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At least 145 records · Page 8

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NASA NTRS2015

Assessing Spontaneous Combustion Instability with Nonlinear Time Series Analysis

Considerable interest lies in the ability to characterize the onset of spontaneous instabilities within liquid propellant rocket engine (LPRE) combustion devices. Linear techniques, such as fast Fourier transforms, various correlation parameters, and critical damping parameters, have been used at great length for over fifty years. Recently, nonlinear time series methods have been applied to deduce information pertaining to instability incipiency hidden in seemingly stochastic combustion noise. A technique commonly used in biological sciences known as the Multifractal Detrended Fluctuation Analysis has been extended to the combustion dynamics field, and is introduced here as a data analysis approach complementary to linear ones. Advancing, a modified technique is leveraged to extract artifacts of impending combustion instability that present themselves a priori growth to limit cycle amplitudes. Analysis is demonstrated on data from J-2X gas generator testing during which a distinct spontaneous instability was observed. Comparisons are made to previous work wherein the data were characterized using linear approaches. Verification of the technique is performed by examining idealized signals and comparing two separate, independently developed tools.

Eberhart, C. J.↗

NASA NTRS1993

Control of nonlinear systems with applications to constrained robots and spacecraft attitude stabilization

This thesis is organized in two parts. In Part 1, control systems described by a class of nonlinear differential and algebraic equations are introduced. A procedure for local stabilization based on a local state realization is developed. An alternative approach to local stabilization is developed based on a classical linearization of the nonlinear differential-algebraic equations. A theoretical framework is established for solving a tracking problem associated with the differential-algebraic system. First, a simple procedure is developed for the design of a feedback control law which ensures, at least locally, that the tracking error in the closed loop system lies within any given bound if the reference inputs are sufficiently slowly varying. Next, by imposing additional assumptions, a procedure is developed for the design of a feedback control law which ensures that the tracking error in the closed loop system approaches zero exponentially for reference inputs which are not necessarily slowly varying. The control design methodologies are used for simultaneous force and position control in constrained robot systems. The differential-algebraic equations are shown to characterize the slow dynamics of a certain nonlinear control system in nonstandard singularly perturbed form. In Part 2, the attitude stabilization (reorientation) of a rigid spacecraft using only two control torques is considered. First, the case of momentum wheel actuators is considered. The complete spacecraft dynamics are not controllable. However, the spacecraft dynamics are small time locally controllable in a reduced sense. The reduced spacecraft dynamics cannot be asymptotically stabilized using continuous feedback, but a discontinuous feedback control strategy is constructed. Next, the case of gas jet actuators is considered. If the uncontrolled principal axis is not an axis of symmetry, the complete spacecraft dynamics are small time locally controllable. However, the spacecraft attitude cannot be asymptotically stabilized using continuous feedback, but a discontinuous stabilizing feedback control strategy is constructed. If the uncontrolled principal axis is an axis of symmetry, the complete spacecraft dynamics cannot be stabilized. However, the spacecraft dynamics are small time locally controllable in a reduced sense. The reduced spacecraft dynamics cannot be asymptotically stabilized using continuous feedback, but again a discontinuous feedback control strategy is constructed.

Krishnan, Hariharan↗

NASA NTRS1997

An Energy-Based Hysteresis Model for Magnetostrictive Transducers

This paper addresses the modeling of hysteresis in magnetostrictive transducers. This is considered in the context of control applications which require an accurate characterization of the relation between input currents and strains output by the transducer. This relation typically exhibits significant nonlinearities and hysteresis due to inherent properties of magnetostrictive materials. The characterization considered here is based upon the Jiles-Atherton mean field model for ferromagnetic hysteresis in combination with a quadratic moment rotation model for magnetostriction. As demonstrated through comparison with experimental data, the magnetization model very adequately quantifies both major and minor loops under various operating conditions. The combined model can then be used to accurately characterize output strains at moderate drive levels. The advantages to this model lie in the small number (six) of required parameters and the flexibility it exhibits in a variety of operating conditions.

Calkins, F. T.↗

NASA NTRS1979

Controllability of delay systems with restrained controls

Using a geometric growth condition, both the function space and Euclidean controllability of a nonlinear delay system which has a compact and convex control set are characterized. This extends analogous results for ordinary differential systems, and it yields conditions under which perturbed nonlinear delay controllable systems are controllable.

Chukwu, E. N.↗

NASA NTRS1990

Self-calibration of robot-sensor system

The process of finding the coordinate transformation between a robot and an external sensor system has been addressed. This calibration is equivalent to solving a nonlinear optimization problem for the parameters that characterize the transformation. A two-step procedure is herein proposed for solving the problem. The first step involves finding a nominal solution that is a good approximation of the final solution. A varational problem is then generated to replace the original problem in the next step. With the assumption that the variational parameters are small compared to unity, the problem that can be more readily solved with relatively small computation effort.

Yeh, Pen-Shu↗

NASA NTRS1991

An inverse dynamic tracking control for bracing a flexible manipulator

The goal of this research is to produce a braced manipulator that is flexible. In order to brace the manipulator against a surface, a tip position tracking control becomes essential to avoid large impacts on contact, and to control the force after contact. If we consider the characteristics of the flexible manipulator, the control task may be characterized as a tracking control of a nonlinear, noncolocated, nonminimum-phase system with uncertainties. First, the author introduces the staged positioning concept and provides a conceptual background for the bracing strategy. Second, a single link flexible manipulator is modeled by the assumed-modes method, and the validity of the model is verified with experimental results. Third, a time domain inverse dynamic method is proposed to cancel out the nonminimum-phase positive zeros which cannot be cancelled by feedback controls. Fourth, a tracking controller is designed to control the end point of a flexible manipulator without any overshoot or residual vibrations. Its perfect tracking or asymptotic tracking performance is analyzed and discussed for zero and non-zero initial condition cases. Finally, impact phenomena are investigated, and contact force control of a flexible bracing manipulator is presented to set up a control scenerio for such a manipulator. The proposed control scheme is implemented on a single link flexible manipulator, and analyzed and evaluated with simulations and experiments.

Source record↗

NASA NTRS1993

Numerical simulation of stability and stability control of high speed compressible rotating couette flow

The nonlinear temporal evolution of disturbances in compressible flow between infinitely long, concentric cylinders is investigated through direct numerical simulations of the full, three-dimensional Navier-Stokes and energy equations. Counter-rotating cylinders separated by wide gaps are considered with supersonic velocities of the inner cylinder. Initially, the primary disturbance grows exponentially in accordance with linear stability theory. As the disturbances evolve, higher harmonics and subharmonics are generated in a cascading order eventually reaching a saturation state. Subsequent highly nonlinear stages of the evolution are governed by the interaction of the disturbance modes, particularly the axial subharmonics. Nonlinear evolution of the disturbance field is characterized by the formation of high-shear layers extending from the inner cylinder towards the center of the gap in the form of jets similar to the ejection events in transitional and turbulent wall-bounded shear flows.

Biringen, Sedat↗

NASA NTRS1995

A Simple Theory of Capillary-Gravity Wave Turbulence

Employing a recently proposed 'multi-wave interaction' theory, inertial spectra of capillary gravity waves are derived. This case is characterized by a rather high degree of nonlinearity and a complicated dispersion law. The absence of scale invariance makes this and some other problems of wave turbulence (e.g., nonlinear inertia gravity waves) intractable by small-perturbation techniques, even in the weak-turbulence limit. The analytical solution obtained in the present work for an arbitrary degree of nonlinearity is shown to be in reasonable agreement with experimental data. The theory explains the dependence of the wave spectrum on wind input and describes the accelerated roll-off of the spectral density function in the narrow sub-range separating scale-invariant regimes of purely gravity and capillary waves, while the appropriate (long- and short-wave) limits yield power laws corresponding to the Zakharov-Filonenko and Phillips spectra.

Glazman, Roman E.↗

NASA NTRS1994

Non-linear numerical analysis of the Iosipescu specimen for composite materials

A nonlinear elastic finite element analysis is presented of the Iosipescu shear specimen tested in the modified Wyoming fixture for unidirectional graphite/epoxy composites. It is shown that the nonlinear effects due to specimen-to-fixture contact interactions and specimen geometry on the overall shear response are negligible. It is proposed that the tangential shear modulus should be used to characterize the shear resistance of composite materials with highly nonlinear shear response. The correction factors, which are needed to compensate for the nonuniformity of the shear stress or strain distribution in the specimen test section for shear modulus measurement, have to be defined carefully. Strain contours in the nonlinear response ranges are presented and the initiation of failure in the notch regions is investigated.

Ho, Henjen↗

NASA NTRS2009

Hybrid NN/SVM Computational System for Optimizing Designs

A computational method and system based on a hybrid of an artificial neural network (NN) and a support vector machine (SVM) (see figure) has been conceived as a means of maximizing or minimizing an objective function, optionally subject to one or more constraints. Such maximization or minimization could be performed, for example, to optimize solve a data-regression or data-classification problem or to optimize a design associated with a response function. A response function can be considered as a subset of a response surface, which is a surface in a vector space of design and performance parameters. A typical example of a design problem that the method and system can be used to solve is that of an airfoil, for which a response function could be the spatial distribution of pressure over the airfoil. In this example, the response surface would describe the pressure distribution as a function of the operating conditions and the geometric parameters of the airfoil. The use of NNs to analyze physical objects in order to optimize their responses under specified physical conditions is well known. NN analysis is suitable for multidimensional interpolation of data that lack structure and enables the representation and optimization of a succession of numerical solutions of increasing complexity or increasing fidelity to the real world. NN analysis is especially useful in helping to satisfy multiple design objectives. Feedforward NNs can be used to make estimates based on nonlinear mathematical models. One difficulty associated with use of a feedforward NN arises from the need for nonlinear optimization to determine connection weights among input, intermediate, and output variables. It can be very expensive to train an NN in cases in which it is necessary to model large amounts of information. Less widely known (in comparison with NNs) are support vector machines (SVMs), which were originally applied in statistical learning theory. In terms that are necessarily oversimplified to fit the scope of this article, an SVM can be characterized as an algorithm that (1) effects a nonlinear mapping of input vectors into a higher-dimensional feature space and (2) involves a dual formulation of governing equations and constraints. One advantageous feature of the SVM approach is that an objective function (which one seeks to minimize to obtain coefficients that define an SVM mathematical model) is convex, so that unlike in the cases of many NN models, any local minimum of an SVM model is also a global minimum.

Rai, Man Mohan↗

NASA NTRS1990

Nonlinear phase-space diffusion approach to turbulent organized structures

The study deals with the approximation of the effect of all velocity-increment moments on the spatial evolution of the pdf for maximally correlated structures by the effect of the second moment alone by assuming independence of separated length scales. The dependence of the two-point velocity statistics on length-scale or separation is found to be governed by the gradients of the stress, rather than of the velocity. This may provide a new approach for predicting the domain patterns observed in turbulent flows and a new means of characterizing or classifying different structures, namely, by their nonlinear diffusion coefficient.

Shen, Hubert H.↗

NASA NTRS1990

Chaos in driven Alfven systems

The chaos in a one-dimensional system, which would be nonlinear stationary Alfven waves in the absence of an external driver, is characterized. The evolution equations are numerically integrated for the transverse wave magnetic field amplitude and phase using the derivative nonlinear Schroedinger equation (DNLS), including resistive wave damping and a long-wavelength monochromatic, circularly polarized driver. A Poincare map analysis shows that, for the nondissipative (Hamiltonian) case, the solutions near the phase space (soliton) separatrices of this system become chaotic as the driver amplitude increases, and 'strong' chaos appears when the driver amplitude is large. The dissipative system exhibits a wealth of dynamical behavior, including quasiperiodic orbits, period-doubling bifurcations leading to chaos, sudden transitions to chaos, and several types of strange attractors.

Hada, T.↗

NASA NTRS1976

Nonlinear effects in thermal stress analysis of a solid propellant rocket motor

Direct characterization procedures were used to determine the relaxation modulus as a function of time, temperature, and state of strain. Using the quasi-elastic method of linearviscoelasticity, these properties were employed in a finite element computer code to analyze a thick-walled, nonlinear viscoelastic cylinder in the state of plane strain bonded to a thin (but stiff) elastic casing and subjected to slow thermal cooling. The viscoelastic solution is then expressed as a sequence of elastic finite element solutions. The strain-dependent character of the relaxation modulus is included by replacing the single relaxation curve used in the linear viscoelastic theory by a family of relaxation functions obtained at various strain levels. These functions may be regarded as a collection of stress histories or responses to specific loads (in this case, step strains) with which the cooldown solution is made to agree by iterations on the modulus and strain level.

Francis, E. C.↗

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.↗

NASA NTRS1995

Bearing defect signature analysis using advanced nonlinear signal analysis in a controlled environment

Utilizing high-frequency data from a highly instrumented rotor assembly, seeded bearing defect signatures are characterized using both conventional linear approaches, such as power spectral density analysis, and recently developed nonlinear techniques such as bicoherence analysis. Traditional low-frequency (less than 20 kHz) analysis and high-frequency envelope analysis of both accelerometer and acoustic emission data are used to recover characteristic bearing distress information buried deeply in acquired data. The successful coupling of newly developed nonlinear signal analysis with recovered wideband envelope data from accelerometers and acoustic emission sensors is the innovative focus of this research.

Zoladz, T.↗

NASA NTRS1979

Simulation of liquid propellant rocket engine combustion instabilities

A simulation technique for studying the high frequency combustion instabilities of liquid propellant rocket engines has been developed and used to investigate various aspects of instability phenomena. Of importance was investigation of the significance of the method of coupling the combustion and the gas dynamics of the system. Two coupling processes were studied: linear response of the combustion process to pressure fluctuations, and the nature of the resulting instabilities; and nonlinear response of the combustion process to velocity fluctuations, and the nature of the resulting instabilities. For the combustion model studied, nonlinear (velocity) coupling was found to more closely characterize liquid propellant instabilities.

Ventrice, M. B.↗

NASA NTRS1989

Shear testing of fiber reinforced metal matrix composites

This paper outlines the elements of a combined experimental/analytical methodology for accurate shear characterization of unidirectional composites in the linear and nonlinear range, with particular attention devoted to metal matrix composites. It is illustrated that consistent results can be obtained for a large class of composites from two commonly employed shear test methods currently in use by composites researchers when the influence of various factors that affect the determination of the actual shear response is properly analyzed. These factors include the effects of material anisotropy, specimen geometry, manner of load introduction, and test fixture design on the stress and deformation fields in the test section of off-axis and Iosipescu specimens. Common errors associated with the measurement of deformation fields and calculation of stress fields are discussed and quantified. Particular problems in the determination of the shear response of unidirectional boron/aluminum using the Iosipescu test are illustrated and discussed.

Pindera, Marek-Jerzy↗

NASA NTRS2001

High Strain Rate Behavior of Polymer Matrix Composites Analyzed

Procedures for modeling the high-speed impact of composite materials are needed for designing reliable composite engine cases that are lighter than the metal cases in current use. The types of polymer matrix composites that are likely to be used in such an application have a deformation response that is nonlinear and that varies with strain rate. To characterize and validate material models that could be used in the design of impactresistant engine cases, researchers must obtain material data over a wide variety of strain rates. An experimental program has been carried out through a university grant with the Ohio State University to obtain deformation data for a representative polymer matrix composite for strain rates ranging from quasi-static to high rates of several hundred per second. This information has been used to characterize and validate a constitutive model that was developed at the NASA Glenn Research Center.

Goldberg, Robert K.↗