Calibration Envelope Modeling for High-Dimensional Control Variables
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Solution Overview
Problem
Calibrating internal combustion engines and other technical systems with a large number of control variables is complex due to non-linear influences and dependencies, making it difficult to determine whether new control variables are within the drivability limit using existing discrete data points, especially in high-dimensional test spaces.
Innovation Solution
The method models a conical data envelope using different opening angles for radial basis functions and interpolation conditions, allowing for efficient checking of whether an optimized test point lies inside or outside the data envelope, even in high-dimensional spaces, and considers data points outside the data shell for more accurate modeling.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Quantity of substance
If discrete data points are used to define the drivability limit, then the calibration can be performed with limited measurements, but it becomes impossible to determine whether new control variable combinations are within the drivability limit
Solution Approach 1:
The patent introduces an implicit function f(u) as an intermediary between the discrete data points and the drivability limit determination. This function acts as a mediator that takes control variable vectors as input and returns a scalar value indicating whether the point lies within the drivability limit, thereby enabling continuous evaluation without requiring exhaustive discrete data coverage
Solution Approach 2:
The patent creates a mathematical model (implicit function) that copies or represents the drivability limit surface defined by the discrete data points. Instead of working directly with the discrete points, the implicit function creates a continuous representation that can be evaluated at any point in the control variable space, allowing determination of drivability limit compliance for new control variable combinations
2Manufacturing precision
If the number of control variables is increased to improve system control, then the calibration accuracy improves, but the computational complexity and dimensionality of the test space increases
Solution Approach 1:
The patent extracts the essential characteristic of the drivability limit by representing it through a single implicit function f(u) = 0 rather than storing and processing all discrete data points. This extraction reduces the computational burden by focusing on the boundary definition rather than the complete data set, making high-dimensional calibration tractable
Solution Approach 2:
The patent changes the parameter representation from discrete data points to a continuous implicit function with parameters that define the drivability limit surface. This parameter transformation allows the system to handle high-dimensional control variable spaces by working with a compact mathematical representation rather than exhaustive data sets
Data Source
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Figure 2
AI summary
In order to be able to check the compliance with a data envelope in a simple and rapid manner when calibrating a technical system, provision is made for the data envelope (D) to be modelled by a function - formula (I) with formula (II) and a predefined centre (c) of the data points (Xn), or formula (III) with a radial base function (ϕ) and coefficients (cn), and for the test point (Zj) to be considered to be within the data envelope (D) if the condition in formula (IV) or formula (V) with a predefined opening angle (cp) or a predefined contour line (f) is satisfied.