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DOE OSTI2020

MASTODON: An Open-Source Software for Seismic Analysis and Risk Assessment of Critical Infrastructure

Seismic analysis and risk assessment of safety-critical infrastructure like hospitals, nuclear power plants, dams, and facilities handling radioactive materials involve computationally intensive numerical models and coupled multiphysics scenarios. They are also performed in a strict regulatory environment that requires high software quality assurance standards, and in the case of safety-related nuclear facilities, a conformance to the American Society of Mechanical Engineers Nuclear Quality Assurance (NQA-1) standard. This paper introduces the open-source finite-element software, MASTODON (Multi-hazard Analysis of Stochastic Time-Domain Phenomena), which implements state-of-the-art seismic analysis and risk assessment tools in a quality-controlled environment. MASTODON is built on MOOSE (Multi-physics Object-Oriented Simulation Environment), which is a highly parallelizable, NQA-1 conforming, coupled multiphysics, finite-element framework developed at Idaho National Laboratory. MASTODON is capable of fault rupture and source-to-site wave propagation using the domain reduction method, nonlinear site response, and soil-structure interaction analysis, implicit and explicit time integration, automated stochastic simulations, and seismic probabilistic risk assessment. When coupled with other MOOSE applications, MASTODON can also solve strongly and weakly coupled multiphysics problems. This paper presents a summary of the capabilities of MASTODON and some demonstrative examples.

42 ENGINEERING↗
DOE OSTI2023

Preliminary Nuclear Containment Vessel Modeling for Multi-Hazard Probabilistic Risk Assessment under Seismic Hazards and Concrete Degradation

The current practice for natural phenomena hazards (NPH) risk assessment of nuclear facilities is to compute the risk for each hazard independently and then compound the total risk as a combination of single hazard risks. This state of practice does not consider correlations between hazards and the cascading impacts to structures, systems, and components (SSCs), and could thus underestimate the NPH risk or overestimate the nuclear facility safety. Events such as the Fukushima Daiichi accident have highlighted the importance of multi-hazard risk considerations to nuclear power plants (NPPs) that quantify the cascading damage effects to SSCs in the risk models. Moreover, the current fleet of NPPs in the United States is aging; these NPPs are now expected to operate well beyond their initially planned design life. Aging-related deterioration can potentially decrease the capacity of critical structures such as containment vessels to withstand NPH. Such aging considerations may not be adequately accounted for by the current NPH risk assessment guidelines. This paper presents a preliminary modeling and simulation of a representative reinforced concrete containment vessel subjected to seismic mainshock and aftershock considering concrete degradation due to alkali silica reaction. The broader aim is to develop multi-hazard time-dependent fragility functions that could be subsequently used in the probabilistic risk assessment (PRA) model. The multi-hazard component comes into play due to the consideration of damage to the containment vessel under seismic loads and concrete degradation. Consideration of concrete degradation also brings into play the time-dependent nature of the containment vessel response. The response of the containment vessel under varying degrees of concrete degradation to seismic loads is investigated. The results presented are simulated using the Multi-hazard Analysis for STOchastic time-DOmaiN phenomena (MASTODON) software for seismic analysis and the Blackbear software for concrete degradation and damage modeling. Both software are open source and developed within the Multiphysics Object-Oriented Simulation Environment (MOOSE).

42 ENGINEERING↗
DOE OSTI2021

Stochastic properties of ultralight scalar field gradients

Ultralight axion-like particles are well-motivated dark matter candidates that are the target of numerous direct detection efforts. In the vicinity of the Solar System, such particles can be treated as oscillating scalar fields. The velocity dispersion of the Milky Way determines a coherence time of about 10 6 oscillations, beyond which the amplitude of the axion field fluctuates stochastically. Any analysis of data from an axion direct detection experiment must carefully account for this stochastic behavior to properly interpret the results. This is especially true for experiments sensitive to the gradient of the axion field that are unable to collect data for many coherence times. Indeed, the direction, in addition to the amplitude, of the axion field gradient fluctuates stochastically. We present the first complete stochastic treatment for the gradient of the axion field, including multiple computationally efficient methods for performing likelihood-based data analysis, which can be applied to any axion signal, regardless of coherence time. Additionally, we demonstrate that ignoring the stochastic behavior of the gradient of the axion field can potentially result in failure to discover a true axion signal

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2021

Observability Analysis of a Power System Stochastic Dynamic Model Using a Derivative-Free Approach

Serving as a prerequisite to power system dynamic state estimation, the observability analysis of a power system dynamic model has recently attracted the attention of many power engineers. However, because this model is typically nonlinear and large-scale, the analysis of its observability is a challenge to the traditional derivative-based methods. Indeed, the linear-approximation-based approach may provide unreliable results while the nonlinear-technique-based approach inevitably faces extremely complicated derivations. Furthermore, because power systems are intrinsically stochastic, the traditional deterministic approaches may lead to inaccurate observability analyses. In this work, facing these challenges, we propose a novel polynomial-chaos-based derivative-free observability analysis approach that not only is free of any linear approximations, but also accounts for the stochasticity of the dynamic model while bringing a low implementation complexity. Furthermore, this approach enables us to quantify the degree of observability of a stochastic model, what conventional deterministic methods cannot do. The excellent performance of the proposed method has been demonstrated by performing extensive simulations using a synchronous generator model with IEEE-DC1A exciter and the TGOV1 turbine governor.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2020

Numerical Validation of an Algorithm for Combined Soiling and Degradation Analysis of Photovoltaic Systems

We describe and demonstrate an open-source algorithm for simultaneously quantifying degradation and soiling of photovoltaic (PV) systems from energy-production time series data. The new analysis is based on year-on-year degradation rate analysis combined with stochastic rate and recovery soiling analysis. The algorithm is designed to fit into the workflow provided by RdTools, a Python module maintained by NREL and collaboratively developed with the community, which provides a framework and functions for degradation and loss-factor analysis of PV field data. We demonstrate the method on numerically simulated PV data sets and show that it reduces the root-mean-square error of the P50 degradation rate estimate when soiling is present.

14 SOLAR ENERGY↗
DOE OSTI2024

Stochastic Distribution Control Theory-Its Potential Application in Risk Management in Financial Systems

Stochastic Distribution Control (SDC) theory [1], originated by the author in 1996, aims at developing modeling and control strategies for dynamic and non-Gaussian stochastic systems by controlling the shape of the probability density functions of some concerned variables and parameters in stochastic systems. It generalizes the capability of standard stochastic differential equations and can therefore be applied to generic non-Gaussian systems. Since it was established in 1996, it has found a wide spectrum of applications in non-Gaussian stochastic system control, data mining, filtering and optimization for uncertain systems. In this short opinion article, discussions will be made on potential applications of SDC theory to financial systems in terms of risk analysis and management.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Instability and turbulent relaxation in a stochastic magnetic field

An analysis of instability dynamics in a stochastic magnetic field is presented for the tractable case of the resistive interchange. Externally prescribed static magnetic perturbations convert the eigenmode problem to a stochastic differential equation, which is solved by the method of averaging. The dynamics are rendered multi-scale, due to the size disparity between the test mode and magnetic perturbations. Maintaining quasi-neutrality at all orders requires that small-scale convective cell turbulence be driven by disparate scale interaction. Here, the cells in turn produce turbulent mixing of vorticity and pressure, which is calculated by fluctuation-dissipation type analyses, and are relevant to pump-out phenomena. The development of correlation between the ambient magnetic perturbations and the cells is demonstrated, showing that turbulence will 'lock on' to ambient stochasticity. Magnetic perturbations are shown to produce a magnetic braking effect on vorticity generation at large scale. Detailed testable predictions are presented. The relations of these findings to the results of available simulations and recent experiments are discussed.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2023

Adaptive, Active Learning, and Multifidelity Monte Carlo Methods in the MOOSE Stochastic Tools Module

MOOSE is an open-source computational platform for constructing multi-physics models and executing them in a massively parallel fashion. It has a stochastic tools module (STM) for forward/inverse uncertainty quantification (UQ) and surrogate modeling. This presentation details some recent developments to the STM with respect to the implementation of adaptive, active learning, and multifidelity Monte Carlo methods for forward UQ of computational models. Specifically, the adaptive Monte Carlo methods include Markov Chain Monte Carlo (MCMC)-driven algorithms like adaptive importance sampling and parallelized subset simulation for statistical QoI estimation, rare events analysis, and stochastic gradient-free optimization. The active learning methods include Gaussian Process (GP) surrogates and their training via Adam optimization, design of acquisition functions, and integration with samplers like Monte Carlo, adaptive importance, and parallelized subset simulation. These active learning methods are also designed to work in a batch mode, wherein, the required calls to the full computational model are executed in parallel whenever a user-specified batch size is met. The multifidelity methods in STM are broadly divided into two categories: hierarchical, where a defined hierarchy exists among the low-fidelity models, and peer, where all the low-fidelity models are treated equally. A GP surrogate is used to learn the differences between the low- and high-fidelity models in both multifidelity categories, and acquisition functions from the active learning classes are used to decide whether to rely on a low-fidelity model or call the expensive high-fidelity model. Alongside the software description and usage, applications are also presented to nuclear engineering computational models including a TRISO nuclear fuel particle, a reactor pressure vessel, and a heat-pipe microreactor.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Data-driven optimization of mixed-integer bi-level multi-follower integrated planning and scheduling problems under demand uncertainty

The coordination of interconnected elements across the different layers of the supply chain is essential for all industrial processes and the key to optimal decision-making. Yet, the modeling and optimization of such interdependent systems are still burdensome. Here we address the simultaneous modeling and optimization of medium-term planning and short-term scheduling problems under demand uncertainty using mixed-integer bi-level multi-follower programming and data-driven optimization. Bi-level multi-follower programs model the natural hierarchy between different layers of supply chain management holistically, while scenario analysis and data-driven optimization allow us to retrieve the guaranteed feasible solutions of the integrated formulation under various demand considerations. We address the data-driven optimization of this challenging class of problems using the DOMINO framework, which was initially developed to solve single-leader single-follower bi-level optimization problems to guaranteed feasibility. This framework is extended to solve single-leader multi-follower stochastic formulations and its performance is characterized by well-known single and multi-product process scheduling case studies. Through our data-driven algorithmic approach, we present guaranteed feasible solutions to linear and nonlinear mixed-integer bi-level formulations of simultaneous planning and scheduling problems and further characterize the effects of the scheduling level complexity on the solution performance, which spans over several hundred continuous and binary variables, and thousands of constraints.

42 ENGINEERING↗
DOE OSTI2020

An Evaluation of the Economic and Resilience Benefits of a Microgrid in Northampton, Massachusetts

Recent developments and advances in distributed energy resource (DER) technologies make them valuable assets in microgrids. This paper presents an innovative evaluation framework for microgrid assets to capture economic benefits from various grid and behind-the-meter services in grid-connecting mode and resilience benefits in islanding mode. In particular, a linear programming formulation is used to model different services and DER operational constraints to determine the optimal DER dispatch to maximize economic benefits. For the resiliency analysis, a stochastic evaluation procedure is proposed to explicitly quantify the microgrid survivability against a random outage, considering uncertainties associated with photovoltaic (PV) generation, system load, and distributed generator failures. Optimal coordination strategies are developed to minimize unserved energy and improve system survivability, considering different levels of system connectedness. The proposed framework has been applied to evaluate a proposed microgrid in Northampton, Massachusetts that would link the Northampton Department of Public Works, Cooley Dickenson Hospital, and Smith Vocational Area High School. The findings of this analysis indicate that over a 20-year economic life, a 441 kW/441 kWh battery energy storage system, and 386 kW PV solar array can generate $2.5 million in present value benefits, yielding a 1.16 return on investment ratio. Results of this study also show that forming a microgrid generally improves system survivability, but the resilience performance of individual facilities varies depending on power-sharing strategies.

25 ENERGY STORAGE↗
DOE OSTI2025

Theory of x-ray photon correlation spectroscopy for multiscale flows

Complex multiscale flows associated with instabilities and turbulence are commonly induced under high-energy density (HED) conditions, but accurate measurement of their transport properties has been challenging. X-ray photon correlation spectroscopy (XPCS) with coherent x-ray sources can, in principle, probe material dynamics to infer transport properties using time autocorrelation of density fluctuations. Here we develop a theoretical framework for utilizing XPCS to study material diffusivity in multiscale flows. We extend single-scale shear flow theories to broadband flows using a multiscale analysis that captures shear and diffusion dynamics. Our theory is validated with simulated XPCS for Brownian particles advected in multiscale flows. We demonstrate the versatility of the method over several orders of magnitude in timescale using sequential-pulse XPCS, single-pulse x-ray speckle visibility spectroscopy (XSVS), and double-pulse XSVS.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2025

Advancing Multi-Hazard Risk and Safety Considerations for Aging Nuclear Facilities (Revision 1)

This project will demonstrate a multi-hazard time-dependent probabilistic risk assessment (PRA) approach for nuclear facilities considering aging-related deterioration of structures. A generic pressurized water reactor (PWR) reactor subjected to seismic mainshock-aftershock sequences considering the aging of the containment structure will be used as a case study to demonstrate the multi-hazard PRA approach. Using advanced modeling and simulation, seismic mainshock-aftershock fragility functions will be simulated for the containment structure considering aging effects. A multi-hazard PRA model for a generic PWR reactor will be built to quantify the multi-hazard core damage frequency (CDF) and large early release frequency (LERF) with explicit time-dependent modeling of event sequences. To date, the cascading impacts of multi-hazards are not adequately accounted for in the PRA models for nuclear facilities. In addition, for both initial and periodic evaluation of facilities to withstand natural phenomena hazards (NPH), deterioration of the SSCs due to aging and other effects is not adequately considered. By advancing multi-hazard considerations accounting for aging effects, this project will contribute to improved understanding of the safety of aging nuclear facilities. Project outcomes such as the multi-hazard CDF and LERF will also allow facility owners to optimize upgrade and retrofit protocols. This project is divided into two components: (1) advanced modeling and simulations; and (2) multi-hazard PRA. For the first component, Idaho National Laboratory’s (INL) Multi-hazard Analysis for STOchastic time-DOmaiN phenomena (MASTODON) and BlackBear codes will be used to simulate the seismic response and damage of a containment structure under cascading mainshock-aftershock sequences with aging effects. Uncertainties related to the seismic inputs, material parameters, and environmental factors such as temperature and humidity will be identified and propagated to the fragility functions. These fragility functions, which consider aging effects, will be time dependent. The second component will take the fragility information from the first component to build a multi-hazard time-dependent PRA model starting from a generic PWR model to evaluate the multi-hazard CDF and LERF and characterize the associated consequences. For this component, OpenPRA Web Application and SAPHIRE code will be used. Events such as the Fukushima Daiichi accident have highlighted the importance of considering the cascading impacts of multi-hazards for PRA. Moreover, many of the reactors in the current nuclear fleet in the United States (US) are already operating well beyond their initially planned design life, and applications for further extensions to operating licenses are being considered. Therefore, considering multi-hazard effects and aging deterioration in the NPH risk assessment process will contribute to the safety of both existing and future nuclear facilities. Outcomes of this project will thus directly benefit the standards DOE-STD-1020-16 and DOE-HDBK-1224-18.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2022

Surface fluctuating hydrodynamics methods for the drift-diffusion dynamics of particles and microstructures within curved fluid interfaces

Here we introduce fluctuating hydrodynamics approaches on surfaces for capturing the drift-diffusion dynamics of particles and microstructures immersed within curved fluid interfaces of spherical shape. We take into account the interfacial hydrodynamic coupling, traction coupling with the surrounding bulk fluid, and thermal fluctuations. For fluid-structure interactions, we introduce Immersed Boundary Methods (IBM) and related Stochastic Eulerian-Lagrangian Methods (SELM) for curved surfaces. We use these approaches to investigate the statistics of surface fluctuating hydrodynamics and microstructures. For velocity autocorrelations, we find characteristic power-law scalings $τ^{-1}, τ^{-2}$, and plateaus can emerge. This depends on the physical regime associated with the geometry, surface viscosity, and bulk viscosity. This differs from the characteristic $τ^{-3/2}$ scaling for bulk three dimensional fluids. We develop theory explaining these observed power-laws associated with time-scales for dissipation within the fluid interface and coupling to the surrounding fluid. We then use our introduced methods to investigate a few example systems and roles of hydrodynamic coupling and thermal fluctuations including for the kinetics of passive particles and active microswimmers in curved fluid interfaces.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Stochastic multiscale modeling for quantifying statistical and model errors with application to composite materials

This paper provides a coherent and efficient computational framework for stochastic multiscale analysis of material systems in the presence of parametric uncertainties and modeling errors. Uncertainty in those model parameters that are not deduced as upscaled quantities is attributed to an uncertainty “germ”. While such parameters can appear at any scale, they are predominant at the finest analysis scale. Additional uncertainties stemming from statistical estimation, attributed to lack of data and model error, are associated with each submodel contributing to the multiscale system. Here, a robust and efficient framework based on a generalized extended polynomial chaos expansion (gEPCE) is proposed to simultaneously propagate all these uncertainties in order to provide a probabilistic representation of specific quantities of interest (QoI). We characterize the full probability distribution of the QoI and the uncertainty in the failure probability pertaining to its tails. By combining gEPCE with kernel density estimation (KDE) and directional derivatives, we construct sensitivity measures that connect these statistical metrics of QoI to the various sources of uncertainty to assess their individual and combined impacts. An illustrative problem featuring three-point bending of a composite beam is investigated to demonstrate the presented approach.

36 MATERIALS SCIENCE↗
DOE OSTI2026

Identification of Solid-Electrolyte Interphase Species by Joint Characterization of Li-Ion Battery Chemistry by Mass Spectrometry and Electrochemical Reaction Networks

The formation and stability of the solid-electrolyte interphase (SEI) play central roles in determining the long-term performance and safety of modern electrochemical energy storage systems. Despite decades of research, the SEI’s heterogeneous, dynamic, and multiphase nature has defied comprehensive molecular-level characterization, creating a critical knowledge gap that limits rational battery design. In this work, we introduce a computational−experimental framework that integrates high-throughput quantum chemistry calculations, data-driven electrochemical reaction networks (eCRNs), stochastic algorithms, and laser desorption/ionization Fourier transform ion cyclotron resonance mass spectrometry (LDI-FTICR-MS) to unravel SEI formation in carbonatebased electrolytes without imposing predefined mechanisms. We constructed the most comprehensive eCRN to date, spanning over 10,000 species and 209 million reactions. Through stochastic network analysis, we successfully recovered 27 species that were previously reported in the literature and predicted 28 novel SEI species nearly doubling our scientific knowledge in this area. Each new species was rigorously confirmed through advanced mass spectral analysis of its distinct molecular and isotopic signatures. We kinetically refined the formation pathways for a select set of both previously reported and novel SEI products, revealing kinetically feasible elementary reaction mechanisms with activation barriers below 1 eV. This computational−experimental approach deepens our molecular-level understanding of SEI chemistry by resolving which species form and through which decomposition mechanisms they emerge. Such knowledge provides the foundation necessary to connect electrolyte composition to the resulting SEI components, a critical step toward a more informed electrolyte development in next-generation lithium-based batteries.

25 ENERGY STORAGE↗
DOE OSTI2020

Thermal fluctuations in the Landau-Lifshitz-Bloch model

A formulation for thermal noise in the stochastic form of the Landau-Lifshitz-Bloch equation used for modeling the magnetization dynamics at elevated temperatures is presented here. The diffusion coefficients for thermal fluctuations are obtained via the Fokker-Plank equation using the mean-field approximation of the field in defining the free energy. The presented model leads to a mean magnetization consistent with the equilibrium magnetization for small and large particles. The distribution of the magnetization magnitude is of the Maxwell-Boltzmann type. The presented model was tested by studying the equilibrium magnetization in macrospin particles at high temperatures. The model is appealing for multiscale modeling, such as modeling heat assisted magnetic recording systems and all-optical magnetization reversal.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2022

Velocity-space compression from Fermi acceleration with Lorentz scattering

The Fermi acceleration model describes how cosmic ray particles accelerate to great speeds by interacting with moving magnetic fields. In this work, we identify a variation of the model where light ions interact with a moving wall while undergoing pitch angle scattering through Coulomb collisions due to the presence of a heavier ionic species. The collisions introduce a stochastic component which adds complexity to the particle acceleration profile and sets it apart from collisionless Fermi acceleration models. The unusual effect captured by this simplified variation of Fermi acceleration is the nonconservation of phase space, with the possibility for a distribution of particles initially monotonically decreasing in energy to exhibit an energy peak upon compression. A peaked energy distribution might have interesting applications, such as to optimize fusion reactivity or to characterize astrophysical phenomena that exhibit nonthermal features.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗