Partial-Derivative Linear Models for Fast Industrial Optimization
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Solution Overview
Problem
Existing methods for simulating and optimizing complex industrial systems with a large number of input variables are inefficient due to high computational requirements and lack of accuracy, particularly in modeling non-linear behaviors.
Innovation Solution
A process that incorporates first-order partial derivatives, cross-term partial derivatives, and square-term partial derivatives into a linear programming model to accurately simulate and optimize industrial systems, allowing for reliable determination of output variables without excessive computational intensity.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If first-principles reference tools are used to simulate complex industrial systems with large numbers of input variables, then the capability to model individual system units and process steps is improved, but the computing time and computational resources required increase excessively
Solution Approach 1:
The patent segments the complex non-linear modeling problem into two distinct parts: (1) using first-principles reference tools to generate training data and determine coefficients for simplified relationships, and (2) using these pre-determined coefficients in a linear programming model for rapid simulation. This segmentation allows the computationally intensive work to be done once offline, while online simulations use the pre-processed information for fast results.
Solution Approach 2:
The patent performs preliminary action by pre-determining the coefficients of the simplified relationships using first-principles reference tools before actual simulation needs arise. The training phase where complex calculations are performed is completed in advance, creating a library of coefficients that can be quickly applied during operational simulations without requiring repeated intensive computing.
2Adaptability or versatility
If the total number of input variables increases in industrial systems, then the complexity and capability to represent real-world processes is improved, but the total number of experiments and trials required increases to a very large number that is infeasible
Solution Approach 1:
The patent creates a simplified copy or representation of the complex industrial system using linear programming models with pre-determined coefficients. Instead of performing exhaustive experiments on the full complex system, the patent uses this simplified model that replicates the essential behavior, allowing rapid analysis and optimization without requiring proportional increases in experimental effort as system complexity grows.
3Productivity
If derived tools with simplified structures are used to reduce computing power requirements, then the computing efficiency is improved, but the capability to model process unit operations based on first-principles and provide heat and material balance information is lost
Solution Approach 1:
The patent applies local quality by using different modeling approaches in different contexts: first-principles reference tools are used locally for the specific purpose of generating training data and determining coefficients, while the linear programming model with pre-determined coefficients is used for the broader purpose of rapid simulation and optimization. Each method is applied where it is most effective, combining the strengths of both approaches.
Data Source
AI summary
Linear programming models utilizing first-order partial derivatives and at least one of cross-term partial derivatives and square-term partial derivatives are disclosed. The models can be more advantageous than models utilizing first-order partial derivatives only and models utilizing regressed coefficients. Effective, accurate, and efficient prediction and optimization of industrial processes, systems, and products can be achieved using the improved models.