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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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All sourcesNASA NTRSDOE OSTI
DOE OSTI2017

Model Order Reduction Algorithm for Estimating the Absorption Spectrum

The ab initio description of the spectral interior of the absorption spectrum poses both a theoretical and computational challenge for modern electronic structure theory. Due to the often spectrally dense character of this domain in the quantum propagator’s eigenspectrum for medium-to-large sized systems, traditional approaches based on the partial diagonalization of the propagator often encounter oscillatory and stagnating convergence. Electronic structure methods which solve the molecular response problem through the solution of spectrally shifted linear systems, such as the complex polarization propagator, offer an alternative approach which is agnostic to the underlying spectral density or domain location. This generality comes at a seemingly high computational cost associated with solving a large linear system for each spectral shift in some discretization of the spectral domain of interest. In this work, we present a novel, adaptive solution to this high computational overhead based on model order reduction techniques via interpolation. Model order reduction reduces the computational complexity of mathematical models and is ubiquitous in the simulation of dynamical systems and control theory. The efficiency and effectiveness of the proposed algorithm in the ab initio prediction of X-ray absorption spectra is demonstrated using a test set of challenging water clusters which are spectrally dense in the neighborhood of the oxygen K-edge. On the basis of a single, user defined tolerance we automatically determine the order of the reduced models and approximate the absorption spectrum up to the given tolerance. We also illustrate that, for the systems studied, the automatically determined model order increases logarithmically with the problem dimension, compared to a linear increase of the number of eigenvalues within the energy window. Furthermore, we observed that the computational cost of the proposed algorithm only scales quadratically with respect to the problem dimension.

IDREAM, K-Edge, theoretical, computational, electr↗
NASA NTRS2016

Model Order Reduction of Aeroservoelastic Model of Flexible Aircraft

This paper presents a holistic model order reduction (MOR) methodology and framework that integrates key technological elements of sequential model reduction, consistent model representation, and model interpolation for constructing high-quality linear parameter-varying (LPV) aeroservoelastic (ASE) reduced order models (ROMs) of flexible aircraft. The sequential MOR encapsulates a suite of reduction techniques, such as truncation and residualization, modal reduction, and balanced realization and truncation to achieve optimal ROMs at grid points across the flight envelope. The consistence in state representation among local ROMs is obtained by the novel method of common subspace reprojection. Model interpolation is then exploited to stitch ROMs at grid points to build a global LPV ASE ROM feasible to arbitrary flight condition. The MOR method is applied to the X-56A MUTT vehicle with flexible wing being tested at NASA/AFRC for flutter suppression and gust load alleviation. Our studies demonstrated that relative to the fullorder model, our X-56A ROM can accurately and reliably capture vehicles dynamics at various flight conditions in the target frequency regime while the number of states in ROM can be reduced by 10X (from 180 to 19), and hence, holds great promise for robust ASE controller synthesis and novel vehicle design.

aeroelasticity↗
DOE OSTI2020

SNS: A Solution-Based Nonlinear Subspace Method for Time-Dependent Model Order Reduction

Several reduced order models have been successfully developed for nonlinear dynamical systems. To achieve a considerable speed-up, a hyper-reduction step is needed to reduce the computational complexity due to nonlinear terms. Many hyper-reduction techniques require the construction of nonlinear term basis, which introduces a computationally expensive offline phase. A novel way of constructing nonlinear term basis within the hyper-reduction process is introduced. In contrast to the traditional hyper-reduction techniques where the collection of nonlinear term snapshots is required, the SNS method avoids collecting the nonlinear term snapshots. Instead, it uses the solution snapshots that are used for building a solution basis, which enables avoiding an extra data compression of nonlinear term snapshots. As a result, the SNS method provides a more efficient offline strategy than the traditional model order reduction techniques, such as the DEIM, GNAT, and ST-GNAT methods. The SNS method is theoretically justified by the conforming subspace condition and the subspace inclusion relation. It is useful for model order reduction of large-scale nonlinear dynamical problems to reduce the offline cost. It is especially useful for ST-GNAT that has shown promising results, such as a good accuracy with a considerable online speed-up for hyperbolic problems in a recent paper by Choi and Carlberg [SIAM J. Sci. Comput., 41 (2019), pp. A26--A58], because ST-GNAT involves an expensive offline cost related to collecting nonlinear term snapshots. Error analysis for the SNS method is presented. Numerical results support that the accuracy of the solution from the SNS method is comparable to the traditional methods and a considerable speed-up (i.e., a factor of two to a hundred) is achieved in the offline phase.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Affine Approximation of Parametrized Kernels and Model Order Reduction for Nonlocal and Fractional Laplace Models

In this work, we consider parametrized problems driven by spatially nonlocal integral operators with parameter-dependent kernels. In particular, kernels with varying nonlocal interaction radius $\delta > 0$ and fractional Laplace kernels, parametrized by the fractional power $s\in(0,1)$, are studied. Furthermore, in order to provide an efficient and reliable approximation of the solution for different values of the parameters, we develop the reduced basis method as a parametric model order reduction approach. Major difficulties arise since the kernels are not affine in the parameters, singular, and discontinuous. Moreover, the spatial regularity of the solutions depends on the varying fractional power $s$. To address this, we derive regularity and differentiability results with respect to $\delta$ and $s$, which are of independent interest for other applications such as optimization and parameter identification. We then use these results to construct affine approximations of the kernels by local polynomials. Finally, we certify the method by providing reliable a posteriori error estimators, which account for all approximation errors, and support the theoretical findings by numerical experiments.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

Model Order Reduction of Nonviscously Damped Structural Dynamic Models

A reduced order modeling capability has been developed to reduce the computational burden associated with time-domain solutions of structural dynamic models with linear viscoelastic materials. The discretized equations-of-motion produce convolution integrals resulting in a linear system with nonviscous damping forces. The challenge associated with the reduction of nonviscously damped, linear systems is the selection and computation of the appropriate modal basis to perform modal projection. The system produces a nonlinear eigenvalue problem that is challenging to solve and requires use of specialized algorithms not readily available in commercial finite element packages. This SAND report summarizes the LDRD discoveries of a reduction scheme developed for monolithic finite element models and provides preliminary investigations to extensions of the method using component mode synthesis. In addition, this report provides a background overview of structural dynamic modeling of structures with linear viscoelastic materials, and provides an overview of a new code capability in Sierra Structural Dynamics to output the system level matrices computed on multiple processors.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2011

Automatic Black-Box Model Order Reduction using Radial Basis Functions

Finite elements methods have long made use of model order reduction (MOR), particularly in the context of fast freqeucny sweeps. In this paper, we discuss a black-box MOR technique, applicable to a many solution methods and not restricted only to spectral responses. We also discuss automated methods for generating a reduced order model that meets a given error tolerance. Numerical examples demonstrate the effectiveness and wide applicability of the method. With the advent of improved computing hardware and numerous fast solution techniques, the field of computational electromagnetics are progressed rapidly in terms of the size and complexity of problems that can be solved. Numerous applications, however, require the solution of a problem for many different configurations, including optimization, parameter exploration, and uncertainly quantification, where the parameters that may be changed include frequency, material properties, geometric dimensions, etc. In such cases, thousands of solutions may be needed, so solve times of even a few minutes can be burdensome. Model order reduction (MOR) may alleviate this difficulty by creating a small model that can be evaluated quickly. Many MOR techniques have been applied to electromagnetic problems over the past few decades, particularly in the context of fast frequency sweeps. Recent works have extended these methods to allow more than one parameter and to allow the parameters to represent material and geometric properties. There are still limitations with these methods, however. First, they almost always assume that the finite element method is used to solve the problem, so that the system matrix is a known function of the parameters. Second, although some authors have presented adaptive methods (e.g., [2]), the order of the model is often determined before the MOR process begins, with little insight about what order is actually needed to reach the desired accuracy. Finally, it not clear how to efficiently extend most methods to the multiparameter case. This paper address the above shortcomings be developing a method that uses a block-box approach to the solution method, is adaptive, and is easily extensible to many parameters.

42 ENGINEERING↗
NASA NTRS2017

Genetic Algorithm-Guided, Adaptive Model Order Reduction of Flexible Aircrafts

This paper presents a methodology for automated model order reduction (MOR) of flexible aircrafts to construct linear parameter-varying (LPV) reduced order models (ROM) for aeroservoelasticity (ASE) analysis and control synthesis in broad flight parameter space. The novelty includes utilization of genetic algorithms (GAs) to automatically determine the states for reduction while minimizing the trial-and-error process and heuristics requirement to perform MOR; balanced truncation for unstable systems to achieve locally optimal realization of the full model; congruence transformation for "weak" fulfillment of state consistency across the entire flight parameter space; and ROM interpolation based on adaptive grid refinement to generate a globally functional LPV ASE ROM. The methodology is applied to the X-56A MUTT model currently being tested at NASA/AFRC for flutter suppression and gust load alleviation. Our studies indicate that X-56A ROM with less than one-seventh the number of states relative to the original model is able to accurately predict system response among all input-output channels for pitch, roll, and ASE control at various flight conditions. The GA-guided approach exceeds manual and empirical state selection in terms of efficiency and accuracy. The adaptive refinement allows selective addition of the grid points in the parameter space where flight dynamics varies dramatically to enhance interpolation accuracy without over-burdening controller synthesis and onboard memory efforts downstream. The present MOR framework can be used by control engineers for robust ASE controller synthesis and novel vehicle design.

Numerical Analysi↗
NASA NTRS1989

Multivariable frequency weighted model order reduction for control synthesis

Quantitative criteria are presented for model simplification, or order reduction, such that the reduced order model may be used to synthesize and evaluate a control law, and the stability robustness obtained using the reduced order model will be preserved when controlling the full-order system. The error introduced due to model simplification is treated as modeling uncertainty, and some of the results from multivariate robustness theory are brought to bear on the model simplification problem. A numerical procedure developed previously is shown to lead to results that meet the necessary criteria. The procedure is applied to reduce the model of a flexible aircraft. Also, the importance of the control law itself, in meeting the modeling criteria, is underscored. An example is included that demonstrates that an apparently robust control law actually amplifies modest modeling errors in the critical frequency region, and leads to undesirable results. The cause of this problem is associated with the canceling of lightly damped transmission zeroes in the plant. An attempt is made to expand on some of the earlier results and to further clarify the theoretical basis behind the proposed methodology.

Schmidt, David K.↗
DOE OSTI2023

Control oriented model order reduction for the hydraulic system of an autonomous wheel loader

Control design for an autonomous wheel loader requires a high-fidelity and low-order dynamics model. The objective of order reduction is to decrease the number of states in the model while maintaining performance comparable to the original model. Of all the power components in a wheel loader, the model order reduction for steering and working hydraulic systems is most demanding due to its nonlinear and stiff dynamical nature. This paper describes a physics-inspired model order reduction method that can reduce the model order by close to thirty percent. It is achieved by discarding orders with fast dynamics and consolidating multiple states into less new states. Furthermore, this method can also be extended to other types of off-road vehicles such as excavators, bulldozers, etc. Simulation results demonstrate that the reduced-order model exhibits very similar performance to the full-order model under typical operating conditions of wheel loaders, with an output error of less than six percent.

42 ENGINEERING↗
DOE OSTI2021

Evaluation of pressure reconstruction techniques for Model Order Reduction in incompressible convective heat transfer

This paper compares pressure reconstruction strategies in Model Order Reduction for incompressible flows with convective heat transfer. The Navier-Stokes equation are reduced along with the passive scalar transport equation for the temperature using the POD-Galerkin technique. Six different pressure reconstruction methods are evaluated, two of which are novel to the best of the authors’ knowledge. Accurate pressure reconstruction is key to avoid error buildup in when solving for the conservation of linear momentum at the reduced level. The six approaches are compared using Direct Numerical Simulations of convective heat exchange processes in a 3D Backward Facing Step with a heated cylinder. Additionally, when comparing time-averaged metrics, we observe that the reconstruction methods that approximate the reduced pressure field using techniques borrowed from full order models (mechanical analogy, pressure Poisson, and velocity supremizers) yield higher errors than the methods that seek to stabilize the reduced systems (reduced residual stabilization, artificial divergence, and Uzawa operator).

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
NASA NTRS1989

Component mode synthesis for model order reduction of nonclassically damped systems

Based on a component mode synthesis approach, a model-order-reduction method for linear structures with arbitrary linear damping has been developed. Projection matrices are introduced to make the method applicable to systems having rigid-body freedom. To test the method, eigenvalues of a reduced-order model of a free-free beam with nonproportional damping were compared to exact eigenvalues and to eigenvalues obtained using two other model-reduction strategies. The present model-reduction strategy proved to be decidedly superior.

Craig, Roy R., Jr.↗
DOE OSTI2022

Parametric model-order-reduction development for unsteady convection

A time-averaged error indicator with POD- h Greedy is developed to drive parametric model order reduction (pMOR) for 2D unsteady natural convection in a high-aspect ratio slot parameterized with the Prandtl number, Rayleigh number, and slot angle with respect to the gravity. The error indicator is extended to accommodate the energy equation and Leray regularization. Despite being two-dimensional and laminar, the target flow regime presents several challenges: 1) there is a bifurcation in the angle parameter space; 2) the solution can be multivalued, even at steady state; and 3) the solution exhibits spatio-temporal chaos at several points in the parameter space. The authors explore several reduced-order models (ROMs) and demonstrate that Leray-regularized Galerkin ROMs provide a robust solution approach for this class of flows. They further demonstrate that error-indicated pMOR can efficiently predict several QOIs, such as mean flow, mean Nusselt number and mean turbulent kinetic energy, even in the presence of a bifurcation. Finally, they show that spatio-temporal chaos can lead to lack of reproducibility in both the full-order model and the reduced-order model and that the variance in the full-order model provides a lower bound on the pMOR error in these cases.

leray regularization↗
DOE OSTI2016

Adaptive model order reduction for the Jacobian calculation in inverse multi-frequency problem for Maxwell's equations

Here this work develops a model order reduction method for a numerical solution of an inverse multi-frequency eddy current problem using a rational interpolation of the transfer function in the complex plane. We use the Pade interpolation in the complex frequency plane; this allows us to speed up the calculation of the frequency-dependent Jacobian in the inversion procedure without loosing accuracy. Interpolating frequencies are chosen adaptively to reduce the maximal approximation error. We use the error indicator that is equivalent to a seminorm of the residual. The efficiency of the developed approach is demonstrated by applying it to the inverse magnetotelluric problem, which is a geophysical electromagnetic remote sensing method used in mineral, geothermal, and groundwater exploration. In this application, the transfer function values are needed for shifts in a purely imaginary interval. Thus we consider the interpolating shifts in the same interval as well as in a purely real interval, containing the spectrum of the operator. Numerical tests show an excellent performance of the proposed methods characterized by a significant reduction of computational time without loss of accuracy of the calculated Jacobian.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Accelerating structural dynamics simulations with localised phenomena through matrix compression and projection‐based model order reduction

In this work, a novel approach is introduced for accelerating the solution of structural dynamics problems in the presence of localised phenomena, such as cracks. For this category of problems, conventional projection-based Model Order Reduction (MOR) methods are either limited with respect to the range of system configurations that can be represented or require frequent solutions of the Full Order Model (FOM) to update the low-dimensional spaces, in which solutions are represented. In the proposed approach, low-dimensional spaces, constructed for the healthy structure, are enriched with appropriately selected columns of the flexibility matrix of the system. It can be shown that these spaces contain the solution to the original problem for the static case, while their dimension is much smaller. In order to allow their online construction for arbitrary localised features, the full flexibility matrix of the system should be available. To this end, a hierarchical representation is used for the matrices involved, allowing to compute the flexibility matrix efficiently and with reduced memory requirements. The resulting method offers significant speedups, without sacrificing the flexibility and accuracy of the full order model. The performance and limitations of the approach are studied through a series of examples in structural dynamics.

fracture mechanics↗
DOE OSTI2024

CI-MOR Final Report: Analysis and Validation of Critical Infrastructure Models using Model Order Reduction

This report summarizes the research and capabilities developed as part of the project “Analysis and Validation of Critical Infrastructure Models using Model Order Reduction” (CI-MOR) LDRD project. CI-MOR research enables the solution of large, complex optimization models that naturally arise in national security challenges involving critical infrastructures. Specifically, CI-MOR researchers developed methods to (1) rigorously approximate complex, nonlinear optimization formulations, (2) identify alternative near-optimal solutions, (3) accelerate optimization workflows used for complex applications, and (4) rigorously integrate domain knowledge in stochastic-process models. This report provides an overview of the research done in CI-MOR, and we describe application exemplars used to illustrate CI-MOR capabilities. Furthermore, we describe the software developed by CI-MOR that researchers can leverage to analyze new applications.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Machine learning for nonintrusive model order reduction of the parametric inviscid transonic flow past an airfoil

Fluid flow in the transonic regime finds relevance in aerospace engineering, particularly in the design of commercial air transportation vehicles. Computational fluid dynamics models of transonic flow for aerospace applications are computationally expensive to solve because of the high degrees of freedom as well as the coupled nature of the conservation laws. While these issues pose a bottleneck for the use of such models in aerospace design, computational costs can be significantly minimized by constructing special, structure-preserving surrogate models called reduced-order models. In this work, we propose a machine learning method to construct reduced-order models via deep neural networks and we demonstrate its ability to preserve accuracy with a significantly lower computational cost. In addition, our machine learning methodology is physics-informed and constrained through the utilization of an interpretable encoding by way of proper orthogonal decomposition. Application to the inviscid transonic flow past the RAE2822 airfoil under varying freestream Mach numbers and angles of attack, as well as airfoil shape parameters with a deforming mesh, shows that the proposed approach adapts to high-dimensional parameter variation well. Notably, the proposed framework precludes the knowledge of numerical operators utilized in the data generation phase, thereby demonstrating its potential utility in the fast exploration of design space for diverse engineering applications. Comparison against a projection-based nonintrusive model order reduction method demonstrates that the proposed approach produces comparable accuracy and yet is orders of magnitude computationally cheap to evaluate, despite being agnostic to the physics of the problem.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2015

An approximate framework for quantum transport calculation with model order reduction

A new approximate computational framework is proposed for computing the non-equilibrium charge density in the context of the non-equilibrium Green's function (NEGF) method for quantum mechanical transport problems. The framework consists of a new formulation, called the X-formulation, for single-energy density calculation based on the solution of sparse linear systems, and a projection-based nonlinear model order reduction (MOR) approach to address the large number of energy points required for large applied biases. The advantages of the new methods are confirmed by numerical experiments.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗