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Results for “Nonlinear approximation”

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 1,585 records · Page 88
All sourcesNASA NTRSDOE OSTI
NASA NTRS1991

Structural behavior of scientific balloons - Finite element simulation and verification

An off-the-shelf nonlinear finite element code was used to analyze fully inflated scientific balloons. The thin balloon film was modeled by shell bending elements. Numerical difficulties caused by insignificant bending stiffness terms were overcome by introducing some artificial bending stiffness. This approximation is justified by the fact that in thin shells with nonzero Gaussian curvature the membrane solution component is essentially independent of the bending solution component. Perturbation of the coveraged solution by increasing the bending stiffness by a full decade verified this assertion. This analytical approach was experimentally verified. As a result of this verification process it was discovered that the generally accepted linearly visco-elastic model for polyethylene film is inappropriate for a significant planar (as opposed to uniaxial) stress state. A linear elastic model presents a good approximation for planar stress states.

Schur, Willi W.↗
NASA NTRS1995

Toward a theory of interstellar turbulence. 2: Strong alfvenic turbulence

We continue to investigate the possibility that interstellar turbulence is caused by nonlinear interactions among shear Alfven waves. Here, we restrict attention to the symmetric case where the oppositely directed waves carry equal energy fluxes. This precludes application to the solar wind in which the outward flux significantly exceeds the ingoing one. All our detailed calculations are carried out for an incompressible magnetized fluid. In incompressible magnetohydrodynamics (MHD), nonlinear interactions only occur between oppositely direct waves. We present a theory for the strong turbulence of shear Alfven waves. It has the following main characteristics. (1) The inertial-stage energy spectrum exhibits a critical balance between linear wave periods and nonlinear turnover timescales. (2) The 'eddies' are elongated in the direction of the field on small spatial scales; the parallel and perpendicular components of the wave vector, k(sub z) and k(perpendicular) are related by k(sub z) approximately equals k(sub perpendicular to)(exp 2/3) L(exp -1/3), where L is the outer scale of the turbulence. (3) The 'one-dimensional' energy spectrum is proportional to k(sub perpendicular)(exp -5/3)-an anisotropic Kolmogorov energy spectrum. Shear Alfvenic turbulence mixes specific entropy as a passive contaminant. This gives rise to an electron density power spectrum whose form mimics the energy spectrum of the turbulence. Radio wave scattering by these electron density fluctuations produces anisotropic scatter-broadened images. Damping by ion-neutral collisions restricts Alfvenic turbulence to highly ionized regions of the interstellar medium.

Goldreich, P.↗
NASA NTRS2009

Methodologies for Adaptive Flight Envelope Estimation and Protection

This paper reports the latest development of several techniques for adaptive flight envelope estimation and protection system for aircraft under damage upset conditions. Through the integration of advanced fault detection algorithms, real-time system identification of the damage/faulted aircraft and flight envelop estimation, real-time decision support can be executed autonomously for improving damage tolerance and flight recoverability. Particularly, a bank of adaptive nonlinear fault detection and isolation estimators were developed for flight control actuator faults; a real-time system identification method was developed for assessing the dynamics and performance limitation of impaired aircraft; online learning neural networks were used to approximate selected aircraft dynamics which were then inverted to estimate command margins. As off-line training of network weights is not required, the method has the advantage of adapting to varying flight conditions and different vehicle configurations. The key benefit of the envelope estimation and protection system is that it allows the aircraft to fly close to its limit boundary by constantly updating the controller command limits during flight. The developed techniques were demonstrated on NASA s Generic Transport Model (GTM) simulation environments with simulated actuator faults. Simulation results and remarks on future work are presented.

Tang, Liang↗
NASA NTRS2012

Implementation of an Integrated On-Board Aircraft Engine Diagnostic Architecture

An on-board diagnostic architecture for aircraft turbofan engine performance trending, parameter estimation, and gas-path fault detection and isolation has been developed and evaluated in a simulation environment. The architecture incorporates two independent models: a realtime self-tuning performance model providing parameter estimates and a performance baseline model for diagnostic purposes reflecting long-term engine degradation trends. This architecture was evaluated using flight profiles generated from a nonlinear model with realistic fleet engine health degradation distributions and sensor noise. The architecture was found to produce acceptable estimates of engine health and unmeasured parameters, and the integrated diagnostic algorithms were able to perform correct fault isolation in approximately 70 percent of the tested cases

Armstrong, Jeffrey B.↗
NASA NTRS2017

Novel Estimation of Pilot Performance Characteristics

Two mechanisms internal to the pilot that affect performance during a tracking task are: 1) Pilot equalization (i.e. lead/lag); and 2) Pilot gain (i.e. sensitivity to the error signal). For some applications McRuer's Crossover Model can be used to anticipate what equalization will be employed to control a vehicle's dynamics. McRuer also established approximate time delays associated with different types of equalization - the more cognitive processing that is required due to equalization difficulty, the larger the time delay. However, the Crossover Model does not predict what the pilot gain will be. A nonlinear pilot control technique, observed and coined by the authors as 'amplitude clipping', is shown to improve stability, performance, and reduce workload when employed with vehicle dynamics that require high lead compensation by the pilot. Combining linear and nonlinear methods a novel approach is used to measure the pilot control parameters when amplitude clipping is present, allowing precise measurement in real time of key pilot control parameters. Based on the results of an experiment which was designed to probe workload primary drivers, a method is developed that estimates pilot spare capacity from readily observable measures and is tested for generality using multi-axis flight data. This paper documents the initial steps to developing a novel, simple objective metric for assessing pilot workload and its variation over time across a wide variety of tasks. Additionally, it offers a tangible, easily implementable methodology for anticipating a pilot's operating parameters and workload, and an effective design tool. The model shows promise in being able to precisely predict the actual pilot settings and workload, and observed tolerance of pilot parameter variation over the course of operation. Finally, an approach is proposed for generating Cooper-Harper ratings based on the workload and parameter estimation methodology.

Human pilot models↗
DOE OSTI2026

Measurement and feedback-driven adaptive dynamics in the classical and quantum kicked top

In classical dynamical systems, stochastic feedback can stabilize otherwise unstable periodic orbits, giving rise to distinct controlled and uncontrolled phases as the rate of control application is varied. In this work, we apply these control protocols in classical, semiclassical, and quantum regimes to the kicked top, a paradigmatic model of quantum chaos. The quantum kicked top, modeled as the dynamics of a spin-S object, naturally interpolates between these regimes with the spin size S acting as an effective Planck constant. We show that the dynamics of the kicked top in classical, semiclassical, and fully quantum limits can all be controlled using stochastic feedback protocols. Comparing the full quantum dynamics to a truncated Wigner approximation that captures quantum noise but neglects interference beyond the Ehrenfest time, we find that low-moment observables are largely accounted for semiclassically, while the remaining discrepancy in higher moments is consistent with contributions from interference and possibly nonlinearities in rare trajectories that explore the compact phase space. We also find rapid purification in the numerics studied for all rates of control considered, suggesting that control quenches the top's ability to encode a qubit of quantum information even in the uncontrolled phase.

Prasad, Mahaveer [Tata Inst.; Singapore U. Tech. D↗
NASA NTRS1990

Overshooting thunderstorm cloud top dynamics as approximated by a linear Lagrangian parcel model with analytic exact solutions

Results are presented from a linear Lagrangian entraining parcel model of an overshooting thunderstorm cloud top. The model, which is similar to that of Adler and Mack (1986), gives analytic exact solutions for vertical velocity and temperature by representing mixing with Rayleigh damping instead of nonlinearly. Model results are presented for various combinations of stratospheric lapse rate, drag intensity, and mixing strength. The results are compared to those of Adler and Mack.

Schlesinger, Robert E.↗
NASA NTRS1997

Nonlinear Waves and Particle Heating in the Auroral Ionosphere

In the two year period, the researchers have developed innovative 2-D simulation codes for modeling the interaction between electron beams and plasma waves and particles in the auroral ionosphere. These new simulations include kinetic wave particles as well as wave-wave interactions near and above approximately 500 km. The principal numerical model consists of partial-differential equations which evolve large amplitude magnetized 2-D Langmuir waves self-consistently with the electron distribution function. Progress was also made in developing 2-D Particle in Cell (PIC) codes.

Goldman, Martin↗
DOE OSTI2021

Optimization of battery swapping infrastructure for e-commerce drone delivery

Drone delivery is widely-researched to alter the current e-commerce delivery convention for providing short delivery lead times. Yet, flight range of drones, constrained by the available battery technology, sets a milestone toward realizing the sole-drone delivery. To tackle with the flight range limitation, locating automated battery swapping machines (ABSM) have been proposed and a few studies modeled the problem. Using the ABSMs, drones can be loaded with fully-charged batteries along the route to a demand location. Here, we introduce a mixed-integer nonlinear program to model the problem. The objective of the program is to optimally select ABSM locations, determine the delivery-mode choices (drone-only, truck-only, and mixed delivery) of demand locations, find drone delivery routes, and approximate the baseline requirements for the number of drones and batteries needed. The program minimizes the overall delivery system costs including: ABSM, delivery, drone ownership, battery inventory, and service congestion. A cutting-plane method is developed to find exact solutions in finite iterations. Computational experiments showed that the method quickly yields the optimal solution to instances with less than 60 ABSM candidates and 20 demand locations. A case study shows that the optimal drone delivery infrastructure can save almost 20% cost compared to the conventional truck-only delivery. Sensitivity analyses were conducted to reveal the impact of key parameters in the decision-making and found that a decrease in the ABSM and drone costs highly affect the system cost.

25 ENERGY STORAGE↗
DOE OSTI2020

An explicit scheme to enforce charge conservation in transient Particle-in-Cell simulations with Maxwell-Boltzmann electrons

The Maxwell-Boltzmann electron model is a very popular approximation of the electronic behavior in electrostatic plasmas, adopted in all cases where the electron dynamics is governed only by a balance between electric and pressure forces. In such a model, the electron dynamics is reduced to solving for a nonlinear Poisson problem together with an additional expression enforcing charge conservation. In this work we derive an expression of charge conservation which can be conveniently applied to explicit schemes to update the reference Boltzmann density, particularly useful when simulating plasma sheaths. The scheme can be equally applied to both steady-state and transient problems. Two examples are shown, a steady-state plasma sheath, and a radio-frequency magnetic presheath. Our proposed scheme allows to enforce global charge conservation locally in time, and can thus be applied to the simulation of transient phenomena.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2020

A Comparison of Interface Growth Models Applied to Rayleigh–Taylor and Richtmyer–Meshkov Instabilities

Sophisticated numerical models that contain fluid interfaces rely upon interface evolution models to approximate the transition to turbulence near interfaces, in the presence of Rayleigh–Taylor (RTI) or Richtmyer–Meshkov (RMI) instability. Semi-analytical models have been developed in recent decades to predict the interface growth from an initial state into the nonlinear regime. Two of these models are considered in this study. They are the Goncharov and the z-models. Both of these interface models have strengths and weaknesses, which are examined here. Both of them have been implemented in the xRAGE compressible flow solver, which models fluid interfaces. The flow solver provides the fluids acceleration as a body force to the interface model. The purpose of such interface model is to evolve the early times of interface position as a subgrid model within a compressible flow simulation in order to then initialize a turbulence model. In this work, the interface models are assessed and compared for their evolution of RTI and RMI. The z-model performed better than the Goncharov model for all cases that were explored.

42 ENGINEERING↗
DOE OSTI2022

Adaptive Space-Time Methods for Large Scale Optimal Design

When modeling complex physical systems with advanced dynamics, such as shocks and singularities, many classic methods for solving partial differential equations can return inaccurate or unusable results. One way to resolve these complex dynamics is through r-adaptive refinement methods, in which a fixed number of mesh points are shifted to areas of high interest. The mesh refinement map can be found through the solution of the Monge-Ampére equation, a highly nonlinear partial differential equation. Due to its nonlinearity, the numerical solution of the Monge-Ampére equation is nontrivial and has previously required computationally expensive methods. In this report, we detail our novel optimization-based, multigrid-enabled solver for a low-order finite element approximation of the Monge-Ampére equation. This fast and scalable solver makes r-adaptive meshing more readily available for problems related to large-scale optimal design. Beyond mesh adaptivity, our report discusses additional applications where our fast solver for the Monge-Ampére equation could be easily applied.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS1972

Discrete-time demodulation of continuous-time signals.

Nonlinear stochastic estimation theory is applied to the problem of obtaining discrete-time demodulator structures for the common types of analog communication signals. A stochastic communication model is presented that can be treated with current results in estimation theory. Approximate algorithms are developed for the estimation problem that yield mathematically realizable receiver structures for the cases of AM, PC, and FM. The digital receivers yield performance characteristics that compare favorably with those of their analog counterparts.

Kelly, C. N.↗
NASA NTRS1975

The Hertzsprung progression in Cepheid calculations

The Hertzsprung bump in Cepheid models has been studied for models of a wide range of mass (M), radius (R), and effective temperature (T sub e). This study showed that the delay of the bump (in days) measured from the time of minimum radius preceding the bump by one plus period is dependent only on M and R and not on T sub e. Over a range of models from M/M solar mass approximately 0.5 and R/R solar radius = 10 to M/M solar mass = 13 and R/R solar radius = 160, the delay of the bump (in days) is approximately proportional to the radius. This is consistent with a picture that the bump results from an acoustic signal that traverses the star from the ionization zone into the center and out again to the surface. The bump and other nonlinear phenomena has been studied over a series of Cepheid models from a period of less than one day to a period of 150 days. The results show characteristic changes in amplitude and in the appearance of bumps and are in good correspondence to actual Cepheids. The masses in this series are, however, characteristically lower than evolutionary masses.

Christy, R. F.↗
NASA NTRS1977

Set-point control of nonlinear systems

A method of nonlinear stochastic control is applied to the problem of providing set-point control. The procedure is illustrated for a nonlinear second-order plant. The controller design uses a variation of the 'multiple-model adaptive control' approach. Specific problems related to the design are investigated, including learning time and set-point accuracy dependence on the number of approximating models, chord versus tangent approximations, and the a priori Markov switching parameter values. Simulations are provided for different situations under various levels of measurement noise.

Vanlandingham, H. F.↗
NASA NTRS1981

On-line optimization of aircraft altitude and flight path angle dynamics

The optimization of aircraft altitude and flight path angle dynamics is addressed in a form suitable for on-line computation and control. The approach here is a direct extension of the work reported by Calise (1979), where singular perturbation methods were used to optimize position, energy and heading dynamics; it thus represents an optimal control solution that models all of the primary trajectory related dynamics. It is pointed out that the resulting algorithm can be regarded as a nonlinear feedback control law. The minimum time intercept of a fixed terminal point is used in setting the framework in which the analytical results are developed. The main theoretical result is that the dynamics, while not completely separable, can be approximated by singular perturbation methods when the control model includes relative position dynamics.

Calise, A. J.↗
NASA NTRS1989

Calculation of steady and unsteady pressures at supersonic speeds with CAP-TSD

A finite difference technique is used to solve the transonic small disturbance flow equation making use of shock capturing to treat wave discontinuities. Thus the nonlinear effects of thickness and angle of attack are considered. Such an approach is made feasible by the development of a new code called CAP-TSD (Computational Aeroelasticity Program - Transonic Small Disturbance), and is based on a fully implicit approximate factorization (AF) finite difference method to solve the time dependent transonic small disturbance equation. The application of the CAP-TSD code to the calculation of low to moderate supersonic steady and unsteady flows is presented. In particular, comparisons with exact linear theory solutions are made for steady and unsteady cases to evaluate shock capturing and other features of the current method. In addition, steady solutions obtained from an Euler code are used to evaluate the small disturbance aspects of the code. Steady and unsteady pressure comparisons are made with measurements for an F-15 wing model and for the RAE tailplane model.

Bennett, Robert M.↗