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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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At least 109 records · Page 6
All sourcesNASA NTRSDOE OSTI
NASA NTRS1993

Improving the reconstruction of the velocity potential and primordial density fluctuations by choice of smoothing windows

Recently considerable attention has been focused on improving algorithms for restoring primordial density fluctuations in the universe or investigating large-scale velocity fields by going to higher order approximations relating nonlinear states to their initial conditions. An alternative approach is to investigate the use of alternative smoothing windows within the context of first-order approximations. I present evidence that the universally used Gaussian smoothing window is far from optimal. A sharp truncation P(k) = 0 for k greater than k(c) leads to a much more direct connection to initial conditions for either 'Gaussianization' methods or use of the Zel'dovich approximation, as discussed in the text.

Melott, Adrian L.↗
NASA NTRS1991

Nonlinear modal resonances in low-gravity slosh-spacecraft systems

Nonlinear models of low gravity slosh, when coupled to spacecraft vibrations, predict intense nonlinear eigenfrequency shifts at zero gravity. These nonlinear frequency shifts are due to internal quadratic and cubic resonances between fluid slosh modes and spacecraft vibration modes. Their existence has been verified experimentally, and they cannot be correctly modeled by approximate, uncoupled nonlinear models, such as pendulum mechanical analogs. These predictions mean that linear slosh assumptions for spacecraft vibration models can be invalid, and may lead to degraded control system stability and performance. However, a complete nonlinear modal analysis will predict the correct dynamic behavior. This paper presents the analytical basis for these results, and discusses the effect of internal resonances on the nonlinear coupled response at zero gravity.

Peterson, Lee D.↗
NASA NTRS1992

A conjugate gradients/trust regions algorithms for training multilayer perceptrons for nonlinear mapping

This paper addresses the issue of applying a globally convergent optimization algorithm to the training of multilayer perceptrons, a class of Artificial Neural Networks. The multilayer perceptrons are trained towards the solution of two highly nonlinear problems: (1) signal detection in a multi-user communication network, and (2) solving the inverse kinematics for a robotic manipulator. The research is motivated by the fact that a multilayer perceptron is theoretically capable of approximating any nonlinear function to within a specified accuracy. The algorithm that has been employed in this study combines the merits of two well known optimization algorithms, the Conjugate Gradients and the Trust Regions Algorithms. The performance is compared to a widely used algorithm, the Backpropagation Algorithm, that is basically a gradient-based algorithm, and hence, slow in converging. The performances of the two algorithms are compared with the convergence rate. Furthermore, in the case of the signal detection problem, performances are also benchmarked by the decision boundaries drawn as well as the probability of error obtained in either case.

Madyastha, Raghavendra K.↗
NASA NTRS1986

Do large rate coefficients for ion-polar neutral reactions have a serious effect on chemical models of dense clouds?

In order to incorporate large ion-polar neutral rate coefficients into existing gas phase reaction networks, it is necessary to utilize simplified theoretical treatments because of the significant number of rate coefficients needed. The authors have used two simple theoretical treatments: the locked dipole approach of Moran and Hamill for linear polar neutrals and the trajectory scaling approach of Su and Chesnavich for nonlinear polar neutrals. The former approach is suitable for linear species because in the interstellar medium these are rotationally relaxed to a large extent and the incoming charged reactants can lock their dipoles into the lowest energy configuration. The latter approach is a better approximation for nonlinear neutral species, in which rotational relaxation is normally less severe and the incoming charged reactants are not as effective at locking the dipoles. The treatments are in reasonable agreement with more detailed long range theories and predict an inverse square root dependence on kinetic temperature for the rate coefficient. Compared with the locked dipole method, the trajectory scaling approach results in rate coefficients smaller by a factor of approximately 2.5.

Herbst, E.↗
NASA NTRS1987

Nonlinear programming extensions to rational function approximations of unsteady aerodynamics

This paper deals with approximating unsteady generalized aerodynamic forces in the equations of motion of a flexible aircraft. Two methods of formulating these approximations are extended to include both the same flexibility in constraining them and the same methodology in optimizing nonlinear parameters as another currently used 'extended least-squares' method. Optimal selection of 'nonlinear' parameters is made in each of the three methods by use of the same nonlinear (nongradient) optimizer. The objective of the nonlinear optimization is to obtain rational approximations to the unsteady aerodynamics whose state-space realization is of lower order than that required when no optimization of the nonlinear terms is performed. The free 'linear' parameters are determined using least-squares matrix techniques on a Lagrange multiplier formulation of an objective function which incorporates selected linear equality constraints. State-space mathematical models resulting from the different approaches are described, and results are presented which show comparative evaluations from application of each of the extended methods to a numerical example. The results obtained for the example problem show a significant (up to 63 percent) reduction in the number of differential equations used to represent the unsteady aerodynamic forces in linear time-invariant equations of motion as compared to a conventional method in which nonlinear terms are not optimized.

Tiffany, Sherwood H.↗
NASA NTRSDate not supplied

Towards Surrogate Modeling of Subgrid Turbulent Transport for 3D Radiative Hydrodynamic Simulations of the Quiet Sun

In this work, we investigate the use of deep learn-ing techniques as surrogate models, to enhance the estimationof effects of subgrid turbulent transport for 3D radiatuve hy-drodynamic simulations of the quiet Sun. We develop two dis-tinct 3D Convolutional Neural Networks (3DCNNs) to capturespatio-temporal dependencies in 3D velocity fields, leveragingdifferent activation functions and architectural designs. Thesemodels integrate both averaged velocity vector components andscalar features such as plasma density to enhance predictionaccuracy. Additionally, a Multilayer Perceptron (MLP) modelis employed to approximate complex nonlinear relationships,offering a comparison in performance between convolutionaland fully connected architectures. Logarithmic transformationis applied to the targets to handle heavily skewed data, im-proving model performance. All models are compared againsta physics-based Gradient Model. Results show that the 3DCNNmodels excel at approximating Reynolds stress tensors, makingthem a candidate for assisting in producing reduced resolutionsimulations, and thereby reducing computational overheadwhile maintaining higher accuracy than the baseline. Thesefindings demonstrate the potential of deep learning, particu-larly CNNs, to advance scalable and accurate simulations ofsolar dynamics, offering a promising alternative to traditionalturbulence models.

Heliophysics↗
NASA NTRS2024

Global Optimization via Quadratic Disjunctive Programming for Water Networks Design with Energy Recovery

Generalized disjunctive programming (GDP) models with bilinear and concave constraints, often seen in water network design, are challenging optimization problems. This work proposes quadratic and piecewise linear approximations for nonlinear terms to reformulate GDP models into quadratic GDP (QGDP) models that suitable solvers may solve more efficiently. We illustrate the benefits of the quadratic reformulation with a water treatment network design problem in which nonconvexities arise from bilinear terms in the mixers’ mass balances and concave investment cost functions of treatment units. Given the similarities with water network design problems, we suggest quadratic approximation for the GDP model for the optimal design of a large-scale reverse electrodialysis (RED) process. This power technology can recover energy from salinity differences between by-product streams of the water sector, such as desalination brine mixed with regenerated wastewater effluents. The solver Gurobi excels in handling QGDP problems, but weighing the problem’s precision and tractability balance is crucial. The piecewise linear approximation yields more accurate, yet larger QGDP models that may require longer optimization times in large-scale process synthesis problems.

Water Networks↗
NASA NTRS1999

Structural Reliability Analysis and Optimization: Use of Approximations

This report is intended for the demonstration of function approximation concepts and their applicability in reliability analysis and design. Particularly, approximations in the calculation of the safety index, failure probability and structural optimization (modification of design variables) are developed. With this scope in mind, extensive details on probability theory are avoided. Definitions relevant to the stated objectives have been taken from standard text books. The idea of function approximations is to minimize the repetitive use of computationally intensive calculations by replacing them with simpler closed-form equations, which could be nonlinear. Typically, the approximations provide good accuracy around the points where they are constructed, and they need to be periodically updated to extend their utility. There are approximations in calculating the failure probability of a limit state function. The first one, which is most commonly discussed, is how the limit state is approximated at the design point. Most of the time this could be a first-order Taylor series expansion, also known as the First Order Reliability Method (FORM), or a second-order Taylor series expansion (paraboloid), also known as the Second Order Reliability Method (SORM). From the computational procedure point of view, this step comes after the design point identification; however, the order of approximation for the probability of failure calculation is discussed first, and it is denoted by either FORM or SORM. The other approximation of interest is how the design point, or the most probable failure point (MPP), is identified. For iteratively finding this point, again the limit state is approximated. The accuracy and efficiency of the approximations make the search process quite practical for analysis intensive approaches such as the finite element methods; therefore, the crux of this research is to develop excellent approximations for MPP identification and also different approximations including the higher-order reliability methods (HORM) for representing the failure surface. This report is divided into several parts to emphasize different segments of the structural reliability analysis and design. Broadly, it consists of mathematical foundations, methods and applications. Chapter I discusses the fundamental definitions of the probability theory, which are mostly available in standard text books. Probability density function descriptions relevant to this work are addressed. In Chapter 2, the concept and utility of function approximation are discussed for a general application in engineering analysis. Various forms of function representations and the latest developments in nonlinear adaptive approximations are presented with comparison studies. Research work accomplished in reliability analysis is presented in Chapter 3. First, the definition of safety index and most probable point of failure are introduced. Efficient ways of computing the safety index with a fewer number of iterations is emphasized. In chapter 4, the probability of failure prediction is presented using first-order, second-order and higher-order methods. System reliability methods are discussed in chapter 5. Chapter 6 presents optimization techniques for the modification and redistribution of structural sizes for improving the structural reliability. The report also contains several appendices on probability parameters.

Grandhi, Ramana V.↗
NASA NTRS1983

Estimation of delays and other parameters in nonlinear functional differential equations

A spline-based approximation scheme for nonlinear nonautonomous delay differential equations is discussed. Convergence results (using dissipative type estimates on the underlying nonlinear operators) are given in the context of parameter estimation problems which include estimation of multiple delays and initial data as well as the usual coefficient-type parameters. A brief summary of some of the related numerical findings is also given.

Banks, H. T.↗
NASA NTRS1989

An approximate analytic solution of a set of nonlinear model alpha-omega-dynamo equations for marginally unstable systems

An approximate analytic solution of a set of nonlinear model alpha-omega-dynamo equations is obtained. The reaction of the Lorentz force on the velocity shear which stretches and, hence, amplifies the magnetic field is incorporated into the model. To single out the effect of the Lorentz force on the omega-effect, the effect of the Lorentz force on the alpha-effect is neglected in this study. The solution represents a nonlinear oscillation with the amplitude and period determined by the dynamo number N. The amplitude is proportional to N - 1, while the period is almost exactly the same as the dissipation time of the unstable mode (proportional to N).

Hinata, S.↗
NASA NTRS1997

Predicting survival in heart failure case and control subjects by use of fully automated methods for deriving nonlinear and conventional indices of heart rate dynamics

BACKGROUND: Despite much recent interest in quantification of heart rate variability (HRV), the prognostic value of conventional measures of HRV and of newer indices based on nonlinear dynamics is not universally accepted. METHODS AND RESULTS: We have designed algorithms for analyzing ambulatory ECG recordings and measuring HRV without human intervention, using robust methods for obtaining time-domain measures (mean and SD of heart rate), frequency-domain measures (power in the bands of 0.001 to 0.01 Hz [VLF], 0.01 to 0.15 Hz [LF], and 0.15 to 0.5 Hz [HF] and total spectral power [TP] over all three of these bands), and measures based on nonlinear dynamics (approximate entropy [ApEn], a measure of complexity, and detrended fluctuation analysis [DFA], a measure of long-term correlations). The study population consisted of chronic congestive heart failure (CHF) case patients and sex- and age-matched control subjects in the Framingham Heart Study. After exclusion of technically inadequate studies and those with atrial fibrillation, we used these algorithms to study HRV in 2-hour ambulatory ECG recordings of 69 participants (mean age, 71.7+/-8.1 years). By use of separate Cox proportional-hazards models, the conventional measures SD (P<.01), LF (P<.01), VLF (P<.05), and TP (P<.01) and the nonlinear measure DFA (P<.05) were predictors of survival over a mean follow-up period of 1.9 years; other measures, including ApEn (P>.3), were not. In multivariable models, DFA was of borderline predictive significance (P=.06) after adjustment for the diagnosis of CHF and SD. CONCLUSIONS: These results demonstrate that HRV analysis of ambulatory ECG recordings based on fully automated methods can have prognostic value in a population-based study and that nonlinear HRV indices may contribute prognostic value to complement traditional HRV measures.

Non-NASA Center↗
NASA NTRS1952

The linearized characteristics method and its application to practical nonlinear supersonic problems

The methods of characteristics has been linearized by assuming that the flow field can be represented as a basic flow field determined by nonlinearized methods and a linearized superposed flow field that accounts for small changes of boundary conditions. The method has been applied to two-dimensional rotational flow where the basic flow is potential flow and to axially symmetric problems where conical flows have been used as the basic flows. In both cases the method allows the determination of the flow field to be simplified and the numerical work to be reduced to a few calculations. The calculations of axially symmetric flow can be simplified if tabulated values of some coefficients of the conical flow are obtained. The method has also been applied to slender bodies without symmetry and to some three-dimensional wing problems where two-dimensional flow can be used as the basic flow. Both problems were unsolved before in the approximation of nonlinear flow.

Ferri, Antonio↗