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NASA NTRS1989

The determination of third order linear models from a seventh order nonlinear jet engine model

Results are presented that demonstrate how good reduced-order models can be obtained directly by recursive parameter identification using input/output (I/O) data of high-order nonlinear systems. Three different methods of obtaining a third-order linear model from a seventh-order nonlinear turbojet engine model are compared. The first method is to obtain a linear model from the original model and then reduce the linear model by standard reduction techniques such as residualization and balancing. The second method is to identify directly a third-order linear model by recursive least-squares parameter estimation using I/O data of the original model. The third method is to obtain a reduced-order model from the original model and then linearize the reduced model. Frequency responses are used as the performance measure to evaluate the reduced models. The reduced-order models along with their Bode plots are presented for comparison purposes.

Lalonde, Rick J.↗

NASA NTRS1998

Reduced-Order Aerodynamic Model and Its Application to a Nonlinear Aeroelastic System

Starting from a finite state model for a two-dimensional aerodynamic flow over an airfoil, the eigenmodes of the aerodynamic flow are determined. Using a small number of these aerodynamic eigenmodes, ie., a reduced-order model, the aeroelastic model is formed by coupling them to a typical section structural model with a trailing-edge flap. A free-play nonlinearity is modeled. Results are shown from the finite state model, the reduced-order model, and previous theoretical and experimental work. All results are in good agreement.

Tang, Deman↗

NASA NTRSDate not supplied

Reduced-Order Aerodynamic Modeling Based on CFD Frequency Responses from Multisine Inputs

A system identification analysis was performed to determine reduced-order models of a computational fluid dynamics (CFD) solver for linear aeroelastic analysis and control design. The application was to the FUN3D code and the flexible half-span wind tunnel test article, in transonic flow conditions, used in the NASA-Boeing collaboration called the Integrated Adaptive Wing Technology Maturation (IAWTM) project. Multiple inputs (structural mode displacements and control surface deflections) were simultaneously excited with orthogonal phase-optimized multisines and multiple outputs (generalized aerodynamic forces) were recorded, from which the matrix of frequency responses were computed using a single CFD run. A state-space model was then fit to the frequency response data using a maximum-likelihood estimator.

System identification↗

NASA NTRSDate not supplied

Reduced-Order Aerodynamic Modeling Based on CFD Frequency Responses from Multisine Inputs

A system identification analysis was performed to determine a reduced-order model (ROM) of a computational fluid dynamics (CFD) solver in support of linear aeroservoelastic model development and feedback control design. The approach was applied to the FUN3D code for the half-span wind tunnel test article used in the NASA-Boeing collaboration called the Integrated Adaptive Wing Technology Maturation (IAWTM) project. In a transonic flow condition, multiple inputs (11 structural mode displacements and 3 control surface deflections) were simultaneously excited with orthogonal phase-optimized multisines while multiple outputs (the corresponding 14 generalized aerodynamic forces) were recorded. From these recorded times series, the matrix of frequency responses was computed and subsequently fit using rational function approximations (RFAs). It was found that the entire (14 x 14) matrix of frequency responses could be determined from a single CFD run and that results generally followed trends predicted using other methods. Differences were attributed to the modeling fidelity and nonlinearities from structural mode and control surface interactions at higher reduced frequencies. More accurate fits of the RFAs to the frequency response data were obtained by making two CFD runs, one with only structural mode excitations and one with only control surface excitations, which reduced the degree of nonlinearity in the modeling data.

Aeroservoelasticity↗

NASA NTRS2020

Solution of the Nonlinear High-Fidelity Generalized Method of Cells Micromechanics Relations via Order-Reduction Techniques

The High-Fidelity Generalized Method of Cells (HFGMC) is one technique, distinct from traditional finite element approaches, for accurately simulating nonlinear composite material behavior. In this work, the HFGMC global system of equations for doubly-periodic repeating unit cells with nonlinear constituents has been reduced in size through the novel application of a Petrov-Galerkin Proper Orthogonal Decomposition order-reduction scheme in order to improve its computational efficiency. Order-reduced models of an E-glass/Nylon 12 composite led to a 4.8 to 6.3x speedup in the equation assembly/solution runtime while maintaining model accuracy. This corresponded to a 21 to 38 percent reduction in total runtime. The significant difference in assembly/solution and total runtimes was attributed to the evaluation of integration point inelastic field quantities; this step was identical between the unreduced and order-reduced models. Nonetheless, order-reduced techniques offer the potential to significantly improve the computational efficiency of multiscale calculations.

Ricks, Trenton M.↗

NASA NTRS1989

Linear analysis of a force reflective teleoperator

Complex force reflective teleoperation systems are often very difficult to analyze due to the large number of components and control loops involved. One mode of a force reflective teleoperator is described. An analysis of the performance of the system based on a linear analysis of the general full order model is presented. Reduced order models are derived and correlated with the full order models. Basic effects of force feedback and position feedback are examined and the effects of time delays between the master and slave are studied. The results show that with symmetrical position-position control of teleoperators, a basic trade off must be made between the intersystem stiffness of the teleoperator, and the impedance felt by the operator in free space.

Biggers, Klaus B.↗

NASA NTRS1991

Error associated with a reduced order linear model of a spur gear pair

The paper proposes a reduced-order analytical model of a spur gear pair which consists of two identical spur gears, two identical flexible shafts, and four identical rolling element bearings of a given radial stiffness. The error associated with the undamped eigensolution is estimated by a comparison with a benchmark finite element model.

Kahraman, A.↗

NASA NTRS1999

Proper Orthogonal Decomposition in Optimal Control of Fluids

In this article, we present a reduced order modeling approach suitable for active control of fluid dynamical systems based on proper orthogonal decomposition (POD). The rationale behind the reduced order modeling is that numerical simulation of Navier-Stokes equations is still too costly for the purpose of optimization and control of unsteady flows. We examine the possibility of obtaining reduced order models that reduce computational complexity associated with the Navier-Stokes equations while capturing the essential dynamics by using the POD. The POD allows extraction of certain optimal set of basis functions, perhaps few, from a computational or experimental data-base through an eigenvalue analysis. The solution is then obtained as a linear combination of these optimal set of basis functions by means of Galerkin projection. This makes it attractive for optimal control and estimation of systems governed by partial differential equations. We here use it in active control of fluid flows governed by the Navier-Stokes equations. We show that the resulting reduced order model can be very efficient for the computations of optimization and control problems in unsteady flows. Finally, implementational issues and numerical experiments are presented for simulations and optimal control of fluid flow through channels.

Ravindran, S. S.↗

NASA NTRS1993

Two-Stage Reduction Of Dynamical Models

No longer necessary to solve eigenvalue problems of high order. Component-mode projection-and-assembly model-reduction (COMPARE) method provides approximation of dynamics of vibrations of complicated, multiple flexible bodies by use of mathematical models of reduced order. Incorporates component-mode synthesis (CMS) method and enhanced projection-and-assembly (EP&A) method, described in "Enhanced Method of Reduction of Dynamical Models" (NPO-18402), providing for somewhat simplified two-stage process in which order of applicable mathematical models reduced. Reduced-order models used to design algorithms of control systems to suppress vibrations or otherwise control structure.

Lee, Allan Y.↗

NASA NTRS2014

Flutter Analysis for Turbomachinery Using Volterra Series

The objective of this paper is to describe an accurate and efficient reduced order modeling method for aeroelastic (AE) analysis and for determining the flutter boundary. Without losing accuracy, we develop a reduced order model based on the Volterra series to achieve significant savings in computational cost. The aerodynamic force is provided by a high-fidelity solution from the Reynolds-averaged Navier-Stokes (RANS) equations; the structural mode shapes are determined from the finite element analysis. The fluid-structure coupling is then modeled by the state-space formulation with the structural displacement as input and the aerodynamic force as output, which in turn acts as an external force to the aeroelastic displacement equation for providing the structural deformation. NASA's rotor 67 blade is used to study its aeroelastic characteristics under the designated operating condition. First, the CFD results are validated against measured data available for the steady state condition. Then, the accuracy of the developed reduced order model is compared with the full-order solutions. Finally the aeroelastic solutions of the blade are computed and a flutter boundary is identified, suggesting that the rotor, with the material property chosen for the study, is structurally stable at the operating condition, free of encountering flutter.

computational fluid dynamics↗

NASA NTRS1991

Improved large perturbation propulsion models for control system design (1988-1989) and large perturbation models of high velocity propulsion systems (1989-1990) and reduced order propulsion models for control system design (1990-1991)

Methods for modeling high speed propulsion systems will be discussed. Included in this category are internal flow propulsion systems without rotating machinery, such as inlets, ramjets, and scramjets. Among the modeling topics discussed are modeling of linear isentropic flow, heat exchange, gasdynamics, lumped parameter systems, and infinite dimensional systems. Furthermore, a generalized overview of modeling high speed propulsion systems is presented in this collection of papers.

Hartley, Tom T.↗

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.↗

NASA NTRS1993

A COMPACT model reduction methodology for articulated, multi-flexible bodies structures

To simulate the dynamical motion of articulated, multiflexible body structures, one can use multibody simulation packages such as DISCOS. To this end, one need appropriate reduced-order models for all the flexible components involved. The component modes projection and assembly model reduction methodology is one way to construct these reduced-order component models. However, the generated reduced-order system models typically contain high frequency extraneous modes. The presence of high frequency extraneous modes in a reduced-order system model forces us to use a small stepsize in the numerical integration of that model, resulting in an increase in the elapsed time of the integration process. To eliminate these high-frequency modes, we first identify and discard the component modes that 'contributed' to the generations of these modes. A sensitivity analysis is then used to determine how the remaining component modes should be perturbed in order to still closely capture the selected system modes. The effectiveness of the proposed methodology has been successfully verified using a finite-element model of the Galileo spacecraft.

Lee, Allan Y.↗

NASA NTRS1991

Physical lumping methods for developing linear reduced models for high speed propulsion systems

In gasdynamic systems, information travels in one direction for supersonic flow and in both directions for subsonic flow. A shock occurs at the transition from supersonic to subsonic flow. Thus, to simulate these systems, any simulation method implemented for the quasi-one-dimensional Euler equations must have the ability to capture the shock. In this paper, a technique combining both backward and central differencing is presented. The equations are subsequently linearized about an operating point and formulated into a linear state space model. After proper implementation of the boundary conditions, the model order is reduced from 123 to less than 10 using the Schur method of balancing. Simulations comparing frequency and step response of the reduced order model and the original system models are presented.

Immel, S. M.↗

NASA NTRS1989

On the control of elastic vehicles - Model simplification and stability robustness

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 and 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 multivariable 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 identified to be associated with the canceling of lightly-damped transmission zeroes in the plant.

Schmidt, David K.↗

NASA NTRSDate not supplied

Usage-based Lifing of Lithium-Ion Battery with HybridPhysics-Informed Neural Networks

Lithium-ion batteries are commonly used to power unmanned aircraft vehicles (UAVs).The ability to model and forecast the remaining useful life of these batteries enables UAV reliability assurance. Building accurate models for battery state of charge and state of health based on first principles is challenging due to the complex electrochemistry that governs battery operations and computational complexity required to solve them. Therefore, reduced order models are often used due to their ability to capture the overall battery discharge. Un-fortunately, these simplifications lead to residual discrepancy between model predictions and observed data. In this paper, we present a hybrid modeling approach merging reduced-order models and neural networks. In this approach, while most of the input-output relationship is captured by Nernst and Butler-Volmer equations, data-driven kernels reduce the gap between predictions and observations. We validate our approach using data publicly available through the NASA Prognostics Center of Excellence repository. Results showed that our hybrid battery prognosis model can be successfully calibrated, even with a limited number of observations.

Lithium-ion Battery↗

NASA NTRSDate not supplied

Computational investigation on the combined effect of pore attributes on strain concentrators in metal additively manufactured materials

Metal additive manufacturing provides a pathway for creating highly optimized components. However, porosity continues to be a prevalent issue for fatigue performance despite best efforts in optimizing process parameters and postprocessing techniques. This work uses finite element analysis to conduct a parametric study to link various pore attributes (i.e., aspect ratio, orientation, and location) to strain concentration factors (SCF) under elastic/plastic deformation during uniaxial loading. Keyhole and lack-of-fusion pores are idealized by prolate and oblate ellipsoids, respectively. Each simulation of the parametric study assumes a single isolated pore in a Ti-6Al-4V material, modeled with J2-plasticity. A reduced-order model is developed to relate pore attributes to SCF, and then used to quantify the variability in SCF for a given experimentally characterized probability distribution of pore attributes. This reduced-order model can be used in a production environment to provide a first-order evaluation to rapidly screen sub-optimally performing components.

Additive Manufacturing↗

NASA NTRSDate not supplied

L'Ralph's Advanced Thermal Model Correlation Using Veritrek

Thermal model correlation uses data from thermal balance tests to better estimate uncertain input parameter values. During the correlation process, input parameters are modified in an iterative manner which can become computationally expensive since this requires that the high-fidelity thermal model be run for each iteration. Depending on the number of thermal balance test points there can be many sets of correlation parameters that satisfy correlation criteria; and having enough data to ascertain the best set of correlation parameters to use, further increases the computational expense. Reduced-order models (ROMs) provide computationally efficient surrogates of high-fidelity models and are often built to reduce development cycle times and cost. By leveraging the speed of reduced-order models and the Correlation Analysis feature in the Veritrek software, the typical computational expense of a traditional thermal model correlation process can be significantly reduced and having access to hundreds of thousands of iteration results provides an advanced means of intelligently determining the best set of correlation parameters to use. The L’Ralph thermal team at NASA Goddard Space Flight Center explored the use of the Veritrek software for their thermal model correlation efforts. The ROM that was created allowed for the variation of 15 input parameters to match 70 temperature sensor readouts from 3 thermal balance plateus and required 125 runs of the high-fidelity Thermal Desktop® model to generate a ROM that could predict the detailed model’s results to within 0.2 K (RMS). The ROM was then used to find dozens of plausible correlation parameter values based on L’Ralph instrument test data within a few seconds. By providing several plausible correlation parameter combinations, Veritrek allowed the thermal team to explore different uncertain parameter value combinations and provided insight into how deterministic each input parameter was. This allowed for a more confident decision on the best set of correlation parameters to use, compared to traditional model correlation techniques. In this presentation, the L’Ralph thermal team will be presenting their experience with the Veritrek software and how the software was utilized to provide additional insights during the correlation process.

Daniel Bae↗