Computational Framework for Stochastic Parameter Estimation
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Solution Overview
Problem
Current methods for estimating key parameters in complex physical processes, such as power generation, are often inaccurate due to their stochastic nature, leading to costly, time-consuming, and labor-intensive offline testing, and are limited by Gaussian assumptions and slow convergence rates, which can result in inappropriate control actions and system failures.
Innovation Solution
A computational framework for efficient and robust statistical estimation of high-dimensional stochastic behaviors, using non-linear dimension reduction, fast uncertainty propagation, and Bayesian inference to generate approximated system variables, allowing for non-standard probability distributions and improved accuracy.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If traditional offline stage-testing based methods are used to generate key parameter values, then measurement precision is improved, but productivity deteriorates due to high cost, time consumption, and labor intensity
Solution Approach 1:
The patent replaces traditional mechanical offline testing systems with a computational framework using polynomial chaos expansion and Bayesian inference. This substitution transforms physical testing into mathematical modeling, achieving accurate parameter estimation without time-consuming physical experiments while maintaining measurement precision.
Solution Approach 2:
The patent changes the parameter representation from deterministic values to probabilistic distributions using polynomial chaos expansion. By representing parameters as random variables with specific probability distribution functions, the method achieves both accuracy and computational efficiency through statistical characterization rather than exhaustive testing.
2Measurement precision
If Markov Chain Monte Carlo (MCMC)-based methods are used for Bayesian inference, then measurement precision is improved through maximum-a-posteriori parameter estimation, but productivity deteriorates due to prohibitive computing times
Solution Approach 1:
The patent uses cheap polynomial chaos expansion approximations instead of expensive MCMC simulations. The polynomial chaos method provides rapid, disposable estimates that can be computed quickly without the prohibitive computational cost of MCMC, while still capturing the essential probabilistic behavior for parameter estimation.
Solution Approach 2:
The patent performs preliminary polynomial chaos expansion to obtain approximate parameter distributions before final Bayesian inference. This preliminary action provides initial estimates and uncertainty quantification that guide subsequent MCMC sampling, reducing the number of iterations needed and significantly cutting computational time while maintaining precision.
3Productivity
If local optimization approach with approximated Gaussian assumption is used, then productivity is improved by reducing computing times, but measurement precision deteriorates due to biased local optima when initial guess is far from true value
Solution Approach 1:
The patent implements feedback through polynomial chaos expansion that continuously updates parameter distributions based on observed data. The method uses measured system responses to update the probability distribution functions of parameters, providing feedback that corrects initial guesses and prevents bias even when starting far from true values, while maintaining computational efficiency.
Solution Approach 2:
The patent transforms the static local optimization problem into a dynamic Bayesian inference process. Instead of fixed Gaussian assumptions, the method dynamically updates polynomial chaos coefficients and probability distributions as new data becomes available, allowing the solution to adapt and converge to accurate values regardless of initial conditions while maintaining computational speed.
4Ease of operation
If conventional approaches assuming Gaussian priors and posteriors are used, then ease of operation is improved, but measurement precision deteriorates due to unreliable solutions when posterior distributions are non-Gaussian
Solution Approach 1:
The patent creates a composite method combining polynomial chaos expansion with Bayesian inference. This composite approach integrates the simplicity of Gaussian-based polynomial chaos with the accuracy of full Bayesian inference, allowing the use of simple polynomial chaos for most computations while incorporating Bayesian updates to correct for non-Gaussian effects and improve precision when needed.
Data Source
AI summary
Techniques, systems, and devices are described for providing a computational frame for estimating high-dimensional stochastic behaviors. In one exemplary aspect, a method for performing numerical estimation includes receiving a set of measurements of a stochastic behavior. The set of correlated measurements follows a non-standard probability distribution and is non-linearly correlated. Also, a non-linear relationship exists between a set of system variables that describes the stochastic behavior and a corresponding set of measurements. The method includes determining, based on the set of measurements, a numerical model of the stochastic behavior. The numerical model comprises a feature space comprising non-correlated features corresponding to the stochastic behavior. The non-correlated features have a dimensionality of M and the set of measurements has a dimensionality of N, M being smaller than N. The method includes generating a set of approximated system variables corresponding to the set of measurements based on the numerical model.