Calibration Space Segmentation for High-Dimensional Data Envelopes
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Solution Overview
Problem
Calibrating high-dimensional technical systems, such as internal combustion engines, is complex due to the large number of control variables and limited data points, making it difficult to determine whether new control variables fall within the drivability limit using existing envelope algorithms like convex data hulls, which become impractical in higher dimensions.
Innovation Solution
Divide the calibration space into smaller sub-calibration spaces to calculate data shells with lower dimensions, allowing for quicker computation using conventional algorithms like QuickHull, and prioritize calibration variables with the greatest constraining influence in the first sub-space.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If conventional envelope algorithms like convex data hulls are used for calibration, then measurement precision is maintained, but computational complexity becomes impractical in high-dimensional spaces
Solution Approach 1:
The calibration space is divided into multiple sub-calibration spaces, each with lower dimensionality. Data envelopes are calculated separately for each sub-space using conventional algorithms like QuickHull, which are computationally feasible. The sub-spaces are then combined to form the complete drivability limit determination, maintaining measurement precision while reducing computational complexity from impractical to manageable levels.
2Productivity
If the calibration space is divided into sub-calibration spaces, then computational effort is reduced, but the complexity of managing multiple spaces increases
Solution Approach 1:
The calibration space is segmented into sub-spaces based on selecting calibration variables with the greatest constraining influence. This segmentation enables parallel or sequential processing of smaller data envelopes, significantly improving computation speed. The management complexity is mitigated by systematically selecting variables for each sub-space based on their constraining impact, providing a clear organizational structure.
Solution Approach 2:
Different sub-calibration spaces are created with different dimensions and variable compositions based on local requirements. Each sub-space focuses on specific calibration variables with the greatest constraining influence, allowing tailored optimization for different regions of the calibration space while maintaining overall system coherence.
3Productivity
If calibration variables with greatest constraining influence are prioritized in the first sub-space, then calibration efficiency is improved, but the selection process becomes more complex
Solution Approach 1:
The approach changes the parameter of variable selection from arbitrary or sequential to priority-based on constraining influence. By identifying and prioritizing calibration variables with the greatest constraining influence for inclusion in the first sub-calibration space, the method optimizes the distribution of computational effort across sub-spaces, improving overall calibration efficiency despite the added complexity of influence assessment.
Data Source
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AI summary
In order to be able to check easily and quickly the observance of a data envelope during the calibration of a technical system, the d-dimensional calibration space, which comprises the calibration variables required for the calibration, is divided into a first sub-calibration space having a dimension dsub < d and at least one further sub-calibration space, and a dsub-dimensional data envelope is calculated using available data points at least for the first sub-calibration space and is checked during the calibration as an auxiliary condition.