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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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100 records · Page 6
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Reduced basis approximations of parameterized dynamical partial differential equations via neural networks

Projection-based reduced order models are effective at approximating parameter-dependent differential equations that are parametrically separable. When parametric separability is not satisfied, which occurs in both linear and nonlinear problems, projection-based methods fail to adequately reduce the computational complexity. Devising alternative reduced order models is crucial for obtaining efficient and accurate approximations to expensive high-fidelity models. In this work, we develop a timestepping procedure for dynamical parameter-dependent problems, in which a neural-network is trained to propagate the coefficients of a reduced basis expansion. This results in an online stage with a computational cost independent of the size of the underlying problem. Here, we demonstrate our method on several parabolic partial differential equations, including a problem that is not parametrically separable.

97 MATHEMATICS AND COMPUTING↗
NASA NTRSDate not supplied

Quantifying Emergent Fluid Dynamics Using Reynolds-Interpolated Fluid Reduced-order Models

Fluid reduced-order models (ROMs) which capture the flow physics within the problem's physical domain are usually constrained in accuracy to only the parameter points, e.g. Reynolds and Mach numbers, at which reference data was provided. Interpolation-focused quantity-of-interest ROMs are often structured differently and fail to provide flow volume data with the same quality - if at all. In this paper, techniques which reside at the intersection of these two ROM schools - flow physics ROMs which can be interpolated within a parameter space of interest - are explored. Using a combination of existing and novel techniques, emergent physics are identified using a fluid ROM at parameter points which are not provided in the ROM's training data.

uncertainty quantification↗
NASA NTRSDate not supplied

Quantifying Emergent Fluid Dynamics Using Reynolds-Interpolated Fluid Reduced-order Models

Fluid reduced-order models (ROMs) which capture the flow physics within the problem's physical domain are usually constrained in accuracy to only the parameter points, e.g. Reynolds and Mach numbers, at which reference data was provided. Interpolation-focused quantity-of-interest ROMs are often structured differently and fail to provide flow volume data with the same quality - if at all. In this paper, techniques which reside at the intersection of these two ROM schools - flow physics ROMs which can be interpolated within a parameter space of interest - are explored. Using a combination of existing and novel techniques, emergent physics are identified using a fluid ROM at parameter points which are not provided in the ROM's training data.

uncertainty quantification↗
NASA NTRS2024

Development of a Data Fusion Methodology for Lineload Aerodynamic Databases for a Launch Vehicle during Liftoff and Transition

The need for databases for the distributed loading on launch vehicles during the early portion of flight necessitates the use of expensive computational flows in regimes where wake effects dominate. While also being expensive, this is a regime that computational tools tend to historically have problems simulating accurately. To help tackle this problem, a method of data fusion to combine computational results to wind tunnel derived force and moment data is developed. Using this method, significant reduction in computational costs and increases in confidence of the final product is possible and has been used to generate several databases for the Space Launch System (SLS) at NASA. While the full details of database generation are not part of this work, the crucial method at its core is developed here. Two SLS geometries are used throughout the work to demonstrate the techniques. These are two of the larger geometries and represent both planned crewed missions to the Moon as well as potential cargo missions to deep space. The method uses principal component analysis (PCA) to generate a reduced ordered model (ROM) to help fill in the full parameter space. Other similar techniques are explored, but were not found to have a significant result on the predictions of the ROM. Because the full number of components are kept to generate the model, this lack of difference is expected. This method is then extended to ensure that predicted surfaces match trusted force and moment data derived from wind tunnel testing. This extension is done by setting up a constrained optimization problem in order to minimize the deviation from the surface resolved computational data while still integrating to the desired values. When generating the constrained optimization problem, a weighting factor to balance these competing needs is introduced. The work compares previously introduced weighting terms from similar work to the proposed terms and shows that the previously used terms do not have as desirable behavior in this flow regime. This method is then expanded by developing a technique to incorporate uncertainty quantification into the developed data fusion methodology. This expansion takes a two pronged approach. One examines transferring the uncertainties in the force and moment database and characterizes how those adjustments change the predicted lineloads. The second looks at model form error and looks how rebuilding the model using slightly different data changes the predictions. These two terms are then combined in order to create an uncertainty model that takes both effects into account. The limitations of the proposed methods is then discussed as well as possible techniques to address these shortcomings.

Launch Vehicles↗
NASA NTRSDate not supplied

Derivation of Integrated Load Distributions from Resampled Computational Data

Principal component analysis (PCA) has been the center of many surrogate models used to characterize fluid flows in recent years. However, little work has been done to character- ize the uncertainty in the PCA transform itself and its effect on derived surrogate models. To explore the uncertainty, a typical interpolated surrogate model is constructed for a represen- tative aerodynamic body from computational data. The computational data is then resampled to explore the robustness of the PCA transformation. The variations of the model predictions during this resampling are analyzed to get a measure of confidence in the PCA transformation, which is then applied to the interpolated surrogate model to get uncertainty on integrated force predictions. An initial test case has been explored with promising results.

Principal Component Analysis↗
NASA NTRSDate not supplied

Derivation of Integrated Load Distributions from Resampled Computational Data

Principal component analysis (PCA) has been the center of many surrogate models used to characterize fluid flows in recent years. However, little work has been done to character- ize the uncertainty in the PCA transform itself and its effect on derived surrogate models. To explore the uncertainty, a typical interpolated surrogate model is constructed for a represen- tative aerodynamic body from computational data. The computational data is then resampled to explore the robustness of the PCA transformation. The variations of the model predictions during this resampling are analyzed to get a measure of confidence in the PCA transformation, which is then applied to the interpolated surrogate model to get uncertainty on integrated force predictions. An initial test case has been explored with promising results.

Computational Fluid Dynamics↗
NASA NTRSDate not supplied

Fluid-Thermal-Structural Interactions Induced by an Asymmetric Shock-Wave/Boundary-Layer Interaction in a Mach-6 Compression Corner

An experimental study is conducted of the fluid-thermal-structural interaction of a clamped compliant panel exposed to a three dimensional shock-wave/boundary-layer interaction (SWBLI) induced by a Mach-6 compression ramp with a spanwise nonuniform incoming boundary layer. The nonuniform boundary layer was produced by placing trips on one side of the upstream flat plate, resulting in largely turbulent flow on the tripped side and transitional flow on the untripped side. Measurements of the flowfield confirmed that the tripped boundary layer contained elevated levels of unsteadiness, and the SWBLI was observed to vary from attached to fully separated as the ramp angle was increased from 10◦ to 38◦; the separation region on the tripped side of the panel was noticeably smaller, showing the elevated turbulence levels of the tripped-side flow to remain relatively localized rather than diffusing across the whole model. Full-field, time-resolved panel deformations were measured using high-speed photogrammetry and the vibrational response at each compression angle was characterized. Although the measured modes conformed largely to those from classical clamped-plate theory, some skewing of the mode shapes was observed. IR thermography highlighted regions of the compliant region where elevated temperatures were likely to promote thermal softening effects to the transient panel response. The quasi-static deformation and stress field was used to characterize the internal stress factor of each mode and showed a meaningful relationship between transient panel response and stress contained within each mode: modes with antinodes lying in high-stress areas of the plate tended to exhibit increases in vibrational frequency and decreases in vibrational power, whereas the opposite was true for modes with antinodes in low-stress areas.

Spectral Proper Orthogonal Decomposition↗
NASA NTRS1994

On determining the spectrum of primordial inhomogeneity from the COBE DMR sky maps: Method

The natural approach to a spectral analysis of data distributed on the sky employs spherical harmonic decomposition. A common problem encountered in practical astronomy is the lack of full sky coverage in the available data. For example, the removal of the Galactic plane data from the Cosmic Background Explorer (COBE) Differential Microwave Radiometer (DMR) sky maps compromises Fourier analysis of the cosmic microwave background (CMB) temperature distribution due to the loss of orthogonality of the spherical harmonics. An explicit method for constructing orthonormal functions on an incomplete (e.g., Galaxy-cut) sphere is presented. These functions should be used in the proper Fourier analysis of the COBE DMR sky maps to provide the correct input for the determination of the spectrum of primordial inhomogeneity. The results of such an analysis are presented in an accompanying Letter. A similar algebraic construction of appropriate functions can be devised for other astronomical applications.

Gorski, Krzysztof M.↗
NASA NTRS1983

Asymptotic unbounded root loci - Formulas and computation

A new geometric way of computing the asymptotic behavior of unbounded root loci of a strictly proper linear time-invariant control system as loop gain goes to infinity is presented. Properties of certain restricted linear maps and nested restrictions of linear maps are developed, and formulas are obtained for the leading coefficient of the asymptotic values of the unbounded multivariable root loci are obtained in terms of eigenvalues of those maps. Published results and a certain simple null structure assumption are used to relate these asymptotic values to the structure at infinity of the Smith-McMillan form of the open loop transfer function. Explicit matrix formulas for the more abstract derived formulas are given and additional geometric insights are developed with orthogonal projections and singular value decomposition. Formulas for the pivots of the unbounded root loci are calculated and shown to have the same form as the coefficients of the unbounded asymptotic root loci.

Sastry, S. S.↗
NASA NTRS1994

A simple suboptimal least-squares algorithm for attitude determination with multiple sensors

Three-axis attitude determination is equivalent to finding a coordinate transformation matrix which transforms a set of reference vectors fixed in inertial space to a set of measurement vectors fixed in the spacecraft. The attitude determination problem can be expressed as a constrained optimization problem. The constraint is that a coordinate transformation matrix must be proper, real, and orthogonal. A transformation matrix can be thought of as optimal in the least-squares sense if it maps the measurement vectors to the reference vectors with minimal 2-norm errors and meets the above constraint. This constrained optimization problem is known as Wahba's problem. Several algorithms which solve Wahba's problem exactly have been developed and used. These algorithms, while steadily improving, are all rather complicated. Furthermore, they involve such numerically unstable or sensitive operations as matrix determinant, matrix adjoint, and Newton-Raphson iterations. This paper describes an algorithm which minimizes Wahba's loss function, but without the constraint. When the constraint is ignored, the problem can be solved by a straightforward, numerically stable least-squares algorithm such as QR decomposition. Even though the algorithm does not explicitly take the constraint into account, it still yields a nearly orthogonal matrix for most practical cases; orthogonality only becomes corrupted when the sensor measurements are very noisy, on the same order of magnitude as the attitude rotations. The algorithm can be simplified if the attitude rotations are small enough so that the approximation sin(theta) approximately equals theta holds. We then compare the computational requirements for several well-known algorithms. For the general large-angle case, the QR least-squares algorithm is competitive with all other know algorithms and faster than most. If attitude rotations are small, the least-squares algorithm can be modified to run faster, and this modified algorithm is faster than all but a similarly specialized version of the QUEST algorithm. We also introduce a novel measurement averaging technique which reduces the n-measurement case to the two measurement case for our particular application, a star tracker and earth sensor mounted on an earth-pointed geosynchronous communications satellite. Using this technique, many n-measurement problems reduce to less than or equal to 3 measurements; this reduces the amount of required calculation without significant degradation in accuracy. Finally, we present the results of some tests which compare the least-squares algorithm with the QUEST and FOAM algorithms in the two-measurement case. For our example case, all three algorithms performed with similar accuracy.

Brozenec, Thomas F.↗