Equation-Constrained System Design via Parameterized Solution Curves
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Solution Overview
Problem
Current optimization and constraint satisfaction technologies in physical system design are inefficient in navigating solution spaces due to unpredictable algorithm behavior and lack of control over initial conditions, and they struggle to provide physically acceptable solutions, especially at early design stages where natural criteria for optimization and uniqueness are absent.
Innovation Solution
A computer-implemented method that partitions variables into fixed and unfixed categories, computes a parameterized curve of solutions, and displays their projections in a 2D domain, allowing real-time navigation and representation of current positions on this curve to facilitate the design of physical systems constrained by equations.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Productivity
If optimization algorithms are used to find the best solution, then the algorithm efficiency is improved, but the designer loses control over the solution space navigation and cannot investigate multiple solutions
Solution Approach 1:
The patent introduces an intermediary representation (the curve C and its projections) that mediates between the complex high-dimensional solution space and the designer's need for control. The curve serves as a structured path through the solution space that maintains algorithmic efficiency while providing the designer with intuitive navigation capabilities through 2D visualizations.
Solution Approach 2:
The patent transforms the high-dimensional solution space navigation problem into a 2D visualization problem by projecting the curve onto coordinate planes. This dimensionality reduction allows designers to control and understand the solution space through familiar 2D graphics while the underlying algorithm operates in the full high-dimensional space.
2Measurement precision
If constraint satisfaction algorithms narrow the solution subset, then the solution precision is improved, but the navigation in the solution subset becomes difficult due to holes and discontinuities
Solution Approach 1:
The patent performs a preliminary action by computing the continuous curve C that represents all solutions before the designer begins navigation. This pre-computation ensures that the solution set is complete and continuous, avoiding the holes and discontinuities that plague traditional constraint satisfaction approaches. The curve is computed once and then used for smooth navigation.
3Productivity
If the designer is asked to provide an initial condition for optimization, then the algorithm can compute a solution, but the solution highly depends on the initial condition and this dependency is out of control
Solution Approach 1:
The patent changes the parameter representation from discrete initial conditions to a continuous curve parameterized by a single parameter λ. Instead of relying on discrete initial guesses that lead to different solutions, the system provides a continuous family of solutions parameterized by λ, making the solution stable and predictable regardless of where on the curve the designer starts.
4Extent of automation
If traditional CAD/CAE systems are used for physical system design, then the design process can be computer-aided, but the systems lack capability to navigate and investigate solution spaces constrained by equations
Solution Approach 1:
The patent creates a universal module that can be integrated into existing CAD/CAE systems to provide solution space navigation capabilities. The curve computation and visualization module is designed to work with any system of equations, making it adaptable to various design domains while maintaining the core functionality of computer-aided design.
Data Source
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AI summary
The invention notably relates to a computer-implemented method for designing a physical system constrained by a system of equations involving variables, the method comprising the steps of partitioning (S10) the variables involved in the equations into fixed variables and unfixed variables, thereby setting the system to a restricted system with a degree of freedom equal to 1, computing (S20) a parameterized curve of solutions of the restricted system in the domain of the unfixed variables, for at least one pair of unfixed variables, displaying (S30) the projection of the curve in the product of the domains of the pair, and navigating (S40) the solutions on the parameterized curve and representing, real-time, the current navigation position on the projection of the curve. Such a method improves the design of a physical system constrained by equations involving variables