Analytical Sensitivity Optimization for External Interventions
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Solution Overview
Problem
Existing automated optimization methods in CAD and CAE systems face inefficiencies and divergence due to the lack of proper accounting for external intervention events between equilibriums in analytical sensitivities, particularly in industries like automotive and aerospace, where preloading significantly influences design outcomes.
Innovation Solution
The method involves defining a model with design variables and sensitivity equations, iteratively optimizing by adding a term for design response sensitivity to account for external intervention events, using either the adjoint or direct method, to ensure consistent inclusion of external factors in sensitivity calculations.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Productivity
If existing automated optimization methods are used without accounting for external intervention events, then the optimization process is simpler, but computational efficiency deteriorates and optimization convergence fails
Solution Approach 1:
The sensitivity calculation is segmented into two distinct parts: the base sensitivity equation and the external intervention term. This segmentation allows the complex problem to be broken down into manageable components that can be computed separately and then combined, improving both computational efficiency and convergence accuracy.
Solution Approach 2:
The external intervention term is pre-calculated and stored before the main optimization loop. By performing this calculation in advance, the method avoids redundant computations during iterative optimization, significantly improving computational efficiency while ensuring accurate convergence.
2Measurement precision
If external intervention events are properly accounted for in sensitivity calculations, then optimization accuracy improves, but computational complexity increases
Solution Approach 1:
An intermediary term representing the external intervention effect is introduced into the sensitivity equation. This intermediary captures the influence of external events (such as preloading) on the optimization process, enabling accurate sensitivity calculations without requiring complete reformulation of the underlying mathematical model.
Solution Approach 2:
The method introduces additional parameters to represent external intervention effects (e.g., preloading forces, boundary condition changes). By treating these as separate parameters that can be independently calculated and incorporated, the approach maintains mathematical rigor while managing equation complexity through systematic parameterization.
Data Source
AI summary
Embodiments provide methods and systems for optimizing a physical system. One such example embodiment begins by defining, in memory of a processor, a model comprising a plurality of design variables where the defined model represents a real-world physical system where behavior of the model is given by an equation that includes corresponding sensitivity equations for the plurality of design variables. The example method continues by iteratively optimizing the model with respect to a given design variable of the plurality, using the equation. In an example embodiment, the optimizing includes the processor accounting for a given external intervention event between equilibriums by adding a term for design response sensitivity of the given one of the plurality of design variables to the corresponding sensitivity equation of the given design variable. Such optimizing results in an improved optimization of the real-world physical model.