Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “nonlinear function”

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 703 records · Page 39
All sourcesNASA NTRSDOE OSTI
NASA NTRS1973

An interative solution of an integral equation for radiative transfer by using variational technique

An effective iterative technique is introduced to solve a nonlinear integral equation frequently associated with radiative transfer problems. The problem is formulated in such a way that each step of an iterative sequence requires the solution of a linear integral equation. The advantage of a previously introduced variational technique which utilizes a stepwise constant trial function is exploited to cope with the nonlinear problem. The method is simple and straightforward. Rapid convergence is obtained by employing a linear interpolation of the iterative solutions. Using absorption coefficients of the Milne-Eddington type, which are applicable to some planetary atmospheric radiation problems. Solutions are found in terms of temperature and radiative flux. These solutions are presented numerically and show excellent agreement with other numerical solutions.

Yoshikawa, K. K.↗
NASA NTRS1975

Jump resonant frequency islands in nonlinear feedback control systems

A new type of jump resonance is predicted and observed in certain nonlinear feedback control systems. The new jump resonance characteristic is described as a 'frequency island' due to the fact that a portion of the input-output transfer characteristic is disjoint from the main body. The presence of such frequency islands was predicted by using a sinusoidal describing function characterization of the dynamics of an inertial gyro employing nonlinear ternary rebalance logic. While the general conditions under which such islands are possible has not been examined, a numerical approach is presented which can aid in establishing their presence. The existence of the frequency islands predicted for the ternary rebalanced gyro was confirmed by simulating the nonlinear system and measuring the transfer function.

Koenigsberg, W. D.↗
DOE OSTI2020

Convex Relaxations for Quadratic On/Off Constraints and Applications to Optimal Transmission Switching

This paper studies mixed-integer nonlinear programs featuring disjunctive constraints and trigonometric functions and presents a strengthened version of the convex quadratic relaxation of the optimal transmission switching problem. We first characterize the convex hull of univariate quadratic on/off constraints in the space of original variables using perspective functions. Next, we introduce new tight quadratic relaxations for trigonometric functions featuring variables with asymmetrical bounds. These results are used to further tighten recent convex relaxations introduced for the optimal transmission switching problem in power systems. Using the proposed improvements, along with bound propagation, on 23 medium-sized test cases in the PGLib benchmark library with a relaxation gap of more than 1%, we reduce the gap to less than 1% on five instances. The tightened model has promising computational results when compared with state-of-the-art formulations.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1991

Computational methods for structural load and resistance modeling

An automated capability for computing structural reliability considering uncertainties in both load and resistance variables is presented. The computations are carried out using an automated Advanced Mean Value iteration algorithm (AMV +) with performance functions involving load and resistance variables obtained by both explicit and implicit methods. A complete description of the procedures used is given as well as several illustrative examples, verified by Monte Carlo Analysis. In particular, the computational methods described in the paper are shown to be quite accurate and efficient for a material nonlinear structure considering material damage as a function of several primitive random variables. The results show clearly the effectiveness of the algorithms for computing the reliability of large-scale structural systems with a maximum number of resolutions.

Thacker, B. H.↗
NASA NTRS2011

Uncertainty Analysis via Failure Domain Characterization: Unrestricted Requirement Functions

This paper proposes an uncertainty analysis framework based on the characterization of the uncertain parameter space. This characterization enables the identification of worst-case uncertainty combinations and the approximation of the failure and safe domains with a high level of accuracy. Because these approximations are comprised of subsets of readily computable probability, they enable the calculation of arbitrarily tight upper and lower bounds to the failure probability. The methods developed herein, which are based on nonlinear constrained optimization, are applicable to requirement functions whose functional dependency on the uncertainty is arbitrary and whose explicit form may even be unknown. Some of the most prominent features of the methodology are the substantial desensitization of the calculations from the assumed uncertainty model (i.e., the probability distribution describing the uncertainty) as well as the accommodation for changes in such a model with a practically insignificant amount of computational effort.

Crespo, Luis G.↗
NASA NTRS1987

Response of joint dominated space structures

An efficient linearization method is presented for calculating the transient response of nonlinear systems due to initial disturbances. The method is an extension of the describing function approach in which the steady state response of the system is calculated by representing the nonlinear element, typically joints in the case of space structures, by impedances which are functions of the amplitude of response. Thus, the problem of solving the differential equation for the steady state response becomes one of solving a set of nonlinear algebraic equations involving the steady state amplitudes and phases of the system. It is shown that for the transient case the steady state impedances can be averaged over the range of responses in order to provide equivalent values of stiffness and damping that, for a given set of initial displacements, may be treated as being constant for purposes of calculating system response. Single degree of freedom system are used to demonstrate the method and to develop an approach for optimizing the joint's characteristics so as to minimize transient response times. The use of this method for response estimation and optimization in multiple degree of freedom systems is investigated.

Source record↗
DOE OSTI2025

Massive νs through the CNN lens: interpreting the field-level neutrino mass information in weak lensing

Modern cosmological surveys probe the Universe deep into the nonlinear regime, where massive neutrinos suppress cosmic structure. Traditional cosmological analyses, which use the 2-point correlation function to extract information, are no longer optimal in the nonlinear regime, and there is thus much interest in extracting beyond-2-point information to improve constraints on neutrino mass. Quantifying and interpreting the beyond-2-point information is thus a pressing task. We study the field-level information in weak lensing convergence maps using convolution neural networks. We find that the network performance increases as higher source redshifts and smaller scales are considered — investigating up to a source redshift of 2.5 and ℓ max ≃ 10 4 — verifying that massive neutrinos leave a distinct effect on weak lensing. However, the performance of the network significantly drops after scaling out the 2-point information from the maps, implying that most of the field-level information can be found in the 2-point correlation function alone. We quantify these findings in terms of the likelihood ratio and also use Integrated Gradient saliency maps to interpret which parts of the map the network is learning the most from. We find that, in the absence of noise, the network extracts a similar amount of information from the most overdense and underdense regions. However, upon adding noise, the information in underdense regions is distorted as noise disproportionately washes out void-like structures.

Golshan, Malika [University of California, Berkele↗
DOE OSTI2023

Analytical Large-Signal Modeling of Inverter-Based Microgrids With Koopman Operator Theory for Autonomous Control

The microgrid (MG) plays a crucial role in the energy transition, but its nonlinearity presents a significant challenge for large-signal power systems studies in the electromagnetic transient (EMT) time scale. In this paper, we develop a large-signal linear MG model that considers the detailed dynamics of the primary and zero-control levels based on the Koopman operator (KO) theory. Firstly, a set of observable functions is carefully designed to capture the nonlinear dynamics of the MG. The corresponding linear KO is then analytically derived based on these observables, resulting in the linear representation of the original nonlinear MG with observables as the new coordinate. The influence of external input on the system dynamics is also considered during the derivation, enabling control of the MG. We solve the voltage control problem using the traditional linear quadratic integrator (LQI) method to demonstrate that textbook linear control techniques can accurately control the original nonlinear MG via the developed KO-linearized MG model. Our proposed KO linearization method is generic and can be easily extended for different control objectives and MG structures using our analytical derivation procedure. Here, we validate the effectiveness of our methodology through various case studies.

25 ENERGY STORAGE↗
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 NTRS1973

Continuous and discrete describing function analysis of the LST system

A describing function of the control moment gyros (CMG) frictional nonlinearity is derived using the analytic torque equation. Computer simulation of the simplified Large Space Telescope (LST) system with the analytic torque expression is discussed along with the transfer functions of the sampled-data LST system, and the discrete describing function of the GMC frictionality.

Kuo, B. C.↗
NASA NTRS1995

Estimating errors in least-squares fitting

While least-squares fitting procedures are commonly used in data analysis and are extensively discussed in the literature devoted to this subject, the proper assessment of errors resulting from such fits has received relatively little attention. The present work considers statistical errors in the fitted parameters, as well as in the values of the fitted function itself, resulting from random errors in the data. Expressions are derived for the standard error of the fit, as a function of the independent variable, for the general nonlinear and linear fitting problems. Additionally, closed-form expressions are derived for some examples commonly encountered in the scientific and engineering fields, namely ordinary polynomial and Gaussian fitting functions. These results have direct application to the assessment of the antenna gain and system temperature characteristics, in addition to a broad range of problems in data analysis. The effects of the nature of the data and the choice of fitting function on the ability to accurately model the system under study are discussed, and some general rules are deduced to assist workers intent on maximizing the amount of information obtained form a given set of measurements.

Richter, P. H.↗
NASA NTRS2016

Wave Amplitude Dependent Engineering Model of Propellant Slosh in Spherical Tanks

Liquid propellant slosh is often a concern for the controllability of flight vehicles. Anti-slosh devices are traditionally included in propellant tank designs to limit the amount of sloshing allowed during flight. These devices and any necessary supports can be quite heavy to meet various structural requirements. Some of the burden on anti-slosh devices can be relieved by exploiting the nonlinear behavior of slosh waves in bare smooth wall tanks. A nonlinear regime slosh model for bare spherical tanks was developed through a joint analytical and experimental effort by NASA/MSFC. The developed slosh model accounts for the large damping inherent in nonlinear slosh waves which is more accurate and drives conservatism from vehicle stability analyses that use traditional bare tank slosh models. A more accurate slosh model will result in more realistic predicted slosh forces during flight reducing or removing the need for active controls during a maneuver or baffles in the tank design. Lower control gains and smaller or fewer tank baffles can reduce cost and system complexity while increasing vehicle performance. Both Computational Fluid Dynamics (CFD) simulation and slosh testing of three different spherical tank geometries were performed to develop the proposed slosh model. Several important findings were made during this effort in addition to determining the parameters to the nonlinear regime slosh model. The linear regime slosh damping trend for spherical tanks reported in NASA SP-106 was shown to be inaccurate for certain regions of a tank. Additionally, transition to the nonlinear regime for spherical tanks was only found to occur at very large wave amplitudes in the lower hemisphere and was a strong function of the propellant fill level in the upper hemisphere. The nonlinear regime damping trend was also found to be a function of the propellant fill level.

Brodnick, Jacob↗
NASA NTRS1984

The ADS general-purpose optimization program

The mathematical statement of the general nonlinear optimization problem is given as follows: find the vector of design variables, X, that will minimize f(X) subject to G sub J (x) + or - 0 j=1,m H sub K hk(X) = 0 k=1,l X Lower I approx less than X sub I approx. less than X U over I i = 1,N. The vector of design variables, X, includes all those variables which may be changed by the ADS program in order to arrive at the optimum design. The objective function F(X) to be minimized may be weight, cost or some other performance measure. If the objective is to be maximized, this is accomplished by minimizing -F(X). The inequality constraints include limits on stress, deformation, aeroelastic response or controllability, as examples, and may be nonlinear implicit functions of the design variables, X. The equality constraints h sub k(X) represent conditions that must be satisfied precisely for the design to be acceptable. Equality constraints are not fully operational in version 1.0 of the ADS program, although they are available in the Augmented Lagrange Multiplier method. The side constraints given by the last equation are used to directly limit the region of search for the optimum. The ADS program will never consider a design which is not within these limits.

Vanderplaats, G. N.↗
NASA NTRSDate not supplied

Recommended Crew Systems Capabilities for a 30 to 90 Day Four-Crew Lunar Surface Mission

For any given surface mission duration, there exists a set of surface capabilities necessary to sustain a four-person crew for the length of time the crew is on the surface. Identifying these capabilities is important to mission planners and spacecraft design engineers responsible for lunar surface habitation elements, who need to know which systems and capabilities must be prioritized for the vehicles they are designing. However, simply identifying the surface capabilities does not necessarily equal a viable surface configuration. These capabilities may or may not satisfy stakeholder expectations or even permit completion of mission objectives. Lunar lander cargo mass constraints are a powerful forcing function that requires significant efforts to reduce the mass of all surface elements, including those supporting crew habitation. The required capabilities do increase as a function of mission duration, but it is a nonlinear growth. There are key points in mission duration, beyond which certain additional capabilities are needed. This forms bands of capability between each point. Within a given band, the same functional capabilities are needed, and the only scaling is that associated with daily consumables. The next higher band requires additional capabilities. This paper will focus on those capabilities needed for missions of 30-90 days. It should be noted that there are some uncertainties interpreting NASA requirements that require capabilities after a certain number of days, as typically this refers to number of days in space, not number of days on the lunar surface. Depending on transportation architecture, the number of days between Earth launch and lunar surface landing may vary, therefore impacting when certain required capabilities are implemented. However, activities to prepare humans for missions to Mars and commercial interest in lunar development may drive progressive increases in surface duration. Missions up to 30 days are expected to follow the initial 6.5-day surface missions and there may be commercial interest in extending to even greater durations. This paper will examine the potential case of a 30-90-day surface mission duration with respect to the systems necessary to support crew living and working on the lunar surface.

Habitat↗
NASA NTRS2012

Simulations of Spray Reacting Flows in a Single Element LDI Injector With and Without Invoking an Eulerian Scalar PDF Method

This paper presents the numerical simulations of the Jet-A spray reacting flow in a single element lean direct injection (LDI) injector by using the National Combustion Code (NCC) with and without invoking the Eulerian scalar probability density function (PDF) method. The flow field is calculated by using the Reynolds averaged Navier-Stokes equations (RANS and URANS) with nonlinear turbulence models, and when the scalar PDF method is invoked, the energy and compositions or species mass fractions are calculated by solving the equation of an ensemble averaged density-weighted fine-grained probability density function that is referred to here as the averaged probability density function (APDF). A nonlinear model for closing the convection term of the scalar APDF equation is used in the presented simulations and will be briefly described. Detailed comparisons between the results and available experimental data are carried out. Some positive findings of invoking the Eulerian scalar PDF method in both improving the simulation quality and reducing the computing cost are observed.

Shih, Tsan-Hsing↗
NASA NTRS1974

Error estimates for approximate dynamic systems

Two approaches are investigated for obtaining estimates on the error between approximate and exact solutions of dynamic systems. The first method is primarily useful if the system is nonlinear and of low dimension. The second requires construction of a system of v-functions but is useful for higher dimensional systems, either linear or nonlinear.

Gunderson, R. W.↗
DOE OSTI2024

Theory of nonlinear terahertz susceptibility in ferroelectrics

An analytical theory is developed for predicting the nonlinear susceptibility of ionic polarization to continuous electromagnetic waves in both bulk and strained thin film ferroelectrics. Using a perturbation method for solving the nonlinear equation of motion for ionic polarization within the framework of Landau-Ginzburg-Devonshire theory, the full second-order nonlinear susceptibility tensor is derived as a function of frequency, temperature, and strain. Here, the theory predicts the coexistence of a significantly enhanced second-order dielectric susceptibility and a relatively low dielectric loss in BaTiO 3 films with a strain-stabilized monoclinic ferroelectric phase and in a strained SrTiO 3 film near its temperature-driven second-order ferroelectric-to-paraelectric phase transition. In this paper, we establish a theoretical framework for predicting and exploiting nonlinear interactions between terahertz waves and ferroelectric materials and, more generally, suggest exciting opportunities to strain-engineer nonlinear dynamical properties of ferroelectrics beyond the static and quasistatic limits.

36 MATERIALS SCIENCE↗