achieved, but stability of the interface between layers deteriorates
Solution Approach 1:
The patent applies preliminary action by pre-calculating and storing the gain matrix for the lower optimization layer before it is needed for interface stabilization. This advance preparation allows the system to quickly compute condition numbers and determine appropriate constraint adjustments when interface stability issues arise, rather than calculating everything in real-time when problems occur
Solution Approach 2:
The patent implements feedback by continuously monitoring the condition number of the gain matrix sub-matrix at the interface between optimization layers. When the condition number exceeds a threshold indicating instability, the system adjusts constraints on variables and recalculates, creating a closed-loop control mechanism that actively maintains interface stability across the hierarchical optimization structure
2Ease of manufacture
If constraints are added to convert non-square sub-matrices into square ones, then mathematical solvability is improved, but system stability deteriorates due to increased condition numbers
Solution Approach 1:
The patent applies parameter changes by dynamically adjusting the constraints on process variables at the optimization layer interface. Instead of using fixed constraints, the system modifies constraint values based on the calculated condition number, selecting which variables to constrain and what constraint levels to apply in order to achieve a square sub-matrix while minimizing the condition number and maintaining stability
3Productivity
If variables are constrained to form a square sub-matrix, then the linear program model becomes solvable, but oscillations in process operations increase
Solution Approach 1:
The patent uses parameter changes by dynamically selecting which variables to constrain and what constraint values to apply, based on minimizing the condition number of the resulting square sub-matrix. This intelligent selection process avoids arbitrary constraint imposition that would cause oscillations, instead choosing constraint parameters that maintain operational stability while ensuring mathematical solvability
Data Source
AI summary
Systems and methods are provided for interfacing multiple layers of optimization for a model of one or more processes in a processing environment to achieve increased or maximized stability in the underlying layer. To improve consistency between the solutions at the different model levels, the lower level of optimization can have extra constraints added to the optimization problem which target variables at their unconstrained values in the upper layer of optimization. The systems and methods can facilitate selection of variables to receive an external target such that stability of the solution is improved or maximized. This can be achieved, at least in part, by identifying variables that provide a reduced or minimized condition number for a sub-matrix in the lower level model when an additional external constraint is applied. The sub-matrix with the reduced or minimized condition number can correspond to a partitioned portion of the gain matrix that corresponds to unconstrained independent variables and constrained dependent variables.