Radial-Symmetric Weighting for Non-Linear Engine Model
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Solution Overview
Problem
Existing methods for modeling non-linear systems, such as combustion engines, are inefficient and require a large number of partial models due to axis-orthogonal subdivisions, leading to excessive processing power and inadequate representation of complex non-linearities.
Innovation Solution
The method employs radial-symmetric weighting functions, such as hyper-ellipsoids, to orient and expand partial models in the n-dimensional space, allowing for better approximation of operating points and reducing the number of partial models by dynamically adjusting their placement and removal based on prediction quality and error, with a focus on achieving a desired statistical prediction quality.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Ease of manufacture
If axis-orthogonal subdivisions are used for modeling non-linear systems, then the model structure is simple to implement, but the number of partial models increases excessively leading to high processing power requirements
Solution Approach 1:
The patent applies radial-symmetric weighting functions with hyper-ellipsoid iso-curves instead of axis-orthogonal subdivisions. This curved, radial approach allows partial models to be oriented and expanded in the n-dimensional space according to the actual distribution of operating points, achieving better approximation with fewer partial models while maintaining implementation feasibility.
Solution Approach 2:
The patent introduces dynamic adjustment mechanisms where partial models are automatically added or removed based on prediction quality and error metrics. This dynamic construction algorithm adapts the model structure to the complexity of the problem, reducing the number of partial models needed compared to static axis-orthogonal approaches.
2Measurement precision
If more partial models are used to represent complex non-linearities, then the prediction accuracy improves, but the computing effort increases excessively
Solution Approach 1:
The patent applies local quality by using radial-symmetric weighting functions that concentrate computational effort in regions where it is most needed. Each partial model is oriented and expanded according to the local distribution of operating points, providing high prediction accuracy in complex non-linear regions while using fewer resources in simpler regions.
Solution Approach 2:
The patent changes the parameterization approach from fixed axis-orthogonal grids to dynamic radial-symmetric functions with hyper-ellipsoid iso-curves. This allows the model to adapt its parameters (orientation, expansion, position) to the actual data distribution, achieving better accuracy with reduced computing effort.
3Ease of manufacture
If axis-orthogonal subdivisions are used, then the model construction is straightforward, but the representation of complex non-linearities becomes inadequate
Solution Approach 1:
The patent replaces straight axis-orthogonal boundaries with curved radial-symmetric weighting functions. The hyper-ellipsoid iso-curves of these functions can orient and expand in any direction in the n-dimensional space, providing much better representation of complex non-linear relationships while maintaining a relatively simple construction algorithm.
Data Source
AI summary
A method for creating a non-linear, stationary or dynamic overall model of a control variable of a combustion engine or partial systems thereof is based on simplified partial model functions that are used to determine in a weighted fashion at each desired operating point the total output quantities from the partial model function with an associated weighting function. The difference between the total output quantity and the real value is determined for all real operating points; and in areas of operating points with an absolute value of this difference that is above the preset value, a further model function with a further associated weighting function is used for which the absolute value of the difference stays below the preset value.The steps for determining the difference between the total output quantity of the associated partial model functions and a real value of the control value as well as the application of a further model and weighting function are executed as many times as needed until the statistically evaluated prediction quality of the overall model has reached a desired value.