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All sourcesNASA NTRSDOE OSTI
NASA NTRS1990

Practical model reduction for flexible structures

The most accepted methods for developing models of flexible structures for the analysis, design and simulation of control systems are finite element methods and extraction from experimental data. Using either of these methods, models are often produced with modes that do not significantly add to the fidelity of the model. This paper presents techniques for eliminating these modes. Particular attention is paid to multiple-input, multiple-output systems. First, control system models developed for flexible structures, using finite element methods and experimental data, are briefly discussed. the shortcomings of using models with unnecessary and/or residual modes are delineated. Then, two techniques for reducing the order of models are presented; the first is applicable to single-input, single-output systems and the second for multiple-input, multiple-output systems. Finally, both are illustrated using model data from the proposed NASA Shuttle-C.

Mitchell, Jerrel R.↗
DOE OSTI2025

Block-Structured Operator Inference for Coupled Multiphysics Model Reduction

This work presents a block-structured formulation of Operator Inference as a way to learn structured reduced-order models for multiphysics systems. The approach specifies the governing equation structure for each physics component and the structure of the coupling terms. Once the multiphysics structure is specified, the reduced-order model is learned from snapshot data following the nonintrusive Operator Inference methodology. In addition to preserving physical system structure, which in turn permits preservation of system properties such as stability and second-order structure, the block-structured approach has the advantages of reducing the overall dimensionality of the learning problem and admitting tailored regularization for each physics component. The numerical advantages of the block-structured formulation over a monolithic Operator Inference formulation are demonstrated for aeroelastic analysis, which couples aerodynamic and structural models. For the benchmark test case of the AGARD 445.6 wing, block-structured Operator Inference provides an average 20% online prediction speedup over monolithic Operator Inference across subsonic and supersonic flow conditions in both the stable and fluttering parameter regimes while preserving the accuracy achieved with monolithic Operator Inference.

42 ENGINEERING↗
NASA NTRS1992

Model reduction for systems with integrators

The reduction algorithm for systems with integrators is derived. The algorithm is based on balancing the antigrammians and has the same computational effectiveness as the regular balancing procedure. It was applied to the reduction of the NASA Deep Space Network antenna model. As a result, the 90-state model has been reduced to a 27-state model, which preserves the full-model properties.

Gawronski, Wodek↗
NASA NTRS1991

A Markov model reduction technique for fault tolerant processor reliability analysis

A fault tolerant processor (FTP) plays a key role in many high performance, safety-critical control system applications. Realistic modeling of an FTP is crucial to gaining a high degree of confidence in the reliability and safety analysis of such a system. While fidelity is clearly a major consideration, a practical model must also be kept to a moderate size to allow its incorporation into the overall system model. This paper presents a systematic reduction technique that starts from a complex, detailed model of a triple, redundant FTP and produces a low order approximation of very high accuracy. The existence of two distinct time scales represents the key to the success of the technique. No eigenvalue solution or coordinate transformation are needed. The reduced model captures all the important features of the detailed model, is amenable to an analytical solution and provides insight into the reconfiguration behavior of an FTP.

Schor, Andrei L.↗
DOE OSTI2020

The Adjoint Petrov–Galerkin method for non-linear model reduction

Here, we formulate a new projection-based reduced-order modeling technique for non-linear dynamical systems. The proposed technique, which we refer to as the Adjoint Petrov–Galerkin (APG) method, is derived by decomposing the generalized coordinates of a dynamical system into a resolved coarse-scale set and an unresolved fine-scale set. A Markovian finite memory assumption within the Mori–Zwanzig formalism is then used to develop a reduced-order representation of the coarse scales. This procedure leads to a closed reduced-order model that displays commonalities with the adjoint stabilization method used in finite elements. The formulation is shown to be equivalent to a Petrov–Galerkin method with a non-linear, time-varying test basis, thus sharing some similarities with the Least-Squares Petrov–Galerkin method. Theoretical analysis examining a priori error bounds and computational cost is presented. Numerical experiments on the compressible Navier–Stokes equations demonstrate that the proposed method can lead to improvements in numerical accuracy, robustness, and computational efficiency over the Galerkin method on problems of practical interest. Improvements in numerical accuracy and computational efficiency over the Least-Squares Petrov–Galerkin method are observed in most cases.

42 ENGINEERING↗
DOE OSTI2020

Closure Learning for Nonlinear Model Reduction Using Deep Residual Neural Network

Developing accurate, efficient, and robust closure models is essential in the construction of reduced order models (ROMs) for realistic nonlinear systems, which generally require drastic ROM mode truncations. We propose a deep residual neural network (ResNet) closure learning framework for ROMs of nonlinear systems. The novel ResNet-ROM framework consists of two steps: (i) In the first step, we use ROM projection to filter the given nonlinear system and construct a spatially filtered ROM. This filtered ROM is low-dimensional, but is not closed. (ii) In the second step, we use ResNet to close the filtered ROM, i.e., to model the interaction between the resolved and unresolved ROM modes. We emphasize that in the new ResNet-ROM framework, data is used only to complement classical physical modeling (i.e., only in the closure modeling component), not to completely replace it. We also note that the new ResNet-ROM is built on general ideas of spatial filtering and deep learning and is independent of (restrictive) phenomenological arguments, e.g., of eddy viscosity type. The numerical experiments for the 1D Burgers equation show that the ResNet-ROM is significantly more accurate than the standard projection ROM. The new ResNet-ROM is also more accurate and significantly more efficient than other modern ROM closure models.

Xie, Xuping↗
NASA NTRS1989

Fatigue strength reduction model: RANDOM3 and RANDOM4 user manual, appendix 2

The FORTRAN programs RANDOM3 and RANDOM4 are documented. They are based on fatigue strength reduction, using a probabilistic constitutive model. They predict the random lifetime of an engine component to reach a given fatigue strength. Included in this user manual are details regarding the theoretical backgrounds of RANDOM3 and RANDOM4. Appendix A gives information on the physical quantities, their symbols, FORTRAN names, and both SI and U.S. Customary units. Appendix B and C include photocopies of the actual computer printout corresponding to the sample problems. Appendices D and E detail the IMSL, Version 10(1), subroutines and functions called by RANDOM3 and RANDOM4 and SAS/GRAPH(2) programs that can be used to plot both the probability density functions (p.d.f.) and the cumulative distribution functions (c.d.f.).

Boyce, Lola↗
NASA NTRS1989

Fatigue strength reduction model: RANDOM3 and RANDOM4 user manual. Appendix 2: Development of advanced methodologies for probabilistic constitutive relationships of material strength models

FORTRAN programs RANDOM3 and RANDOM4 are documented in the form of a user's manual. Both programs are based on fatigue strength reduction, using a probabilistic constitutive model. The programs predict the random lifetime of an engine component to reach a given fatigue strength. The theoretical backgrounds, input data instructions, and sample problems illustrating the use of the programs are included.

Boyce, Lola↗
NASA NTRS1991

Numerical and literal aeroelastic-vehicle-model reduction for feedback control synthesis

The simplification of a high-order, literal model for large flexible aircraft is discussed. Areas of model fidelity that are critical if the model is to be used for control law synthesis are presented. Several simplification techniques, some new and some widely available, that can deliver the necessary model fidelity are presented and applied to a model from the literature. The techniques include both numerical and analytical approaches. An analytical approach, based on first-order sensitivity theory, is shown to lead not only to excellent numerical results, but also to closed-form analytical expressions for key system dynamic properties such as the pole/zero factors of the vehicle transfer-function matrix. The analytical results are expressed in terms of vehicle vibrational characteristics and rigid-body and aeroelastic stability derivatives, thus providing insight into the underlying causes for critical dynamic characteristics.

Newman, Brett↗
NASA NTRS1988

Closed-form Grammians and model reduction for flexible space structures

Analytical expression are derived for the Grammians of a model in modal coordinates for the dynamics of a flexible space structure (FSS). These exact results provide insight into the dynamics of such systems and reduce the known approximate expressions in the case of lightly damped, widely separated modes. A novel algorithm is outlined that uses these to compute a dominant reduced-order model for such a system in an efficient manner.

Williams, Trevor↗
NASA NTRS1985

An Overview of Latest Model Reduction and Control Methods of Large Flexible Space Structures

The latest trends and theoretical developments involved with the modeling and control of Large Flexible Space Structures (LFSS) are described. The paper addresses first the basic problems, characteristics, and difficulties inherent in modeling and control of LFSS. Major sources of difficulties and errors are the stiffness and damping operators of the dynamic model. Extensions of Linear Quadratic Gaussian (LQG) theory as applied to LFSS are presented, including frequency-shaped cost functionals and perturbation methods. The minimum data/maximum entropy approach which uses a stochastic design model to overcome difficulties found in the LQG-based methods is described. Latest trends in system theory including balanced realization and singular-value analysis are used to determine reduced order controllers and models. Ad hoc methods such as component cost analysis and modal cost analysis are discussed in context with the closed-loop reduction problem of controller order versus performance. The minimum data/maximum entropy approach also addresses controller order versus performance. Those areas of control science and large scale systems that appear to have an important role in understanding and solving LFSS modeling and control are also identified.

Santiago, J. M.↗
DOE OSTI2020

Turbulence model reduction by deep learning

A defining problem of turbulence theory is to produce a predictive model for turbulent fluxes. These have profound implications for virtually all aspects of the turbulence dynamics. In magnetic confinement devices, drift-wave turbulence produces anomalous fluxes via cross-correlations between fluctuations. In this work, we introduce an alternative, data-driven method for parametrizing these fluxes. The method uses deep supervised learning to infer a reduced mean-field model from a set of numerical simulations. We apply the method to a simple drift-wave turbulence system and find a significant new effect which couples the particle flux to the local gradient of vorticity. Notably, here, this effect is much stronger than the oft-invoked shear suppression effect. We also recover the result via a simple calculation. The vorticity gradient effect tends to modulate the density profile. In addition, our method recovers a model for spontaneous zonal flow generation by negative viscosity, stabilized by nonlinear and hyperviscous terms. We highlight the important role of symmetry to implementation of the new method.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2022

Projection-Based Model Reduction for Coupled Conduction—Enclosure Radiation Systems

We report a projection-based reduced order model (pROM) methodology has been developed for transient heat transfer problems involving coupled conduction and enclosure radiation. The approach was demonstrated on two test problems of varying complexity. The reduced order models demonstrated substantial speedups (up to 185×) relative to the full order model with good accuracy (less than 3% L ∞ error). An attractive feature of pROMs is that there is a natural error indicator for the ROM solution: the final residual norm at each time-step of the converged ROM solution. Using example test cases, we discuss how to interpret this error indicator to assess the accuracy of the ROM solution. The approach shows promise for many-query applications, such as uncertainty quantification and optimization. The reduced computational cost of the ROM relative to the full-order model (FOM) can enable the analysis of larger and more complex systems as well as the exploration of larger parameter spaces.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS1990

Multibody model reduction by component mode synthesis and component cost analysis

The classical assumed-modes method is widely used in modeling the dynamics of flexible multibody systems. According to the method, the elastic deformation of each component in the system is expanded in a series of spatial and temporal functions known as modes and modal coordinates, respectively. This paper focuses on the selection of component modes used in the assumed-modes expansion. A two-stage component modal reduction method is proposed combining Component Mode Synthesis (CMS) with Component Cost Analysis (CCA). First, each component model is truncated such that the contribution of the high frequency subsystem to the static response is preserved. Second, a new CMS procedure is employed to assemble the system model and CCA is used to further truncate component modes in accordance with their contribution to a quadratic cost function of the system output. The proposed method is demonstrated with a simple example of a flexible two-body system.

Spanos, J. T.↗
DOE OSTI2025

Ground-state-based model reduction with unitary circuits

Here, we present a method to numerically obtain low-energy effective models based on a unitary transformation of the ground state. The algorithm finds a unitary circuit that transforms the ground state of the original model to a projected wavefunction with only the low-energy degrees of freedom. The effective model can then be derived using the unitary transformation encoded in the circuit. We test our method on the one-dimensional and two-dimensional square-lattice Hubbard model at half-filling, and obtain more accurate effective spin models than the standard perturbative approach.

Hubbard model↗
NASA NTRS1990

Finite element model reduction application to parametric studies and optimization of rotorcraft structures

As a result of this work, a reduction procedure has been developed which can be applied to large finite element model of airframe type structures. This procedure, which is tailored to be used with MSC/NASTRAN finite element code, is applied to the full airframe dynamic finite element model of AH-64A Attack Helicopter. The applicability of the resulting reduced model to parametric and optimization studies is examined. Through application of the design sensitivity analysis, the viability and efficiency of this reduction technique has been demonstrated in a vibration reduction study.

Hashemi-Kia, M.↗
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.↗