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NASA NTRS1992

A fundamental theorem for the model reduction of nonlinear systems

A simple, but fundamental, theorem is given on the extent to which a nonlinear system model can have its order reduced. Essentially, the result is that the order, or the dimension of the state space representation, cannot be reduced to, or below, the dimension of the system's attractor. Several examples are given to illustrate this point. The result is especially applicable to higher order systems such as the infinite dimensional systems arising from the modeling of distributed parameter systems.

Mossayebi, Faramarz↗
NASA NTRS1985

Polynomic nonlinear dynamical systems - A residual sensitivity method for model reduction

The motivation for using polynomic combinations of system states and inputs to model nonlinear dynamics systems is founded upon the classical theories of analysis and function representation. A feature of such representations is the need to make available all possible monomials in these variables, up to the degree specified, so as to provide for the description of widely varying functions within a broad class. For a particular application, however, certain monomials may be quite superfluous. This paper examines the possibility of removing monomials from the model in accordance with the level of sensitivity displayed by the residuals to their absence. Critical in these studies is the effect of system input excitation, and the effect of discarding monomial terms, upon the model parameter set. Therefore, model reduction is approached iteratively, with inputs redesigned at each iteration to ensure sufficient excitation of remaining monomials for parameter approximation. Examples are reported to illustrate the performance of such model reduction approaches.

Yurkovich, S.↗
NASA NTRS1984

Mixed Models and Reduction Techniques for Large-Rotation, Nonlinear Analysis of Shells of Revolution with Application to Tires

An effective computational strategy is presented for the large-rotation, nonlinear axisymmetric analysis of shells of revolution. The three key elements of the computational strategy are: (1) use of mixed finite-element models with discontinuous stress resultants at the element interfaces; (2) substantial reduction in the total number of degrees of freedom through the use of a multiple-parameter reduction technique; and (3) reduction in the size of the analysis model through the decomposition of asymmetric loads into symmetric and antisymmetric components coupled with the use of the multiple-parameter reduction technique. The potential of the proposed computational strategy is discussed. Numerical results are presented to demonstrate the high accuracy of the mixed models developed and to show the potential of using the proposed computational strategy for the analysis of tires.

Noor, A. K.↗
NASA NTRS1990

Experimental validation of Order (n) DISCOS

An order (n) algorithm is developed for use in the industry-standard DISCOS (Dynamics Interaction Simulation of Controls and Structures) program for flexible multibody system dynamics simulation. This version should be more computationally efficient than conventional DISCOS for problems where a large number of bodies are involved. Program-dependent changes to DISCOS are described for reducing the number of bodies required to model gear reduction and nonlinear stiffness as internal effects. The gear reduction modification can be extended to general applications, such as gear box, rack and pinion, lever joint, and screw rotation models. Upgrading DISCOS for future use include the addition of robotics capabilities such as event-driven topology changes, surface sliding, pick-and-place, and multiarm hand-off.

Chun, Hon M.↗
NASA NTRS2006

Computational Aeroelastic Modeling of Airframes and TurboMachinery: Progress and Challenges

Computational analyses such as computational fluid dynamics and computational structural dynamics have made major advances toward maturity as engineering tools. Computational aeroelasticity is the integration of these disciplines. As computational aeroelasticity matures it too finds an increasing role in the design and analysis of aerospace vehicles. This paper presents a survey of the current state of computational aeroelasticity with a discussion of recent research, success and continuing challenges in its progressive integration into multidisciplinary aerospace design. This paper approaches computational aeroelasticity from the perspective of the two main areas of application: airframe and turbomachinery design. An overview will be presented of the different prediction methods used for each field of application. Differing levels of nonlinear modeling will be discussed with insight into accuracy versus complexity and computational requirements. Subjects will include current advanced methods (linear and nonlinear), nonlinear flow models, use of order reduction techniques and future trends in incorporating structural nonlinearity. Examples in which computational aeroelasticity is currently being integrated into the design of airframes and turbomachinery will be presented.

Bartels, R. E.↗
NASA NTRS2003

Aeroservoelastic Model Validation and Test Data Analysis of the F/A-18 Active Aeroelastic Wing

Model validation and flight test data analysis require careful consideration of the effects of uncertainty, noise, and nonlinearity. Uncertainty prevails in the data analysis techniques and results in a composite model uncertainty from unmodeled dynamics, assumptions and mechanics of the estimation procedures, noise, and nonlinearity. A fundamental requirement for reliable and robust model development is an attempt to account for each of these sources of error, in particular, for model validation, robust stability prediction, and flight control system development. This paper is concerned with data processing procedures for uncertainty reduction in model validation for stability estimation and nonlinear identification. F/A-18 Active Aeroelastic Wing (AAW) aircraft data is used to demonstrate signal representation effects on uncertain model development, stability estimation, and nonlinear identification. Data is decomposed using adaptive orthonormal best-basis and wavelet-basis signal decompositions for signal denoising into linear and nonlinear identification algorithms. Nonlinear identification from a wavelet-based Volterra kernel procedure is used to extract nonlinear dynamics from aeroelastic responses, and to assist model development and uncertainty reduction for model validation and stability prediction by removing a class of nonlinearity from the uncertainty.

Brenner, Martin J.↗
NASA NTRS2020

Application of Quasi-Static Modal Analysis to an Orion Multi-Purpose Crew Vehicle Test

Bolted structural joints often exhibit load-dependent stiffness and energy dissipation that leads to nonlinear, amplitude dependent frequency and damping in the structure. As an alternative to direct integration of the nonlinear equations of motion, quasi-static modal analysis (QSMA) determines the dependence of frequency and damping on response amplitude using loading behavior from nonlinear static analyses. QSMA has previously been demonstrated to substantially reduce computational cost and maintain accuracy relative to full nonlinear dynamic simulation. This work explores the applicability of QSMA to a complex, large-scale aerospace structure. QSMA is employed to analyze a nonlinear model of test hardware developed to support the Orion Multi-Purpose Crew Vehicle program, which exhibited nonlinear behavior during dynamic testing at flight-like load levels. In addition to the extraction of amplitude-dependent frequency and damping curves, a Bouc-Wen hysteresis model was used in conjunction with the quasi-static results to develop nonlinear, uncoupled, time-domain modal equations of motion for the structure. Excellent agreement was observed between the reduced and full-order nonlinear models, encouraging future employment of QSMA to support accurate and efficient model reduction of structures with bolted joint nonlinearities.

QSMA↗
NASA NTRS1983

Assessment of current state of the art in modeling techniques and analysis methods for large space structures

Advances in continuum modeling, progress in reduction methods, and analysis and modeling needs for large space structures are covered with specific attention given to repetitive lattice trusses. As far as continuum modeling is concerned, an effective and verified analysis capability exists for linear thermoelastic stress, birfurcation buckling, and free vibration problems of repetitive lattices. However, application of continuum modeling to nonlinear analysis needs more development. Reduction methods are very effective for bifurcation buckling and static (steady-state) nonlinear analysis. However, more work is needed to realize their full potential for nonlinear dynamic and time-dependent problems. As far as analysis and modeling needs are concerned, three areas are identified: loads determination, modeling and nonclassical behavior characteristics, and computational algorithms. The impact of new advances in computer hardware, software, integrated analysis, CAD/CAM stems, and materials technology is also discussed.

Noor, A. K.↗
NASA NTRS2020

Modeling Whitecaps on Global Scale

Whitecaps play an important role in the surface-atmosphere interactions across the ocean. They are directly linked to the energy dissipation rate during wave breaking and transfer of heat, momentum, and gas/aerosol exchange from the wind to the sea surface. Although the first models of W were dependent only on wind speeds, a large number of diverse models based on wind and sea state which include wave height, wave age, friction velocity, and stability effects have been proposed since then. However, it is recognized that most of the proposed W models have strong systematic (e.g., zonal bias) and random errors when compared against observations. This is partly due to the differences in environmental conditions, measurement techniques, and geographical locations among these studies. But, some of these biases are linked to the inability of the proposed models to capture the variability in W in certain wind/wave regimes. Despite the knowledge of existing biases, W residual relationships from the models with wind and wave fields remain highly uncertain, with residual trends varying between the published studies. Here, we take advantage of the availability of relatively dense observations of W from WindSat microwave satellite retrievals in combination with the University of Miami wave model which was recently incorporated within the NASA GMAO/GEOS system (GEOS-UMWM). We use Windsat W retrievals to assess and constrain the previously published W models and understand the relationships of residuals from models in different wind/wave regimes. We link these unexplained residual variations to additional factors such as swell index, drag coefficient etc and add information to the existing whitecap models. Since Windsat retrievals cover wide range of environmental conditions, it helps to reduce the uncertainties associated with differences in measurement techniques. Regression of wind-wave fields against all Windsat data points (CTL) results in larger residuals for lower wave age and W is overestimated upto ~4% for wave age < 10 and underestimated by upto ~2% as wave age increases. We attest to this bias by considering two approaches. One is to perform regression separately for different stages of wave development such as developing sea, fully developed, and wind sea regimes thereby understanding the sensitivity of regression coefficients to sea state (EXP1). Another is to derive coefficients of W models in EXP1 as a function of additional wind/wave factors such as swell index, drag coefficient, and mean squared slope, deriving more nonlinear W models (EXP2). EXP2 provides reduction in Root Mean Squared Error (RMSE) by 0.1-0.3%. Sea surface drag has a stronger relationship with regression coefficients compared to swell index.These additional factors provide improved parameterizations in different wind and wave age regimes, with smaller unexplained/residual variations in W that has been a major concern in the W community.

Raman, Aishwarya↗
NASA NTRSDate not supplied

Aeroservoelastic Control Law Development for the Integrated Adaptive Wing Technology Maturation Wind-Tunnel Test

The NASA Advanced Air Transport Technology (AATT) Project seeks to “explore and develop technologies and concepts for improved energy efficiency and environmental compatibility for fixed wing subsonic transports” [1]. The IAWTM project is a subproject within AATT and is a joint Boeing/NASA effort to, in part, demonstrate the active control systems necessary to employ high-aspect ratio wings for improved aerodynamic efficiency. The aircraft configuration under study for the IAWTM project is a generic jet transport based on the NASA Common Research Model (CRM) whose wing aspect ratio has been increased to 13.5 (as opposed to nominal CRM aspect ratio of 9) and whose development is given in Ref. [2]. A semi-span model of the high-aspect-ratio CRM with 10 trailing edge control surfaces is currently being fabricated and will be delivered to the NASA Langley Transonic Dynamics Tunnel (TDT). There, several tests will be conducted to demonstrate maneuver load alleviation (MLA), gust load alleviation (GLA), active flutter suppression (AFS), and drag reduction, all at transonic conditions. A layout of the wind tunnel model is shown in Fig. 1. The wind-tunnel model is a spar/pod wing design with a relatively rigid fuselage attached to a mounting structure (seen in Fig. 1), which in turn is attached to a load balance behind the tunnel wall. Shims exist that can be attached to force the load to go through the fuselage rather than through the balance so as not to damage the balance in the event of flutter. The spar/pod design is similar to that used in the Boeing truss-braced wing aeroelastic model tested in the TDT in 2013 [3]. There is a central spar running the span of the wing to which the pods are attached that form the aerodynamic shape of the wing. The pods are constructed of ribs for attachment to the spar and skins to create the outer mold line. There are ten active control surfaces that will be used for the test objectives discussed above. Three of these (two outboard ailerons and one inboard aileron) are high-speed electrohydraulic actuators, and the remaining seven are low-speed mini-plane flaps, which have slower servo motors that will be used primarily for drag and maneuver load reductions. Control laws must be developed for each test (MLA, GLA, AFS, and drag reduction) and must be able to work in tandem when two or more control strategies are being tested simultaneously (e.g., when control laws to mitigate maneuver loads and gust loads operate simultaneously). The development of these control laws requires accurate mathematical representations of the aerodynamics, structural dynamics, and control surface dynamics of the system. Taken together, this mathematical representation—which is often in state-space form— is the ASE model. Three low-order ASE models of differing fidelities were developed for the IAWTM test and will be presented here. The differences in fidelity appeared in the aerodynamic modeling—one model assumed purely linear aerodynamics, while the other two models used different techniques to linearize the aerodynamics about a nonlinear mean. Furthermore, simple observer-based full-state feedback controllers for each test (MLA, GLA, AFS, and drag reduction) were designed from these low-order ASE models and implemented in a higher-order, nonlinear computational ASE simulation to assess the effectiveness of each controller. Observers were designed from each of the three lower-order ASE models, and each (linear) observer was then used as an estimate of the nonlinear dynamics of the system. Using the estimated states and the full-state feedback controller, control surface commands were fed back to the higher-order, nonlinear ASE system. The insight gained during this development will be applied to control law development for the physical IAWTM wind-tunnel test.

Josiah M Waite↗
NASA NTRS1981

Recent advances in reduction methods for nonlinear problems

Status and some recent developments in the application of reduction methods to nonlinear structural mechanics problems are summarized. The aspects of reduction methods discussed herein include: (1) selection of basis vectors in nonlinear static and dynamic problems, (2) application of reduction methods in nonlinear static analysis of structures subjected to prescribed edge displacements, and (3) use of reduction methods in conjunction with mixed finite element models. Numerical examples are presented to demonstrate the effectiveness of reduction methods in nonlinear problems. Also, a number of research areas which have high potential for application of reduction methods are identified.

Noor, A. K.↗
NASA NTRS1983

Finite element modeling and analysis of tires

Predicting the response of tires under various loading conditions using finite element technology is addressed. Some of the recent advances in finite element technology which have high potential for application to tire modeling problems are reviewed. The analysis and modeling needs for tires are identified. Reduction methods for large-scale nonlinear analysis, with particular emphasis on treatment of combined loads, displacement-dependent and nonconservative loadings; development of simple and efficient mixed finite element models for shell analysis, identification of equivalent mixed and purely displacement models, and determination of the advantages of using mixed models; and effective computational models for large-rotation nonlinear problems, based on a total Lagrangian description of the deformation are included.

Noor, A. K.↗
NASA NTRS1993

Optimal fixed-finite-dimensional compensator for Burgers' equation with unbounded input/output operators

The problem of using reduced order dynamic compensators to control a class of nonlinear parabolic distributed parameter systems was considered. Concentration was on a system with unbounded input and output operators governed by Burgers' equation. A linearized model was used to compute low-order-finite-dimensional control laws by minimizing certain energy functionals. Then these laws were applied to the nonlinear model. Standard approaches to this problem employ model/controller reduction techniques in conjunction with linear quadratic Gaussian (LQG) theory. The approach used is based on the finite dimensional Bernstein/Hyland optimal projection theory which yields a fixed-finite-order controller.

Burns, John A.↗
NASA NTRS1979

Generation of linear dynamic models from a digital nonlinear simulation

The results and methodology used to derive linear models from a nonlinear simulation are presented. It is shown that averaged positive and negative perturbations in the state variables can reduce numerical errors in finite difference, partial derivative approximations and, in the control inputs, can better approximate the system response in both directions about the operating point. Both explicit and implicit formulations are addressed. Linear models are derived for the F 100 engine, and comparisons of transients are made with the nonlinear simulation. The problem of startup transients in the nonlinear simulation in making these comparisons is addressed. Also, reduction of the linear models is investigated using the modal and normal techniques. Reduced-order models of the F 100 are derived and compared with the full-state models.

Daniele, C. J.↗
NASA NTRS1992

Expert systems for automated maintenance of a Mars oxygen production system

Application of expert system concepts to a breadboard Mars oxygen processor unit have been studied and tested. The research was directed toward developing the methodology required to enable autonomous operation and control of these simple chemical processors at Mars. Failure detection and isolation was the key area of concern, and schemes using forward chaining, backward chaining, knowledge-based expert systems, and rule-based expert systems were examined. Tests and simulations were conducted that investigated self-health checkout, emergency shutdown, and fault detection, in addition to normal control activities. A dynamic system model was developed using the Bond-Graph technique. The dynamic model agreed well with tests involving sudden reductions in throughput. However, nonlinear effects were observed during tests that incorporated step function increases in flow variables. Computer simulations and experiments have demonstrated the feasibility of expert systems utilizing rule-based diagnosis and decision-making algorithms.

Huang, Jen-Kuang↗