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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 289 records · Page 16
All sourcesNASA NTRSDOE OSTI
NASA NTRS1991

Image inversion analysis of the HST OTA (Hubble Space Telescope Optical Telescope Assembly), phase A

Technical work during September-December 1990 consisted of: (1) analyzing HST point source images obtained from JPL; (2) retrieving phase information from the images by a direct (noniterative) technique; and (3) characterizing the wavefront aberration due to the errors in the Hubble Space Telescope (HST) mirrors, in a preliminary manner. This work was in support of JPL design of compensating optics for the next generation wide-field planetary camera on HST. This digital technique for phase retrieval from pairs of defocused images, is based on the energy transport equation between these image planes. In addition, an end-to-end wave optics routine, based on the JPL Code 5 prescription of the unaberrated HST and WFPC, was derived for output of the reference phase front when mirror error is absent. Also, the Roddier routine unwrapped the retrieved phase by inserting the required jumps of +/- 2(pi) radians for the sake of smoothness. A least-squares fitting routine, insensitive to phase unwrapping, but nonlinear, was used to obtain estimates of the Zernike polynomial coefficients that describe the aberration. The phase results were close to, but higher than, the expected error in conic constant of the primary mirror suggested by the fossil evidence. The analysis of aberration contributed by the camera itself could be responsible for the small discrepancy, but was not verified by analysis.

Litvak, M. M.↗
NASA NTRS1994

The Accuracy of Parameter Estimation in System Identification of Noisy Aircraft Load Measurement

This thesis focuses on the subject of the accuracy of parameter estimation and system identification techniques. Motivated by a complicated load measurement from NASA Dryden Flight Research Center, advanced system identification techniques are needed. The objective of this problem is to accurately predict the load experienced by the aircraft wing structure during flight determined from a set of calibrated load and gage response relationship. We can then model the problem as a black box input-output system identification from which the system parameter has to be estimated. Traditional LS (Least Square) techniques and the issues of noisy data and model accuracy are addressed. A statistical bound reflecting the change in residual is derived in order to understand the effects of the perturbations on the data. Due to the intrinsic nature of the LS problem, LS solution faces the dilemma of the trade off between model accuracy and noise sensitivity. A method of conflicting performance indices is presented, thus allowing us to improve the noise sensitivity while at the same time configuring the degredation of the model accuracy. SVD techniques for data reduction are studied and the equivalence of the Correspondence Analysis (CA) and Total Least Squares Criteria are proved. We also looked at nonlinear LS problems with NASA F-111 data set as an example. Conventional methods are neither easily applicable nor suitable for the specific load problem since the exact model of the system is unknown. Neural Network (NN) does not require prior information on the model of the system. This robustness motivated us to apply the NN techniques on our load problem. Simulation results for the NN methods used in both the single load and the 'warning signal' problems are both useful and encouraging. The performance of the NN (for single load estimate) is better than the LS approach, whereas no conventional approach was tried for the 'warning signals' problems. The NN design methodology is also presented. The use of SVD, CA and Collinearity Index methods are used to reduce the number of neurons in a layer.

Kong, Jeffrey↗
DOE OSTI2021

Non-intrusive data-driven model reduction for differential–algebraic equations derived from lifting transformations

In this paper we present a non-intrusive data-driven approach for model reduction of nonlinear systems. The approach considers the particular case of nonlinear partial differential equations (PDEs) that form systems of partial differential–algebraic equations (PDAEs) when lifted to polynomial form. Such systems arise, for example, when the governing equations include Arrhenius reaction terms (e.g., in reacting flow models) and thermodynamic terms (e.g., the Helmholtz free energy terms in a phase-field solidification model). Using the known structured form of the lifted algebraic equations, the approach computes the reduced operators for the algebraic equations explicitly, using straightforward linear algebra operations on the basis matrices. The reduced operators for the differential equations are inferred from lifted snapshot data using operator inference, which solves a linear least squares regression problem. The approach is illustrated for the nonlinear model of solidification of a pure material. The lifting transformations reformulate the solidification PDEs as a system of PDAEs that have cubic structure. The operators of the lifted system for this solidification example have affine dependence on key process parameters, permitting us to learn a parametric reduced model with operator inference. Numerical experiments show the effectiveness of the resulting reduced models in capturing key aspects of the solidification dynamics.

42 ENGINEERING↗
DOE OSTI2020

Online Parameter Estimation Methods for Adaptive Cruise Control Systems

Modeling Adaptive Cruise Control (ACC) vehicles enables the understanding of the impact of these vehicles on traffic flow. In this work, two online methods are used to provide real time system identification of ACC enabled vehicles. The first technique is a recursive least squares (RLS) approach, while the second method solves a nonlinear joint state and parameter estimation problem via particle filtering (PF). We provide a parameter identifiability analysis for both methods to analytically show that the model parameters are not identifiable using equilibrium driving. The accuracy and computational runtime of the online methods are compared to a commonly used offline simulation-based optimization (i.e., batch optimization) approach. The methods are tested on synthetic data as well as on empirical data collected directly from a 2019 model year ACC vehicle using data from sensors that are part of the stock ACC system. The online methods are scalable and provide comparable accuracy to the batch method. RLS runs in real time and is two orders of magnitude faster than the batch method for modest sized (e.g., 15 min) datasets. The particle filter also runs in real- time, and is also suitable in streaming applications in which the datasets can grow arbitrarily large.

33 ADVANCED PROPULSION SYSTEMS↗
DOE OSTI2025

Kernel Manifolds: Nonlinear‐Augmentation Dimensionality Reduction Using Reproducing Kernel Hilbert Spaces

This paper generalizes recent advances on quadratic manifold (QM) dimensionality reduction by developing kernel methods-based nonlinear-augmentation dimensionality reduction. QMs, and more generally feature map-based nonlinear corrections, augment linear dimensionality reduction with a nonlinear correction term in the reconstruction map to overcome approximation accuracy limitations of purely linear approaches. While feature map-based approaches typically learn a least squares optimal polynomial correction term, we generalize this approach by learning an optimal nonlinear correction from a user-defined reproducing kernel Hilbert space. Our approach allows one to impose arbitrary nonlinear structure on the correction term, including polynomial structure, and includes feature map and radial basis function-based corrections as special cases. Furthermore, our method has relatively low training cost and has monotonically decreasing error as the latent space dimension increases. In conclusion, we compare our approach to proper orthogonal decomposition and several recent QM approaches on data from several example problems.

kernel methods↗
NASA NTRS1988

Parameter estimation in nonlinear distributed systems - Approximation theory and convergence results

An abstract approximation framework and convergence theory is described for Galerkin approximations applied to inverse problems involving nonlinear distributed parameter systems. Parameter estimation problems are considered and formulated as the minimization of a least-squares-like performance index over a compact admissible parameter set subject to state constraints given by an inhomogeneous nonlinear distributed system. The theory applies to systems whose dynamics can be described by either time-independent or nonstationary strongly maximal monotonic operators defined on a reflexive Banach space which is densely and continuously embedded in a Hilbert space. It is demonstrated that if readily verifiable conditions on the system's dependence on the unknown parameters are satisfied, and the usual Galerkin approximation assumption holds, then solutions to the approximating problems exist and approximate a solution to the original infinite-dimensional identification problem.

Banks, H. T.↗
NASA NTRS1984

Objective scatterometer wind ambiguity removal using smoothness and dynamical constraints

In the present investigation, a variational analysis method (VAM) is used to remove the ambiguity of the Seasat-A Satellite Scatterometer (SASS) winds. At each SASS data point, two, three, or four wind vectors (termed ambiguities) are retrieved. It is pointed out that the VAM is basically a least squares method for fitting data. The problem may be nonlinear. The best fit to the data and constraints is obtained on the basis of a minimization of the objective function. The VAM was tested and tuned at 12 h GMT Sept. 10, 1978. Attention is given to a case study involving an intense cyclone centered south of Japan at 138 deg E.

Hoffman, R. N.↗
NASA NTRS1986

Constraints on geomagnetic secular variation modeling from electromagnetism and fluid dynamics of the Earth's core

A spherical harmonic representation of the geomagnetic field and its secular variation for epoch 1980, designated GSFC(9/84), is derived and evaluated. At three epochs (1977.5, 1980.0, 1982.5) this model incorporates conservation of magnetic flux through five selected patches of area on the core/mantle boundary bounded by the zero contours of vertical magnetic field. These fifteen nonlinear constraints are included like data in an iterative least squares parameter estimation procedure that starts with the recently derived unconstrained field model GSFC (12/83). Convergence is approached within three iterations. The constrained model is evaluated by comparing its predictive capability outside the time span of its data, in terms of residuals at magnetic observatories, with that for the unconstrained model.

Benton, E. R.↗
NASA NTRS1990

Efficient Implementation of Minimal Polynomial and Reduced Rank Extrapolation Methods

The minimal polynomial extrapolation (MPE) and reduced rank extrapolation (RRE) are two effective techniques that have been used in accelerating the convergence of vector sequences, such as those that are obtained from iterative solution of linear and nonlinear systems of equation. Their definitions involve some linear least squares problems, and this causes difficulties in their numerical implementation. Timewise efficient and numerically stable implementations for MPE and RRE are developed. A computer program written in FORTRAN 77 is also appended and applied to some model problems.

Sidi, Avram↗
NASA NTRS1987

Vortex breakdown simulation based on a nonlinear inviscid model

It is shown that the inviscid equations governing steady axisymmetric flow with swirl, admit solutions with closed streamlines. Results are obtained using two different numerical algorithms. The first is based on a multigrid method for nonlinear eigenvalue problems, while the second is based on a least squares formulation.

Hafez, M. M.↗
NASA NTRS1982

Computer modeling of multiple-channel input signals and intermodulation losses caused by nonlinear traveling wave tube amplifiers

The multiple channel input signal to a soft limiter amplifier as a traveling wave tube is represented as a finite, linear sum of Gaussian functions in the frequency domain. Linear regression is used to fit the channel shapes to a least squares residual error. Distortions in output signal, namely intermodulation products, are produced by the nonlinear gain characteristic of the amplifier and constitute the principal noise analyzed in this study. The signal to noise ratios are calculated for various input powers from saturation to 10 dB below saturation for two specific distributions of channels. A criterion for the truncation of the series expansion of the nonlinear transfer characteristic is given. It is found that he signal to noise ratios are very sensitive to the coefficients used in this expansion. Improper or incorrect truncation of the series leads to ambiguous results in the signal to noise ratios.

Stankiewicz, N.↗
DOE OSTI2024

Prediction of Dielectric Constant in Series of Polymers by Quantitative Structure-Property Relationship (QSPR)

This work is devoted to the investigation of dielectric permittivity which is influenced by electronic, ionic, and dipolar polarization mechanisms, contributing to the material’s capacity to store electrical energy. In this study, an extended dataset of 86 polymers was analyzed, and two quantitative structure–property relationship (QSPR) models were developed to predict dielectric permittivity. From an initial set of 1273 descriptors, the most relevant ones were selected using a genetic algorithm, and machine learning models were built using the Gradient Boosting Regressor (GBR). In contrast to Multiple Linear Regression (MLR)- and Partial Least Squares (PLS)-based models, the gradient boosting models excel in handling nonlinear relationships and multicollinearity, iteratively optimizing decision trees to improve accuracy without overfitting. The developed GBR models showed high R2 coefficients of 0.938 and 0.822, for the training and test sets, respectively. An Accumulated Local Effect (ALE) technique was applied to assess the relationship between the selected descriptors—eight for the GB_A model and six for the GB_B model, and their impact on target property. ALE analysis revealed that descriptors such as TDB09m had a strong positive effect on permittivity, while MLOGP2 showed a negative effect. These results highlight the effectiveness of the GBR approach in predicting the dielectric properties of polymers, offering improved accuracy and interpretability.

Ascencio-Medina, Estefania↗
NASA NTRS1974

Least squares adjustment with relatively large observation errors, inaccurate initial approximations, or both

Least squares adjustment problems are considered in which the condition equations are nonlinear in both the observations and the adjustment parameters ('unknowns'). A solution algorithm is presented which takes into account the second (as well as the first) order derivatives in the adjustment residuals (observation errors) and the corrections to the initially available approximations to the adjustment parameters. The inclusion of second-order terms in the adjustment residuals is necessary whenever the adjustment residuals themselves cannot be regarded as negligible as compared to the adjustment parameters, i.e., whenever the linearized condition equations would no longer be practically equivalent to the rigorous ones. The consideration of second-order terms in the parameter corrections is completely independent of the second-order terms in the adjustment residuals.

Eichhorn, H.↗
NASA NTRS2012

Real-Time Frequency Response Estimation Using Joined-Wing SensorCraft Aeroelastic Wind-Tunnel Data

A new method is presented for estimating frequency responses and their uncertainties from wind-tunnel data in real time. The method uses orthogonal phase-optimized multi- sine excitation inputs and a recursive Fourier transform with a least-squares estimator. The method was first demonstrated with an F-16 nonlinear flight simulation and results showed that accurate short period frequency responses were obtained within 10 seconds. The method was then applied to wind-tunnel data from a previous aeroelastic test of the Joined- Wing SensorCraft. Frequency responses describing bending strains from simultaneous control surface excitations were estimated in a time-efficient manner.

Grauer, Jared A↗
NASA NTRS1972

The lunar conductivity profile and the nonuniqueness of electromagnetic data inversion.

A review of the theory for the electromagnetic functional used to date to determine the lunar conductivity profile from spectral analyses of lunar magnetometer data. The 'hard' boundary condition used by Sonett et al. (1971) and others appears to be a good approximation for the sunlit lunar hemisphere. The use of the spectral data in conjunction with the functional to find a least squares conductivity profile is examined from the point of view of the nonuniqueness of nonlinear estimation. An unsuccessful search was carried out to find models that were both geophysically reasonable and consistent with the data. It is asserted that the failure to find these models is due to the inadequacy of the functional. Of the models generated, those that best fit the data all have a conductivity peak at a depth of 240 km similar to that of the model discussed by Sonett et al. However, all of these models are quite distinct elsewhere in the profile. It is shown how such models are dependent on both the nature of the functional as well as the initial guess in the least squares procedure. A correlation analysis shows that the only resolvable features from this type of model are a low conductivity crust, a high conductivity peak of limited radial extent, and a low conductivity zone beneath the peak.

Phillips, R. J.↗
DOE OSTI2024

A fast and accurate domain decomposition nonlinear manifold reduced order model

Here, this paper integrates nonlinear-manifold reduced order models (NM-ROMs) with domain decomposition (DD). NM ROMs approximate the full order model (FOM) state in a nonlinear-manifold by training a shallow, sparse autoencoder using FOM snapshot data. These NM-ROMs can be advantageous over linear-subspace ROMs (LS-ROMs) for problems with slowly decaying Kolmogorov n-width. However, the number of NM-ROM parameters that need to be trained scales with the size of the FOM. Moreover, for “extreme-scale” problems, the storage of high-dimensional FOM snapshots alone can make ROM training expensive. To alleviate the training cost, this paper applies DD to the FOM, computes NM-ROMs on each subdomain, and couples them to obtain a global NM-ROM. This approach has several advantages: Subdomain NM-ROMs can be trained in parallel, involve fewer parameters to be trained than global NM-ROMs, require smaller subdomain FOM dimensional training data, and can be tailored to subdomain specific features of the FOM. The shallow, sparse architecture of the autoencoder used in each subdomain NM-ROM allows application of hyper-reduction (HR), reducing the complexity caused by nonlinearity and yielding computational speedup of the NM-ROM. This paper provides the first application of NM-ROM (with HR) to a DD problem. In particular, this paper details an algebraic DD reformulation of the FOM, training a NM-ROM with HR for each sub domain, and a sequential quadratic programming (SQP) solver to evaluate the coupled global NM-ROM. Theoretical convergence results for the SQP method and a priori and a posteriori error estimates for the DD NM-ROM with HR are provided. The proposed DD NM-ROM with HR approach is numerically compared to a DD LS-ROM with HR on the 2D steady-state Burgers’ equation, showing an order of magnitude improvement in accuracy of the proposed DD NM-ROM over the DD LS-ROM.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1999

Optimal System Realization in Frequency Domain

Several approaches are presented to identify an experimental system model directly from frequency response data. The formulation begins with a matrix-fraction description as the model structure. Frequency weighting such as exponential weighting is introduced to solve a weighted least-squares problem to obtain the coefficient matrices for the matrix-fraction description. A multi-variable state-space model can then be formed using the coefficient matrices of the matrix-fraction description. An approach is introduced to fine-tune the model using non-linear programming methods to minimize the desired cost function. The method deals with the model in the real Schur or modal form and reassigns a subset of system poles using a nonlinear optimizer. At every optimization step, the input and output influence matrices are refined through least-squares procedures. The proposed approaches are used to identify an analytical model for a NASA testbed from experimental data.

Juang, Jer-Nan↗