Constitutive Equation Learning with Feasibility Constraints
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Solution Overview
Problem
Current system modeling approaches, particularly in partially known physical systems, face challenges in learning constitutive equations of acausal components due to lack of direct access to component variables and proprietary constraints, limiting the generation of complete system models necessary for analytics like controls, diagnostics, and prognostics.
Innovation Solution
An iterative procedure is proposed that focuses on exploring the feasibility set initially, then shifts to parameter estimation, using constraints to encourage exploration of points with higher uncertainty, and employs binary classification models like logistic regression or neural networks with softmax functions to learn both parameters and their feasibility set representation.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Ease of manufacture
If a pure machine learning approach is used to build causal black-box models, then the model can be built without physical semantics, but the model lacks physical interpretability and cannot support model-based analytics
Solution Approach 1:
The patent transforms the modeling approach by changing the parameters from purely data-driven to physics-constrained parameters. The constitutive equations are parameterized with physical meaning, and the learning process optimizes these parameters within physically feasible regions, thereby achieving both ease of model building and retention of physical semantics.
Solution Approach 2:
The patent introduces constitutive equations as an intermediary between raw data and the final system model. These equations serve as a bridge that incorporates physical semantics into the machine learning framework, allowing the model to learn from data while maintaining physical interpretability and supporting model-based analytics.
2Reliability
If the feasibility set is explored extensively to learn constraints, then the search space is well-understood, but the process requires many iterations and computational resources
Solution Approach 1:
The patent performs preliminary action by initializing the feasibility set based on prior physical knowledge and constraints before the main learning process. This preliminary setup reduces the search space and allows the iterative process to converge faster while maintaining constraint accuracy.
Solution Approach 2:
The patent implements feedback mechanisms where the learned constraints from each iteration are used to refine the feasibility set for the next iteration. This feedback loop allows the system to progressively improve constraint accuracy while reducing the number of iterations needed, as the search space becomes better understood over time.
3Stability of the object's composition
If constraints are enforced strictly to maintain physical feasibility, then the model remains physically valid, but the exploration of uncertain regions is limited
Solution Approach 1:
The patent applies dynamics by making the constraint enforcement adaptive rather than static. The feasibility set and constraints are dynamically adjusted during the learning process, allowing stricter enforcement in well-understood regions and more flexible exploration in uncertain regions. This dynamic approach maintains physical validity while enabling exploration of uncertain regions.
Solution Approach 2:
The patent implements local quality by applying different levels of constraint strictness to different regions of the parameter space. In regions where the feasibility is well-established, strict physical constraints are enforced to maintain validity. In uncertain regions, the constraints are relaxed to allow exploration, thereby balancing physical validity with exploration capability.
Data Source
AI summary
The following relates generally to system modeling. Some embodiments described herein learn a representation of the parameter feasibility space that make model parameter tuning easier by constraining the search space, thus enabling physical interpretation of the learned model. They also enable model-based system analytics (controls, diagnosis, prognostics) by providing a system model.