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At least 289 records · Page 16
All sourcesNASA NTRSDOE OSTI
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↗
NASA NTRS1993

Reduction of Model Complexity by Active Control

The mathematical models of many dynamic systems of interest in the aerospace industry are inherently complex and of high order. Rather than grapple with the full-complexity models for such systems, the control designers often elect to derive low-order, reduced-complexity models for which a control system can be designed. The subject of model-order reduction has received a significant amount of attention in control engineering literature. This paper describes and demonstrates a novel active-control methodology that can be used to design a control system that automatically forces the original system to behave like a chosen reduced-complexity model by treating the effects of the original complexity-related terms as disturbances acting on the reduced-complexity system. The method is demonstrated by several worked examples involving both linear and nonlinear systems, supported by simulation results.

Bukley, Angelia P.↗
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 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↗
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.↗
NASA NTRS1991

Model order reduction applied to a hot-bench simulation of an aeroelastic wind-tunnel model

Simulations of an aeroelastically scaled wind-tunnel model were developed for hot-bench testing of a digital controller. The digital controller provided active flutter-suppression, rolling-maneuver-load alleviation, and plant estimation. To achieve an acceptable time scale for the hot-bench application, the mathematical model of the wind-tunnel model was reduced from 220 states to approximately 130 states while assuring that the required accuracy was preserved for all combinations of 10 inputs and 56 outputs. The reduction was achieved by focussing on a linear, aeroelastic submodel of the full mathematical model and by applying a method based on the internally balanced realization of a dynamic system. The error-bound properties of the internally balanced realization significantly contribute to its utility in the model reduction process. The reduction method and the results achieved are described.

Buttrill, Carey S.↗
DOE OSTI2023

DRIPS: A framework for dimension reduction and interpolation in parameter space

Reduced-order models are often used to describe the behavior of complex systems, whose simulation with a full model is too expensive, or to extract salient features from the full model’s output. We introduce a new model-reduction framework DRIPS (dimension reduction and interpolation in parameter space) that combines the offline local model reduction with the online parameter interpolation of reduced-order bases (ROBs). The offline step of this framework relies on dynamic mode decomposition (DMD) to build a low-rank linear surrogate model, equipped with a local ROB, for quantities of interest derived from the training data generated by repeatedly solving the (nonlinear) high-fidelity model for multiple parameter points. The online step consists of the construction of a parametric reduced-order model for each target/test point in the parameter space, with the interpolation of ROBs done on a Grassman manifold and the interpolation of reduced-order operators done on a matrix manifold. The DMD component enables DRIPS to model (typically low-dimensional) quantities of interest directly, without having to access the (typically high-dimensional and possibly nonlinear) operators in a high-fidelity model that governs the dynamics of the underlying high-dimensional state variables, as required in projection-based reduced-order modeling. A series of numerical experiments suggests that DRIPS yields a model reduction, which is computationally more efficient than the commonly used projection-based proper orthogonal decomposition; it does so without requiring a prior knowledge of the governing equation for quantities of interest. Furthermore, for the nonlinear systems considered, DRIPS is more accurate than Gaussian-process interpolation (Kriging).

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2020

Sampling Low-Dimensional Markovian Dynamics for Preasymptotically Recovering Reduced Models from Data with Operator Inference

This work introduces a method for learning low-dimensional models from data of high-dimensional black-box dynamical systems. The novelty is that the learned models are exactly the reduced models that are traditionally constructed with classical projection-based model reduction techniques. Thus, the proposed approach learns models that are guaranteed to have the well-studied properties of reduced models known from model reduction, without requiring full knowledge of the governing equations and without requiring the operators of the high-dimensional systems. The key ingredient is a new data sampling scheme to obtain re-projected trajectories of high-dimensional systems that correspond to Markovian dynamics in low-dimensional subspaces. The exact recovery of reduced models from these re-projected trajectories is guaranteed pre-asymptotically under certain conditions for finite amounts of data and for a large class of systems with polynomial nonlinear terms. Numerical results demonstrate that the low-dimensional models learned with the proposed approach match reduced models from traditional model reduction up to numerical errors in practice. In conclusion, the numerical results further indicate that low-dimensional models fitted to re-projected trajectories are predictive even in situations where models fitted to trajectories without re-projection are inaccurate and unstable.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1990

A decentralized linear quadratic control design method for flexible structures

A decentralized suboptimal linear quadratic control design procedure which combines substructural synthesis, model reduction, decentralized control design, subcontroller synthesis, and controller reduction is proposed for the design of reduced-order controllers for flexible structures. The procedure starts with a definition of the continuum structure to be controlled. An evaluation model of finite dimension is obtained by the finite element method. Then, the finite element model is decomposed into several substructures by using a natural decomposition called substructuring decomposition. Each substructure, at this point, still has too large a dimension and must be reduced to a size that is Riccati-solvable. Model reduction of each substructure can be performed by using any existing model reduction method, e.g., modal truncation, balanced reduction, Krylov model reduction, or mixed-mode method. Then, based on the reduced substructure model, a subcontroller is designed by an LQ optimal control method for each substructure independently. After all subcontrollers are designed, a controller synthesis method called substructural controller synthesis is employed to synthesize all subcontrollers into a global controller. The assembling scheme used is the same as that employed for the structure matrices. Finally, a controller reduction scheme, called the equivalent impulse response energy controller (EIREC) reduction algorithm, is used to reduce the global controller to a reasonable size for implementation. The EIREC reduced controller preserves the impulse response energy of the full-order controller and has the property of matching low-frequency moments and low-frequency power moments. An advantage of the substructural controller synthesis method is that it relieves the computational burden associated with dimensionality. Besides that, the SCS design scheme is also a highly adaptable controller synthesis method for structures with varying configuration, or varying mass and stiffness properties.

Su, Tzu-Jeng↗
DOE OSTI2024

Learning Nonlinear Reduced Models from Data with Operator Inference

This review discusses Operator Inference, a nonintrusive reduced modeling approach that incorporates physical governing equations by defining a structured polynomial form for the reduced model, and then learns the corresponding reduced operators from simulated training data. The polynomial model form of Operator Inference is sufficiently expressive to cover a wide range of nonlinear dynamics found in fluid mechanics and other fields of science and engineering, while still providing efficient reduced model computations. The learning steps of Operator Inference are rooted in classical projection-based model reduction; thus, some of the rich theory of model reduction can be applied to models learned with Operator Inference. This connection to projection-based model reduction theory offers a pathway toward deriving error estimates and gaining insights to improve predictions. Furthermore, through formulations of Operator Inference that preserve Hamiltonian and other structures, important physical properties such as energy conservation can be guaranteed in the predictions of the reduced model beyond the training horizon. This review illustrates key computational steps of Operator Inference through a large-scale combustion example.

Mechanics↗
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↗
DOE OSTI2025

The Effects of Compounded Model Size Reductions on Adversarial Robustness

Recent advances in Edge AI and Tiny Machine Learning (TinyML) have enabled the deployment of machine learning models on resource-constrained environments. However, deploying these models on edge devices, such as micro-controllers, requires significant model footprint reduction through a variety of techniques such as quantization, pruning, and clustering. While these optimization methods offer considerable advantages, they potentially introduce AI-related security vulnerabilities, particularly concerning model robustness with respect to adversarial AI attacks. Prior research has extensively examined the impact of quantization on adversarial robustness; however, the effects of alternative reduction techniques and their combinations remain understudied. This paper investigates the impact of model size reduction techniques on adversarial robustness, when applied individually and combined. We utilized Fast Gradient Sign Method (FGSM) and Projected Gradient Descent (PGD) attacks to generate adversarial perturbations for both training and testing data, and then evaluated the models' accuracy under adversarial training conditions. Our findings revealed that reduction techniques generally diminished robustness; although, combining techniques was not found to make robustness any worse than when applied individually. Moreover, specific techniques can potentially enhance resistance to small size perturbations. This research provides insights into the trade-offs between model size reduction and security, establishing a foundation for future investigations into improving adversarial training techniques and methodologies for maintaining robustness while preserving memory footprint benefits.

Austria, Phillipe [ORNL] (ORCID:0000000236223973)↗
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

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

Polyethylene Blends for Improved Oxygen Barrier: Processing-Dependent Microstructure and Gas Permeability

Here this work demonstrates a greater than expected enhancement of oxygen barrier properties in linear low-density polyethylene (LLDPE)-based materials by blending LLDPE with high-density polyethylene (HDPE). The films made by melt pressing the LLDPE/HDPE blends had a greater reduction in oxygen permeability coefficients (PO 2 ) than predicted using common permeability reduction models, i.e., the harmonic average model and zero-permeability nanofiller model. The reduction of PO 2 was attributed to the presence of spherulite crystal structures, as revealed by atomic force microscopy combined with infrared spectroscopy (AFM-IR). The LLDPE matrix exhibited significant spherulite formation even at a relatively low addition of HDPEs, which likely formed tortuous pathways for diffusing oxygen molecules. Transport results from melt-pressed films contrast with the results from films with similar compositions prepared by film blowing, which did not show barrier enhancement beyond expectation. AFM-IR revealed that the blown films lacked spherulite crystals likely due to stretching in the machine direction followed by rapid cooling. These findings demonstrate the role of processing in controlling microstructures and thus the oxygen barrier performance. This work offers the possibility of achieving easily recyclable LLDPE-based packaging materials by simple blending of polyethylenes with different crystalline content.

36 MATERIALS SCIENCE↗
NASA NTRS1990

A Hankel singular value approach for identification of low level dynamics in flexible structures

The intensity of dynamics in a flexible structure is characterized by its Hankel singular values. Low level dynamics may be caused by generic properties of a structure or by its actuator and sensor configurations. In the latter case, it is shown that the dynamics can significantly be amplified by small perturbations of actuator and/or sensor configurations. In the presented examples, the variations of sensor configuration of 0.05 or less caused an increase of Hankel singular values of order 1000. This approach is useful for model reduction and model order determination in the presence of noise.

Gawronski, W.↗
NASA NTRS2012

Constructing an Efficient Self-Tuning Aircraft Engine Model for Control and Health Management Applications

Self-tuning aircraft engine models can be applied for control and health management applications. The self-tuning feature of these models minimizes the mismatch between any given engine and the underlying engineering model describing an engine family. This paper provides details of the construction of a self-tuning engine model centered on a piecewise linear Kalman filter design. Starting from a nonlinear transient aerothermal model, a piecewise linear representation is first extracted. The linearization procedure creates a database of trim vectors and state-space matrices that are subsequently scheduled for interpolation based on engine operating point. A series of steady-state Kalman gains can next be constructed from a reduced-order form of the piecewise linear model. Reduction of the piecewise linear model to an observable dimension with respect to available sensed engine measurements can be achieved using either a subset or an optimal linear combination of "health" parameters, which describe engine performance. The resulting piecewise linear Kalman filter is then implemented for faster-than-real-time processing of sensed engine measurements, generating outputs appropriate for trending engine performance, estimating both measured and unmeasured parameters for control purposes, and performing on-board gas-path fault diagnostics. Computational efficiency is achieved by designing multidimensional interpolation algorithms that exploit the shared scheduling of multiple trim vectors and system matrices. An example application illustrates the accuracy of a self-tuning piecewise linear Kalman filter model when applied to a nonlinear turbofan engine simulation. Additional discussions focus on the issue of transient response accuracy and the advantages of a piecewise linear Kalman filter in the context of validation and verification. The techniques described provide a framework for constructing efficient self-tuning aircraft engine models from complex nonlinear simulations.Self-tuning aircraft engine models can be applied for control and health management applications. The self-tuning feature of these models minimizes the mismatch between any given engine and the underlying engineering model describing an engine family. This paper provides details of the construction of a self-tuning engine model centered on a piecewise linear Kalman filter design. Starting from a nonlinear transient aerothermal model, a piecewise linear representation is first extracted. The linearization procedure creates a database of trim vectors and state-space matrices that are subsequently scheduled for interpolation based on engine operating point. A series of steady-state Kalman gains can next be constructed from a reduced-order form of the piecewise linear model. Reduction of the piecewise linear model to an observable dimension with respect to available sensed engine measurements can be achieved using either a subset or an optimal linear combination of "health" parameters, which describe engine performance. The resulting piecewise linear Kalman filter is then implemented for faster-than-real-time processing of sensed engine measurements, generating outputs appropriate for trending engine performance, estimating both measured and unmeasured parameters for control purposes, and performing on-board gas-path fault diagnostics. Computational efficiency is achieved by designing multidimensional interpolation algorithms that exploit the shared scheduling of multiple trim vectors and system matrices. An example application illustrates the accuracy of a self-tuning piecewise linear Kalman filter model when applied to a nonlinear turbofan engine simulation. Additional discussions focus on the issue of transient response accuracy and the advantages of a piecewise linear Kalman filter in the context of validation and verification. The techniques described provide a framework for constructing efficient self-tuning aircraft engine models from complex nonlinear simulatns.

Armstrong, Jeffrey B.↗