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NASA NTRS1992

On-line implementation of nonlinear parameter estimation for the Space Shuttle main engine

We investigate the performance of a nonlinear estimation scheme applied to the estimation of several parameters in a performance model of the Space Shuttle Main Engine. The nonlinear estimator is based upon the extended Kalman filter which has been augmented to provide estimates of several key performance variables. The estimated parameters are directly related to the efficiency of both the low pressure and high pressure fuel turbopumps. Decreases in the parameter estimates may be interpreted as degradations in turbine and/or pump efficiencies which can be useful measures for an online health monitoring algorithm. This paper extends previous work which has focused on off-line parameter estimation by investigating the filter's on-line potential from a computational standpoint. ln addition, we examine the robustness of the algorithm to unmodeled dynamics. The filter uses a reduced-order model of the engine that includes only fuel-side dynamics. The on-line results produced during this study are comparable to off-line results generated previously. The results show that the parameter estimates are sensitive to dynamics not included in the filter model. Off-line results using an extended Kalman filter with a full order engine model to address the robustness problems of the reduced-order model are also presented.

Buckland, Julia H.↗

NASA NTRS2025

Shock-Stationary Application of Pseudoshock Models During High-Amplitude Combustion-Driven Unsteadiness

The isolator pseudo-shock provides necessary compression within a dual-mode scramjet engine and buffers the engine system against unstart. Quasi-1D flux-conserved models are the state-of-the-art reduced-order model for optimization and online control of dual-mode scramjet engines. The stability and efficacy of this modeling approach is evaluated against data from a combustor-driven direct-connect experiment. The experiment exhibited strong combustor-driven unsteadiness that produced upstream propagating weak shocks into the isolator, interacting with the pseudo-shock. While this configuration resulted in unsteadiness that is atypical of standard operation, the experiment provided an opportunity to evaluate the modeling techniques in highly transient states. Such transients could occur during maneuvering or result from unexpected combustor events. A flexible quasi-1D formulation, the Fievet flux-conserved model is fit using Bayesian inference in the laboratory and shock-stationary reference frames. Model performance is analyzed using the Bayesian posteriors and model evaluations over the measured shock train speed range. It is concluded that to produce consistent isolator pressure profile estimates in this unsteady environment, the model must be implemented in a shock-stationary reference frame. Implementing this conclusion in model-based engine controllers may reduce needed unstart safety margins and increase maximum performance.

Bayesian↗

NASA NTRS1992

An unsymmetric Lanczos algorithm for damped structural dynamics systems

A one-sided, unsymmetric block Lanczos algorithm is proposed for the model reduction of structural dynamics systems with unsymmetric damping and/or stiffness matrices. The algorithm is a three-term iteration scheme, which transforms the system matrix into an almost skew-symmetric, block-tridiagonal form. The Lanczos reduced-order model is guaranteed to be stable if the full-order system is stable. For unstable systems, a shifting method is available. Also, the algorithm offers flexibility in the choice of starting vectors and thus can yield more accurate reduced-order models. A linear system example and a plane truss structure example are used to show the efficacy of the proposed method.

Su, Tzu-Jeng↗

NASA NTRS1978

Procedures for generation and reduction of linear models of a turbofan engine

A real time hybrid simulation of the Pratt & Whitney F100-PW-F100 turbofan engine was used for linear-model generation. The linear models were used to analyze the effect of disturbances about an operating point on the dynamic performance of the engine. A procedure that disturbs, samples, and records the state and control variables was developed. For large systems, such as the F100 engine, the state vector is large and may contain high-frequency information not required for control. This, reducing the full-state to a reduced-order model may be a practicable approach to simplifying the control design. A reduction technique was developed to generate reduced-order models. Selected linear and nonlinear output responses to exhaust-nozzle area and main-burner fuel flow disturbances are presented for comparison.

Seldner, K.↗

NASA NTRS2008

Cryogenic Pressure Control Modeling for Ellipsoidal Space Tanks in Reduced Gravity

A computational fluid dynamics (CFD) model is developed to simulate pressure control of an ellipsoidal-shaped liquid hydrogen tank under external heating in low gravity. Pressure control is provided by an axial jet thermodynamic vent system (TVS) centered within the vessel that injects cooler liquid into the tank, mixing the contents and reducing tank pressure. The two-phase cryogenic tank model considers liquid hydrogen in its own vapor with liquid density varying with temperature only and a fully compressible ullage. The axisymmetric model is developed using a custom version of the commercially available FLOW-3D software and simulates low gravity extrapolations of engineering checkout tests performed at Marshall Space Flight Center in 1999 in support of the Solar Thermal Upper Stage Technology Demonstrator (STUSTD) program. Model results illustrate that stable low gravity liquid-gas interfaces are maintained during all phases of the pressure control cycle. Steady and relatively smooth ullage pressurization rates are predicted. This work advances current low gravity CFD modeling capabilities for cryogenic pressure control and aids the development of a low cost CFD-based design process for space hardware.

Hedayat, Ali↗

NASA NTRS2013

Developing an Accurate CFD Based Gust Model for the Truss Braced Wing Aircraft

The increased flexibility of long endurance aircraft having high aspect ratio wings necessitates attention to gust response and perhaps the incorporation of gust load alleviation. The design of civil transport aircraft with a strut or truss-braced high aspect ratio wing furthermore requires gust response analysis in the transonic cruise range. This requirement motivates the use of high fidelity nonlinear computational fluid dynamics (CFD) for gust response analysis. This paper presents the development of a CFD based gust model for the truss braced wing aircraft. A sharp-edged gust provides the gust system identification. The result of the system identification is several thousand time steps of instantaneous pressure coefficients over the entire vehicle. This data is filtered and downsampled to provide the snapshot data set from which a reduced order model is developed. A stochastic singular value decomposition algorithm is used to obtain a proper orthogonal decomposition (POD). The POD model is combined with a convolution integral to predict the time varying pressure coefficient distribution due to a novel gust profile. Finally the unsteady surface pressure response of the truss braced wing vehicle to a one-minus-cosine gust, simulated using the reduced order model, is compared with the full CFD.

Bartels, Robert E.↗

NASA NTRS1987

State-space formulation of multi-shaker modal analysis

As modal testing techniques have improved in recent years, the demands placed on the accuracy of modal test results have increased. This paper describes a new multi-input, multi-output modal parameter estimation algorithm suitable for the identification of reduced-order models of structures. The method described is a frequency-domain method based on excitation and response spectra. The principal features of the algorithm are: (1) applicability to general linear, time-invariant systems, (2) direct use of multiple input and multiple response data, (3) identification of reduced-order models with minimum user interaction through the use of two automatic model-reduction techniques, (4) identification of a consistent set of modal parameters through the use of numerically stable least-squares techniques, and (5) complete user documentation.

Craig, Roy R., Jr.↗

NASA NTRS2015

Application of Transfer Matrix Approach to Modeling and Decentralized Control of Lattice-Based Structures

This paper presents a modeling and control of aerostructure developed by lattice-based cellular materials/components. The proposed aerostructure concept leverages a building block strategy for lattice-based components which provide great adaptability to varying ight scenarios, the needs of which are essential for in- ight wing shaping control. A decentralized structural control design is proposed that utilizes discrete-time lumped mass transfer matrix method (DT-LM-TMM). The objective is to develop an e ective reduced order model through DT-LM-TMM that can be used to design a decentralized controller for the structural control of a wing. The proposed approach developed in this paper shows that, as far as the performance of overall structural system is concerned, the reduced order model can be as e ective as the full order model in designing an optimal stabilizing controller.

Transfer Matrix Method↗

NASA NTRS1989

LQG and direct rate feedback control with model reduction on a flexible laboratory grid structure

This paper presents experimental and theoretical comparisons of three control laws applied to a complex laboratory structure. A reduced finite element model was generated for designing the control systems and then corrected based on measured mode shapes and frequencies. A standard time-invariant linear quadratic regulator with state estimation was investigated first. Two simple direct rate feedback control laws both guaranteeing stability were also designed using the reduced model. One minimizes the maximum control force and the other minimizes the same quadratic performance index as the linear quadratic regulator. The three control laws have comparable performance indices with the direct rate feedback designs having better spillover properties. Experimental results for all designs were obtained with digital implementation. It was shown that the performance of the control system designed on the basis of the corrected finite element model agreed better with experimental results than the performance of the control system designed on the basis of the uncorrected model.

Schamel, G. C., II↗

NASA NTRS1978

NASTRAN analysis of Tokamak vacuum vessel using interactive graphics

Isoparametric quadrilateral and triangular elements were used to represent the vacuum vessel shell structure. For toroidally symmetric loadings, MPCs were employed across model boundaries and rigid format 24 was invoked. Nonsymmetric loadings required the use of the cyclic symmetry analysis available with rigid format 49. NASTRAN served as an important analysis tool in the Tokamak design effort by providing a reliable means for assessing structural integrity. Interactive graphics were employed in the finite element model generation and in the post-processing of results. It was felt that model generation and checkout with interactive graphics reduced the modelling effort and debugging man-hours significantly.

Miller, A.↗

NASA NTRS1981

Parameter estimation of large flexible aerospace structures with application to the control of the Maypole Deployable Reflector

Systems such as the Maypole deployable reflector have a distributed parameter nature. The flexible column and hoop structure and the circular antenna of 30-100 meter diameter which it supports are described by partial, rather than ordinary, differential equations. Progress completed in reduced order modelling andd controller design and digital parameter estimation and control is summarized. Topics covered include depolyment and on-orbit operation; quasi-static (steady state) operation; dynamic distributed parameter system; autoregressive moving average identification; frequency domain procedures; direct or implicit active control; adaptive observers; parameter estimation using a linear reinforcement learning factor; feedback control; and reduced order modeling for nonlinear systems.

Balas, M. J.↗

NASA NTRS1983

Current status of system identification methodology

Large space structures, system identification, model formulation, experimental design, model order and structure determination, parameter estimation, reduced order modeling, and closed loops are considered.

Larimore, W. E.↗

NASA NTRS1981

A function space approach to smoothing with applications to model error estimation for flexible spacecraft control

A function space approach to smoothing is used to obtain a set of model error estimates inherent in a reduced-order model. By establishing knowledge of inevitable deficiencies in the truncated model, the error estimates provide a foundation for updating the model and thereby improving system performance. The function space smoothing solution leads to a specification of a method for computation of the model error estimates and development of model error analysis techniques for comparison between actual and estimated errors. The paper summarizes the model error estimation approach as well as an application arising in the area of modeling for spacecraft attitude control.

Rodriguez, G.↗

NASA NTRS1988

Discrete analysis of spatial-sensitivity models

Procedures for reducing the computational burden of current models of spatial vision are described, the simplifications being consistent with the prediction of the complete model. A method for using pattern-sensitivity measurements to estimate the initial linear transformation is also proposed which is based on the assumption that detection performance is monotonic with the vector length of the sensor responses. It is shown how contrast-threshold data can be used to estimate the linear transformation needed to characterize threshold performance.

Nielsen, Kenneth R. K.↗

NASA NTRS2000

A Shell/3D Modeling Technique for the Analysis of Delaminated Composite Laminates

A shell/3D modeling technique was developed for which a local solid finite element model is used only in the immediate vicinity of the delamination front. The goal was to combine the accuracy of the full three-dimensional solution with the computational efficiency of a shell finite element model. Multi-point constraints provided a kinematically compatible interface between the local 3D model and the global structural model which has been meshed with shell finite elements. Double Cantilever Beam, End Notched Flexure, and Single Leg Bending specimens were analyzed first using full 3D finite element models to obtain reference solutions. Mixed mode strain energy release rate distributions were computed using the virtual crack closure technique. The analyses were repeated using the shell/3D technique to study the feasibility for pure mode I, mode II and mixed mode I/II cases. Specimens with a unidirectional layup and with a multidirectional layup were simulated. For a local 3D model, extending to a minimum of about three specimen thicknesses on either side of the delamination front, the results were in good agreement with mixed mode strain energy release rates obtained from computations where the entire specimen had been modeled with solid elements. For large built-up composite structures the shell/3D modeling technique offers a great potential for reducing the model size, since only a relatively small section in the vicinity of the delamination front needs to be modeled with solid elements.

Krueger, Ronald↗

NASA NTRS2003

Macroscopic Models of Radiative Transfer as Applied to Computation of the Radiation Field in the Solar Atmosphere

In this paper a new three dimensional half-moment model for radiative transfer is presented for a gray medium. It describes the evolution of the zeroth and first directional half moments of the radiative intensity. The closure is provided, similarly to Dubroca and Klar, by the maximum entropy concept. This work generalizes that model to three dimensions. The model presented here (the derivation being done in Ripoll and Wray, called the M(sup 1/2)(sub 1) model, is a hyperbolic system consisting of a total of eight equations in three dimensions, four equations for each direction. Each half model has the classical form of a macroscopic moment model in which the pressure tensor is constructed from the well-known Eddington tensor with a particular Eddington factor. Moreover, different source and border terms occur. The latter introduce couplings between the macroscopic and microscopic quantities and between the + and - streams, through the intensity in the plane perpendicular to the flux. The main theoretical application of the half moment model, treated in this paper, is its reduction to a full moment model, called M(sup +)(sub 1), for the particular but important case of a hot, opaque source radiating in a cold transparent (or semi-transparent) medium for very specific applications, such as stellar interiors or atmospheres, or combustion problems. The structure of the paper is as follows. In section 2, the model M(sup 1/2)(sub 1) is presented. In section 3, for the particular case of a hot, opaque source radiating into a cold medium, the half moment model is reduced to the M(sup +)(sub 1) model. In section 4, we first solve a simple and academic problem to validate the models, followed by a simplified solar atmosphere.

Ripoll, J.-F.↗

NASA NTRS2001

A Shell/3D Modeling Technique for the Analyses of Delaminated Composite Laminates

A shell/3D modeling technique was developed for which a local three-dimensional solid finite element model is used only in the immediate vicinity of the delamination front. The goal was to combine the accuracy of the full three-dimensional solution with the computational efficiency of a plate or shell finite element model. Multi-point constraints provided a kinematically compatible interface between the local three-dimensional model and the global structural model which has been meshed with plate or shell finite elements. Double Cantilever Beam (DCB), End Notched Flexure (ENF), and Single Leg Bending (SLB) specimens were modeled using the shell/3D technique to study the feasibility for pure mode I (DCB), mode II (ENF) and mixed mode I/II (SLB) cases. Mixed mode strain energy release rate distributions were computed across the width of the specimens using the virtual crack closure technique. Specimens with a unidirectional layup and with a multidirectional layup where the delamination is located between two non-zero degree plies were simulated. For a local three-dimensional model, extending to a minimum of about three specimen thicknesses on either side of the delamination front, the results were in good agreement with mixed mode strain energy release rates obtained from computations where the entire specimen had been modeled with solid elements. For large built-up composite structures modeled with plate elements, the shell/3D modeling technique offers a great potential for reducing the model size, since only a relatively small section in the vicinity of the delamination front needs to be modeled with solid elements.

Krueger, Ronald↗

NASA NTRS2006

A New Empirical Thermospheric Density Model JB2006 using New Solar Indices

A new empirical atmospheric density model is developed using the CIRA72 (Jacchia 71) model as the basis for the diffusion equations. New solar indices based on orbit based sensor data are used for the solar irradiances in the extreme and far ultraviolet wavelengths. New exospheric temperature and semiannual density equations are employed to represent the major thermospheric density variations. Temperature correction equations are also developed for diurnal and latitudinal effects, and finally density correction factors are used for model corrections required at high altitude (1500-4000 km). The new model, Jacchia-Bowman 2006, is validated through comparisons of accurate daily density drag data previously computed for numerous satellite. For 400 km altitude the standard deviation of 16% for the standard Jacchia model is reduced to 10% for the new JB2006 model for periods of low geomagnetic storm activity.

Bowman, Bruce R.↗