SEARCH · Engineering Papers

Results for “partial least squares”

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.

SourceResearch connectionFrom yearThrough year

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 217 records · Page 12

All sources NASA NTRS DOE OSTI

NASA NTRS1974

Sequential filter design for precision orbit determination and physical constant refinement

Earth-based spacecraft tracking data have historically been processed with classical least squares filtering techniques both for navigation purposes and for physical constant determination. The small, stochastic nongravitational forces acting on the spacecraft are described to motivate the use of sequential estimation as an alternative to the least squares fitting procedures. The stochastic forces are investigated both in terms of their effect on the tracking data and their influence on estimation accuracy. A flexible sequential filter design which leaves the existing trajectory, variational equations, data observable and partial computations undisturbed is described. A detailed filter design is presented that meets the precision demands and flexibility requirements of deep space navigation and of scientific problems.

Curkendall, D. W.↗

NASA NTRS1985

Structural parameter identification of distributed systems using finite element approximation

A system identification technique is developed for classes of distributed systems using finite element approximations. Vibrating systems represented by partial differential equations have physical parameters associated with mass, stiffness, and damping distributions which need to be known in order to properly control and design mathematical models of the system. In order to identify these parameters a weighted least-squares algorithm and modified Newton-Raphson method is used for the identification process. The theory and technique is demonstrated by estimating the system parameters of a vibrating cantilever beam made up of several different structural properties.

Lee, K. Y.↗

DOE OSTI2020

Retrieval of Cloud Liquid Water Using Microwave Signals from LEO Satellites: A Feasibility Study through Simulations

A novel method, using low Earth orbit (LEO) satellite microwave communication links for cloud liquid water measurements, is introduced in this paper. The feasibility of this approach is studied through simulations of the retrieval system including a LEO satellite communicating with a group of ground receivers equipped with signal-to-noise ratio (SNR) estimators, a synthetic cloud attenuation field and a tomographic retrieval algorithm. Rectangular and Gaussian basis functions are considered to define the targeted field. Simulation results suggest that the proposed least-squares based retrieval algorithm produces satisfactory outcomes for both types of basis functions. The root-mean-square error of the retrieved field is around 0.2 dB/km, with the range of the reference field as 0 to 2.35 dB/km. It is also confirmed that the partial retrieval of the cloud field is achievable when a limited number of receivers with restricted locations are available. The retrieval outcomes exhibit properties of high resolution and low error, indicating that the proposed approach has great potential for cloud observations.

54 ENVIRONMENTAL SCIENCES↗

NASA NTRS1989

Numerical algorithms for steady and unsteady incompressible Navier-Stokes equations

The numerical analysis of the incompressible Navier-Stokes equations are becoming important tools in the understanding of some fluid flow problems which are encountered in research as well as in industry. With the advent of the supercomputers, more realistic problems can be studied with a wider choice of numerical algorithms. An alternative formulation is presented for viscous incompressible flows. The incompressible Navier-Stokes equations are cast in a velocity/vorticity formulation. This formulation consists of solving the Poisson equations for the velocity components and the vorticity transport equation. Two numerical algorithms for the steady two-dimensional laminar flows are presented. The first method is based on the actual partial differential equations. This uses a finite-difference approximation of the governing equations on a staggered grid. The second method uses a finite element discretization with the vorticity transport equation approximated using a Galerkin approximation and the Poisson equations are obtained using a least squares method. The equations are solved efficiently using Newton's method and a banded direct matrix solver (LINPACK). The method is extended to steady three-dimensional laminar flows and applied to a cubic driven cavity using finite difference schemes and a staggered grid arrangement on a Cartesian mesh. The equations are solved iteratively using a plane zebra relaxation scheme. Currently, a two-dimensional, unsteady algorithm is being developed using a generalized coordinate system. The equations are discretized using a finite-volume approach. This work will then be extended to three-dimensional flows.

Hafez, Mohammed↗

NASA NTRS1986

Simulation and study of small numbers of random events

Random events were simulated by computer and subjected to various statistical methods to extract important parameters. Various forms of curve fitting were explored, such as least squares, least distance from a line, maximum likelihood. Problems considered were dead time, exponential decay, and spectrum extraction from cosmic ray data using binned data and data from individual events. Computer programs, mostly of an iterative nature, were developed to do these simulations and extractions and are partially listed as appendices. The mathematical basis for the compuer programs is given.

Shelton, R. D.↗

NASA NTRS1988

GaussFit - A system for least squares and robust estimation

GaussFit is a new computer program for solving least-squares and robust estimation problems. It has a number of unique features, including a complete programming language designed especially to formulate estimation problems, a built-in compiler and interpreter to support the programming language, and a built-in algebraic manipulator for calculating the required partial derivatives analytically. These features make GaussFit very easy to use, so that even complex problems can be set up and solved with minimal effort. GaussFit can correctly handle many cases of practical interest: nonlinear models, exact constraints, correlated observations, and models where the equations of condition contain more than one observed quantity. An experimental robust estimation capability is built into GaussFit so that data sets contaminated by outliers can be handled simply and efficiently.

Jefferys, W. H.↗

NASA NTRS2004

An Evaluation of Quantitative Methods of Determining the Degree of Melting Experienced by a Chondrule

Many workers have considered the degree to which partial melting occurred in chondrules they have studied, and this has led to attempts to find reliable methods of determining the degree of melting. At least two quantitative methods have been used in the literature: a convolution index (CVI), which is a ratio of the perimeter of the chondrule as seen in thin section divided by the perimeter of a circle with the same area as the chondrule, and nominal grain size (NGS), which is the inverse square root of the number density of olivines and pyroxenes in a chondrule (again, as seen in thin section). We have evaluated both nominal grain size and convolution index as melting indicators. Nominal grain size was measured on the results of a set of dynamic crystallization experiments previously described, where aliquots of LEW97008(L3.4) were heated to peak temperatures of 1250, 1350, 1370, and 1450 C, representing varying degrees of partial melting of the starting material. Nominal grain size numbers should correlate with peak temperature (and therefore degree of partial melting) if it is a good melting indicator. The convolution index is not directly testable with these experiments because the experiments do not actually create chondrules (and therefore they have no outline on which to measure a CVI). Thus we had no means to directly test how well the CVI predicted different degrees of melting. Therefore, we discuss the use of the CVI measurement and support the discussion with X-ray Computed Tomography (CT) data.

Nettles, J. W.↗

NASA NTRS1997

Exponential Approximations Using Fourier Series Partial Sums

The problem of accurately reconstructing a piece-wise smooth, 2(pi)-periodic function f and its first few derivatives, given only a truncated Fourier series representation of f, is studied and solved. The reconstruction process is divided into two steps. In the first step, the first 2N + 1 Fourier coefficients of f are used to approximate the locations and magnitudes of the discontinuities in f and its first M derivatives. This is accomplished by first finding initial estimates of these quantities based on certain properties of Gibbs phenomenon, and then refining these estimates by fitting the asymptotic form of the Fourier coefficients to the given coefficients using a least-squares approach. It is conjectured that the locations of the singularities are approximated to within O(N(sup -M-2), and the associated jump of the k(sup th) derivative of f is approximated to within O(N(sup -M-l+k), as N approaches infinity, and the method is robust. These estimates are then used with a class of singular basis functions, which have certain 'built-in' singularities, to construct a new sequence of approximations to f. Each of these new approximations is the sum of a piecewise smooth function and a new Fourier series partial sum. When N is proportional to M, it is shown that these new approximations, and their derivatives, converge exponentially in the maximum norm to f, and its corresponding derivatives, except in the union of a finite number of small open intervals containing the points of singularity of f. The total measure of these intervals decreases exponentially to zero as M approaches infinity. The technique is illustrated with several examples.

Banerjee, Nana S.↗

DOE OSTI2021

Parameter dependencies of the experimental nitrogen concentration required for detachment on ASDEX Upgrade and JET

While current tokamak experiments are beginning to use real-time feedback control systems to manage the plasma exhaust, future tokamaks still require validation of theoretical models used to predict the threshold impurity concentration required to sufficiently reduce the power and particle fluxes to the divertor. This work exploits new spectroscopic measurements of the divertor nitrogen concentration, c n , in partially detached N 2 -seeded H-mode plasmas on ASDEX Upgrade (AUG) and JET with the ITER-Like Wall (JET-ILW) to test the parameter dependencies of the power flowing to the outer divertor, P div,outer , and the separatrix electron density, n e.sep . A least-squares regression of the AUG measurements demonstrates that the threshold c n required for detachment scales as $c_n∝P^{1.19±0.32}_{div,outer}n^{-2.77±0.36}_{e,sep}$. This scaling of n e,sep is also consistent with the measurements from JET which, at constant P div,outer , show $c_n∝n^{-2.43±0.27}_{e,sep}$. The dependencies of P div,outer and n e.sep is demonstrated over at least a factor of two change in both parameters and indicates a stronger dependence on n e.sep in comparison to the Lengyel model, which could be due to the assumption in this model that the heat flux channel width is independent of density. This first assessment of detachment scaling with impurity seeding highlights the need for further analysis of the systematic uncertainties of the measurement and more consistent scenarios from more tokamaks to investigate the machine size scaling.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2021

Efficient ptychographic phase retrieval via a matrix-free Levenberg-Marquardt algorithm

The phase retrieval problem, where one aims to recover a complex-valued image from far-field intensity measurements, is a classic problem encountered in a range of imaging applications. Modern phase retrieval approaches usually rely on gradient descent methods in a nonlinear minimization framework. Calculating closed-form gradients for use in these methods is tedious work, and formulating second order derivatives is even more laborious. Additionally, second order techniques often require the storage and inversion of large matrices of partial derivatives, with memory requirements that can be prohibitive for data-rich imaging modalities. We use a reverse-mode automatic differentiation (AD) framework to implement an efficient matrix-free version of the Levenberg-Marquardt (LM) algorithm, a longstanding method that finds popular use in nonlinear least-square minimization problems but which has seen little use in phase retrieval. Furthermore, we extend the basic LM algorithm so that it can be applied for more general constrained optimization problems (including phase retrieval problems) beyond just the least-square applications. Since we use AD, we only need to specify the physics-based forward model for a specific imaging application; the first and second-order derivative terms are calculated automatically through matrix-vector products, without explicitly forming the large Jacobian or Gauss-Newton matrices typically required for the LM method. We demonstrate that this algorithm can be used to solve both the unconstrained ptychographic object retrieval problem and the constrained “blind” ptychographic object and probe retrieval problems, under the popular Gaussian noise model as well as the Poisson noise model. We compare this algorithm to state-of-the-art first order ptychographic reconstruction methods to demonstrate empirically that this method outperforms best-in-class first-order methods: it provides excellent convergence guarantees with (in many cases) a superlinear rate of convergence, all with a computational cost comparable to, or lower than, the tested first-order algorithms.

36 MATERIALS SCIENCE↗

NASA NTRS1993

Improved Nystrom Integrators

New formulation for Nystrom integrators offers increased precision and speed of computation. Formulation takes advantage of capabilities of modern electronic computers. Independent and dependent variables and various partial and total derivatives expressed via compact tensor notation. In this approach, typical set of constraint equations derived in about 1 day. Solution of constraint equations speeded by SEARCH computer program. Is general-purpose optimization program, which maximizes or minimizes cost function defined by user. Used successfully, to make least-squares fit of about 4,000 equations in 12 unknowns.

Lear, William M.↗

NASA NTRS1992

Optimal moving grids for time-dependent partial differential equations

Various adaptive moving grid techniques for the numerical solution of time-dependent partial differential equations were proposed. The precise criterion for grid motion varies, but most techniques will attempt to give grids on which the solution of the partial differential equation can be well represented. Moving grids are investigated on which the solutions of the linear heat conduction and viscous Burgers' equation in one space dimension are optimally approximated. Precisely, the results of numerical calculations of optimal moving grids for piecewise linear finite element approximation of PDE solutions in the least-squares norm are reported.

Wathen, A. J.↗

NASA NTRS1986

Open system magnetic evolution of the taos plateau volcanic field, Northern New Mexico. I - The petrology and geochemistry of the servilleta basalt

MULTIFIT, an embodiment of the conceptual structure needed in modeling multisource and multiprocess magmatic systems, is described. This program, which uses familiar materials balance methodology and the equilibrium form of the Rayleigh equations, links evolutionary arrays, which is turn collectively relate the starting and final compositions of a given magmatic system. Moreover, MULTIFIT incorporates variations within major element data arrays; the linkage between them can be tested using an extension of the least squares algorithm, which selects the best branch point according to the minimum-sum-of-squared-residuals criterion. Advantages and disadvantages of the materials balance approach used in this program are discussed, an example is provided, and equations utilized by MULTIFIT are summarized. While MULTIFIT may not be the best approach for poorly constrained models involving partial melting for complex mixing, it may ultimately prove useful for ascertaining trace element partition coefficients in magnetic systems.

Dungan, M. A.↗

DOE OSTI2025

Bayesian learning with Gaussian processes for low-dimensional representations of time-dependent nonlinear systems

This work presents a data-driven method for learning low-dimensional time-dependent physics-based surrogate models whose predictions are endowed with uncertainty estimates. We use the operator inference approach to model reduction that poses the problem of learning low-dimensional model terms as a regression of state space data and corresponding time derivatives by minimizing the residual of reduced system equations. Standard operator inference models perform well with accurate training data that are dense in time, but producing stable and accurate models when the state data are noisy and/or sparse in time remains a challenge. Another challenge is the lack of uncertainty estimation for the predictions from the operator inference models. Our approach addresses these challenges by incorporating Gaussian process surrogates into the operator inference framework to (1) probabilistically describe uncertainties in the state predictions and (2) procure analytical time derivative estimates with quantified uncertainties. The formulation leads to a generalized least-squares regression and, ultimately, reduced-order models that are described probabilistically with a closed-form expression for the posterior distribution of the operators. The resulting probabilistic surrogate model propagates uncertainties from the observed state data to reduced-order predictions. Furthermore, we demonstrate the method is effective for constructing low-dimensional models of two nonlinear partial differential equations representing a compressible flow and a nonlinear diffusion–reaction process, as well as for estimating the parameters of a low-dimensional system of nonlinear ordinary differential equations representing compartmental models in epidemiology.

Data-driven model reduction↗

NASA NTRS1988

Kinetics of thermochemical gas-solid reactions important in the Venus sulfur cycle

The thermochemical net reaction CaCO3 + SO2 yields CaSO4 + CO is predicted to be an important sink for incorporation of SO2 into the Venus crust. The reaction rate law was established to understand the dependence of rate on experimental variables such as temperature and partial pressure of SO2, CO2, and O2. The experimental approach was a variant of the thermogravimetric method often employed to study the kinetics of thermochemical gas-solid reactions. Clear calcite crystals were heated at constant temperature in SO2-bearing gas streams for varying time periods. Reaction rate was determined by three independent methods. A weighted linear least squares fit to all rate data yielded a rate equation. Based on the Venera 13, 14 and Vega 2 observations of CaO content of the Venus atmosphere, SO2 at the calculated rate would be removed from the Venus atmosphere in about 1,900,00 years. The most plausible endogenic source of the sulfur needed to replenish atmospheric SO2 is volcanism. The annual amount of erupted material needed for the replenishment depends on sulfur content; three ratios are used to calculate rates ranging from 0.4 to 11 cu km/year. This geochemically derived volcanism rate can be used to test if geophysically derived rates are correct. The work also suggests that Venus is less volcanically active than the Earth.

Fegley, Bruce, Jr.↗

NASA NTRS1975

Computer-oriented synthesis of wide-band non-uniform negative resistance amplifiers

This paper presents a synthesis procedure which provides design values for broad-band amplifiers using non-uniform negative resistance devices. Employing a weighted least squares optimization scheme, the technique, based on an extension of procedures for uniform negative resistance devices, is capable of providing designs for a variety of matching network topologies. It also provides, for the first time, quantitative results for predicting the effects of parameter element variations on overall amplifier performance. The technique is also unique in that it employs exact partial derivatives for optimization and sensitivity computation. In comparison with conventional procedures, significantly improved broad-band designs are shown to result.

Branner, G. R.↗

NASA NTRS2007

Sensitivity Testing of the NSTAR Ion Thruster

During the Extended Life Test of the DS1 flight spare ion thruster, the engine was subjected to sensitvity testing in order to characterize the macroscopic dependence of discharge chamber sensitivity to a +\-3% vatiation in main flow, cathode flow and beam current, and to +\5% variation in beam and accelerator voltage, was determined for the minimum- (THO), half- (TH8) and full power (TH15) throttle levels. For each power level investigared, 16 high/low operating conditions were chosen to vary the flows, beam current, and grid voltages in in a matrix that mapped out the entire parameter space. The matrix of data generated was used to determine the partial derivative or senitivity of the dependent parameters--discharge voltage, discharge current, discharge loss, double-to-single-ion current ratio, and neutralizer-keeper voltage--to the variation in the independent parameters--main flow, cathode flow, beam current, and beam voltage. The sensititivities of each dependent parameter with respect to each independent parameter were determined using a least-square fit routine. Variation in these sensitivities with thruster runtime was recorded over the duration of the ELT, to detemine if discharge performance changed with thruster wear. Several key findings have been ascertained from the sensitivity testing. Discharge operation is most sensitve to changes in cathode flow and to a lesser degree main flow. The data also confirms that for the NSTAR configuration plasma production is limited by primary electron input due to the fixed neutral population. Key sensitivities along with their change with thruster wear (operating time) will be presented. In addition double ion content measurements with an ExB probe will also be presented to illustrate beam ion production and content sensitivity to the discharge chamber operating parameteres.

electric propulsion↗

NASA NTRS1982

Toward autonomous spacecraft

Ways in which autonomous behavior of spacecraft can be extended to treat situations wherein a closed loop control by a human may not be appropriate or even possible are explored. Predictive models that minimize mean least squared error and arbitrary cost functions are discussed. A methodology for extracting cyclic components for an arbitrary environment with respect to usual and arbitrary criteria is developed. An approach to prediction and control based on evolutionary programming is outlined. A computer program capable of predicting time series is presented. A design of a control system for a robotic dense with partially unknown physical properties is presented.

Fogel, L. J.↗