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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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All sourcesNASA NTRSDOE OSTI
NASA NTRS1988

Dynamic structural correlation via nonlinear programming techniques

A solution to the correlation between structural dynamic test results and finite element analyses of the same components is presented in this paper. Basically, the method can be categorized as a Levenberg-Marquardt type Gauss-Newton method which requires only the differences between FE modal analyses and test results and their first derivatives with respect to preassigned design variables. With proper variable normalization and equation scaling, the method has been made numerically better-conditioned and the inclusion of the Levenberg-Marquardt technique overcomes any remaining difficulty encountered in inverting singular or near-singular matrices. An important feature is that each iteration requires only one function evaluation along with the associated design sensitivity analysis and so the procedure is computationally efficient.

Ting, T.↗
NASA NTRS1995

A General Method for Solving Systems of Non-Linear Equations

The method of steepest descent is modified so that accelerated convergence is achieved near a root. It is assumed that the function of interest can be approximated near a root by a quadratic form. An eigenvector of the quadratic form is found by evaluating the function and its gradient at an arbitrary point and another suitably selected point. The terminal point of the eigenvector is chosen to lie on the line segment joining the two points. The terminal point found lies on an axis of the quadratic form. The selection of a suitable step size at this point leads directly to the root in the direction of steepest descent in a single step. Newton's root finding method not infrequently diverges if the starting point is far from the root. However, the current method in these regions merely reverts to the method of steepest descent with an adaptive step size. The current method's performance should match that of the Levenberg-Marquardt root finding method since they both share the ability to converge from a starting point far from the root and both exhibit quadratic convergence near a root. The Levenberg-Marquardt method requires storage for coefficients of linear equations. The current method which does not require the solution of linear equations requires more time for additional function and gradient evaluations. The classic trade off of time for space separates the two methods.

Nachtsheim, Philip R.↗
DOE OSTI2025

Implementation of Stochastic Gradient Descent in an Automated Glow Peak Identification Software for Multiple Thermoluminescent Dosimeter Types

A glow-curve analysis code was previously developed in C++ to analyze thermoluminescent dosimeter glow curves using automated peak detection while applying a first-order kinetics model. A newer version of this code was implemented to improve the automated peak detection and curve fitting models. The Stochastic Gradient Descent Algorithm was introduced to replace the prior approach of taking first and second-order derivatives for peak detection. Additionally, early stopping mechanisms were invoked to improve the previously used Levenberg-Marquardt Algorithm employed for curve fitting. The two software versions were compared through glow curve analysis of different thermoluminescent dosimeter materials and calculation of the corresponding figures of merit. Altogether improvements were shown, namely an increase in the number of peaks detected and a reduction of the mean figure of merit by approximately 46%.

137Cs↗
DOE OSTI2024

Role of the likelihood for elastic scattering uncertainty quantification

In the last decade, uncertainty quantification (UQ) for optical model potentials (OMPs) has become a focal point for nuclear reaction theory, and several competing approaches for OMP UQ have recently been developed. Here, we clarify recent efforts to compare frequentist and Bayesian approaches in the context of OMP UQ [G. B. King et al., Phys. Rev. Lett. 122, 232502 (2019)]. We replicate a portion of that OMP UQ study but use independent statistical tools. Specifically, we compare two methods for OMP parameter inference from elastic scattering data: the Levenberg-Marquardt algorithm for χ 2 minimization on one hand and Markov chain Monte Carlo (MCMC) sampling on the other. Separately, we assess the common practice of using a renormalized likelihood (χ 2 /N), N being the number of data points, instead of the canonical weighted-least-squares likelihood (χ 2 ), as a way of accounting for unknown data correlations. Here, we show that for a generic linear model and for a five-parameter OMP analysis, frequentist and uniform-prior Bayesian approaches recover the same optimum and uncertainty estimates—not systematically larger uncertainties for the Bayesian approach, as was concluded in G. B. King et al., Phys. Rev. Lett. 122, 232502 (2019). Further, we show that if an additional, near-degenerate parameter is introduced into the same OMP analysis such that the parameter posterior becomes non-Gaussian, then covariance-based estimates of uncertainty become unreliable. Finally, we show that regardless of optimization approach, if χ 2 /N is used for the likelihood, the resulting parametric uncertainties increase by $\sqrt{N}$, and that this is responsible for the conclusions drawn in the revisited study. Based on our replication results, we find that a fortuitous cancellation of unreported errors and the renormalization factor can lead to improvement in empirical coverages, as was the case in the original comparative study. We emphasize that developing and applying a realistic likelihood function is an essential task in a UQ analysis, and that several recent UQ studies that employed a renormalized likelihood (i.e., including a 1/N factor) may have yielded unrealistically large uncertainties for elastic-scattering observables. If the parameter posterior deviates from multivariate-normal, a sampling-based approach like MCMC has a clear advantage over methods that assume the Laplace approximation holds. We note that empirical coverage can serve as an important internal check for the analyst whose model or data may have additional, unaccounted-for uncertainties.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2026

RegularizedOptimization.jl: A Julia framework for regularized and nonsmooth optimization

RegularizedOptimization.jl is a Julia package that implements families of quadratic regularization and trust-region methods for solving the nonsmooth optimization problem $^{\textrm{minimize}}_{𝑥∈ℝ^𝑛}$ 𝑓(𝑥) + ℎ(𝑥) subject to 𝑐(𝑥) = 0, (1) where 𝑓 ∶ ℝ 𝑛 → ℝ and 𝑐 ∶ ℝ 𝑛 → ℝ 𝑚 are continuously differentiable, and ℎ ∶ ℝ 𝑛 → ℝ∪{+∞} is lower semi-continuous. The nonsmooth objective ℎ can be a regularizer, such as a sparsity inducing penalty, model simple constraints, such as 𝑥 belonging to a simple convex set, or can be a combination of both. All 𝑓, ℎ, and 𝑐 can be nonconvex. RegularizedOptimization.jl provides a modular and extensible framework for solving (1), and developing novel solvers. Currently, the following solvers are implemented: • Trust-region solvers TR and TRDH (Aravkin et al., 2022; Leconte & Orban, 2025) • Quadratic regularization solvers R2, R2DH and R2N (Aravkin et al., 2022; Diouane, Habiboullah, et al., 2024) • Levenberg-Marquardt solvers LM and LMTR (Aravkin et al., 2024) used when 𝑓 is a least-squares residual. • Augmented Lagrangian solver AL (De Marchi et al., 2023). All solvers rely on first derivatives of 𝑓 and 𝑐, and optionally on their second derivatives in the form of Hessian-vector products. If second derivatives are not available, quasi-Newton approximations can be used. In addition, the proximal mapping of the nonsmooth part ℎ, or adequate models thereof, must be evaluated. At each iteration, a step is computed by solving a subproblem of the form (1) inexactly, in which 𝑓, ℎ, and 𝑐 are replaced with appropriate models around the current iterate. The solvers R2, R2DH, and TRDH are particularly well suited to solve the subproblems, though they are general enough to solve (1). All solvers are allocation-free, so re-solves incur no additional allocations. To illustrate our claim of extensibility, a first version of the AL solver was implemented by an external contributor. Furthermore, a nonsmooth penalty approach, described in Diouane, Gollier, et al. (2024), is currently being developed, that relies on the library to efficiently solve the subproblems.

Gollier, Maxence [Polytechnique Montréal, QC (Cana↗
NASA NTRS1979

NLSCIDNT user's guide maximum likehood parameter identification computer program with nonlinear rotorcraft model

A nonlinear, maximum likelihood, parameter identification computer program (NLSCIDNT) is described which evaluates rotorcraft stability and control coefficients from flight test data. The optimal estimates of the parameters (stability and control coefficients) are determined (identified) by minimizing the negative log likelihood cost function. The minimization technique is the Levenberg-Marquardt method, which behaves like the steepest descent method when it is far from the minimum and behaves like the modified Newton-Raphson method when it is nearer the minimum. Twenty-one states and 40 measurement variables are modeled, and any subset may be selected. States which are not integrated may be fixed at an input value, or time history data may be substituted for the state in the equations of motion. Any aerodynamic coefficient may be expressed as a nonlinear polynomial function of selected 'expansion variables'.

Source record↗
NASA NTRS1989

Inference of stratospheric aerosol composition and size distribution from SAGE II satellite measurements

A method for inferring stratospheric aerosol composition and size distribution from the water vapor concentration and aerosol extinction measurements obtained in the Stratospheric Aerosol and Gas Experiment (SAGE) II and the associated temperature from the NMC. The aerosols are assumed to be sulfuric acid-water droplets. A modified Levenberg-Marquardt algorithm is used to determine model size distribution parameters based on the SAGE II multiwavelength aerosol extinctions. It is found that the best aerosol size information is contained in the aerosol radius range between about 0.25 and 0.80 micron.

Wang, Pi-Huan↗
NASA NTRS1991

A method for the retrieval of atomic oxygen density and temperature profiles from ground-based measurements of the O(+)(2D-2P) 7320 A twilight airglow

This paper describes a technique for extracting thermospheric profiles of the atomic-oxygen density and temperature, using ground-based measurements of the O(+)(2D-2P) doublet at 7320 and 7330 A in the twilight airglow. In this method, a local photochemical model is used to calculate the 7320-A intensity; the method also utilizes an iterative inversion procedure based on the Levenberg-Marquardt method described by Press et al. (1986). The results demonstrate that, if the measurements are only limited by errors due to Poisson noise, the altitude profiles of neutral temperature and atomic oxygen concentration can be determined accurately using currently available spectrometers.

Fennelly, J. A.↗
NASA NTRS1991

A parametric sensitivity and optimization study for the active flexible wing wind-tunnel model flutter characteristics

In this paper an effort is made to improve the analytical open-loop flutter predictions for the Active Flexible Wing wind-tunnel model using a sensitivity based optimization approach. The sensitivity derivatives of the flutter frequency and dynamic pressure of the model with respect to the lag terms appearing in the Roger's unsteady aerodynamics approximations are evaluated both analytical and by finite differences. Then, the Levenberg-Marquardt method is used to find the optimum values for these lag-terms. The results obtained here agree much better with the experimental (wind tunnel) results than those found in the previous studies.

Rais-Rohani, Masoud↗
NASA NTRS1997

Reducing Wind Tunnel Data Requirements Using Neural Networks

The use of neural networks to minimize the amount of data required to completely define the aerodynamic performance of a wind tunnel model is examined. The accuracy requirements for commercial wind tunnel test data are very severe and are difficult to reproduce using neural networks. For the current work, multiple input, single output networks were trained using a Levenberg-Marquardt algorithm for each of the aerodynamic coefficients. When applied to the aerodynamics of a 55% scale model of a U.S. Air Force/ NASA generic fighter configuration, this scheme provided accurate models of the lift, drag, and pitching-moment coefficients. Using only 50% of the data acquired during, the wind tunnel test, the trained neural network had a predictive accuracy equal to or better than the accuracy of the experimental measurements.

Ross, James C.↗
NASA NTRS1997

System and Method for Modeling the Flow Performance Features of an Object

The method and apparatus includes a neural network for generating a model of an object in a wind tunnel from performance data on the object. The network is trained from test input signals (e.g., leading edge flap position, trailing edge flap position, angle of attack, and other geometric configurations, and power settings) and test output signals (e.g., lift, drag, pitching moment, or other performance features). In one embodiment, the neural network training method employs a modified Levenberg-Marquardt optimization technique. The model can be generated 'real time' as wind tunnel testing proceeds. Once trained, the model is used to estimate performance features associated with the aircraft given geometric configuration and/or power setting input. The invention can also be applied in other similar static flow modeling applications in aerodynamics, hydrodynamics, fluid dynamics, and other such disciplines. For example, the static testing of cars, sails, and foils, propellers, keels, rudders, turbines, fins, and the like, in a wind tunnel, water trough, or other flowing medium.

Jorgensen, Charles↗
NASA NTRS1998

Two-Dimensional High-Lift Aerodynamic Optimization Using Neural Networks

The high-lift performance of a multi-element airfoil was optimized by using neural-net predictions that were trained using a computational data set. The numerical data was generated using a two-dimensional, incompressible, Navier-Stokes algorithm with the Spalart-Allmaras turbulence model. Because it is difficult to predict maximum lift for high-lift systems, an empirically-based maximum lift criteria was used in this study to determine both the maximum lift and the angle at which it occurs. The 'pressure difference rule,' which states that the maximum lift condition corresponds to a certain pressure difference between the peak suction pressure and the pressure at the trailing edge of the element, was applied and verified with experimental observations for this configuration. Multiple input, single output networks were trained using the NASA Ames variation of the Levenberg-Marquardt algorithm for each of the aerodynamic coefficients (lift, drag and moment). The artificial neural networks were integrated with a gradient-based optimizer. Using independent numerical simulations and experimental data for this high-lift configuration, it was shown that this design process successfully optimized flap deflection, gap, overlap, and angle of attack to maximize lift. Once the neural nets were trained and integrated with the optimizer, minimal additional computer resources were required to perform optimization runs with different initial conditions and parameters. Applying the neural networks within the high-lift rigging optimization process reduced the amount of computational time and resources by 44% compared with traditional gradient-based optimization procedures for multiple optimization runs.

Greenman, Roxana M.↗
NASA NTRS1998

Accelerated Training for Large Feedforward Neural Networks

In this paper we introduce a new training algorithm, the scaled variable metric (SVM) method. Our approach attempts to increase the convergence rate of the modified variable metric method. It is also combined with the RBackprop algorithm, which computes the product of the matrix of second derivatives (Hessian) with an arbitrary vector. The RBackprop method allows us to avoid computationally expensive, direct line searches. In addition, it can be utilized in the new, 'predictive' updating technique of the inverse Hessian approximation. We have used directional slope testing to adjust the step size and found that this strategy works exceptionally well in conjunction with the Rbackprop algorithm. Some supplementary, but nevertheless important enhancements to the basic training scheme such as improved setting of a scaling factor for the variable metric update and computationally more efficient procedure for updating the inverse Hessian approximation are presented as well. We summarize by comparing the SVM method with four first- and second- order optimization algorithms including a very effective implementation of the Levenberg-Marquardt method. Our tests indicate promising computational speed gains of the new training technique, particularly for large feedforward networks, i.e., for problems where the training process may be the most laborious.

Stepniewski, Slawomir W.↗
NASA NTRS2001

Calibration of Gyros with Temperature Dependent Scale Factors

The general problem of gyro calibration can be stated as the estimation of the scale factors, misalignments, and drift-rate biases of the gyro using the on-orbit sensor measurements. These gyro parameters have been traditionally treated as temperature-independent in the operational flight dynamics ground systems at NASA Goddard Space Flight Center (GSFC), a scenario which has been successfully applied in the gyro calibration of a large number of missions. A significant departure from this is the Microwave Anisotropy Probe (MAP) mission where, due to the high thermal variations expected during the mission phase, it is necessary to model the scale factors as functions of temperature. This paper addresses the issue of gyro calibration for the MAP gyro model using a manufacturer-supplied model of the variation of scale factors with temperature. The problem is formulated as a least squares problem and solved using the Levenberg-Marquardt algorithm in the MATLAB(R) library function NLSQ. The algorithm was tested on simulated data with Gaussian noise for the quaternions as well as the gyro rates and was found to consistently converge close to the true values. Significant improvement in accuracy was noticed due to the estimation of the temperature-dependent scale factors as against constant scale factors.

Belur, Sheela V.↗
NASA NTRS2001

Short-Term Dynamical Interactions Among Extrasolar Planets

We show that short-term perturbations among massive planets in multiple planet systems can result in radial velocity variations of the central star which differ substantially from velocity variations derived assuming the planets are executing independent Keplerian motions. We discuss two alternate fitting methods which can lead to an improved dynamical description of multiple planet systems. In the first method, the osculating orbital elements are determined via a Levenberg-Marquardt minimization scheme driving an N-body integrator. The second method is an improved analytic model in which orbital elements such as the periods and longitudes of periastron are allowed to vary according to a simple model for resonant interactions between the planets. Both of these methods can potentially determine the true masses for the planets by eliminating the sin(i) degeneracy inherent in fits that assume independent Keplerian motions. As more radial velocity data is accumulated from stars such as GJ876, these methods should allow for unambiguous determination of the planetary masses and relative inclinations.

Laughlin, Gregory↗
NASA NTRS1998

High-Lift Optimization Design Using Neural Networks on a Multi-Element Airfoil

The high-lift performance of a multi-element airfoil was optimized by using neural-net predictions that were trained using a computational data set. The numerical data was generated using a two-dimensional, incompressible, Navier-Stokes algorithm with the Spalart-Allmaras turbulence model. Because it is difficult to predict maximum lift for high-lift systems, an empirically-based maximum lift criteria was used in this study to determine both the maximum lift and the angle at which it occurs. Multiple input, single output networks were trained using the NASA Ames variation of the Levenberg-Marquardt algorithm for each of the aerodynamic coefficients (lift, drag, and moment). The artificial neural networks were integrated with a gradient-based optimizer. Using independent numerical simulations and experimental data for this high-lift configuration, it was shown that this design process successfully optimized flap deflection, gap, overlap, and angle of attack to maximize lift. Once the neural networks were trained and integrated with the optimizer, minimal additional computer resources were required to perform optimization runs with different initial conditions and parameters. Applying the neural networks within the high-lift rigging optimization process reduced the amount of computational time and resources by 83% compared with traditional gradient-based optimization procedures for multiple optimization runs.

Greenman, Roxana M.↗
NASA NTRS2003

Terrain Model Registration for Single Cycle Instrument Placement

This paper presents an efficient and robust method for registration of terrain models created using stereo vision on a planetary rover. Our approach projects two surface models into a virtual depth map, rendering the models as they would be seen from a single range sensor. Correspondence is established based on which points project to the same location in the virtual range sensor. A robust norm of the deviations in observed depth is used as the objective function, and the algorithm searches for the rigid transformation which minimizes the norm. An initial coarse search is done using rover pose information from odometry and orientation sensing. A fine search is done using Levenberg-Marquardt. Our method enables a planetary rover to keep track of designated science targets as it moves, and to hand off targets from one set of stereo cameras to another. These capabilities are essential for the rover to autonomously approach a science target and place an instrument in contact in a single command cycle.

Deans, Matthew↗
NASA NTRS1993

bpshape wk4: a computer program that implements a physiological model for analyzing the shape of blood pressure waveforms

We describe the theory and computer implementation of a newly-derived mathematical model for analyzing the shape of blood pressure waveforms. Input to the program consists of an ECG signal, plus a single continuous channel of peripheral blood pressure, which is often obtained invasively from an indwelling catheter during intensive-care monitoring or non-invasively from a tonometer. Output from the program includes a set of parameter estimates, made for every heart beat. Parameters of the model can be interpreted in terms of the capacitance of large arteries, the capacitance of peripheral arteries, the inertance of blood flow, the peripheral resistance, and arterial pressure due to basal vascular tone. Aortic flow due to contraction of the left ventricle is represented by a forcing function in the form of a descending ramp, the area under which represents the stroke volume. Differential equations describing the model are solved by the method of Laplace transforms, permitting rapid parameter estimation by the Levenberg-Marquardt algorithm. Parameter estimates and their confidence intervals are given in six examples, which are chosen to represent a variety of pressure waveforms that are observed during intensive-care monitoring. The examples demonstrate that some of the parameters may fluctuate markedly from beat to beat. Our program will find application in projects that are intended to correlate the details of the blood pressure waveform with other physiological variables, pathological conditions, and the effects of interventions.

Non-NASA Center↗