Sensor-Based Technical System Modeling With Interpretable Symbolic Regression
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Solution Overview
Problem
Current mathematical models for technical systems are limited by low interpretability, accuracy, high computing power requirements, and low generalizability, making them unsuitable for reliable and exact control strategies in industrial applications.
Innovation Solution
A method using measured sensor data to generate data-based models through symbolic regression with a genetic algorithm and Smoothed Grid Regression, optimizing models for efficiency and complexity, and selecting models from a Pareto front to balance accuracy and complexity, which are then implemented on control units for system regulation.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If popular modeling techniques such as neural networks or Gaussian process models are used, then some limitations are overcome, but interpretability remains low and computing power consumption is high
Solution Approach 1:
The patent changes the parameter space by using symbolic regression to discover mathematical models with explicit parameters and structures, rather than using fixed-structure neural networks. This allows the model to adapt its parameters while maintaining interpretability and reducing computing requirements during deployment.
Solution Approach 2:
The patent creates simplified mathematical models that can be easily deployed on resource-constrained embedded control units. These models are computationally inexpensive compared to neural networks, enabling their use in industrial control applications where computing resources are limited.
2Measurement precision
If complex mathematical models are used to improve accuracy, then model precision increases, but interpretability and generalizability decrease
Solution Approach 1:
The patent replaces complex black-box modeling approaches (neural networks) with interpretable mathematical models discovered through symbolic regression. The resulting models use standard mathematical operations and functions that can be understood and verified by domain experts, maintaining both accuracy and interpretability.
Solution Approach 2:
The patent segments the model discovery process into two phases: using machine learning to identify candidate model structures and parameters, then validating and selecting models based on interpretability criteria. This segmentation allows the system to achieve high accuracy while maintaining human-understandable model structures.
3Reliability
If high-accuracy models are created, then control reliability improves, but computing resources and memory consumption increase
Solution Approach 1:
The patent creates lightweight mathematical models that consume minimal memory and computing resources, making them suitable for deployment on embedded control units in industrial applications. The symbolic regression process discovers compact model representations that maintain accuracy while reducing resource requirements.
4Ease of manufacture
If existing models are used for control strategies, then implementation is straightforward, but generalizability to similar systems is low
Solution Approach 1:
The patent creates a universal modeling framework using symbolic regression that can be applied to different technical systems and control problems. The discovered mathematical models use general mathematical operations and can be adapted to various systems, improving generalizability while maintaining ease of implementation through automated model discovery.
Data Source
AI summary
A method for creating a model of a technical system as a function of measured sensor data of the technical system. The method includes the following steps: initializing a symbolic regression problem. A list of mathematical functions is established, including at least one linear and/or non-linear function and/or at least a one-dimensional parameterizable characteristic curve. The at least one-dimensional characteristic curve is implemented by a Smoothed Grid Regression (SGR) model. Solving the symbolic regression problem with the aid of a genetic algorithm.