Functional analysis of systems characterized by nonlinear differential equations
Functional analysis of nonlinear systems characterized by differential equations
NONLINEAR SYSTEM↗
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.
Optimal estimation for discrete time jump processes
Optimum estimates of nonobservable random variables or random processes which influence the rate functions of a discrete time jump process (DTJP) are obtained. The approach is based on the a posteriori probability of a nonobservable event expressed in terms of the a priori probability of that event and of the sample function probability of the DTJP. A general representation for optimum estimates and recursive equations for minimum mean squared error (MMSE) estimates are obtained. MMSE estimates are nonlinear functions of the observations. The problem of estimating the rate of a DTJP when the rate is a random variable with a probability density function of the form cx super K (l-x) super m and show that the MMSE estimates are linear in this case. This class of density functions explains why there are insignificant differences between optimum unconstrained and linear MMSE estimates in a variety of problems.
Vaca, M. V.↗
On the Class of Admissable Nonlinearities for Lur'e's Problem
Imposition of conditions on nonlinear function of scalar so that system will be stable or asymptotically stable
STABILITY↗
Theory and Simulation of Self- and Mutual-Diffusion of Carrier Density and Temperature in Semiconductor Lasers
Carrier diffusion and thermal conduction play a fundamental role in the operation of high-power, broad-area semiconductor lasers. Restricted geometry, high pumping level and dynamic instability lead to inhomogeneous spatial distribution of plasma density, temperature, as well as light field, due to strong light-matter interaction. Thus, modeling and simulation of such optoelectronic devices rely on detailed descriptions of carrier dynamics and energy transport in the system. A self-consistent description of lasing and heating in large-aperture, inhomogeneous edge- or surface-emitting lasers (VCSELs) require coupled diffusion equations for carrier density and temperature. In this paper, we derive such equations from the Boltzmann transport equation for the carrier distributions. The derived self- and mutual-diffusion coefficients are in general nonlinear functions of carrier density and temperature including many-body interactions. We study the effects of many-body interactions on these coefficients, as well as the nonlinearity of these coefficients for large-area VCSELs. The effects of mutual diffusions on carrier and temperature distributions in gain-guided VCSELs will be also presented.
Li, Jian-Zhong↗
The effects of bandpass limiters on n-phase tracking systems
The combination of a bandpass limiter and an n(th) power tracking loop is considered. It is shown that the performance of the combination does not depend on the form of the nonlinear function used to create the n(th) harmonic signal so long as some energy in that zone is produced. Furthermore, the order in which the limiter and n(th) power nonlinearity occur is unimportant so that the results apply equally well to the n-phase Costas type of implementation of the n(th) power loops. Closed form expressions for the signal suppression factors are obtained and it is shown that the coherent and noncoherent SNR's out of the n(th) power-limiter combination can be expressed in terms of two of these suppression factors. This later point enables one to estimate the loop SNR of an n(th) power-limiter phase locked loop by simply calculating the suppression factors for n(th) and 2n(th) power loops. Finally, n(th) power phase locked loops without limiters are compared with similar loops with limiters where it is shown that the presence of the limiter can actually enhance the output SNR at moderate to large values of input SNR.
Butman, S. A.↗
The effects of bandpass limiters on n-phase tracking systems
The combination of a bandpass limiter and an n-th power tracking loop is considered. Performance of the combination does not depend on the form of the nonlinear function used to create the n-th harmonic signal as long as some energy in that zone is produced. The order in which the limiter and n-th power nonlinearity occur is unimportant so that the results apply equally well to the n-phase Costas type of implementations of the n-th power loops. Closed form expressions for the signal suppression factors are obtained. Coherent and noncoherent SNR's out of the n-th power-limiter combination can be expressed in terms of two of these suppression factors. The loop SNR of an n-th power-limited phase locked loop is estimated by simply calculating the suppression factors for n-th and 2n-th power loops. Finally, n-th power phase locked loops without limiters are compared with similar loops with limiters; the limiter can actually enhance output SNR at moderate to large input SNR.
Butman, S. A.↗
Optimal estimation for discrete time jump processes
Optimum estimates of nonobservable random variables or random processes which influence the rate functions of a discrete time jump process (DTJP) are derived. The approach used is based on the a posteriori probability of a nonobservable event expressed in terms of the a priori probability of that event and of the sample function probability of the DTJP. Thus a general representation is obtained for optimum estimates, and recursive equations are derived for minimum mean-squared error (MMSE) estimates. In general, MMSE estimates are nonlinear functions of the observations. The problem is considered of estimating the rate of a DTJP when the rate is a random variable with a beta probability density function and the jump amplitudes are binomially distributed. It is shown that the MMSE estimates are linear. The class of beta density functions is rather rich and explains why there are insignificant differences between optimum unconstrained and linear MMSE estimates in a variety of problems.
Vaca, M. V.↗
Digital modeling of human operator dynamics via class of Liapunov functions
A technique is described which is utilized for modeling human operator dynamics. The technique is based upon a model-reference system configuration and a class of Liapunov functions formulated for this purpose which possess variable characteristics. It is shown how such a class of Liapunov functions and their time derivatives is formulated. The crux of the formulation lies in three variable positive definite matrices used for the construction of the class of Liapunov functions. The form and order of these matrices depend upon the form and order of the error differential equation of the human operator model-reference system. These matrices can be modified to include nonlinear functions of the human operator model.
Mekel, R.↗
Influence of dissolved organic materials on turbid water optical properties and remote-sensing reflectance
The effects of dissolved organic materials on turbid-water optical properties are assessed, by means of field measurements and laboratory simulations in which upwelled reflectance, attenuation, absorption, and backscatter spectral properties at wavelengths from 450 to 800 nm are examined in relation to water chemistry. The data show that dissolved organic materials decrease upwelled reflectance from turbid waters, and that the decrease in reflectance is a nonlinear function of concentration with the largest gradients at low carbon concentrations, depending on wavelength. Upwelled reflectance is found to be highly correlated with two backscatter-absorption parameters used in some optical models, which are nonlinear with dissolved organic material concentration change.
Witte, W. G.↗
A nonlinear control design for energy sink simulation in the Euler-Poinsot problem
A nonlinear control design is presented for the purpose of quantitatively simulating the effects of internal damping mechanisms modeled as energy sinks on the attitude dynamics of rigid body spacecraft. Damping is important because it is often the driving mechanism behind passive attitude acquisition maneuvers. Introduction of the controller into the Euler attitude equations of motion allows for the explicit representation of damping without the introduction of additional degrees of freedom required for a physical damping mechanism. This result is significant because perturbation techniques which rely on the closed form solution of the unperturbed problem can then be used to analyze the effects of perturbations upon a damped system. The controller is designed to dissipate kinetic energy while maintaining the magnitude of the angular momentum vector. Control torques are nonlinear functions of the angular momentum components expressed in a body-fixed frame. A numerical simulation of an actual damping mechanism during a decay from minor axis spin into a flat spin is presented showing that the nonlinear controller gives a good qualitative representation and, in many instances, a good quantitative approximation of the attitude motion of a representative spacecraft containing a damping mechanism.
Kammer, Daniel C.↗
Temperature, density, and composition in the disturbed thermosphere from Esro 4 gas analyzer measurements - A global model
An analysis of density measurements of Ar, N2, O, and He made at 280 km with the gas analyzer aboard the polar-orbiting satellite Esro 4 has yielded a global model of the variations in temperature, density, and composition that occur in the disturbed thermosphere. In the model the increase of temperature over quiet conditions is a nonlinear function of the planetary geomagnetic index, its latitude profile being approximated by a fourth-power sin phi law, where phi is the 'invariant' magnetic latitude. A density wave proceeding from high latitudes is approximated by a fourth power cos phi law. A strong nonlinearity in the relation between the temperature variations and the variations in the height of the homopause explains a previously found behavioral difference in the variation of atomic oxygen during magnetic storms and during periods of sustained geomagnetic activity.
Jacchia, L. G.↗
Aerodynamic characteristics of missile control fins in nonlinear flow fields
Recent experimental results show that the control effectiveness of a missile fin in supersonic flow at moderate-to-high angles of attack is a strong nonlinear function of free-stream Mach number, body incidence angle, fin bank angle and fin deflection angle. Analysis of the experimental results using an Euler finite-difference computer code with flow separation together with the equivalent angle-of-attack concept indicates that the observed nonlinearities are due to the variation of local dynamic pressure and local Mach number around the missile body alone. The nonlinearities are shown to be a strong source of control cross-coupling for high Mach number, high angle-of-attack combinations. The analysis suggests a relatively simple yet comprehensive approach for accurately accounting for these nonlinear effects.
Hemsch, M. J.↗
Spectral properties of mixtures of montmorillonite and dark grains - Implications for remote sensing minerals containing chemically and physically adsorbed water
The spectral properties from 0.4 to 3 microns of montmorillonite plus dark carbon grains (called opaques) of various sizes are studied as a function of the weight fraction of opaques present. The reflectance level and band depths of the 1.4-, 1.9-, 2.2-, and 2.8-micron water and/or OH absorption features are analyzed using derived empirical relationships and scattering theory. It is found that the absorption band depths and reflectance level are a very nonlinear function of the weight fraction of opaques present but can be predicted in many cases by simple scattering theory. The 2.8-micron bound water fundamental band is the most difficult absorption feature to suppress. The overtone absorptions are suppressed a greater amount than the fundamental but are still apparent even when 10-20 wt pct opaques are present. The relationships observed and the simple scattering theory presented show that quantitative compositional remote sensing studies are feasible for surfaces containing complex mineral mixtures.
Clark, R. N.↗
Theoretical and Analog Studies of the Effects of Nonlinear Stability Derivatives on the Longitudinal Motions of an Aircraft in Response to Step Control Deflections and to the Influence of Proportional Automatic Control
Through theoretical and analog results the effects of two nonlinear stability derivatives on the longitudinal motions of an aircraft have been investigated. Nonlinear functions of pitching-moment and lift coefficients with angle of attack were considered. Analog results of aircraft motions in response to step elevator deflections and to the action of the proportional control systems are presented. The occurrence of continuous hunting oscillations was predicted and demonstrated for the attitude stabilization system with proportional control for certain nonlinear pitching-moment variations and autopilot adjustments.
Curfman, Howard J , Jr↗
Static and Dynamic Effects of Lateral Carrier Diffusion in Semiconductor Lasers
Electron and hole diffusions in the plane of semiconductor quantum wells play an important part in the static and dynamic operations of semiconductor lasers. It is well known that the value of diffusion coefficients affects the threshold pumping current of a semiconductor laser. At the same time, the strength of carrier diffusion process is expected to affect the modulation bandwidth of an AC-modulated laser. It is important not only to investigate the combined DC and AC effects due to carrier diffusion, but also to separate the AC effects from that of the combined effects in order to provide design insights for high speed modulation. In this presentation, we apply a hydrodynamic model developed by the present authors recently from the semiconductor Bloch equations. The model allows microscopic calculation of the lateral carrier diffusion coefficient, which is a nonlinear function of the carrier density and plasma temperature. We first studied combined AC and DC effects of lateral carrier diffusion by studying the bandwidth dependence on diffusion coefficient at a given DC current under small signal modulation. The results show an increase of modulation bandwidth with decrease in the diffusion coefficient. We simultaneously studied the effects of nonlinearity in the diffusion coefficient. To clearly identify how much of the bandwidth increase is a result of decrease in the threshold pumping current for smaller diffusion coefficient, thus an effective increase of DC pumping, we study the bandwidth dependence on diffusion coefficient at a given relative pumping. A detailed comparison of the two cases will be presented.
Li, Jian-Zhong↗
Adaptive Filtering Using Recurrent Neural Networks
A method for adaptive (or, optionally, nonadaptive) filtering has been developed for estimating the states of complex process systems (e.g., chemical plants, factories, or manufacturing processes at some level of abstraction) from time series of measurements of system inputs and outputs. The method is based partly on the fundamental principles of the Kalman filter and partly on the use of recurrent neural networks. The standard Kalman filter involves an assumption of linearity of the mathematical model used to describe a process system. The extended Kalman filter accommodates a nonlinear process model but still requires linearization about the state estimate. Both the standard and extended Kalman filters involve the often unrealistic assumption that process and measurement noise are zero-mean, Gaussian, and white. In contrast, the present method does not involve any assumptions of linearity of process models or of the nature of process noise; on the contrary, few (if any) assumptions are made about process models, noise models, or the parameters of such models. In this regard, the method can be characterized as one of nonlinear, nonparametric filtering. The method exploits the unique ability of neural networks to approximate nonlinear functions. In a given case, the process model is limited mainly by limitations of the approximation ability of the neural networks chosen for that case. Moreover, despite the lack of assumptions regarding process noise, the method yields minimum- variance filters. In that they do not require statistical models of noise, the neural- network-based state filters of this method are comparable to conventional nonlinear least-squares estimators.
Parlos, Alexander G.↗
Curvilinear Displacement Transfer Functions for Deformed Shape Predictions of Curved Structures Using Distributed Surface Strains
Curvilinear Displacement Transfer Functions were formulated for deformed shape predictions of different curved structures using surface strains. The embedded curved beam (depth-wise cross section of a curved structure along a surface strain-sensing line) was discretized into multiple small domains, with domain junctures matching the strain-sensing stations. Thus, the surface strain distribution can be described with a piecewise linear or a piecewise nonlinear function. The discrete approach enabled piecewise integrations of a curvature-strain differential equation for the embedded curved beam to yield closed-form Curvilinear Displacement Transfer Functions, which are written in terms of embedded curved-beam geometrical parameters and surface strains. By inputting the surface strain data, the Curvilinear Displacement Transfer Functions can transform surface strains into deflections along each embedded curved beam for mapping out the overall structural deformed shapes. The finite-element method was used to analytically generate the surface strains of the curved beams. The deformed shape prediction accuracies were then determined by comparing the theoretical deflections with the finite-element-generated deflections, which were used as yardsticks. By introducing the correction factors in simple mathematical forms, the Curvilinear Displacement Transfer Functions can be quite accurate for shape predictions of different curved-beam structures ranging from limit case of straight beam up to semicircular curved beam.
Ko, William L.↗
Large-Deformation Displacement Transfer Functions for Shape Predictions of Highly Flexible Slender Aerospace Structures
Large deformation displacement transfer functions were formulated for deformed shape predictions of highly flexible slender structures like aircraft wings. In the formulation, the embedded beam (depth wise cross section of structure along the surface strain sensing line) was first evenly discretized into multiple small domains, with surface strain sensing stations located at the domain junctures. Thus, the surface strain (bending strains) variation within each domain could be expressed with linear of nonlinear function. Such piecewise approach enabled piecewise integrations of the embedded beam curvature equations [classical (Eulerian), physical (Lagrangian), and shifted curvature equations] to yield closed form slope and deflection equations in recursive forms.
Deflection equations↗