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At least 613 records · Page 34
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Development of Segregated Thermal-Hydraulics Solvers in MOOSE

The simulation of fluid flows is an essential part of the design and analysis of nuclear systems. Algorithms able to simulate flows at different fidelity levels are available in the Multiphysics Object-Oriented Simulation Environment (MOOSE) and MOOSE-based applications such as Pronghorn \cite{novak2018pronghorn}, Pronghorn-Subchannel, RELAP-7, and SAM. Currently, significant effort is being invested in the development of coarse-mesh Computational Fluid Dynamics (CFD) capabilities within MOOSE and Pronghorn for the simulation of Generation IV nuclear reactors. Traditionally, the solution algorithms in MOOSE have relied on Newton or quasi-Newton methods (such as the preconditioned Jacobian-free Newton-Krylov method) where residuals and Jacobians (or approximations thereof) are constructed. Both Newton and quasi-Newton methods require the solution of a linear system at each nonlinear Newton iteration with the Jacobian as the system matrix. The Jacobian contains blocks originating from all variables in the problem (i.e., for thermal-hydraulics at least pressure, velocities, and temperature). Due to the formulation of the problem in a general multiphysics setting on unstructured mesh, creating a good preconditioner for the linear system can be challenging, thus many fluid applications have utilized direct solver-based methods such as LU factorization. However, with increasing system size and complexity in multi-dimensional problems, the direct solution of linear systems becomes computationally expensive both in execution time and and memory. For this reason, recent effort has focused on adapting segregated solution algorithms for CFD problems in MOOSE. These algorithms use fixed-point iteration between segregated systems whose assembly and preconditioning are easier those of the monolithic system. Initial results show that the segregated solution algorithm outperforms the monolithic approach in terms of memory usage and for large 3D problems in terms of CPU time as well.

42 ENGINEERING↗
DOE OSTI2016

The value of continuity: Refined isogeometric analysis and fast direct solvers

Here, we propose the use of highly continuous finite element spaces interconnected with low continuity hyperplanes to maximize the performance of direct solvers. Starting from a highly continuous Isogeometric Analysis (IGA) discretization, we introduce C0-separators to reduce the interconnection between degrees of freedom in the mesh. By doing so, both the solution time and best approximation errors are simultaneously improved. We call the resulting method “refined Isogeometric Analysis (rIGA)”. To illustrate the impact of the continuity reduction, we analyze the number of Floating Point Operations (FLOPs), computational times, and memory required to solve the linear system obtained by discretizing the Laplace problem with structured meshes and uniform polynomial orders. Theoretical estimates demonstrate that an optimal continuity reduction may decrease the total computational time by a factor between p 2 and p 3 , with pp being the polynomial order of the discretization. Numerical results indicate that our proposed refined isogeometric analysis delivers a speed-up factor proportional to p 2 . In a 2D mesh with four million elements and p=5, the linear system resulting from rIGA is solved 22 times faster than the one from highly continuous IGA. In a 3D mesh with one million elements and p=3, the linear system is solved 15 times faster for the refined than the maximum continuity isogeometric analysis.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

Representation of Solutions of Systems of Linear Differential Equations with Multiple Delays and Linear Parts Given by Nonpermutable Matrices

In recent results on representation of the solutions of systems of delayed differential equations, the condition that the linear parts are given by pairwise permutable matrices was assumed. We show how this strong condition can be avoided and derive a representation of solutions of systems of differential equations with nonconstant coefficients and variable delays. The results are applied to a system with two constant delays. In addition, the nonexistence of blow-up solutions is proved for nonlinear systems.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Predicting Flow in Fracture Networks With Quantum Algorithms

Uncertainty quantification plays a crucial role in the modeling of subsurface flow. For instance, uncertainties in the properties of geologic fracture networks significantly impact flow, requiring numerous simulations to accurately estimate quantities of interest. However, each simulation is computationally expensive because it requires solving a large linear system to capture features that involve both small and large fractures. An example is in percolation, where the interaction of many small fractures (which cumulatively can have a large surface area) with the rock matrix must be modeled precisely. Quantum computing is an emerging tool with the potential to address this issue. Quantum algorithms offer a significant speedup in solving linear systems, achieving efficiencies that are challenging to match with classical approaches. These classical approaches include direct solvers, such as LU decomposition, and iterative methods, notably preconditioned conjugate gradient, commonly used in subsurface modeling to solve large sparse systems. However, applying quantum algorithms to geologic fracture flow requires careful attention to algorithmic and problem-specific constraints to fully realize this quantum advantage. In this work we describe a quantum algorithm for generalized Monte Carlo applications with a quadratic speedup over the classical approaches which can be combined with the quantum speedup, currently under investigation, for solving quantum linear systems for subsurface flow. We show that for quantum algorithms the computational cost of estimating a quantity of interest for a statistical ensemble of networks is roughly the same as that of a single realization, essentially implying that one can get uncertainty quantification for free.

58 GEOSCIENCES↗
DOE OSTI2023

Sensor Anomaly Detection for Nuclear Reactor Systems Utilizing Linear Regression and K-Means Unsupervised Machine Learning

Nuclear reactors and related systems are becoming increasingly complex due to advancing technologies in next-generation power reactors. This increased complexity necessitates enhanced automation and data management capabilities. To successfully realize autonomous systems, methods must be developed to handle vast volumes of data and effectively distinguish anomalous data from noise and expected data. While impressive models utilizing digital twins and similar approaches are under development, here we propose a simplified model for analyzing fundamental methods and techniques. Initially, we created a general dataset by using initial data from PCTRAN in order to represent ideal steady-state conditions. We then inserted anomalies based on prevalent sensor anomaly types (e.g., point anomalies, linear drift, and downward deviations), along with unusual anomalies such as exponential drift and upward deviations. To detect anomalies, we developed a program that employs data partitioning and linear regression to preprocess and filter the anomalous data. A K-Means machine learning (ML) method was then applied to separate and count the data within the anomalous partition. The results from all datasets—apart from exponential growth—demonstrated positive outcomes, with each returning multiple instances of greaterthan-95% accuracy. We conducted further investigations using Idaho National Laboratory’s RAVEN software to perform a sensitivity analysis on the input variables (R 2 Tolerance, Slope Tolerance, and Window Size) and found that the output variables (Accuracy and Time) were most sensitive to the Window Size. Despite the promising results published, further development is required to effectively apply these methods to nuclear systems. Nevertheless, the strengths of this approach are evident and hold promise for future applications in the field.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
NASA NTRS1974

Discretized partial differential equations - Examples of control systems defined on modules

The purpose of this paper is to show how the important problems of linear system theory can be solved concisely for a particular class of linear systems, namely block circulant systems, by exploiting the algebraic structure. This type of system arises in lumped approximations to linear partial differential equations. The computation of the transition matrix, the variation of constants formula, observability, controllability, pole allocation, realization theory, stability and quadratic optimal control are discussed. In principle, all questions which are solved here could also be solved by standard methods; the present paper clearly exposes the structure of the solution, and thus permits various savings in computational effort.

Brockett, R. W.↗
DOE OSTI2014

A semi-local spectral/hp element solver for linear elasticity problems:

We develop an efficient semi-local method for speeding up the solution of linear systems arising in spectral/hp element discretization of the linear elasticity equations. The main idea is to approximate the element-wise residual distribution with a localization operator we introduce in this paper, and subsequently solve the local linear system. Additionally, we decouple the three directions of displacement in the localization operator, hence enabling the use of an efficient low energy preconditioner for the conjugate gradient solver. This approach is effective for both nodal and modal bases in the spectral/hp element method, but here, we focus on the modal hierarchical basis. In numerical tests, we verify that there is no loss of accuracy in the semi-local method, and we obtain good parallel scalability and substantial speed-up compared to the original formulation. In particular, our tests include both structure-only and fluid-structure interaction problems, with the latter modeling a 3D patient-specific brain aneurysm. Copyright © 2014 John Wiley & Sons, Ltd.

Engineering↗
DOE OSTI2014

Self-consistent field theory based molecular dynamics with linear system-size scaling

We present an improved field-theoretic approach to the grand-canonical potential suitable for linear scaling molecular dynamics simulations using forces from self-consistent electronic structure calculations. It is based on an exact decomposition of the grand canonical potential for independent fermions and does neither rely on the ability to localize the orbitals nor that the Hamilton operator is well-conditioned. Hence, this scheme enables highly accurate all-electron linear scaling calculations even for metallic systems. The inherent energy drift of Born-Oppenheimer molecular dynamics simulations, arising from an incomplete convergence of the self-consistent field cycle, is circumvented by means of a properly modified Langevin equation. The predictive power of the present approach is illustrated using the example of liquid methane under extreme conditions.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2018

Synchronization of Coupled Dynamical Systems: Tolerance to Weak Connectivity and Arbitrarily Bounded Time-Varying Delays

We study synchronization of coupled linear systems over networks with weak connectivity and time-varying delays. We focus on the case that the internal dynamics are time-varying but non-expansive. Both uniformly connected and infinitely connected communication topologies are considered. A new concept of P-synchronization is introduced and we first show that global asymptotic P-synchronization can be achieved over directed networks with uniform joint connectivity and arbitrarily bounded delays. We then study the case of the infinitely jointly connected communication topology. In particular, for the undirected communication topologies, it turns out that the existence of a uniform time interval for the communication topology is not necessary and P-synchronization can be achieved when the time varying delays are arbitrarily bounded. Simulations are given to validate the theoretical results.

Linear time-varying system, Synchronization, Switc↗
NASA NTRS1999

A Critical Examination of Wind-Wave Spectral Functional Form

Traditionally, data from random ocean waves are presented in spectral functions. The spectra are the result of Fourier analysis. Fourier spectral analysis has dominated data analysis for, at least, the last hundred years. It has been the standard method for is examining the global amplitude-frequency distributions. Although Fourier transform valid under extremely general conditions, there are some crucial restrictions for the Fourier spectral analysis. The system must be linear, and the data must be stationary- otherwise, the resulting spectrum will make little physical sense. The stationarity requirement is also a common required criterion for most of other available data analysis methods. Nevertheless, few, if any, natural phenomena are linear and stationary. To compound these complications is the imperfection of our probes or numerical schemes the interactions of the imperfect probes even with a perfect linear system can make the final data nonlinear. Furthermore, all the available data are usually of finite duration. Under these conditions, Fourier analysis is of limited use, For lack of alternatives, however, Fourier analysis is still used to process such data. The loose application of Fourier analysis and the insouciant adoption of the stationary and linear assumptions may lead to misleading conclusions. Ocean waves are know to be nonlinear, and the wind system generating the wave field are seldom stationary- As a result, the traditional examination of the spectral form hardly made physical sense. A new method for analyzing nonlinear and nonstationary data has been developed. The key part is the Empirical Mode Decomposition (EMD) method with which any complicated data set can be decomposed into a finite and often small number of Intrinsic Mode Functions (IMF) that serve as the basis of the representation of the data, This decomposition method is adaptive, and, therefore, highly efficient. The IMFs admit well-behaved Hilbert transforms, and yield instantaneous energy and frequency as functions of time that give sharp identifications of imbedded structures. The final presentation of the results is an energy-frequency-time distribution, designated as the Hilbert Spectrum. Among the main conceptual innovations is the introduction of the instantaneous frequencies for complicated data sets, which eliminate the need of spurious harmonics to represent nonlinear and nonstationary signals. The spectral forms of the ocean waves are very different. This new method offers the first physical meaningful view of the wave spectrum. Data from laboratory and field will be presented to illustrate the differences.

Huang, Norden E.↗
NASA NTRS1972

On the determination of optimal costly measurement strategies for linear stochastic systems.

This paper presents the formulation of a class of optimization problems dealing with selecting, at each instant of time, one measurement provided by one out of many sensors. Each measurement has an associated measurement cost. The basic problem is then to select an optimal measurement policy, during a specified observation time interval, so that a weighted combination of prediction accuracy and accumulated observation cost is optimized. The current analysis is limited to the class of linear stochastic dynamic systems and measurement subsystems. The problem of selecting the optimal measurement strategy can be transformed into a deterministic optimal control problem. It is shown that the optimal measurement policy and the associated matched Kalman-type filter can be precomputed.

Athans, M.↗
DOE OSTI2022

Preconditioned least‐squares Petrov–Galerkin reduced order models

Abstract In this article, we introduce a methodology for improving the accuracy and efficiency of reduced order models (ROMs) constructed using the least‐squares Petrov–Galerkin (LSPG) projection method through the introduction of preconditioning. Unlike prior related work, which focuses on preconditioning the linear systems arising within the ROM numerical solution procedure to improve linear solver performance, our approach leverages a preconditioning matrix directly within the minimization problem underlying the LSPG formulation. Applying preconditioning in this way has the potential to improve ROM accuracy for several reasons. First, preconditioning the LSPG formulation changes the norm defining the residual minimization, which can improve the residual‐based stability constant bounding the ROM solution's error. The incorporation of a preconditioner into the LSPG formulation can have the additional effect of scaling the components of the residual being minimized to make them roughly of the same magnitude, which can be beneficial when applying the LSPG method to problems with disparate scales (e.g., dimensional equations, multi‐physics problems). Importantly, we demonstrate that an “ideal preconditioned” LSPG ROM (a ROM in which the preconditioner is the inverse of the Jacobian of its corresponding full order model) emulates projection of the full order model solution increment onto the reduced basis. This quantity defines a lower bound on the error of a ROM solution for a given reduced basis. By designing preconditioners that approximate the Jacobian inverse—as is common in designing preconditioners for solving linear systems—it is possible to obtain a ROM whose error approaches this lower bound. The proposed approach is evaluated on several mechanical and thermo‐mechanical problems implemented within the Albany HPC code and run in the predictive regime, with prediction across material parameter space. We demonstrate numerically that the introduction of simple Jacobi, Gauss‐Seidel, and ILU preconditioners into the proper orthogonal decomposition/LSPG formulation reduces significantly the ROM solution error, the reduced Jacobian condition number, the number of nonlinear iterations required to reach convergence, and the wall time (thereby improving efficiency). Moreover, our numerical results reveal that the introduction of preconditioning can deliver a robust and accurate solution for test cases in which the unpreconditioned LSPG method fails to converge.

Lindsay, Payton↗
NASA NTRS1962

A REPORT ON THREE SERIES OF EXPERIMENTS AND THE DESCRIPTION OF A SIMPLIFIED MODEL OF THE THIN WALL CYLINDER AND CONE BUCKLING MECHANISM

Three series of experiments were performed to investigate the nature of the buckling phenomenon. They were: a) influence of an increasing dimple on the buckling load of a cylinder; b) investigation of the strain distribution on one cylinder, after one or more waves were imposed on it; c) measurements of lateral deflections at buckling. The results of such experiments give some support to the idea of a buckling model, which can be of eventual interest to the thin wall cylinder and cone buckling problem, where a non-linear system (the buckled band) is considered in series with a linear system (the unbuckled portion of the cylinder, plus the testing-machine )

CYLINDER↗
NASA NTRS1989

Robust control design for aerospace applications

Time-domain control design for stability robustness of linear systems with structured uncertainty is addressed. Upper bounds on the linear perturbation of an asymptotically stable linear system are obtained, making it possible to maintain stability by using the structural information of the uncertainty. A quantitative measure called the stability robustness index is introduced and used to design controllers for robust stability. The proposed state feedback control design algorithm can be used, for a given set of perturbations, to select the range of control effort for which the system is stability-robust. Conversely it can be used, for a given control effort, to determine the size of the tolerable perturbation. The algorithm is illustrated with examples from aircraft control and large-space-structure control problems.

Yedavalli, Rama K.↗
NASA NTRS1983

Linear approximations of nonlinear systems

The development of a method for designing an automatic flight controller for short and vertical take off aircraft is discussed. This technique involves transformations of nonlinear systems to controllable linear systems and takes into account the nonlinearities of the aircraft. In general, the transformations cannot always be given in closed form. Using partial differential equations, an approximate linear system called the modified tangent model was introduced. A linear transformation of this tangent model to Brunovsky canonical form can be constructed, and from this the linear part (about a state space point x sub 0) of an exact transformation for the nonlinear system can be found. It is shown that a canonical expansion in Lie brackets about the point x sub 0 yields the same modified tangent model.

Hunt, L. R.↗