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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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Jacobi matrix method for calculating zeros, coefficients, Christoffel numbers, and derivatives of orthogonal polynomials
Construction of orthogonal matrices using integer as elements for nonbinary coding
Orthogonal polynomials on finite pointset - algorithm for polynomial least square fit
Quantitative description of climatic element field by orthogonal functions
Arbitrary quasi-orthogonals for calculating flow distribution in turbomachine, noting digital computer calculations
Arbitrary quasi-orthogonals for calculating flow distribution in turbomachine, noting digital computer calculations
Core integral and electron repulsion integral for 2p-p1 Slater-type orbitals of allyl radical and benzene molecule transformed to Lowdin orthogonalized basis set of atomic orbitals
N-orthogonal phase-modulated codes generalized from first-order Reed-Muller codes and biorthogonal signals
Proper rotations of three-dimensional orthogonal frame
Hilberts method of solving linear integral equations using system of orthogonal functions
Extension of Hilbert method of linear functional equations to orthogonal systems of functions
The paper proposes the use of the orthogonal arrays for neural network learning. Learning can be seen as a search for the neural weights that give an optimal network performance.
Empirical orthogonal function modeling is explained and applied to identify compact discrete-time nonlinear unsteady aerodynamic models from data generated by an unsteady three-dimensional compressible Navier-Stokes flow solver for an airfoil undergoing various pitching motions. Model structures, model parameter estimates, and model parameter uncertainty estimates for nondimensional lift, drag, and pitching moment coefficient models were determined autonomously and directly from the data. Prediction tests using data that were not used in the modeling process showed that the identified models exhibited excellent prediction capability, which is a strong indicator of an accurate model.
A novel method for three-dimensional flowfield reconstruction is presented that utilizes spectral proper orthogonal decomposition (SPOD). The time-resolved PIV data are acquired in multiple two-dimensional spanwise planes, with adequate streamwise spacing to resolve the out-of-plane wavelength. Knowledge of the out-of-plane phase speed is also required, and for the present case this value was obtained using instantaneous hot-wire measurements. The method is validated by comparing phase-averaged results acquired with a forcing signal to the SPOD reconstructed results using the same data. The method is also applied to data with no forcing applied, and the results are shown to be similar to the forced case. This method is particularly useful for cases in which there are multiple frequencies of interest, or cases in which the phenomena occur over a broad range of frequencies. This method allows reconstruction of the frequencies of interest without the need for a forcing signal, so the flow can be studied in its natural (undisturbed) state.
This presentation discusses Spectral Proper Orthogonal Decomposition (SPOD) of Unsteady Pressure-Sensitive Paint (uPSP) measurements in the Space Launch System (SLS) Ascent Transient Aerodynamics Test (ATAT) and its application in the structural dynamics analysis.
This paper discusses Spectral Proper Orthogonal Decomposition (SPOD) of the Unsteady Pressure-Sensitive Paint (uPSP) measurements in recent NASA Ames wind tunnel test. The uPSP measurements were collected using Innovative Scientific Solutions, Inc. (ISSI) Porous, Fast-Response Pressure-Sensitive Paint (FP-XXX), 40 ISSI four-inch air-cooled Light-Emitting Diodes (LEDs), and 8 Phantom v2512 high-speed cameras at 10,000 frames per second in the Launch Vehicle Demo Test (LVDT) of the Space Launch System (SLS) Block 1B crew vehicle in the 11-by 11-foot transonic test section of the Unitary Plan Wind Tunnel (UPWT) at NASA Ames Research Center in April 2024. Fig. 1 shows the scale model of the SLS launch vehicle installed in the wind tunnel during the test.
Arbitrary quasi-orthogonals for calculating flow distribution in meridional plane of turbomachine
Turbomachine blade surface flow distribution analysis by arbitrary quasi-orthogonals - radial inflow turbine Fortran computer program