Computational framework for modeling of physical process
Inventors
Chen, Xiao • Huang, Can • Min, Liang • Thimmisetty, Charanraj • Tong, Charles • Xu, Yijun • Mili, Lamine
Assignees
Virginia Tech Intellectual Properties Inc • Lawrence Livermore National Security LLC • Virginia Polytechnic Institute and State University
Publication Number
US-11914937-B2
Publication Date
2024-02-27
Expiration Date
2039-12-19
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Abstract
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.
Core Innovation
The invention provides a computational framework for efficient and robust numerical estimation of high-dimensional stochastic behaviors, particularly in modeling physical systems such as power grids. This technique receives a set of measurements that are non-linearly correlated and follow a non-standard probability distribution. There exists a non-linear relationship between a set of system variables describing the stochastic behavior and the corresponding set of measurements. The method determines a numerical model with a feature space of non-correlated features, where this reduced-dimensional feature space allows efficient representation and estimation of the system's stochastic state.
The disclosed approach addresses limitations of traditional and current techniques in uncertainty quantification, parameter estimation, and model inversion, particularly the computational intractability of Bayesian inference for high-dimensional, non-Gaussian, and non-linearly correlated sources. It enables dimensionality reduction using statistical transformations such as kernel principal component analysis, Karhunen-Loeve expansion, or manifold-learning based Isomap, to convert correlated high-dimensional measurements to a lower-dimensional, uncorrelated feature space. This facilitates subsequent processing steps utilizing statistical inference methods such as combined Langevin and adaptive Markov Chain Monte Carlo (MCMC) algorithms.
The system and method offer advanced capabilities for generating posterior probability distributions, enabling risk assessment, model validation, and the identification of system variables necessary for controlling actions in physical power systems. The approach is further extendable to various configurations, including surrogate modeling via polynomial chaos expansion, sampling schemes using importance sampling, hybrid surrogate-original modeling, and application of Gaussian process emulators for stochastic economic dispatch in power systems with renewable energy resources.
Claims Coverage
There are two primary independent inventive features claimed, addressing a method and a system for modeling stochastic behaviors in physical power systems using reduced-dimensional feature spaces and advanced statistical inference techniques.
Generating approximated system variables for a physical power system using reduced-dimensional non-correlated feature space and hybrid Langevin and adaptive MCMC
A method comprising: - Receiving measurements relating to one or more power grids in a physical power system, where the measurements are non-linearly correlated and follow a non-standard probability distribution. - Determining a numerical model of the stochastic behavior based on the measurements, with the numerical model including a feature space of non-correlated features having a dimensionality less than the original measurements. - Sampling the numerical model using a statistical inference approach that combines a Langevin Markov Chain Monte Carlo (MCMC) approach and an adaptive MCMC that calibrates covariance based on Markov Chain history. - Generating approximated system variables from the sampled model and applying them to the physical power system for controlling actions.
System for generating a model of a power system with dimensionality reduction and combined Langevin/adaptive MCMC sampling
A system comprising: - A plurality of sensors to collect measurements of a power system, where the measurements are non-linearly correlated and have a non-standard probability distribution, with a non-linear relationship to system variables. - A processor and memory with executable code to: - Determine a numerical model of the stochastic behavior from the measurements, where the model includes a feature space of non-correlated features (M) with dimensionality less than that of the measurements (N), M < N. - Sample the numerical model using a statistical inference approach that combines Langevin MCMC and adaptive MCMC calibrated via Markov Chain history. - Generate approximated system variables corresponding to the measurements and apply them to the power system for control.
The claims establish a computational approach and system for high-dimensional, non-Gaussian, non-linear modeling of power system behavior by leveraging dimensionality reduction and advanced statistical inference, notably combining Langevin and adaptive MCMC samplers, to enable efficient state estimation and control.
Stated Advantages
The techniques enable efficient and robust statistical estimation for high-dimensional and nonlinearly correlated sources with non-standard probability distributions.
They overcome the computational intractability of Bayesian inference in high-dimensional, non-Gaussian, and nonlinearly correlated systems.
The methods provide a probabilistic characterization of solutions that include detailed posterior distributions, rather than just deterministic point estimates.
The approach achieves a significant speedup in solution time compared to traditional Bayesian inference methods, with up to three orders of magnitude improvement reported.
The framework is applicable to scenarios with rare events and system topological changes (e.g., branch outages), maintaining accuracy while reducing computational cost.
The dimensionality reduction enables tractable modeling and estimation even in very large-scale systems.
Documented Applications
Modeling stochastic behavior and state estimation in physical power systems, including power grids with renewable energy sources.
Advanced state estimation systems for power grids, specifically addressing non-Gaussian measurement errors and dynamic, diverse distribution networks.
Probabilistic power-flow analysis and dynamic parameter estimation in power grids, including decentralized modeling and risk assessment for failure events.
Stochastic economic dispatch (SED) problems in power systems, particularly for systems with high penetration of renewable energy resources.
Estimation of wave speed fields using waveform measurements.
Derivation of subsurface permeability fields utilizing pressure sensor data.
Determination of subsurface structure based on measurements of surface deformations.
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