Error Propagation Evaluation for Coordinate Measurement
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Solution Overview
Problem
Current methods for estimating uncertainty in three-dimensional coordinate measurement machines are inefficient, costly, and have low precision, particularly due to high calculation loads and reliance on experimental methods or Monte Carlo simulations, which are not reliable for complex data processing.
Innovation Solution
A method involving numerical differentiation to obtain a Jacobian matrix and error matrices, allowing for the calculation of error propagation from input to output data, enabling precise error estimation with a small calculation load and applicability to various software applications.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If Monte Carlo simulation or experimental design is used to estimate output error, then estimation reliability is improved, but calculation load and time consumption increase significantly
Solution Approach 1:
The patent changes the fundamental parameter of the estimation method from statistical simulation (Monte Carlo) to analytical error propagation. By transforming the problem into calculating partial derivatives and propagating input errors through the computational model, the method achieves reliable error estimation without the time-consuming iterative simulations characteristic of Monte Carlo methods.
Solution Approach 2:
The patent replaces the mechanical simulation process (Monte Carlo sampling and repeated computations) with an analytical mathematical approach. Instead of mechanically generating random samples and running numerous simulations, the method uses error propagation formulas with partial derivatives to directly compute output errors, substituting a computational mechanical system with an analytical mathematical one.
2Measurement precision
If experimental methods are used to estimate uncertainty, then measurement precision is improved, but device complexity and cost increase
Solution Approach 1:
The patent creates a virtual computational model that copies the measurement system's mathematical relationships. Instead of requiring complex physical experimental setups with multiple measurement devices and procedures, the method uses a computational representation of the measurement model that propagates errors through the same mathematical relationships, achieving precise uncertainty estimation without physical experimental complexity.
Solution Approach 2:
The patent introduces error propagation calculations as an intermediary between input data and output results. This intermediary computational layer automatically traces how errors from various input sources propagate through the measurement model to affect output uncertainty, eliminating the need for complex coordinated experimental procedures while maintaining precision.
3Measurement precision
If complex data processing is performed to improve output precision, then measurement accuracy is improved, but calculation load increases
Solution Approach 1:
The patent performs preliminary error analysis by calculating partial derivatives of the computational model with respect to input parameters before actual measurement data processing. This preliminary action establishes the error propagation relationships in advance, allowing the system to efficiently process measurement data without repeatedly performing complex computational operations during the main data processing phase.
Data Source
AI summary
Method of evaluating precision of output data using error propagation includes performing numerical differentiation using input data in data processing, and thereby obtaining a Jacobian matrix J of the data processing; estimating variance-covariance of errors of the input data, and thereby obtaining an error matrix D of the input data; and calculating an error matrix from the Jacobian matrix J and the error matrix D of the input data, the error matrix R representing variance-covariance of errors of output data.