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NASA NTRS2010

An Algorithm for the Fitting of Planet Models to Kepler Light Curves

We describe an algorithm which fits model planetary system parameters to light curves from Kepler Mission target stars. The algorithm begins by producing an initial model of the system which is used to seed the fit,with particular emphasis on obtaining good transit timing parameters. An attempt is then made to determine whether the observed transits are more likely due to a planet or an eclipsing binary. In the event that the transits are consistent with a transiting planet, an iterative fitting process is initiated: a wavelet-based whitening filter is used to eliminate stellar variations on timescales long compared to a transit; a robust nonlinear fitter operating on the whitened light curve produces a new model of the system; and the procedure iterates until convergence upon a self-consistent whitening filter and planet model. The fitted transits are removed from the light curve anda search for additional planet candidates is performed upon the residual light curve. The fitted models are used in additional tests which identify false positive planet detections: multiple planet candidates with near-identical fitted periods are far more likely to be an eclipsing binary, for example, while target stars in which the model lightcurve is correlated with the star centroid position may indicate a background eclipsing binary, and subtraction of all model planet candidates yields a light curve of pure noise and stellar variability, which can be used to study the probability that the planet candidates result from statistical fluctuations in the data.

Exoplanet↗

NASA NTRS2013

Applications of Automation Methods for Nonlinear Fracture Test Analysis

Using automated and standardized computer tools to calculate the pertinent test result values has several advantages such as: 1. allowing high-fidelity solutions to complex nonlinear phenomena that would be impractical to express in written equation form, 2. eliminating errors associated with the interpretation and programing of analysis procedures from the text of test standards, 3. lessening the need for expertise in the areas of solid mechanics, fracture mechanics, numerical methods, and/or finite element modeling, to achieve sound results, 4. and providing one computer tool and/or one set of solutions for all users for a more "standardized" answer. In summary, this approach allows a non-expert with rudimentary training to get the best practical solution based on the latest understanding with minimum difficulty.Other existing ASTM standards that cover complicated phenomena use standard computer programs: 1. ASTM C1340/C1340M-10- Standard Practice for Estimation of Heat Gain or Loss Through Ceilings Under Attics Containing Radiant Barriers by Use of a Computer Program 2. ASTM F 2815 - Standard Practice for Chemical Permeation through Protective Clothing Materials: Testing Data Analysis by Use of a Computer Program 3. ASTM E2807 - Standard Specification for 3D Imaging Data Exchange, Version 1.0 The verification, validation, and round-robin processes required of a computer tool closely parallel the methods that are used to ensure the solution validity for equations included in test standard. The use of automated analysis tools allows the creation and practical implementation of advanced fracture mechanics test standards that capture the physics of a nonlinear fracture mechanics problem without adding undue burden or expense to the user. The presented approach forms a bridge between the equation-based fracture testing standards of today and the next generation of standards solving complex problems through analysis automation.

Allen, Phillip A.↗

NASA NTRS1983

Formulation and solution of rotary-wing aeroelastic stability and response problems

The state of the art in the formulation and solution of rotary-wing aeroelastic stability and response problems is reviewed in detail. The approximations used in the structural, inertia and aerodynamic operators are discussed. The important role of geometric nonlinearities, due to moderate deflections, and aerodynamic stall in the aeroelastic stability and response problem are identified. It is also shown that geometric nonlinearities are of primary importance in aeroelastic stability calculations, and have a more limited, though important, role in response calculations. Next, formulation of coupled rotor/fuselage problems is described, for both air and ground resonance type problems. Both topics, the isolated blade problem and the coupled rotor/fuselage problem, are treated for both hover and forward flight. Solution of aeroelastic stability and response problems proceeds in two stages. First, the spatial dependence is eliminated by using Galerkin's method, or by using the finite element method. Next the nonlinear, or linear, ordinary differential equation with periodic coefficients have to be solved for stability or response. Efficient numerical methods for accomplishing these objectives are presented in a comprehensive manner. The paper contains a number of illustrative numerical results which are intended to clarify various aspects of the modeling process and serve as representative results for both aeroelastic stability and response calculations for a variety of blade and rotor configurations.

Friedmann, P. P.↗

NASA NTRS1978

Filtering of non-linear instabilities

For Courant numbers larger than one and cell Reynolds numbers larger than two, oscillations and in some cases instabilities are typically found with implicit numerical solutions of the fluid dynamics equations. This behavior has sometimes been associated with the loss of diagonal dominance of the coefficient matrix. It is shown that these problems can be related to the choice of the spatial differences, with the resulting instability related to aliasing or nonlinear interaction. Appropriate filtering can reduce the intensity of these oscillations and possibly eliminate the instability. These filtering procedures are equivalent to a weighted average of conservation and nonconservation differencing. The entire spectrum of filtered equations retains a three point character as well as second order spatial accuracy. Burgers equation was considered as a model.

Khosla, P. K.↗

NASA NTRS1989

Renormalization group analysis of turbulence

The objective is to understand and extend a recent theory of turbulence based on dynamic renormalization group (RNG) techniques. The application of RNG methods to hydrodynamic turbulence was explored most extensively by Yakhot and Orszag (1986). An eddy viscosity was calculated which was consistent with the Kolmogorov inertial range by systematic elimination of the small scales in the flow. Further, assumed smallness of the nonlinear terms in the redefined equations for the large scales results in predictions for important flow constants such as the Kolmogorov constant. It is emphasized that no adjustable parameters are needed. The parameterization of the small scales in a self-consistent manner has important implications for sub-grid modeling.

Smith, Leslie M.↗

NASA NTRS2015

Position Estimation Using Image Derivative

This paper describes an image processing algorithm to process Moon and/or Earth images. The theory presented is based on the fact that Moon hard edge points are characterized by the highest values of the image derivative. Outliers are eliminated by two sequential filters. Moon center and radius are then estimated by nonlinear least-squares using circular sigmoid functions. The proposed image processing has been applied and validated using real and synthetic Moon images.

Mortari, Daniele↗

NASA NTRS1991

Correlation techniques to determine model form in robust nonlinear system realization/identification

The fundamental challenge in identification of nonlinear dynamic systems is determining the appropriate form of the model. A robust technique is presented which essentially eliminates this problem for many applications. The technique is based on the Minimum Model Error (MME) optimal estimation approach. A detailed literature review is included in which fundamental differences between the current approach and previous work is described. The most significant feature is the ability to identify nonlinear dynamic systems without prior assumption regarding the form of the nonlinearities, in contrast to existing nonlinear identification approaches which usually require detailed assumptions of the nonlinearities. Model form is determined via statistical correlation of the MME optimal state estimates with the MME optimal model error estimates. The example illustrations indicate that the method is robust with respect to prior ignorance of the model, and with respect to measurement noise, measurement frequency, and measurement record length.

Stry, Greselda I.↗

NASA NTRS1972

Bounded state space

This investigation is divided functionally into three different areas: (1) study of bounded state space, (2) nonlinear smoothing theory, and (3) system identification. (1) Study of bounded state space: necessary and sufficient conditions for an optimal control are obtained for a bounded state space optimal control problem. The difficulty of determining the so-called jump conditions is eliminated; however, the problem of determining the points where the response either enters or leaves the boundary still remains unsolved. (2) Nonlinear smoothing theory: nonlinear fixed-interval, fixed-point and fixed-lag smoothing of a random signal generated by a stochastic differential equation are investigated. Results on the asymptotic stability of a linear constant-parameter fixed-interval smoothing filter are obtained. (3) System identification: a particular stochastic modelling problem is solved. An Ito stochastic integral equation is used to mathematically model a black box having multiple inputs and multiple outputs. A new method for identifying system parameters is presented.

Eyman, E. D.↗

NASA NTRS1977

Flight test data for light aircraft spoiler roll control systems

The results of flight tests to determine the characteristics of spoiler roll control systems on three different light aircraft are summarized. Comparisons are made with wind tunnel data where available. Flight tests indicate that excellent roll characteristics can be achieved with spoilers. Yaw coupling with roll control inputs is virtually eliminated. Roll rates remain high when flaps are deployed at low speed. Very mild nonlinearities in control effectiveness exist, and there was no deadband or lag detected.

Kohlman, D. L.↗

NASA NTRS1977

Flight test data for light aircraft spoiler roll control systems

Kohlman, D. L.↗

NASA NTRS1988

Renormalization-group theory for the eddy viscosity in subgrid modeling

Renormalization-group theory is applied to incompressible three-dimensional Navier-Stokes turbulence so as to eliminate unresolvable small scales. The renormalized Navier-Stokes equation now includes a triple nonlinearity with the eddy viscosity exhibiting a mild cusp behavior, in qualitative agreement with the test-field model results of Kraichnan. For the cusp behavior to arise, not only is the triple nonlinearity necessary but the effects of pressure must be incorporated in the triple term. The renormalized eddy viscosity will not exhibit a cusp behavior if it is assumed that a spectral gap exists between the large and small scales.

Zhou, YE↗

NASA NTRS1992

Reasoning about energy in qualitative simulation

While possible behaviors of a mechanism that are consistent with an incomplete state of knowledge can be predicted through qualitative modeling and simulation, spurious behaviors corresponding to no solution of any ordinary differential equation consistent with the model may be generated. The present method for energy-related reasoning eliminates an important source of spurious behaviors, as demonstrated by its application to a nonlinear, proportional-integral controlled. It is shown that such qualitative properties of such a system as stability and zero-offset control are captured by the simulation.

Fouche, Pierre↗

NASA NTRS1999

Structural Optimization for Reliability Using Nonlinear Goal Programming

This report details the development of a reliability based multi-objective design tool for solving structural optimization problems. Based on two different optimization techniques, namely sequential unconstrained minimization and nonlinear goal programming, the developed design method has the capability to take into account the effects of variability on the proposed design through a user specified reliability design criterion. In its sequential unconstrained minimization mode, the developed design tool uses a composite objective function, in conjunction with weight ordered design objectives, in order to take into account conflicting and multiple design criteria. Multiple design criteria of interest including structural weight, load induced stress and deflection, and mechanical reliability. The nonlinear goal programming mode, on the other hand, provides for a design method that eliminates the difficulty of having to define an objective function and constraints, while at the same time has the capability of handling rank ordered design objectives or goals. For simulation purposes the design of a pressure vessel cover plate was undertaken as a test bed for the newly developed design tool. The formulation of this structural optimization problem into sequential unconstrained minimization and goal programming form is presented. The resulting optimization problem was solved using: (i) the linear extended interior penalty function method algorithm; and (ii) Powell's conjugate directions method. Both single and multi-objective numerical test cases are included demonstrating the design tool's capabilities as it applies to this design problem.

El-Sayed, Mohamed E.↗

NASA NTRS1984

Element-by-element Solution Procedures for Nonlinear Structural Analysis

Element-by-element approximate factorization procedures are proposed for solving the large finite element equation systems which arise in nonlinear structural mechanics. Architectural and data base advantages of the present algorithms over traditional direct elimination schemes are noted. Results of calculations suggest considerable potential for the methods described.

Hughes, T. J. R.↗

NASA NTRS1986

Purely cubic action for string field theory

It is shown that Witten's (1986) open-bosonic-string field-theory action and a closed-string analog can be written as a purely cubic interaction term. The conventional form of the action arises by expansion around particular solutions of the classical equations of motion. The explicit background dependence of the conventional action via the Becchi-Rouet-Stora-Tyutin operator is eliminated in the cubic formulation. A closed-form expression is found for the full nonlinear gauge-transformation law.

Horowitz, G. T.↗

NASA NTRS1991

Application and flight test of linearizing transformations using measurement feedback to the nonlinear control problem

The design of nonlinear controllers has relied on the use of detailed aerodynamic and engine models that must be associated with the control law in the flight system implementation. Many of these controllers were applied to vehicle flight path control problems and have attempted to combine both inner- and outer-loop control functions in a single controller. An approach to the nonlinear trajectory control problem is presented. This approach uses linearizing transformations with measurement feedback to eliminate the need for detailed aircraft models in outer-loop control applications. By applying this approach and separating the inner-loop and outer-loop functions two things were achieved: (1) the need for incorporating detailed aerodynamic models in the controller is obviated; and (2) the controller is more easily incorporated into existing aircraft flight control systems. An implementation of the controller is discussed, and this controller is tested on a six degree-of-freedom F-15 simulation and in flight on an F-15 aircraft. Simulation data are presented which validates this approach over a large portion of the F-15 flight envelope. Proof of this concept is provided by flight-test data that closely matches simulation results. Flight-test data are also presented.

Antoniewicz, Robert F.↗

NASA NTRS1999

Semi-monolithic cavity for external resonant frequency doubling and method of performing the same

The fabrication of an optical cavity for use in a laser, in a frequency doubling external cavity, or any other type of nonlinear optical device, can be simplified by providing the nonlinear crystal in combination with a surrounding glass having an index of refraction substantially equal to that of the nonlinear crystal. The closed optical path in this cavity is formed in the surrounding glass and through the nonlinear crystal which lies in one of the optical segments of the light path. The light is transmitted through interfaces between the surrounding glass in the nonlinear crystal through interfaces which are formed at the Brewster-angle to minimize or eliminate reflection.

Hemmati, Hamid↗

NASA NTRS1987

The error associated with use of various forms of the divergence equation to diagnose geopotential and temperature

This study utilizes a model-generated data set to evaluate the errors associated with the diagnosis of geopotential height using three approximate forms of the divergence equation (DE). The DE was solved on the original sigma-coordinate surfaces of the model to exclude any error produced in the process of interpolating the data from observation points to the coordinate surface of the DE. An inviscid, nonlinear, divergent DE produced rms geopotential height errors as large as 3 m and rms temperature errors of over 26 C in the lower planetary boundary layer (PBL), with minimal errors above 800 mb. Elimination of the isobaric divergence in the velocity field caused additional height errors of 5-6 m and temperature errors of 0.4-1.2 C in the free troposphere. Use of a further-degraded DE without nonlinear terms caused height errors of 10-15 m in the upper troposphere with modestly increased temperature errors. Error fields at all levels had synoptic-scale features, with some mesoalpha structure. No spatial noise was apparent. Use of a temporal spectral filter to eliminate high-frequency modes from the model-generated data did not significantly influence the error associated with use of various forms of the DE.

Modica, George M.↗