Robust Surface Fitting from Noisy Data via Segmentation
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Solution Overview
Problem
Existing surface fitting methods struggle with noisy data sets, leading to inaccurate extrapolations and uncertainties, especially when dealing with data sets containing erroneous or misleading values.
Innovation Solution
The method involves determining a frequency distribution of the input data set, identifying continuous sections, and fitting equations using a weighted least squares approach, with iterative outlier rejection and plane fitting techniques to enhance data set fidelity and accuracy.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If conventional surface fitting methods (e.g., least squares) are used on noisy data sets, then processing is simpler and faster, but accuracy and reliability of the fitted surface deteriorate due to erroneous values
Solution Approach 1:
The method segments the data set into multiple subsets based on frequency distribution analysis. By dividing the data into groups with similar characteristics and fitting surfaces to each subset separately, the method achieves higher accuracy while managing complexity through systematic data organization rather than complex algorithms
Solution Approach 2:
The method performs preliminary analysis of the frequency distribution of the data set before applying surface fitting. This preliminary step identifies and separates erroneous values by detecting discontinuities in the frequency distribution, allowing the fitting process to work with cleaned data subsets, thereby improving accuracy without requiring complex iterative correction during fitting
2Reliability
If conventional surface fitting methods are used on noisy data, then processing speed is maintained, but reliability of extrapolation results deteriorates due to higher error rates
Solution Approach 1:
The method performs preliminary filtering of erroneous values by analyzing frequency distribution discontinuities before the main fitting process. This upfront preparation removes unreliable data points that would otherwise compromise extrapolation reliability, ensuring that subsequent fitting operates on high-quality data subsets
Solution Approach 2:
By segmenting the data into reliable subsets based on frequency distribution continuity, the method ensures that extrapolation is performed only on validated data groups. This segmentation approach maintains high reliability by excluding erroneous values while keeping processing efficient through focused fitting on smaller, cleaner data sets
3Measurement precision
If frequency distribution analysis and continuous section identification are performed, then accuracy of surface fitting improves by reducing outlier influence, but processing complexity and time increase
Solution Approach 1:
The frequency distribution analysis segments data into continuous sections that represent reliable data groups. This segmentation approach improves accuracy by ensuring each fitted surface operates on homogeneous data subsets, while the systematic nature of the segmentation provides computational efficiency through clear separation of processing tasks
Solution Approach 2:
The method performs frequency distribution analysis as a preliminary step to identify continuous sections before main fitting. This upfront organization of data into reliable groups eliminates the need for complex iterative outlier detection during fitting, improving accuracy while maintaining processing speed through efficient pre-processing
Data Source
AI summary
Various embodiments of methods and apparatus for fitting a surface to a data set are disclosed. A frequency distribution of an input data set is determined. Determining the frequency distribution includes assigning each data point of the input data set to a category representing a value of a variable for the respective data point. Responsive to identifying one or more discontinuities of the frequency distribution, a continuous section of the frequency distribution is identified as a first data set. A first equation is fit to the first data set.