Stochastic Plausibility Checking for Measurement Variable Test Solutions
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Solution Overview
Problem
Existing stochastic model simulations face challenges in accurately checking the plausibility of stochastic test solutions for measurement variables in technical systems, particularly due to inefficiencies in uncertainty quantification procedures and the need for robust statistical characterization.
Innovation Solution
A procedure that involves determining a first stochastic reference solution using an initial uncertainty quantification method, followed by a second stochastic reference solution via regression methods, and then comparing these solutions to check the plausibility of a stochastic test solution using more efficient uncertainty quantification procedures.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If a first uncertainty quantification method (e.g., Standard Monte Carlo or Latin Hypercube Sampling) is used to determine a stochastic reference solution, then a comprehensive statistical characterization is achieved, but the computational effort and time are significantly increased
Solution Approach 1:
The patent applies preliminary action by first generating a stochastic reference solution using a comprehensive but computationally intensive uncertainty quantification method (Standard Monte Carlo or Latin Hypercube Sampling). This reference solution is prepared in advance to serve as a benchmark for subsequent plausibility checks of test solutions, avoiding the need to repeatedly execute expensive simulations for each test case.
Solution Approach 2:
The patent introduces an intermediary approach by using polynomial chaos expansion as a surrogate model that bridges the gap between comprehensive statistical characterization and efficient computation. The polynomial chaos expansion approximates the stochastic behavior based on the pre-computed reference solution, enabling fast plausibility checks without directly executing expensive Monte Carlo simulations for each test solution.
2Reliability
If traditional uncertainty quantification methods are used for plausibility checking, then comprehensive statistical analysis is performed, but the development time for stochastic simulation models is extended
Solution Approach 1:
The method performs preliminary uncertainty quantification to establish a reference solution before conducting plausibility checks. This upfront comprehensive analysis creates a reliable benchmark that enables faster subsequent validation of test solutions using polynomial chaos expansion, improving overall development efficiency.
Solution Approach 2:
The patent changes the computational parameters by switching from direct Monte Carlo sampling to polynomial chaos expansion for the actual plausibility checking process. This parameter change maintains statistical rigor while dramatically reducing computational time, thus improving productivity without sacrificing reliability.
3Productivity
If polynomial chaos regression is used to determine a second stochastic reference solution, then computational efficiency is improved, but the complexity of the regression method increases
Solution Approach 1:
Polynomial chaos expansion serves as an intermediary mathematical framework that translates complex stochastic behavior into a structured polynomial representation. This intermediary formulation simplifies the computational task by reducing the problem to coefficient determination through regression, making the complex stochastic analysis more tractable while maintaining efficiency.
Solution Approach 2:
The patent transforms the complex stochastic simulation problem into a regression problem with polynomial basis functions. By changing the mathematical parameters and representation form, the method achieves computational efficiency through closed-form solutions and reduced sampling requirements, despite the increased mathematical sophistication of the regression approach.
Data Source
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AI summary
The invention relates to a method for checking the plausibility of a stochastic test solution for a measured variable of a technical system. The invention further relates to a computer program, a device, and a storage medium for this purpose.