Flat Rolled Stock Evaluation Using Robust Error Metrics
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Solution Overview
Problem
Existing methods for determining functions from measurement data of flat rolled materials are prone to being heavily influenced by disturbances, leading to inaccurate evaluations and control issues in rolling mills.
Innovation Solution
An evaluation method that minimizes the sum of individual ratings, where each rating increases less than quadratically with the difference between measurement data and the function value, using recursively reweighted least squares methods and weighting factors to reduce the impact of outliers.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If the least squares method is used to determine function parameters from measurement data, then the function can be determined mathematically, but the evaluation becomes heavily influenced by disturbances and outliers leading to inaccurate results
Solution Approach 1:
The patent changes the evaluation criterion from minimizing the sum of squared deviations (quadratic) to minimizing the sum of absolute deviations (linear). This parameter change in the optimization objective function transforms the least squares method into a least absolute deviations method, which is inherently more robust to outliers and disturbances in the measurement data.
Solution Approach 2:
The patent converts the harmful effect of outliers and disturbances into a benefit by using an evaluation criterion that is less sensitive to extreme values. The linear evaluation criterion naturally downweights the influence of large deviations, turning what would be harmful disturbances into manageable variations that do not dominate the optimization result.
2Ease of manufacture
If quadratic evaluation criterion is used, then mathematical optimization is straightforward, but disturbances have excessive influence on the result
Solution Approach 1:
The patent changes the exponent parameter in the evaluation criterion from 2 (quadratic) to 1 (linear). This simple parameter change maintains mathematical tractability while fundamentally altering the sensitivity to disturbances, reducing the harmful influence of outliers on the optimization result.
3Reliability
If linear increase of individual evaluation with deviation amount is used, then robustness against outliers is improved, but mathematical optimization becomes more complex
Solution Approach 1:
The patent replaces the quadratic mechanical analogy (minimizing squared errors) with a linear statistical approach (minimizing absolute errors). This substitution maintains the core optimization framework while changing the mathematical foundation to one that is more robust to outliers, achieving improved reliability without excessive complexity increase.
Data Source
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AI summary
A detection device (3) acquires measurement data (yi) of a flat rolled stock (1), each data point being assigned to a specific location (xi) in the longitudinal (rL) and/or lateral (rB) direction and/or thickness (rD) direction of the flat rolled stock (1), such that the measurement data (yi) form a corresponding spatially resolved distribution. An evaluation device (4) receives the measurement data (yi) from the detection device (3). The evaluation device defines parameters (a) for a function (f) that varies with the location (xi) in the longitudinal (rL) and/or lateral (rB) direction and/or thickness (rD) direction of the flat rolled stock (1) such that the deviation of the function (f) parameterized with the optimized values (aopt) of the parameters (a) from the measurement data (yi) is minimized according to an evaluation criterion. Based on the function (f), the evaluation device (4) performs further evaluations.The assessment measure is determined by a sum of individual ratings (di). The evaluation unit (4) determines the individual ratings (di) based on the absolute value of the difference between a given measurement date (yi) and the value of the function (f) at that measurement date (yi). While the individual rating (di) does increase with the absolute value of the difference between the given measurement date (yi) and the value of the function (f) at that measurement date (yi), the increase is less than quadratic.