Search NASA⌕ Search

SEARCH · Search NASA

Results for “methods - statistical”

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.

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

At least 577 records · Page 32
All sourcesNASA NTRSDOE OSTI
DOE OSTI2019

A Homotopy-Based Method for Robust Computation of Controlling Unstable Equilibrium Points

This paper proposes a homotopy-based method for efficiently computing and precisely determining controlling unstable equilibrium points (CUEPs) in transient stability analysis and screening using direct methods. The proposed method is intended to overcome potential numerical convergence problems associated with computing CUEPs. These convergence problems are mostly due to irregularities in the region of convergence of CUEPs which make it difficult to determine suitable initial points. The most commonly used initial points in computing CUEPs are minimum gradient points (MGPs) on the stability boundary which in turn rely on the determination of exit points (EPs-points at which sustained-fault trajectories exit system stability boundaries). However, determination of MGPs and EPs are computationally involved and sophisticated numerical methods have been introduced such as stability-boundary-following procedure and shadowing method to correct the solution trajectory. The proposed method does not depend on MGPs and also does not require accurate EPs. The proposed method maps the solution from EPs to the CUEPs. The proposed method is applied on several known systems including the NE 39 bus system and the reduced WECC system and the results are provided. The results are compared with the traditional methods such as Boundary of stability region based CUEP method (BCU method).

42 ENGINEERING↗
DOE OSTI2022

Assessment of four strain energy decomposition methods for phase field fracture models using quasi-static and dynamic benchmark cases

Abstract Strain energy decomposition methods in phase field fracture models separate strain energy that contributes to fracture from that which does not. However, various decomposition methods have been proposed in the literature, and it can be difficult to determine an appropriate method for a given problem. The goal of this work is to facilitate the choice of strain decomposition method by assessing the performance of three existing methods (spectral decomposition of the stress or the strain and deviatoric decomposition of the strain) and one new method (deviatoric decomposition of the stress) with several benchmark problems. In each benchmark problem, we compare the performance of the four methods using both qualitative and quantitative metrics. In the first benchmark, we compare the predicted mechanical behavior of cracked material. We then use four quasi-static benchmark cases: a single edge notched tension test, a single edge notched shear test, a three-point bending test, and a L-shaped panel test. Finally, we use two dynamic benchmark cases: a dynamic tensile fracture test and a dynamic shear fracture test. All four methods perform well in tension, the two spectral methods perform better in compression and with mixed mode (though the stress spectral method performs the best), and all the methods show minor issues in at least one of the shear cases. In general, whether the strain or the stress is decomposed does not have a significant impact on the predicted behavior.

Zhang, Shuaifang↗
DOE OSTI2026

Refining a Novel Process Monitoring Method to Safeguard Continuously Cycling Designs Using Isotopic Ratios

In advanced reactor (AR) designs, a common feature is continuous chemical processing and circulation of the nuclear material. This work bridges a significant measurement gap in safeguarding reactors with circulating fuel or continuous refueling by leveraging and building on the isotope ratio method first developed by our team under an FY21 Advanced Reactors International Safeguards Engagement (ARISE) project (Uribe et al. 2021). In circulating fuel designs, the radioisotope inventory changes from traditional effects (e.g., radioactive decay, fission) but also includes material transport due to pressure and temperature gradients. Such designs may also require regular or continuous additions or removals during operation, which significantly increases the rate of inventory change compared to traditional pressurized water reactor (PWR)s. Thus, directly tracking the nuclear inventory is ineffective since the isotopes are continuously added and removed. The isotope ratio method instead focuses on detecting changes to the input and output flows of radioisotopes. Previous work showed that for well-chosen pairs of isotopes, the isotopic ratio provides a sensitive and lasting indicator of deviation from normal conditions (e.g., startup, shutdown, diversion). The isotope ratio method is a process monitoring method with potential for application in for forward-looking approaches to International Atomic Energy Agency (IAEA) safeguards. The original process monitoring method was developed for a specific case—the decay tank of a thorium-fueled molten salt breeder reactor. In this expanded work, we explored other types of reactors and processes with nonstationary (e.g., flowing) nuclear material, which are difficult to safeguard with traditional methods because of the transient nature of the systems. The goal of the present work is to generalize the isotope ratio method for use in processes with continuously flowing nuclear material. All continuous processes have an average time for isotopes to be replaced in the system. The isotope ratio method works by choosing radioisotopes with half-lives both above and below the processing time. The present work seeks to explore which isotopes are suitable for the method by simulating the nuclear inventory, radioisotope emissions, and detector responses for several classes of advanced reactors. While the method can in principle be applied to other processes (e.g., enrichment or reprocessing facilities), the present work limits scope to ARs with continuously flowing fuel. Section 2 details the mathematics supporting the isotope ratio method, and Section 3 introduces the representative ARs selected for this work. Section 4 discusses how each reactor was analyzed, and Section 5 showcases the results for each representative reactor. Finally, Section 6 provides concluding remarks and suggests pathways for further analysis.

98 NUCLEAR DISARMAMENT, SAFEGUARDS, AND PHYSICAL P↗
NASA NTRS1973

An historical survey of computational methods in optimal control.

Review of some of the salient theoretical developments in the specific area of optimal control algorithms. The first algorithms for optimal control were aimed at unconstrained problems and were derived by using first- and second-variation methods of the calculus of variations. These methods have subsequently been recognized as gradient, Newton-Raphson, or Gauss-Newton methods in function space. A much more recent addition to the arsenal of unconstrained optimal control algorithms are several variations of conjugate-gradient methods. At first, constrained optimal control problems could only be solved by exterior penalty function methods. Later algorithms specifically designed for constrained problems have appeared. Among these are methods for solving the unconstrained linear quadratic regulator problem, as well as certain constrained minimum-time and minimum-energy problems. Differential-dynamic programming was developed from dynamic programming considerations. The conditional-gradient method, the gradient-projection method, and a couple of feasible directions methods were obtained as extensions or adaptations of related algorithms for finite-dimensional problems. Finally, the so-called epsilon-methods combine the Ritz method with penalty function techniques.

Polak, E.↗
NASA NTRS1987

Comparison of three explicit multigrid methods for the Euler and Navier-Stokes equations

Three explicit multigrid methods, Ni's method, Jameson's finite-volume method, and a finite-difference method based on Brandt's work, are described and compared for two model problems. All three methods use an explicit multistage Runge-Kutta scheme on the fine grid, and this scheme is also described. Convergence histories for inviscid flow over a bump in a channel for the fine-grid scheme alone show that convergence rate is proportional to Courant number and that implicit residual smoothing can significantly accelerate the scheme. Ni's method was slightly slower than the implicitly-smoothed scheme alone. Brandt's and Jameson's methods are shown to be equivalent in form but differ in their node versus cell-centered implementations. They are about 8.5 times faster than Ni's method in terms of CPU time. Results for an oblique shock/boundary layer interaction problem verify the accuracy of the finite-difference code. All methods slowed considerably on the stretched viscous grid but Brandt's method was still 2.1 times faster than Ni's method.

Chima, Rodrick V.↗
NASA NTRS1987

Comparison of three explicit multigrid methods for the Euler and Navier-Stokes equations

Three explicit multigrid methods, Ni's method, Jameson's finite-volume method, and a finite-difference method based on Brandt's work, are described and compared for two model problems. All three methods use an explicit multistage Runge-Kutta scheme on the fine grid, and this scheme is also described. Convergence histories for inviscid flow over a bump in a channel for the fine-grid scheme alone show that convergence rate is proportional to Courant number and that implicit residual smoothing can significantly accelerate the scheme. Ni's method was slightly slower than the implicitly-smoothed scheme alone. Brandt's and Jameson's methods are shown to be equivalent in form but differ in their node versus cell-centered implementations. They are about 8.5 times faster than Ni's method in terms of CPU time. Results for an oblique shock/boundary layer interaction problem verify the accuracy of the finite-difference code. All methods slowed considerably on the stretched viscous grid but Brandt's method was still 2.1 times faster than Ni's method.

Chima, Rodrick V.↗
NASA NTRS1988

Leapfrog variants of iterative methods for linear algebra equations

Two iterative methods are considered, Richardson's method and a general second order method. For both methods, a variant of the method is derived for which only even numbered iterates are computed. The variant is called a leapfrog method. Comparisons between the conventional form of the methods and the leapfrog form are made under the assumption that the number of unknowns is large. In the case of Richardson's method, it is possible to express the final iterate in terms of only the initial approximation, a variant of the iteration called the grand-leap method. In the case of the grand-leap variant, a set of parameters is required. An algorithm is presented to compute these parameters that is related to algorithms to compute the weights and abscissas for Gaussian quadrature. General algorithms to implement the leapfrog and grand-leap methods are presented. Algorithms for the important special case of the Chebyshev method are also given.

Saylor, Paul E.↗
NASA NTRS1989

A hybrid perturbation-Galerkin method for differential equations containing a parameter

A two-step hybrid perturbation-Galerkin method to solve a variety of differential equations which involve a parameter is presented and discussed. The method consists of: (1) the use of a perturbation method to determine the asymptotic expansion of the solution about one or more values of the parameter; and (2) the use of some of the perturbation coefficient functions as trial functions in the classical Bubnov-Galerkin method. This hybrid method has the potential of overcoming some of the drawbacks of the perturbation method and the Bubnov-Galerkin method when they are applied by themselves, while combining some of the good features of both. The proposed method is illustrated first with a simple linear two-point boundary value problem and is then applied to a nonlinear two-point boundary value problem in lubrication theory. The results obtained from the hybrid method are compared with approximate solutions obtained by purely numerical methods. Some general features of the method, as well as some special tips for its implementation, are discussed. A survey of some current research application areas is presented and its degree of applicability to broader problem areas is discussed.

Geer, James F.↗
NASA NTRS1991

Nonequilibrium radiative heating prediction method for aeroassist flowfields with coupling to flowfield solvers

A method for predicting radiation adsorption and emission coefficients in thermochemical nonequilibrium flows is developed. The method is called the Langley optimized radiative nonequilibrium code (LORAN). It applies the smeared band approximation for molecular radiation to produce moderately detailed results and is intended to fill the gap between detailed but costly prediction methods and very fast but highly approximate methods. The optimization of the method to provide efficient solutions allowing coupling to flowfield solvers is discussed. Representative results are obtained and compared to previous nonequilibrium radiation methods, as well as to ground- and flight-measured data. Reasonable agreement is found in all cases. A multidimensional radiative transport method is also developed for axisymmetric flows. Its predictions for wall radiative flux are 20 to 25 percent lower than those of the tangent slab transport method, as expected, though additional investigation of the symmetry and outflow boundary conditions is indicated. The method was applied to the peak heating condition of the aeroassist flight experiment (AFE) trajectory, with results comparable to predictions from other methods. The LORAN method was also applied in conjunction with the computational fluid dynamics (CFD) code LAURA to study the sensitivity of the radiative heating prediction to various models used in nonequilibrium CFD. This study suggests that radiation measurements can provide diagnostic information about the detailed processes occurring in a nonequilibrium flowfield because radiation phenomena are very sensitive to these processes.

Hartung, Lin C.↗
NASA NTRS1994

Tensor-GMRES method for large sparse systems of nonlinear equations

This paper introduces a tensor-Krylov method, the tensor-GMRES method, for large sparse systems of nonlinear equations. This method is a coupling of tensor model formation and solution techniques for nonlinear equations with Krylov subspace projection techniques for unsymmetric systems of linear equations. Traditional tensor methods for nonlinear equations are based on a quadratic model of the nonlinear function, a standard linear model augmented by a simple second order term. These methods are shown to be significantly more efficient than standard methods both on nonsingular problems and on problems where the Jacobian matrix at the solution is singular. A major disadvantage of the traditional tensor methods is that the solution of the tensor model requires the factorization of the Jacobian matrix, which may not be suitable for problems where the Jacobian matrix is large and has a 'bad' sparsity structure for an efficient factorization. We overcome this difficulty by forming and solving the tensor model using an extension of a Newton-GMRES scheme. Like traditional tensor methods, we show that the new tensor method has significant computational advantages over the analogous Newton counterpart. Consistent with Krylov subspace based methods, the new tensor method does not depend on the factorization of the Jacobian matrix. As a matter of fact, the Jacobian matrix is never needed explicitly.

Feng, Dan↗
NASA NTRS1995

Non-LTE line-blanketed model atmospheres of hot stars. 1: Hybrid complete linearization/accelerated lambda iteration method

A new munerical method for computing non-Local Thermodynamic Equilibrium (non-LTE) model stellar atmospheres is presented. The method, called the hybird complete linearization/accelerated lambda iretation (CL/ALI) method, combines advantages of both its constituents. Its rate of convergence is virtually as high as for the standard CL method, while the computer time per iteration is almost as low as for the standard ALI method. The method is formulated as the standard complete lineariation, the only difference being that the radiation intensity at selected frequency points is not explicity linearized; instead, it is treated by means of the ALI approach. The scheme offers a wide spectrum of options, ranging from the full CL to the full ALI method. We deonstrate that the method works optimally if the majority of frequency points are treated in the ALI mode, while the radiation intensity at a few (typically two to 30) frequency points is explicity linearized. We show how this method can be applied to calculate metal line-blanketed non-LTE model atmospheres, by using the idea of 'superlevels' and 'superlines' introduced originally by Anderson (1989). We calculate several illustrative models taking into accont several tens of thosands of lines of Fe III to Fe IV and show that the hybrid CL/ALI method provides a robust method for calculating non-LTE line-blanketed model atmospheres for a wide range of stellar parameters. The results for individual stellar types will be presented in subsequent papers in this series.

Hubeny, I.↗
NASA NTRS2003

New Laboratory Methods for Characterizing the Immersion Factors for Irradiance

The experimental determination of the immersion factor, I(sub f)(lambda), of irradiance collectors is a requirement of any in-water radiometer. The eighth SeaWiFS Intercalibration Round-Robin Experiment (SIRREX-8) showed different implementations, at different laboratories, of the same I(sub f)(lambda) measurement protocol. The different implementations make use of different setups, volumes, and water types. Consequently, they exhibit different accuracies and require different execution times for characterizing an irradiance sensor. In view of standardizing the characterization of I(sub f)(lambda) values for in-water radiometers, together with an increase in the accuracy of methods and a decrease in the execution time, alternative methods are presented, and assessed versus the traditional method. The proposed new laboratory methods include: a) the continuous method, in which optical measurements taken with discrete water depths are substituted by continuous profiles created by removing the water from the water vessel at a constant flow rate (which significantly reduces the time required for the characterization of a single radiometer); and b) the Compact Portable Advanced Characterization Tank (ComPACT) method, in which the commonly used large tanks are replaced by a small water vessel, thereby allowing the determination of I(sub f)(lambda) values with a small water volume, and more importantly, permitting I(sub f)(lambda) characterizations with pure water. Intercomparisons between the continuous and the traditional method showed results within the variance of I(sub f) (lambda) determinations. The use of the continuous method, however, showed a much shorter realization time. Intercomparisons between the ComPACT and the traditional method showed generally higher I(sub f)(lambda) values for the former. This is in agreement with the generalized expectations of a reduction in scattering effects, because of the use of pure water with the ComPACT method versus the use of tap water with the traditional method.

Hooker, Stanford B.↗
NASA NTRS2006

Less-Complex Method of Classifying MPSK

An alternative to an optimal method of automated classification of signals modulated with M-ary phase-shift-keying (M-ary PSK or MPSK) has been derived. The alternative method is approximate, but it offers nearly optimal performance and entails much less complexity, which translates to much less computation time. Modulation classification is becoming increasingly important in radio-communication systems that utilize multiple data modulation schemes and include software-defined or software-controlled receivers. Such a receiver may "know" little a priori about an incoming signal but may be required to correctly classify its data rate, modulation type, and forward error-correction code before properly configuring itself to acquire and track the symbol timing, carrier frequency, and phase, and ultimately produce decoded bits. Modulation classification has long been an important component of military interception of initially unknown radio signals transmitted by adversaries. Modulation classification may also be useful for enabling cellular telephones to automatically recognize different signal types and configure themselves accordingly. The concept of modulation classification as outlined in the preceding paragraph is quite general. However, at the present early stage of development, and for the purpose of describing the present alternative method, the term "modulation classification" or simply "classification" signifies, more specifically, a distinction between M-ary and M'-ary PSK, where M and M' represent two different integer multiples of 2. Both the prior optimal method and the present alternative method require the acquisition of magnitude and phase values of a number (N) of consecutive baseband samples of the incoming signal + noise. The prior optimal method is based on a maximum- likelihood (ML) classification rule that requires a calculation of likelihood functions for the M and M' hypotheses: Each likelihood function is an integral, over a full cycle of carrier phase, of a complicated sum of functions of the baseband sample values, the carrier phase, the carrier-signal and noise magnitudes, and M or M'. Then the likelihood ratio, defined as the ratio between the likelihood functions, is computed, leading to the choice of whichever hypothesis - M or M'- is more likely. In the alternative method, the integral in each likelihood function is approximated by a sum over values of the integrand sampled at a number, 1, of equally spaced values of carrier phase. Used in this way, 1 is a parameter that can be adjusted to trade computational complexity against the probability of misclassification. In the limit as 1 approaches infinity, one obtains the integral form of the likelihood function and thus recovers the ML classification. The present approximate method has been tested in comparison with the ML method by means of computational simulations. The results of the simulations have shown that the performance (as quantified by probability of misclassification) of the approximate method is nearly indistinguishable from that of the ML method (see figure).

Hamkins, Jon↗
NASA NTRS2016

Simple Test Functions in Meshless Local Petrov-Galerkin Methods

Two meshless local Petrov-Galerkin (MLPG) methods based on two different trial functions but that use a simple linear test function were developed for beam and column problems. These methods used generalized moving least squares (GMLS) and radial basis (RB) interpolation functions as trial functions. These two methods were tested on various patch test problems. Both methods passed the patch tests successfully. Then the methods were applied to various beam vibration problems and problems involving Euler and Beck's columns. Both methods yielded accurate solutions for all problems studied. The simple linear test function offers considerable savings in computing efforts as the domain integrals involved in the weak form are avoided. The two methods based on this simple linear test function method produced accurate results for frequencies and buckling loads. Of the two methods studied, the method with radial basis trial functions is very attractive as the method is simple, accurate, and robust.

Raju, Ivatury S.↗
NASA NTRSDate not supplied

Monthly Mean DNI and GTI Derived from Monthly Mean GHI and DHI Using Two Methods: Comparisons with the BSRN Data and the Results Derived from the CERES Hourly Data

Monthly mean Global Horizontal Irradiances (GHI) and Diffuse Horizontal Irradiances (DHI) are more widely available than monthly mean Direct Normal Irradiances (DNI) and Global Tilted Irradiances (GTI). Empirical methods have been developed to derive monthly mean DNI and GTI from monthly mean GHI or from GHI and DHI. In this paper, we evaluate two such methods. The first one was the Whitlock Method developed by Charles H. Whitlock (2005) for the NASA POWER project by means of regression of the BSRN data. The method expresses the monthly mean DHI-to-GHI ratio as polynomial functions of monthly mean clearness index, sunset hour angle and noon solar elevation angle on the monthly-average-day. The monthly mean DNI is calculated by dividing the monthly mean GHI-DHI difference, or DirHI, by the cosine of the solar zenith angle at the mid-time between sunrise and solar noon on the monthly-average-day. The second method is the LJCR Method developed by Liu and Jorden (1960) and Collares-Pereira and Rabl (1979), and this method empirically splits monthly mean GHI and DHI into hourly means on the monthly-average-day, and the resulting hourly mean GHI and DHI and their difference, DirHI, can then be used to compute the monthly mean DNI, GTI and the global solar tracker irradiance (GTrI). This method is also used by RETScreen. We recently produced a set of hourly DNI and DHI by bias-correcting the CERES hourly DNI and DHI, and computed hourly GTI and GTrI as well. The data span twenty plus years from March 2000 to near present on a 1 by 1 grid system. The monthly mean CERES GHI and the corrected DHI are used as inputs to the above two methods to compute monthly mean DNI, GTI and GTrI. Through comparisons with the BSRN data, it is found that the Whitlock Method, with slight modification, and the LJCR Method can produce results that are nearly as good as the results derived from the CERES hourly data.

Taiping Zhang↗
DOE OSTI2024

Meshfree Methods

Meshfree methods have undergone substantial development and have received much attention in the last two decades. This new family of numerical methods is designed to inherit the main advantages of the finite element method such as compact supports of shape functions and good approximation properties while, at the same time, overcome the main disadvantages of the finite element method caused by the mesh dependence. The meshfree methods share a common feature that no mesh is needed and shape functions are constructed from sets of points, thus eliminating the need for time consuming mesh generation. The most significant advantage of meshfree methods is the flexibility in customizing approximation functions for desired regularity and for capturing essential physics and features of the particular problems of interest. Adaptivity formulation and multiple-scale solution strategies also can be implemented with relative ease. It has become clear that the meshfree methods provide considerable advantages over the conventional finite element methods in solving problems involving moving discontinuities, evolving material interfaces, multiple-scale phenomena, large material distortion and structural deformation, and fracture and damage processes. This Chapter gives an overview of many classes of meshfree methods, with more detailed discussions on Smoothed Particle Hydrodynamics (SPH), the Reproducing Kernel Particle Method (RKPM), Peridynamics (PD), the Material Point Method (MPM), as well as their applications in various challenging engineering problems.2

Chen, Jiun-Shyan↗
DOE OSTI2021

Implicit-Explicit Multirate Infinitesimal GARK Methods

This work focuses on the development of a new class of high-order accurate methods for multirate time integration of systems of ordinary differential equations. Unlike other recent work in this area, the proposed methods support mixed implicit-explicit (IMEX) treatment of the slow time scale. In addition to allowing this slow time scale flexibility, the proposed methods utilize a so-called infinitesimal formulation for the fast time scale through definition of a sequence of modified “fast" initial-value problems that may be solved using any viable algorithm. We name the proposed class as implicit-explicit multirate infinitesimal generalized-structure additive Runge--Kutta (IMEX-MRI-GARK) methods. In addition to defining these methods, we prove that they may be viewed as specific instances of GARK methods and derive a set of order conditions on the IMEX-MRI-GARK coefficients to guarantee both third and fourth order accuracy for the overall multirate method. Additionally, we provide three specific IMEX-MRI-GARK methods, two of order three and one of order four. We conclude with numerical simulations on two multirate test problems, demonstrating the methods' predicted convergence rates and comparing their efficiency against both legacy IMEX multirate schemes and recent third and fourth order implicit MRI-GARK methods.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

A unified framework of stabilized finite element method for solving the Boltzmann transport equation

This paper presents a unified framework of stabilized finite element method for solving the Boltzmann transport equation. Unlike the traditional Petrov-Galerkin finite element method which modifies the test function to construct the stabilization term, we derive the stabilization methods from the standard Galerkin weak form with Sub-grid scale model. The basic idea of this method is to decompose the unknowns into its numerical solution and residual, with an approximation for the residual and embeds it in the Galerkin weak form to yield a stabilized variational formula. Different approximations of the residual lead to different stabilization methods, all the frequently used stabilized methods, including the Streamline Upwinding Petrov-Galerkin (SUPG) method, Galerkin/Least-Square (GLS) method, and Algebraic Sub-Grid Scale (ASGS) method can be obtained from this framework. The similarities and differences of the different approximations are compared in this paper. The numerical results show that the behaviors of the different methods area similar with the same stabilization parameter, and all these stabilized techniques can obtain a correct and stable solution. (authors)

22 GENERAL STUDIES OF NUCLEAR REACTORS↗