Hilbert Curve Model Generation for Multi-Parameter Systems
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Solution Overview
Problem
Conventional quasi-stationary measurement techniques struggle to generate accurate models for objects with multiple control parameters, as they can only collect data for one parameter at a time, leading to difficulties in expressing correlations between parameters and generating accurate models, especially when parameters exhibit high nonlinearity.
Innovation Solution
A system that uses a Hilbert curve to generate measurement conditions in a normalized space, allowing for comprehensive changes in multiple control parameters, collecting quasi-stationary data and discarding affected data points to create a model of the object being measured.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Loss of time
If quasi-stationary measurement is performed for multiple control parameters, then measurement time is reduced, but model generation becomes difficult due to inability to express parameter correlations
Solution Approach 1:
The measurement space is segmented into multiple regions based on control parameter ranges. The Hilbert curve is divided into segments that correspond to different parameter combinations, allowing systematic coverage of multiple parameters while maintaining quasi-stationary measurement benefits. This segmentation enables the measurement path to visit different regions systematically, collecting data that reflects parameter correlations.
Solution Approach 2:
The patent introduces a new dimension by mapping multiple control parameters onto a normalized space using Hilbert curve geometry. This dimensional transformation allows the measurement system to handle multiple parameters simultaneously while maintaining the quasi-stationary measurement approach. The Hilbert curve provides a space-filling property that enables comprehensive parameter exploration in a structured manner.
2Stability of the object's composition
If measurement points are uniformly distributed, then measurement coverage is even, but prediction accuracy decreases in specific important areas
Solution Approach 1:
The measurement path is designed to have non-uniform point distribution where specific areas receive more measurement points based on their importance. The Hilbert curve structure allows for localized densification in regions that require higher measurement density for accurate prediction, while maintaining reasonable coverage in other areas. This local quality adjustment optimizes the balance between measurement coverage and prediction accuracy.
3Quantity of substance
If data from all measurement points is used, then data utilization is maximized, but model accuracy decreases due to hysteresis effects from parameter changes
Solution Approach 1:
The patent extracts and removes data points that are affected by hysteresis effects from the measurement data. By identifying and excluding these problematic data points, the system maintains model accuracy while still utilizing the majority of valuable measurement data. This extraction approach preserves the benefits of comprehensive data collection while eliminating the harmful effects of hysteresis-induced inaccuracies.
Solution Approach 2:
The patent converts the harmful hysteresis effects into a beneficial filtering mechanism. By systematically identifying data points that exhibit hysteresis behavior and excluding them, the system transforms a source of error into a quality control feature. This approach maintains the comprehensive nature of data collection while ensuring that only high-quality data is used for model generation.
Data Source
AI summary
A non-transitory computer-readable recording medium stores a model generation program that causes a computer to execute a process. The process includes obtaining measurement data on measurement points sequentially measured along a measurement path curve generated from a Hilbert curve laid out in a normalized space in which measurement target ranges of respective plurality of control parameters related to control of an object to be measured are normalized, the measurement points being more in number in a specific area of the measurement target ranges than in an area other than the specific area, and the numbers of measurement points lying on two sides in each group of two adjacent sides of the measurement path curve and where a control parameter changes in opposite directions being balanced; and generating a control model of the object to be measured on the basis of the obtained measurement data of the measurement points.