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Results for “Stochastic modelling”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2020

Explaining persistent incomplete mixing in multicomponent reactive transport with Eulerian stochastic model

We present an Eulerian stochastic advection–diffusion–reaction (SADR) model and use it to explain incomplete mixing typically observed in transport experiments with bimolecular reactions. Unlike traditional advection– dispersion–reaction (ADR) models, the SADR model describes mechanical and diffusive mixing as two separate processes. In the SADR model, mechanical mixing is driven by random advective velocity whose variance is given by the coefficient of mechanical dispersion. The diffusive mixing is modeled as a Fickian diffusion process with the effective diffusion coefficient. We demonstrate that the sum of the two coefficients is equal to the dispersion coefficient, but only the effective diffusion coefficient contributes to the mixing-controlled reactions. We use experimental results of Gramling et al. * * to show that for transport and bimolecular reactions in porous media, the SADR model is significantly more accurate than the ADR model, which overestimates the concentration of the reaction product by as much as 60%. We also show that the SADR model predicts an experimentally observed bell- shaped spatial distribution of the reactive product concentration, while the ADR model results in a concentration distribution with an unphysical kink.

Bimolecular reactions, incomplete mixing, Stochast↗
DOE OSTI2023

Stochastic modeling and statistical calibration with model error and scarce data

This paper introduces a procedure to assess the predictive accuracy of stochastic models subject to model error and sparse data. Model error is introduced as uncertainty on the coefficients of appropriate polynomial chaos expansions (PCE). The error associated with finite sample size allows us to conceive of these coefficients as statistics of the data that we describe as random variables whose influence on output quantities of interest is evaluated through the extended polynomial chaos expansion (EPCE). A Bayesian data assimilation scheme is introduced to update these expansions by considering the resulting nested chaos expansion as a hierarchical probabilistic model. Stochastic models of quantities of interest (QoI) are thus constructed and efficiently evaluated. Here, the Metropolis–Hastings Markov chain Monte Carlo procedure is used to sample the posterior. Two illustrative analytical and numerical problems are used to demonstrate the proposed approach.

Bayesian inference↗
DOE OSTI2022

Stochastic Modeling in a Multimaterial Continuum Mixture Shock Physics Code

Stochastic modelling approaches are presented to capture random effects at multiple time and length scales. Random processes that occur at the microscale produce nondeterministic effects at the macroscale. Here we present three stochastic modeling approaches that describe random processes at microscopic length scales and map these processes to the macroscopic length scale. The first stochastic modeling approach is based upon a particle based numerical technique to solve a Stochastic Differential Equation (SDE) using an arbitrary diffusion process to capture random processes at the microstructural level. The second approach prescribes a Probability Density Function (PDF) for the drift and diffusion of the random variable derived using the forward and backward Kolmogorov equations. This method requires mean and drift evolution PDF transport equations. The third approach is the coupling of multiple random variables which are dependent on each other. The relationship of the PDFs and a coupling function, known as a copula, produces a Joint Probability Density Function (JPDF). These stochastic modeling approaches are implemented into a Multiple Component (MC) shock physics computational code and used to model statistical fracture and reactive flow applications.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

Understanding the Drivers of Atlantic Multidecadal Variability using a Stochastic Model Hierarchy

The relative importance of ocean and atmospheric dynamics in generating Atlantic Multidecadal Variability (AMV) remains an open question. Comparisons between climate models with SLAB and fully-dynamic (FULL) ocean components are often used to explore this question, but cannot reveal how individual ocean processes generate these differences. We build a hierarchy of physically interpretable stochastic models to investigate the contribution of two upper-ocean processes to AMV: the role of seasonal variation and mixed-layer entrainment. This interpretability arises from the stochastic model’s simplified representation of sea surface temperature (SST), considering only the local upper ocean response to white-noise atmospheric forcing and its impact on surface heat exchange. We focus on understanding differences between SLAB and FULL non-eddy resolving pre-industrial control simulations of the Community Earth System Model 1 (CESM), and estimate the stochastic model parameters from each respective simulation. Despite its simplicity, the stochastic model reproduces temporal characteristics of SST variability in the SPG, including reemergence, seasonal-to-interannual persistence and power spectra. Furthermore, unrealistically persistent SST of the CESM-SLAB ocean simulation is reproduced in the equivalent stochastic model configuration where the mixed-layer depth (MLD) is constant. The stochastic model also reveals that vertical entrainment primarily damps SST variability, thus explaining why SLAB exhibits larger SST variance than FULL. Here, the stochastic model driven by temporally stochastic, spatially coherent forcing patterns reproduces the canonical AMV pattern. However, the amplitude of low-frequency variability remains underestimated, suggesting a role for ocean dynamics beyond entrainment.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2022

On analysis and stochastic modeling of the particle kinetic energy equation in particle-laden isotropic turbulent flows

In this study, we analyze three-dimensional particle-laden, isotropic turbulence to develop an understanding of inertial particle dynamics from a kinetic energy perspective. Data trends implying inhomogeneous sampling of the flow by particles are identified and used to support a proposed particle behavior: particles appear to accumulate in regions of low flow kinetic energy over time because they lose kinetic energy and slow down in such regions, ultimately causing them to spend more time there. To elucidate this behavior, we derive a particle kinetic energy equation from the particle momentum equation, which incorporates inertial effects through the Schiller–Naumann drag correlation. Upon extracting fundamental physics from this equation, hypotheses regarding the role of the Stokes number in the temporal change of particle kinetic energy and the previously proposed particle behavior are evaluated using simulation data considering three Stokes numbers. Finally, a Fokker–Planck equation is used to derive the steady-state probability density function of the particle kinetic energy. The model fits the simulation data well and provides a tool for further investigation into understanding preferential concentration, as well as a reduced order model for predicting particle kinetic energy in turbulent flows.

42 ENGINEERING↗
DOE OSTI2023

A stochastic model of future extreme temperature events for infrastructure analysis

Applying extreme temperature events for future conditions is not straightforward for infrastructure resilience analyses. This work introduces a stochastic model that fills this gap. The model uses at least 50 years of daily extreme temperature records, climate normals with 10%-90% confidence intervals, and shifts/offsets for increased frequency and intensity of heat wave events. Intensity and frequency are shifted based on surface temperature anomaly from 1850-1900 for 32 models from CMIP6. A case study for Worcester, Massachusetts passed 85% of cases using the two-sided Kolmogorov-Smirnov -value test with 95% confidence for both temperature and duration. Future shifts for several climate scenarios to 2020, 2040, 2060, and 2080 had acceptable errors between the shifted model and 10- and 50-year extreme temperature event thresholds with the largest error being 2.67 degrees C. The model is likely to be flexible enough for other patterns of extreme weather such as extreme precipitation and hurricanes.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗
DOE OSTI2025

Stochastic Model Predictive Control With Gaussian Wind Direction Preview for Wake Steering

This article addresses the problem of wake steering control for wind farms that explicitly consider the tradeoff between farm-level power generation and yaw duty cycle under variable and uncertain wind conditions. A novel stochastic model predictive control (MPC) algorithm is presented, which utilizes a stochastic model of the freestream wind field components in a receding horizon framework to compute optimal yaw set points that maximize the expected value of the farm power while constraining the yaw actuation. Different configurations of the algorithm are evaluated using a steady-state wind farm simulator. The proposed stochastic MPC algorithm can plan control actions over a future prediction horizon based on probabilistic estimates of the incoming wind magnitude and direction.

17 WIND ENERGY↗
DOE OSTI2023

Stochastic Models, Indices & Optimization Algorithms for Pricing & Hedging Reliability Risks in Modern Power Grids: Data Plan - Princeton

We collected and cleaned the synthetic grid data produced by NREL for the Texas and New York synthetic grids. We developed a high dimensional joint stochastic model for load at the zone level, and solar and wind power productions at the asset level, capturing the spatial and temporal dependencies between all the variables, and demonstrated how such a model could be fitted to historical data. We designed and implemented a simulation engine which can produce Monte Carlo scenarios for the hourly day-ahead values of load, and solar and wind power productions at the spatial and temporal resolutions of the historical data used to fit the model. Finally we developed an open-source Python package which can, from an input grid model, efficiently use forecasts and large numbers of Monte Carlo scenarios to provide unit commitment and economic dispatch for each of these scenarios. The high dimensional stochastic model and the subsequent Monte Carlo simulation engine were implemented in the package PGscen and the corresponding UC and ED optimization programs in the package Vatic.

14 SOLAR ENERGY↗
DOE OSTI2026

Near-Optimal Performance of Stochastic Model Predictive Control

Here, this article presents a regret analysis for stochastic model predictive control (SMPC) in linear systems with quadratic performance index and additive and multiplicative uncertainties. Under a finite support assumption, the problem can be cast as a finite-dimensional quadratic program, but the problem becomes quickly intractable as the problem size grows exponentially in the horizon length. SMPC aims to compute approximate solutions by solving a sequence of problems with truncated prediction horizons and committing the solution in a receding-horizon fashion. Although this approach is widely used in practice, its performance relative to the optimal solution is not well understood. This article reports for the first time a rigorous near-optimal performance guarantee of SMPC: under stabilizability and detectability conditions, the regret of SMPC is exponentially small in the prediction horizon length, allowing SMPC to achieve near-optimal performance at a substantially reduced computational expense.

93E20, 93B45↗
DOE OSTI2020

Characterization of flow and transport in a fracture network at the EGS Collab field experiment through stochastic modeling of tracer recovery

Energy extraction from subsurface reservoirs is important for addressing the increasing energy demand and environmental concerns such as global warming. However, the characterization of subsurface reservoirs, particularly reservoirs dominated by fracture networks remains a challenge due to the lack of means to directly observe subsurface processes. This study explores the feasibility and efficacy of characterizing fracture flow and transport processes in an enhanced geothermal system (EGS) testbed through stochastic tracer modeling. There are two enabling factors that allow application of stochastic modeling to characterize a subsurface reservoir. First, an abundance of geological and geophysical measurements enables the development of a high-fidelity and well-constrained fracture network model. Second, high-performance computing (HPC) allows running massive realizations efficiently. Six conservative tracer tests were stochastically modeled and produced satisfactory realizations that successfully reproduce field tracer recovery data from each tracer test. The evolution of flow and transport processes in the fracture network was then analyzed from these satisfactory realizations. This work demonstrates that stochastic tracer modeling on a high-fidelity fracture network model is feasible and can provide important insights regarding flow and transport characteristics in subsurface fractured reservoirs.

58 GEOSCIENCES↗
DOE OSTI2022

Stochastic Model for High Temperature Oxidation of Cr–Ni Austenitic Steels Assisted by Spallation

Abstract Cr–Ni austenitic steels offer significant high temperature corrosion protection by forming a surface oxide layer. However, above critical service conditions (temperature, atmosphere, thermal cycling), oxidized surface can experience intensive degradation because of scale spallation, which could be detrimental to the in-service life. To predict the effect of scale spallation on oxidation kinetics, a simulation was implemented using a stochastic model. The model considers topological parameters and intensity of spallation which can occur, while delivering a true oxidation constant. The experimental procedure identified the amount of formed spalled scale and topology of spallation based on the use of element mapping of the surface. This information was used to determine a true kinetic constant for a corresponding spallation intensity in oxidized Cr–Ni austenitic steel. To illustrate the capability of the stochastic model, a parametric analysis was performed. The model verified how the spallation parameters could change the oxidation processes from parabolic growth of an adhered oxide layer without spallation to a mixed linear-parabolic, or with a constant thickness of residual scale at high spallation intensity. The spallation model will be used in a separate article to characterize high temperature surface degradation of several Cr–Ni austenitic steels during harsh oxidation environments.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Solving inverse problems in stochastic models using deep neural networks and adversarial training

Inverse problems associated with stochastic models constitute a significant portion of scientific and engineering applications. In such cases the unknown quantities are distributions. The applicability of traditional methods is limited because of their demanding assumptions or prohibitive computational consumption; for example, maximum likelihood methods require closed-form density functions, and Markov Chain Monte Carlo needs a large number of simulations. We propose a new method that estimates the unknown distribution by matching the statistical properties between observed and simulated random processes. We leverage the expressive power of neural networks to approximate the unknown distribution and use a discriminative neural network for computing the statistical discrepancies between the observed and simulated random processes. Here we demonstrated numerically that the proposed methods can estimate both the model parameters and learn complicated unknown distributions.

42 ENGINEERING↗
DOE OSTI2021

Battery Control Using Stochastic Model Predictive Control

Stationary batteries in residential and commercial buildings are often used to smooth customer load profiles and to lower customer electricity bills. Controllers for these battery systems should account for customer energy consumption, rate structures, and high internal battery temperatures, which can lead to reduced performance over the battery lifetime. It is important to consider the uncertainty in forecasting energy consumption and temperature, especially for customers with highly variable and uncertain loads. We propose a novel battery controller using stochastic model predictive control that accounts for these uncertainties and can handle complex rate structures, including demand charges. We show that the controller performs better than standard model predictive control when there is significant uncertainty in the forecast. We also show improvements in the performance with more accurate forecasts and with a more aggressive control strategy.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2020

Time-of-Use and Demand Charge Battery Controller Using Stochastic Model Predictive Control

Stationary batteries in residential and commercial buildings are often used to smooth customer load profiles and to lower customer electricity bills. Controllers for these battery systems should account for customer energy consumption, rate structures, and high internal battery temperatures, which can lead to reduced performance over the battery lifetime. It is important to consider the uncertainty in forecasting energy consumption and temperature, especially for customers with highly variable and uncertain loads. We propose a novel battery controller using stochastic model predictive control that accounts for these uncertainties and can handle complex rate structures, including demand charges. We show that the controller performs better than standard model predictive control when there is significant uncertainty in the forecast. We also show improvements in the performance with more accurate forecasts and with a more aggressive control strategy.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2020

Time-of-Use and Demand Charge Battery Controller Using Stochastic Model Predictive Control: Preprint

Stationary batteries in residential and commercial buildings are often used to smooth customer load profiles and to lower customer electricity bills. Controllers for these battery systems should account for customer energy consumption, rate structures, and high internal battery temperatures, which can lead to reduced performance over the battery lifetime. It is important to consider the uncertainty in forecasting energy consumption and temperature, especially for customers with highly variable and uncertain loads. We propose a novel battery controller using stochastic model predictive control that accounts for these uncertainties and can handle complex rate structures, including demand charges. We show that the controller performs better than standard model predictive control when there is significant uncertainty in the forecast. We also show improvements in the performance with more accurate forecasts and with a more aggressive control strategy.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2020

Numerically modeling stochastic inflation in slow-roll and beyond

In this work, we present a complete numerical treatment of inflationary dynamics under the influence of stochastic corrections from sub-Hubble modes. We discuss how to exactly model the stochastic noise terms arising from the sub-Hubble quantum modes that give rise to the coarse-grained inflaton dynamics in the form of stochastic differential equations. The stochastic differential equations are solved event by event on a discrete time grid. We then compute the power spectrum of curvature perturbations that can be compared with the power spectrum computed in the traditional fashion using the Mukhanov-Sasaki equation by canonically quantizing the inflaton fluctuations. Our numerical procedure helps us to easily extend the formalism to ultra slow-roll inflation and study the possibility of primordial black hole formation.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2022

A hierarchical stochastic modeling approach for representing point bar geometries and petrophysical property variations

The flow of fluids in point bars is affected by the existence of heterogeneities like shale drapes that are found on the surfaces of inclined heterolithic stratifications. In fact, these shale drapes can act as fluid flow baffles; therefore, developing a framework for modeling point bars and their associated heterogeneities is vital. In this study, a stochastic process-based modeling approach is presented for capturing the main point bar heterogeneities: accretion surfaces (i.e., the aerial heterogeneity) and inclined heterolithic stratifications (i.e., the vertical heterogeneity). The former was modeled using a sine-generation function and the latter, with a sigmoidal function after which they were combined into a 3D point bar model. To ensure proper modeling of petrophysical properties, we developed a more representative gridding scheme which generates curvilinear grids representative of the point bar geometry. This grid was then transformed into a rectilinear grid to allow for geostatistical simulation after which all petrophysical properties were mapped back into the original curvilinear grid. An essential element of this modeling approach is the stochastic representation of shale drapes at the interface between successive accretion surfaces. The workflow was tested using a real field dataset for the Cranfield field, Mississippi. The constructed model was then subjected to a flow simulation study mimicking a CO 2 storage scenario. Various sensitivities were simulated to evaluate the effect of heterogeneities on CO 2 flow within the point-bar. Results demonstrate the importance of representing point-bar related heterogeneity and the spatial distribution of shale drapes on CO 2 plume migration and storage.

58 GEOSCIENCES↗
DOE OSTI2024

Versatile stochastic model for predictive KMC simulation of fcc metal nanostructure evolution with realistic kinetics

Stochastic lattice-gas models provide the natural framework for analysis of the surface diffusion-mediated evolution of crystalline metal nanostructures on the appropriate time scale (often 10 1 –10 4 s) and length scale. Model behavior can be precisely assessed by kinetic Monte Carlo simulation, typically incorporating a rejection-free algorithm to efficiently handle the broad range of Arrhenius rates for hopping of surface atoms. The model should realistically prescribe these rates, or the associated barriers, for a diversity of local surface environments. However, commonly used generic choices for barriers fail, even qualitatively, to simultaneously describe diffusion for different low-index facets, for terrace vs step edge diffusion, etc. We introduce an alternative Unconventional Interaction–Conventional Interaction formalism to prescribe these barriers, which, even with few parameters, can realistically capture most aspects of behavior. Here, the model is illustrated for single-component fcc metal systems, mainly for the case of Ag. It is quite versatile and can be applied to describe both the post-deposition evolution of 2D nanostructures in homoepitaxial thin films (e.g., reshaping and coalescence of 2D islands) and the post-synthesis evolution of 3D nanocrystals (e.g., reshaping of nanocrystals synthesized with various faceted non-equilibrium shapes back to 3D equilibrium Wulff shapes).

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗