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NASA NTRS1979

Generation of linear dynamic models from a digital nonlinear simulation

The results and methodology used to derive linear models from a nonlinear simulation are presented. It is shown that averaged positive and negative perturbations in the state variables can reduce numerical errors in finite difference, partial derivative approximations and, in the control inputs, can better approximate the system response in both directions about the operating point. Both explicit and implicit formulations are addressed. Linear models are derived for the F 100 engine, and comparisons of transients are made with the nonlinear simulation. The problem of startup transients in the nonlinear simulation in making these comparisons is addressed. Also, reduction of the linear models is investigated using the modal and normal techniques. Reduced-order models of the F 100 are derived and compared with the full-state models.

Daniele, C. J.↗

DOE OSTI2020

Risk-Informed Applications and Science – Past, Present, & Future

This is a presentation to be made at the University of Tokyo. The Idaho National Laboratory is creating the next-generation reliability- and risk-assessment methods and tools that support risk-informed decision-making by combining physics-based models with probabilistic quantification approaches. Integrating these two worlds of physics and probability using a simulation framework leads us to predictions based upon an approach called “computational risk assessment” which will serve as the technical basis for the future of reliability and risk approaches. The driving factors for this new approach includes: temporal (timing issues), spatial (location issues), mechanistic (physics issues), and topological (complexity issues). By combining phenomenology directly with stochastic quantification, we are able to perform advanced uncertainty analysis directly on both parameters and models. In addition, new tools allow for the creation of reduced order models that mimic high-fidelity engineering models while still permitting the realization of thousands of simulation iterations in short run-times on current workstation-class computers. While these advanced methods and tools can provide increased realism in our engineering safety and risk approaches, their greater benefit is to provide a risk-informed engineering framework for design and operation. This talk will briefly review the history of risk assessment and risk-informed applications, describe some of the current research and development found at the Idaho National Laboratory, and discuss potential future applications and approaches for advanced methods and tools.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2017

Self-consistent clustering analysis: an efficient multiscale scheme for inelastic heterogeneous materials

A predictive computational theory is shown for modeling complex, hierarchical materials ranging from metal alloys to polymer nanocomposites. The theory can capture complex mechanisms such as plasticity and failure that span across multiple length scales. This general multiscale material modeling theory relies on sound principles of mathematics and mechanics, and a cutting-edge reduced order modeling method named self-consistent clustering analysis (SCA) [Zeliang Liu, M.A. Bessa, Wing Kam Liu, “Self-consistent clustering analysis: An efficient multi-scale scheme for inelastic heterogeneous materials,” Comput. Methods Appl. Mech. Engrg. 306 (2016) 319–341]. SCA reduces by several orders of magnitude the computational cost of micromechanical and concurrent multiscale simulations, while retaining the microstructure information. This remarkable increase in efficiency is achieved with a data-driven clustering method. Computationally expensive operations are performed in the so-called offline stage, where degrees of freedom (DOFs) are agglomerated into clusters. The interaction tensor of these clusters is computed. In the online or predictive stage, the Lippmann-Schwinger integral equation is solved cluster-wise using a self-consistent scheme to ensure solution accuracy and avoid path dependence. To construct a concurrent multiscale model, this scheme is applied at each material point in a macroscale structure, replacing a conventional constitutive model with the average response computed from the microscale model using just the SCA online stage. A regularized damage theory is incorporated in the microscale that avoids the mesh and RVE size dependence that commonly plagues microscale damage calculations. The SCA method is illustrated with two cases: a carbon fiber reinforced polymer (CFRP) structure with the concurrent multiscale model and an application to fatigue prediction for additively manufactured metals. For the CFRP problem, a speed up estimated to be about 43,000 is achieved by using the SCA method, as opposed to FE2, enabling the solution of an otherwise computationally intractable problem. The second example uses a crystal plasticity constitutive law and computes the fatigue potency of extrinsic microscale features such as voids. This shows that local stress and strain are capture sufficiently well by SCA. This model has been incorporated in a process-structure-properties prediction framework for process design in additive manufacturing.

Liu, Z.↗

DOE OSTI2025

Bayesian learning with Gaussian processes for low-dimensional representations of time-dependent nonlinear systems

This work presents a data-driven method for learning low-dimensional time-dependent physics-based surrogate models whose predictions are endowed with uncertainty estimates. We use the operator inference approach to model reduction that poses the problem of learning low-dimensional model terms as a regression of state space data and corresponding time derivatives by minimizing the residual of reduced system equations. Standard operator inference models perform well with accurate training data that are dense in time, but producing stable and accurate models when the state data are noisy and/or sparse in time remains a challenge. Another challenge is the lack of uncertainty estimation for the predictions from the operator inference models. Our approach addresses these challenges by incorporating Gaussian process surrogates into the operator inference framework to (1) probabilistically describe uncertainties in the state predictions and (2) procure analytical time derivative estimates with quantified uncertainties. The formulation leads to a generalized least-squares regression and, ultimately, reduced-order models that are described probabilistically with a closed-form expression for the posterior distribution of the operators. The resulting probabilistic surrogate model propagates uncertainties from the observed state data to reduced-order predictions. Furthermore, we demonstrate the method is effective for constructing low-dimensional models of two nonlinear partial differential equations representing a compressible flow and a nonlinear diffusion–reaction process, as well as for estimating the parameters of a low-dimensional system of nonlinear ordinary differential equations representing compartmental models in epidemiology.

Data-driven model reduction↗

DOE OSTI2018

Machine Learning–Based Reduce Order Crystal Plasticity Modeling for ICME Applications

Abstract Crystal plasticity simulation is a widely used technique for studying the deformation processing of polycrystalline materials. However, inclusion of crystal plasticity simulation into design paradigms such as integrated computational materials engineering (ICME) is hindered by the computational cost of large-scale simulations. In this work, we present a machine learning (ML) framework using the material information platform, Open Citrination, to develop and calibrate a reduced order crystal plasticity model for face-centered cubic (FCC) polycrystalline materials, which can be both rapidly exercised and easily inverted. The reduced order model takes crystallographic texture, constitutive model parameters, and loading condition as inputs and returns the stress-strain curve and final texture. The model can also be inverted and take a stress-strain curve, loading condition, and final texture as inputs and return the initial texture and constitutive model parameters as outputs. Principal component analysis (PCA) is used to develop an efficient description of the crystallographic texture. A viscoplastic self-consistent (VPSC) crystal plasticity solver is used to create the training data by modeling the stress-strain behavior and evolution of texture during deformation processing.

Yuan, Mengfei↗

DOE OSTI2024

Dissolution zone model of the oxide structure in additively manufactured dispersion-strengthened alloys

The structural evolution of oxides in dispersion-strengthened superalloys during laser-powder bed fusion is considered in detail. Alloy chemistry and process parameter effects on oxide structure are assessed through a parameter study on the model alloy Ni-20Cr, doped with varying concentrations of Y 2 O 3 and Al. Small angle neutron scattering measurements of the dispersoid size distribution show the dispersoid size increases with higher laser power, slower scan speed, and increasing Y 2 O 3 and Al content. Complementary electron microscopy measurements reveal reactions between Y 2 O 3 and Al, even in nanoscale dispersoids, and the presence of micron-scale oxide slag inclusions in select specimens. A scaling analysis of mass and momentum transport within the melt pool, presented here, establishes that diffusional structural evolution mechanisms dominate for nanoscale dispersoids, while fluid forces and advection become significant for larger slag inclusions. These findings are developed into a theory of dispersoid structural evolution, integrating quantitative models of diffusional processes – dispersoid dissolution, nucleation, growth, coarsening – with a reduced order model of time-temperature trajectories of fluid parcels within the melt pool. Calculations of the dispersoid size in single-pass melting reveal a zone in the center of the melt track in which the oxide feedstock fully dissolves. Within this zone the final Y 2 O 3 size is independent of feedstock size and determined by nucleation and growth kinetics. If the dissolution zones of adjacent melt tracks overlap sufficiently with each other to dissolve large oxides, formed during printing or present in the powder feedstock, then the dispersoid structure throughout the build volume is homogeneous and matches that from a single pass within the dissolution zone. Gaps between adjacent dissolution zones result in oxide accumulation into larger slag inclusions. Predictions of final dispersoid size and slag formation using this dissolution zone model match the present experimental data and explain process-structure linkages speculated in the open literature.

36 MATERIALS SCIENCE↗

DOE OSTI2026

A mechanistic, multiscale model for predicting Pd penetration in TRISO fuels using BISON

TRistructural ISOtropic (TRISO) particles use silicon carbide (SiC) as the primary structural member and barrier against metallic fission product (FP) release. palladiums (PDs), produced by fission in the fuel kernel, can diffuse to and chemically interact with the SiC layer, degrading its structural integrity and ability to contain radioactive FPs. Existing temperature-dependent correlations for predicting Pd penetration rely on experimental data with significant scatter due to varying conditions, potentially complicating ongoing fuel qualification and licensing efforts for advanced reactors that would subject TRISO fuels to operating conditions outside of those examined in the experiments. A mechanistic model of Pd production, transport, and reaction is developed in this work to better understand and predict PD attack of SiC in TRISO particles. molecular dynamicss (MDs) simulations are utilized to calculate the Pd diffusivity in SiC grain bulk and grain boundaries. A mesoscale phase-field diffusion model, informed by the MD diffusivities, is used to develop a reduced order model (ROM) for the effect of SiC microstructure on the Pd penetration rate. The engineering scale BISON model calculates Pd production and transport, utilizing the ROM to predict penetration rates consistent with experimental data. This novel mechanistic ROM captures the effect of temperature, microstructure, and irradiation history on Pd penetration. In conclusion, these new capabilities are expected to support ongoing qualification and licensing efforts associated with near-term TRISO-fueled reactor applications.

11 - NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2024

A Variable Eddington Factor Model for Thermal Radiative Transfer with Closure Based on Data-Driven Shape Function

Here, a new variable Eddington factor (VEF) model is presented for nonlinear problems of thermal radiative transfer (TRT). The VEF model is data-driven and acts on known (a-priori) radiation-diffusion solutions for material temperatures in the TRT problem. A linear auxiliary problem is constructed for the radiative transfer equation (RTE) whose emission source and opacities are evaluated at these known material temperatures. The solution to this RTE approximates the specific intensity distribution in phase-space and time. It is applied as a shape function to define the Eddington tensor for the presented VEF model. The shape function computed via the auxiliary RTE problem will capture some degree of transport effects within the TRT problem. The VEF moment equations closed with this approximate Eddington tensor will thus carry with them these captured transport effects. In this study, the temperature data comes from multigroup P 1 , P 1/3 , and flux-limited diffusion radiative transfer models. The proposed VEF model can be interpreted as a transport-corrected diffusion reduced-order model. Numerical results are presented on the Fleck-Cummings test problem which models a supersonic wavefront of radiation. The VEF model is shown to improve accuracy by 1–2 orders of magnitude compared to the considered radiation-diffusion model solutions to the TRT problem.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2018

Network Reduction Algorithm for Developing Distribution Feeders for Real-Time Simulators

As advanced grid-support functions (AGF) become more widely used in grid-connected photovoltaic (PV) inverters, utilities are increasingly interested in their impacts when implemented in the field. These effects can be understood by modeling feeders in real-time simulators and test PV inverters using power hardware-in-the-loop (PHIL) techniques. This paper presents a novel feeder model reduction algorithm using a ruin & reconstruct methodology that enables large feeders to be solved and operated on real-time computing platforms. Two Hawaiian Electric feeder models in Synergi Electric's load flow software were converted to reduced order models in OpenDSS, and subsequently implemented in the OPAL-RT real-time digital testing platform. Smart PV inverters were added to the realtime model with AGF responses modeled after characterizing commercially available hardware inverters. Finally, hardware inverters were tested in conjunction with the real-time model using PHIL techniques so that the effects of AGFs on the feeders could be analyzed.

14 SOLAR ENERGY↗

DOE OSTI2022

SWP Summary Report for Individual Legacy Well Leakage Risk Analysis at Farnsworth Unit Site: Open Well Scenario

This report summarizes results of the individual legacy well leakage risk analysis of the Farnsworth Unit site (FWU) for Open Well scenario. NRAP tools Integrated Assessment Model for Carbon Storage (NRAP-IAM-CS) and Reservoir Reduced-Order Model Generator (RROMGen) were used (Dilmore et al., 2016; Pawar et al., 2016; King, 2016). This is part one of the additional analysis addressing SWP BP4 Subtask 7.4.1.2: Extend quantitative brine and CO2 leakage calculations (Chu et al., 2020).

58 GEOSCIENCES↗

DOE OSTI2023

Comprehensive Review of DPF-based Flash Neutron Radiography Viability

MJOLNIR (MegaJOule Neutron Imaging Radiography) is a Dense Plasma Focus (DPF) being developed by LLNL as a prototype to assess the viability of a DPF as a flash neutron radiography source. To date, MJOLNIR has discharged up to 1.3 MJ of stored energy into a deuterium plasma load and achieved yields up to 1.2 × 10 12 neutrons per discharge. The MJOLNIR pulse length already meets the preliminary requirements for flash neutron radiography and we demonstrate in this report plausible paths forward to meet the yield requirement in a deuterium plasma. MJOLNIR’s neutron spot size has been characterized to be a factor of two greater than radiography requirements and presents the greatest challenge. A path forward to sufficiently shrinking spot size is outlined in this report, using a combination of gas dopants and a smaller anode implosion radius. A DPF is a plasma device with coaxial electrodes whose discharge ends with a stagnated hot and dense plasma column on-axis, at the tip of the central anode. Inside the MJOLNIR DPF plasma column, both thermal and beam target processes generate neutrons. To understand the underlying physics of neutron generation inside the DPF, we model the experiment using a combination of kinetic, fluid, and reduced-order models we have been developing for over ten years at LLNL. Our numerical tools are also pivotal to charting the path forward because they allow us to numerically test out which modifications would improve the DPF’s characteristic output.

42 ENGINEERING↗

DOE OSTI2023

Engineering-scale Modeling of High-Temperature Creep and Creep Crack Growth in Alloy 316H

This document demonstrates completion of the goals described in the technical narrative of the Department of Energy’s Industry Funding Opportunity Announcement (iFOA) project entitled “Modeling and Simulation Development Pathways to Accelerating KP-FHR Licensing,” which relates to the development and demonstration of capabilities for conducting engineering-scale simulations of Alloy 316H components under high-temperature conditions. This work encompassed two major aspects: integrating and testing constitutive models for the creep response of 316H at high temperatures, and developing tools for modeling creep crack growth (CCG) in 316H. Two classes of constitutive models were used in this effort: phenomenological models based on behavior observed at the engineering scale, and reduced-order models (ROMs) that represent the nonlinear response of mesoscale models that capture the sensitivity to material microstructure and processing. Likewise, the approaches employed for CCG modeling considered both simplified engineering approaches and detailed simulations of creep and damage ahead of the crack tip. These developments, which were performed by utilizing the Grizzly code as well as the open-source libraries it depends on, strengthen Grizzly’s ability to support licensing and safety analyses of high-temperature reactor components.

316H↗

NASA NTRS1982

Eigenspace techniques for active flutter suppression

Mathematical models to be used in the control system design were developed. A computer program, which takes aerodynamic and structural data for the ARW-2 aircraft and converts these data into state space models suitable for use in modern control synthesis procedures, was developed. Reduced order models of inboard and outboard control surface actuator dynamics and a second order vertical wind gust model were developed. An analysis of the rigid body motion of the ARW-2 was conducted. The deletion of the aerodynamic lag states in the rigid body modes resulted in more accurate values for the eigenvalues associated with the plunge and pitch modes than were obtainable if the lag states were retained.

Garrard, W. L.↗

NASA NTRS1989

Model reduction and control of flexible structures using Krylov subspaces

Krylov vectors and the concept of parameter-matching are combined to develop a model reduction algorithm for a damped structural dynamics system. The reduced-order model obtained matches a certain number of low-frequency moments of the full-order system. The major application of the present method is to the control of flexible structures. It is shown that, in the control of flexible structures, there generally exist three types of control energy spillover, namely, the control spillover, the observation spillover, and dynamic spillover. The formulation based on Krylov subspaces can eliminate the control and the observation spillover, while leaving only the dynamic spillover to be considered. Two examples are used to illustrate the efficacy of the Krylov method.

Craig, Roy R., Jr.↗

DOE OSTI2017

Network Reduction Algorithm for Developing Distribution Feeders for Real-Time Simulators: Preprint

As advanced grid-support functions (AGF) become more widely used in grid-connected photovoltaic (PV) inverters, utilities are increasingly interested in their impacts when implemented in the field. These effects can be understood by modeling feeders in real-time systems and testing PV inverters using power hardware-in-the-loop (PHIL) techniques. This paper presents a novel feeder model reduction algorithm using a Monte Carlo method that enables large feeders to be solved and operated on real-time computing platforms. Two Hawaiian Electric feeder models in Synergi Electric's load flow software were converted to reduced order models in OpenDSS, and subsequently implemented in the OPAL-RT real-time digital testing platform. Smart PV inverters were added to the real-time model with AGF responses modeled after characterizing commercially available hardware inverters. Finally, hardware inverters were tested in conjunction with the real-time model using PHIL techniques so that the effects of AGFs on the choice feeders could be analyzed.

14 SOLAR ENERGY↗

DOE OSTI2019

Model Structural Inference Using Local Dynamic Operators

This paper focuses on the problem of quantifying the effects of model-structure uncertainty in the context of time-evolving dynamical systems. This is motivated by multi-model uncertainty in computer physics simulations: developers often make different modeling choices in numerical approximations and process simplifications, leading to different numerical codes that ostensibly represent the same underlying dynamics. We consider model-structure inference as a two-step methodology: the first step is to perform system identification on numerical codes for which it is possible to observe the full state; the second step is structural uncertainty quantification, in which the goal is to search candidate models "close" to the numerical code surrogates for those that best match a quantity of interest (QOI) from some empirical data sets. Here, we (1) define a discrete, local representation of the structure of a partial differential equation, which we refer to as the "local dynamical operator" (LDO); (2) identify model structure nonintrusively from numerical code output; (3) nonintrusively construct a reduced-order model (ROM) of the numerical model through POD-DEIM-Galerkin projection; (4) perturb the ROM dynamics to approximate the behavior of alternate model structures; and (5) apply Bayesian inference and energy conservation laws to calibrate a LDO to a given QOI. We demonstrate these techniques using the two-dimensional rotating shallow water equations as an example system.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS2012

Uncertainty Due to Unsteady Fluid/Structure Interaction for the Ares I Vehicle Traversing the Transonic Regime

Rapid reduced-order numerical models are being investigated as candidates to simulate the dynamics of a flexible launch vehicle during atmospheric ascent. There has also been the extension of these new approaches to include gust response. These methods are used to perform aeroelastic and gust response analyses at isolated Mach numbers. Such models require a method to time march through a succession of ascent Mach numbers. An approach is presented for interpolating reduced-order models of the unsteady aerodynamics at successive Mach numbers. The transonic Mach number range is considered here since launch vehicles can suffer the highest dynamic loads through this range. Realistic simulations of the flexible vehicle behavior as it traverses this Mach number range are presented. The response of the vehicle due to gusts is computed. Uncertainties in root mean square and maximum bending moment and crew module accelerations are presented due to assumed probability distributions in design parameters, ascent flight conditions, gusts. The primary focus is on the uncertainty introduced by modeling fidelity. It is found that an unsteady reduced order model produces larger excursions in the root mean square loading and accelerations than does a quasi-steady reduced order model.

Bartels, Robert E.↗

NASA NTRS1994

Adaptive model reduction for continuous systems via recursive rational interpolation

A method for adaptive identification of reduced-order models for continuous stable SISO and MIMO plants is presented. The method recursively finds a model whose transfer function (matrix) matches that of the plant on a set of frequencies chosen by the designer. The algorithm utilizes the Moving Discrete Fourier Transform (MDFT) to continuously monitor the frequency-domain profile of the system input and output signals. The MDFT is an efficient method of monitoring discrete points in the frequency domain of an evolving function of time. The model parameters are estimated from MDFT data using standard recursive parameter estimation techniques. The algorithm has been shown in simulations to be quite robust to additive noise in the inputs and outputs. A significant advantage of the method is that it enables a type of on-line model validation. This is accomplished by simultaneously identifying a number of models and comparing each with the plant in the frequency domain. Simulations of the method applied to an 8th-order SISO plant and a 10-state 2-input 2-output plant are presented. An example of on-line model validation applied to the SISO plant is also presented.

Lilly, John H.↗