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Results for “natural spline”

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 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2016

Using In Vitro High‐Throughput Screening Data for Predicting Benzo[k]Fluoranthene Human Health Hazards

Today there are more than 80,000 chemicals in commerce and the environment. The potential human health risks are unknown for the vast majority of these chemicals as they lack human health risk assessments, toxicity reference values, and risk screening values. We aim to use computational toxicology and quantitative high‐throughput screening (qHTS) technologies to fill these data gaps, and begin to prioritize these chemicals for additional assessment. In this pilot, we demonstrate how we were able to identify that benzo[k]fluoranthene may induce DNA damage and steatosis using qHTS data and two separate adverse outcome pathways (AOPs). We also demonstrate how bootstrap natural spline‐based meta‐regression can be used to integrate data across multiple assay replicates to generate a concentration–response curve. We used this analysis to calculate an in vitro point of departure of 0.751 μM and risk‐specific in vitro concentrations of 0.29 μM and 0.28 μM for 1:1,000 and 1:10,000 risk, respectively, for DNA damage. Based on the available evidence, and considering that only a single HSD17B4 assay is available, we have low overall confidence in the steatosis hazard identification. This case study suggests that coupling qHTS assays with AOPs and ontologies will facilitate hazard identification. Combining this with quantitative evidence integration methods, such as bootstrap meta‐regression, may allow risk assessors to identify points of departure and risk‐specific internal/ in vitro concentrations. These results are sufficient to prioritize the chemicals; however, in the longer term we will need to estimate external doses for risk screening purposes, such as through margin of exposure methods.

Burgoon, Lyle D.↗
DOE OSTI2021

DELVE-ing into the Jet: A Thin Stellar Stream on a Retrograde Orbit at 30 kpc

We perform a detailed photometric and astrometric analysis of stars in the Jet stream using data from the first data release of the DECam Local Volume Exploration Survey DR1 and Gaia EDR3. We discover that the stream extends over ∼ 29° on the sky (increasing the known length by 18°), which is comparable to the kinematically cold Phoenix, ATLAS, and GD-1 streams. Using blue horizontal branch stars, we resolve a distance gradient along the Jet stream of 0.2 kpc deg$^{−1}$, with distances ranging from D $_{⊙}$ ∼ 27–34 kpc. We use natural splines to simultaneously fit the stream track, width, and intensity to quantitatively characterize density variations in the Jet stream, including a large gap, and identify substructure off the main track of the stream. Furthermore, we report the first measurement of the proper motion of the Jet stream and find that it is well aligned with the stream track, suggesting the stream has likely not been significantly perturbed perpendicular to the line of sight. Finally, we fit the stream with a dynamical model and find that it is on a retrograde orbit, and is well fit by a gravitational potential including the Milky Way and Large Magellanic Cloud. These results indicate the Jet stream is an excellent candidate for future studies with deeper photometry, astrometry, and spectroscopy to study the potential of the Milky Way and probe perturbations from baryonic and dark matter substructure.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2022

From the Fire: A Deeper Look at the Phoenix Stream

We use 6 yr of data from the Dark Energy Survey to perform a detailed photometric characterization of the Phoenix stellar stream, a 15° long, thin, dynamically cold, low-metallicity stellar system in the Southern Hemisphere. We use natural splines, a nonparametric modeling technique, to simultaneously fit the stream track, width, and linear density. This updated stream model allows us to improve measurements of the heliocentric distance (17.4 ± 0.1 (stat.) ±0.8 (sys.) kpc) and distance gradient (−0.009 ± 0.006 kpc deg$^{−1}$) of Phoenix, which corresponds to a small change of 0.13 ± 0.09 kpc in heliocentric distance along the length of the stream. We measure linear intensity variations on degree scales, as well as deviations in the stream track on ∼2° scales, suggesting that the stream may have been disturbed during its formation and/or evolution. We recover three peaks and one gap in linear intensity along with fluctuations in the stream track. Compared to other thin streams, the Phoenix stream shows more fluctuations and, consequently, the study of Phoenix offers a unique perspective on gravitational perturbations of stellar streams. We discuss possible sources of perturbations to Phoenix, including baryonic structures in the Galaxy and dark matter subhalos.

79 ASTRONOMY AND ASTROPHYSICS↗
NASA NTRS1976

Cubic spline reflectance estimates using the Viking lander camera multispectral data

A technique was formulated for constructing spectral reflectance estimates from multispectral data obtained with the Viking lander cameras. The output of each channel was expressed as a linear function of the unknown spectral reflectance producing a set of linear equations which were used to determine the coefficients in a representation of the spectral reflectance estimate as a natural cubic spline. The technique was used to produce spectral reflectance estimates for a variety of actual and hypothetical spectral reflectances.

Park, S. K.↗
DOE OSTI2017

Analyzing degradation data with a random effects spline regression model

This study proposes using a random effects spline regression model to analyze degradation data. Spline regression avoids having to specify a parametric function for the true degradation of an item. A distribution for the spline regression coefficients captures the variation of the true degradation curves from item to item. We illustrate the proposed methodology with a real example using a Bayesian approach. The Bayesian approach allows prediction of degradation of a population over time and estimation of reliability is easy to perform.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1976

A spectral reflectance estimation technique using multispectral data from the Viking lander camera

A technique is formulated for constructing spectral reflectance curve estimates from multispectral data obtained with the Viking lander camera. The multispectral data are limited to six spectral channels in the wavelength range from 0.4 to 1.1 micrometers and most of these channels exhibit appreciable out-of-band response. The output of each channel is expressed as a linear (integral) function of the (known) solar irradiance, atmospheric transmittance, and camera spectral responsivity and the (unknown) spectral responsivity and the (unknown) spectral reflectance. This produces six equations which are used to determine the coefficients in a representation of the spectral reflectance as a linear combination of known basis functions. Natural cubic spline reflectance estimates are produced for a variety of materials that can be reasonably expected to occur on Mars. In each case the dominant reflectance features are accurately reproduced, but small period features are lost due to the limited number of channels. This technique may be a valuable aid in selecting the number of spectral channels and their responsivity shapes when designing a multispectral imaging system.

Park, S. K.↗
NASA NTRS1977

Estimation of spectral reflectance curves from multispectral image data

A technique is presented for estimating spectral reflectance curves from multispectral image data even if the spectral samples are obtained from channels whose spectral responsivity is not narrowband. It is demonstrated that these reflectance estimates can be written as a linear combination of the spectral samples and that, analogous to Shannon's sampling theorem, if the spectral reflectance is a natural cubic spline, it can be estimated exactly provided the number of spectral channels is sufficiently large. Simulation results suggest that the accuracy of the spectral reflectance estimates is quite good and very insensitive to the spectral responsivity shapes.

Park, S. K.↗
NASA NTRS1985

A Natural Bias Approach to Cardinal Spline Curves

The cardinal spline approach to defining interpolatory curves is of interest in the application of computer graphics to modelling and animation problems. The formulation of this interpolation problem (C) a vector valued function V is obtained which forms a C1 map from 0,n into the plane in such a way that V(i) and V prime (i) attain prespecified (vector) values P sub i and T sub i for the integers i=0, 1,...n. The intent is that the planar curves V(s) pass through each point P sub i in the direction corresponding to T sub i. In actual practice it is common for only the interpolation points P sub i to be user specified. Suitable tangents T sub i are then provided by some heuristic to complete the specification of (C). A convex control polygon yields a convex interpolant. Examples exist where the interpolant fails to be convex if the tangents are left unbiased.

Fletcher, G. Y.↗
DOE OSTI2020

Soft x-ray spectrum unfold of K-edge filtered x-ray diode arrays using cubic splines

Cubic spline interpolation is able to recover temporally and spectrally resolved soft x-ray flux from an array of K-edge filtered x-ray diodes without the need for a priori assumptions about the spectrum or the geometry of the emitting volume. The mathematics of the cubic spline interpolation is discussed in detail. The analytic nature of the cubic spline solution allows for analytical error propagation, and the method of calculating the error for radiation temperature, spectral power, and confidence intervals of the unfolded spectrally resolved flux is explained. An unfold of a blackbody model demonstrates the accuracy of the cubic spline unfold. Tests of cubic spline performance using spectrally convolved detailed atomic model simulation results have been performed to measure the method's ability to conserve spectral power to within a factor of 2 or better in line-dominated regimes. The unfold is also demonstrated to work when information from the x-ray diode array is limited due to high signal-to-noise ratios or lack of signal due to over-attenuation or over-filtration of the x-ray diode signal. Here, the robustness of the unfold with respect to background subtraction and raw signal processing, signal alignment between diode traces, limited signal information, and initial conditions is discussed. Results from an example analysis of a halfraum drive are presented to demonstrate the capabilities of the unfold in comparison with previously established methods.

47 OTHER INSTRUMENTATION↗
NASA NTRS1985

Spline-based Rayleigh-Ritz methods for the approximation of the natural modes of vibration for flexible beams with tip bodies

Rayleigh-Ritz methods for the approximation of the natural modes for a class of vibration problems involving flexible beams with tip bodies using subspaces of piecewise polynomial spline functions are developed. An abstract operator theoretic formulation of the eigenvalue problem is derived and spectral properties investigated. The existing theory for spline-based Rayleigh-Ritz methods applied to elliptic differential operators and the approximation properties of interpolatory splines are useed to argue convergence and establish rates of convergence. An example and numerical results are discussed.

Rosen, I. G.↗
NASA NTRS1986

Spline-based Rayleigh-Ritz methods for the approximation of the natural modes of vibration for flexible beams with tip bodies

Rayleigh-Ritz methods for the approximation of the natural modes for a class of vibration problems involving flexible beams with tip bodies using subspaces of piecewise polynomial spline functions are developed. An abstract operator-theoretic formulation of the eigenvalue problem is derived and spectral properties investigated. The existing theory for spline-based Rayleigh-Ritz methods applied to elliptic differential operators and the approximation properties of interpolatory splines are used to argue convergence and establish rates of convergence. An example and numerical results are discussed.

Rosen, I. G.↗
NASA NTRS1984

A numerical scheme for the identification of hybrid systems describing the vibration of flexible beams with tip bodies

A cubic spline based Galerkin-like method is developed for the identification of a class of hybrid systems which describe the transverse vibration to flexible beams with attached tip bodies. The identification problem is formulated as a least squares fit to data subject to the system dynamics given by a coupled system of ordnary and partial differential equations recast as an abstract evolution equation (AEE) in an appropriate infinite dimensional Hilbert space. Projecting the AEE into spline-based subspaces leads naturally to a sequence of approximating finite dimensional identification problems. The solutions to these problems are shown to exist, are relatively easily computed, and are shown to, in some sense, converge to solutions to the original identification problem. Numerical results for a variety of examples are discussed.

Rosen, I. G.↗
NASA NTRS1994

Splines and control theory

In this work, the relationship between splines and the control theory has been analyzed. We show that spline functions can be constructed naturally from the control theory. By establishing a framework based on control theory, we provide a simple and systematic way to construct splines. We have constructed the traditional spline functions including the polynomial splines and the classical exponential spline. We have also discovered some new spline functions such as trigonometric splines and the combination of polynomial, exponential and trigonometric splines. The method proposed in this paper is easy to implement. Some numerical experiments are performed to investigate properties of different spline approximations.

Zhang, Zhimin↗
DOE OSTI2017

Generating short-term probabilistic wind power scenarios via nonparametric forecast error density estimators: Generating short-term probabilistic wind power scenarios via nonparametric forecast error density estimators

Forecasts of available wind power are critical in key electric power systems operations planning problems, including economic dispatch and unit commitment. Such forecasts are necessarily uncertain, limiting the reliability and cost effectiveness of operations planning models based on a single deterministic or “point” forecast. A common approach to address this limitation involves the use of a number of probabilistic scenarios, each specifying a possible trajectory of wind power production, with associated probability. We present and analyze a novel method for generating probabilistic wind power scenarios, leveraging available historical information in the form of forecasted and corresponding observed wind power time series. We estimate non-parametric forecast error densities, specifically using epi-spline basis functions, allowing us to capture the skewed and non-parametric nature of error densities observed in real-world data. We then describe a method to generate probabilistic scenarios from these basis functions that allows users to control for the degree to which extreme errors are captured.We compare the performance of our approach to the current state-of-the-art considering publicly available data associated with the Bonneville Power Administration, analyzing aggregate production of a number of wind farms over a large geographic region. Finally, we discuss the advantages of our approach in the context of specific power systems operations planning problems: stochastic unit commitment and economic dispatch. Here, our methodology is embodied in the joint Sandia – University of California Davis Prescient software package for assessing and analyzing stochastic operations strategies.

17 WIND ENERGY↗
DOE OSTI2024

Forward variable selection enables fast and accurate dynamic system identification with Karhunen-Loève decomposed Gaussian processes

A promising approach for scalable Gaussian processes (GPs) is the Karhunen-Loève (KL) decomposition, in which the GP kernel is represented by a set of basis functions which are the eigenfunctions of the kernel operator. Such decomposed kernels have the potential to be very fast, and do not depend on the selection of a reduced set of inducing points. However KL decompositions lead to high dimensionality, and variable selection thus becomes paramount. This paper reports a new method of forward variable selection, enabled by the ordered nature of the basis functions in the KL expansion of the Bayesian Smoothing Spline ANOVA kernel (BSS-ANOVA), coupled with fast Gibbs sampling in a fully Bayesian approach. It quickly and effectively limits the number of terms, yielding a method with competitive accuracies, training and inference times for tabular datasets of low feature set dimensionality. Theoretical computational complexities are O ( N P 2 ) in training and O ( P ) per point in inference, where N is the number of instances and P the number of expansion terms. The inference speed and accuracy makes the method especially useful for dynamic systems identification, by modeling the dynamics in the tangent space as a static problem, then integrating the learned dynamics using a high-order scheme. The methods are demonstrated on two dynamic datasets: a ‘Susceptible, Infected, Recovered’ (SIR) toy problem, along with the experimental ‘Cascaded Tanks’ benchmark dataset. Comparisons on the static prediction of time derivatives are made with a random forest (RF), a residual neural network (ResNet), and the Orthogonal Additive Kernel (OAK) inducing points scalable GP, while for the timeseries prediction comparisons are made with LSTM and GRU recurrent neural networks (RNNs) along with the SINDy package.

Hayes, Kyle↗
NASA NTRS1989

The computation of generalized cross-validation functions through householder tridiagonalization with applications to the fitting of interaction spline models

An efficient algorithm for computing the generalized cross-validation function for the general cross-validated regularization/smoothing problem is provided. This algorithm is appropriate for problems where no natural structure is available, and the regularization/smoothing problem is solved (exactly) in a reproducing kernel Hilbert space. It is particularly appropriate for certain multivariate smoothing problems with irregularly spaced data, and certain remote sensing problems, such as those that occur in meteorology, where the sensors are arranged irregularly. The algorithm is applied to the fitting of interaction spline models with irregularly spaced data and two smoothing parameters; favorable timing results are presented. The algorithm may be extended to the computation of certain generalized maximum likelihood (GML) functions. Application of the GML algorithm to a problem in numerical weather forecasting, and to a broad class of hypothesis testing problems, is noted.

Gu, Chong↗
NASA NTRS1994

Automation of reverse engineering process in aircraft modeling and related optimization problems

During the year of 1994, the engineering problems in aircraft modeling were studied. The initial concern was to obtain a surface model with desirable geometric characteristics. Much of the effort during the first half of the year was to find an efficient way of solving a computationally difficult optimization model. Since the smoothing technique in the proposal 'Surface Modeling and Optimization Studies of Aerodynamic Configurations' requires solutions of a sequence of large-scale quadratic programming problems, it is important to design algorithms that can solve each quadratic program in a few interactions. This research led to three papers by Dr. W. Li, which were submitted to SIAM Journal on Optimization and Mathematical Programming. Two of these papers have been accepted for publication. Even though significant progress has been made during this phase of research and computation times was reduced from 30 min. to 2 min. for a sample problem, it was not good enough for on-line processing of digitized data points. After discussion with Dr. Robert E. Smith Jr., it was decided not to enforce shape constraints in order in order to simplify the model. As a consequence, P. Dierckx's nonparametric spline fitting approach was adopted, where one has only one control parameter for the fitting process - the error tolerance. At the same time the surface modeling software developed by Imageware was tested. Research indicated a substantially improved fitting of digitalized data points can be achieved if a proper parameterization of the spline surface is chosen. A winning strategy is to incorporate Dierckx's surface fitting with a natural parameterization for aircraft parts. The report consists of 4 chapters. Chapter 1 provides an overview of reverse engineering related to aircraft modeling and some preliminary findings of the effort in the second half of the year. Chapters 2-4 are the research results by Dr. W. Li on penalty functions and conjugate gradient methods for quadratic programming problems.

Li, W.↗
NASA NTRS2003

Automated CFD Database Generation for a 2nd Generation Glide-Back-Booster

A new software tool, AeroDB, is used to compute thousands of Euler and Navier-Stokes solutions for a 2nd generation glide-back booster in one week. The solution process exploits a common job-submission grid environment using 13 computers located at 4 different geographical sites. Process automation and web-based access to the database greatly reduces the user workload, removing much of the tedium and tendency for user input errors. The database consists of forces, moments, and solution files obtained by varying the Mach number, angle of attack, and sideslip angle. The forces and moments compare well with experimental data. Stability derivatives are also computed using a monotone cubic spline procedure. Flow visualization and three-dimensional surface plots are used to interpret and characterize the nature of computed flow fields.

Chaderjian, Neal M.↗