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NASA NTRS1985

Optimal symmetric flight studies

Several topics in optimal symmetric flight of airbreathing vehicles are examined. In one study, an approximation scheme designed for onboard real-time energy management of climb-dash is developed and calculations for a high-performance aircraft presented. In another, a vehicle model intermediate in complexity between energy and point-mass models is explored and some quirks in optimal flight characteristics peculiar to the model uncovered. In yet another study, energy-modelling procedures are re-examined with a view to stretching the range of validity of zeroth-order approximation by special choice of state variables. In a final study, time-fuel tradeoffs in cruise-dash are examined for the consequences of nonconvexities appearing in the classical steady cruise-dash model. Two appendices provide retrospective looks at two early publications on energy modelling and related optimal control theory.

Weston, A. R.↗

NASA NTRS1993

Ignition and subsequent flame spread over a thin cellulosic material

Both ignition and flame spread on solid fuels are processes that not only are of considerable scientific interest but that also have important fire safety applications. Both types of processes, ignition and flame spread, are complicated by strong coupling between chemical reactions and transport processes, not only in the gas phase but also in the condensed phase. In most previous studies, ignition and flame spread were studied separately with the result that there has been little understanding of the transition from ignition to flame spread. In fire safety applications this transition is crucial to determine whether a fire will be limited to a localized, temporary burn or will transition into a growth mode with a potential to become a large fire. In order to understand this transition, the transient mechanisms of ignition and subsequent flame spread must be studied. However, there have been no definitive experimental or modeling studies, because of the complexity of the flow motion generated by buoyancy near the heated sample surface. One must solve the full Navier-Stokes equations over an extended region to represent accurately the highly unstable buoyant plume and entrainment of surrounding gas from far away. In order to avoid the complicated nature of the starting plume problem under normal gravity, previous detailed radiative ignition models were assumed to be one-dimensional or were applied at a stagnation point. Thus, these models cannot be extended to include the transition to flame spread. The mismatch between experimental and calculated geometries means that theories cannot be compared directly with experimental results in normal gravity. To overcome the above difficulty, theoretical results obtained without buoyancy can be directly compared with experimental data measured in a microgravity environment. Thus, the objective of this study is to develop a theoretical model for ignition and the transition to flame spread and to make predictions using the thermal and chemical characteristics of a cellulosic material which are measured in normal gravity.

Nakabe, Kazuyoshi↗

NASA NTRS2005

Shock Waves in a Bose-Einstein Condensate

A paper presents a theoretical study of shock waves in a trapped Bose-Einstein condensate (BEC). The mathematical model of the BEC in this study is a nonlinear Schroedinger equation (NLSE) in which (1) the role of the wave function of a single particle in the traditional Schroedinger equation is played by a space- and time-dependent complex order parameter (x,t) proportional to the square root of the density of atoms and (2) the atoms engage in a repulsive interaction characterized by a potential proportional to | (x,t)|2. Equations that describe macroscopic perturbations of the BEC at zero temperature are derived from the NLSE and simplifying assumptions are made, leading to equations for the propagation of sound waves and the transformation of sound waves into shock waves. Equations for the speeds of shock waves and the relationships between jumps of velocity and density across shock fronts are derived. Similarities and differences between this theory and the classical theory of sound waves and shocks in ordinary gases are noted. The present theory is illustrated by solving the equations for the example of a shock wave propagating in a cigar-shaped BEC.

Kulikov, Igor↗

NASA NTRS1984

Andean tectonics: Implications for Satellite Geodesy

Current knowledge and theories of large scale Andean tectonics as they relate to site planning for the NASA Crustal Dynamics Program's proposed high precision geodetic measurements of relative motions between the Nazca and South American plates are summarized. The Nazca Plate and its eastern margin, the Peru-Chile Trench, is considered a prototype plate marked by rapid motion, strong seismicity and well defined boundaries. Tectonic activity across the Andes results from the Nazca Plate subducting under the South American plate in a series of discrete platelets with different widths and dip angles. This in turn, is reflected in the tectonic complexity of the Andes which are a multitutde of orogenic belts superimposed on each other since the Precambrian. Sites for Crustal Dynamics Program measurements are being located to investigate both interplate and extraplate motions. Observing operations have already been initiated at Arequipa, Peru and Easter Island, Santiago and Cerro Tololo, Chile. Sites under consideration include Iquique, Chile; Oruro and Santa Cruz, Bolivia; Cuzco, Lima, Huancayo and Bayovar, Peru; and Quito and the Galapagos Islands, Ecuador. Based on scientific considerations, Santa Cruz, Huancayo (or Lima), Quito and the Galapagos Islands should be replaced by Isla San Felix, Chile; Brazilia or Petrolina, Brazil; and Guayaquil, Ecuador. If resources permit, additional important sites would be Buenaventura and Villavicencio or Puerto La Concordia, Colombia; and Mendoza and Cordoba, Argentina.

Allenby, R. J.↗

NASA NTRS1983

The birthline for low-mass stars

Using the results of protostar theory, the locus in the Hertzsprung-Russell diagram is found where pre-main-sequence stars of subsolar mass should begin their quasi-static contraction phase and first appear as visible objects. This 'birthline' is in striking agreement with observations of T Tauri stars, providing a strong confirmation of the fact that these stars are indeed contracting along Hayashi tracks. The assumption that most T Tauri stars first appear along this line forces a recalibration of their ages. This recalibration removes the puzzling dip in present-day star formation seen in age histograms of several cloud complexes. Since the underlying protostar calculation assumes that the parent cloud was only thermally supported prior to its collapse, the observed location of the birthline places severe restrictions on the degree of extrathermal support provided by rotation, magnetic fields, or turbulence. In addition, the hypothesis that the collapse from thermally supported clouds to low-mass stars proceeds through protostellar disks appears untenable, since the disk accretion process almost certainly produces pre-main-sequence stars with radii well below the observed birthline.

Stahler, S. W.↗

NASA NTRS1985

Study of photon emission by electron capture during solar nuclei acceleration, 1: Temperature-dependent cross section for charge changing processes

The study of charge changing cross sections of fast ions colliding with matter provides the fundamental basis for the analysis of the charge states produced in such interactions. Given the high degree of complexity of the phenomena, there is no theoretical treatment able to give a comprehensive description. In fact, the involved processes are very dependent on the basic parameters of the projectile, such as velocity charge state, and atomic number, and on the target parameters, the physical state (molecular, atomic or ionized matter) and density. The target velocity, may have also incidence on the process, through the temperature of the traversed medium. In addition, multiple electron transfer in single collisions intrincates more the phenomena. Though, in simplified cases, such as protons moving through atomic hydrogen, considerable agreement has been obtained between theory and experiments However, in general the available theoretical approaches have only limited validity in restricted regions of the basic parameters. Since most measurements of charge changing cross sections are performed in atomic matter at ambient temperature, models are commonly based on the assumption of targets at rest, however at Astrophysical scales, temperature displays a wide range in atomic and ionized matter. Therefore, due to the lack of experimental data , an attempt is made here to quantify temperature dependent cross sections on basis to somewhat arbitrary, but physically reasonable assumptions.

Perez-Peraza, J.↗

NASA NTRS1984

Computation of eigenpairs of Ax = lambda Bx for vibrations of spinning deformable bodies

It is shown that, when linear theory is used, the general eigenvalue problem related with the free vibrations of spinning deformable bodies is of the type AX = lambda Bx, where A is Hermitian, and B is real positive definite. Since the order n of the matrices may be large, and A and B are banded or block banded, due to the economics of the numerical solution, one is interested in obtaining only those eigenvalues which fall within the frequency band of interest of the problem. The paper extends the well known method of bisections and iteration of R to the n power to n dimensional complex spaces, i.e., to C to the n power, so that it can be applied to the present problem.

Utku, S.↗

NASA NTRS2004

Validation of Inlet and Exhaust Boundary Conditions for a Cartesian Method

Inlets and exhaust nozzles are often omitted in aerodynamic simulations of aircraft due to the complexities involved in the modeling of engine details and flow physics. However, the omission is often improper since inlet or plume flows may have a substantial effect on vehicle aerodynamics. A method for modeling the effect of inlets and exhaust plumes using boundary conditions within an inviscid Cartesian flow solver is presented. This approach couples with both CAD systems and legacy geometry to provide an automated tool suitable for parameter studies. The method is validated using two and three-dimensional test problems which are compared with both theoretical and experimental results. The numerical results demonstrate excellent agreement with theory and available data, even for extremely strong jets and very sensitive inlets.

Pandya, Shishir A.↗

NASA NTRS2010

Multiple Kernel Learning for Heterogeneous Anomaly Detection: Algorithm and Aviation Safety Case Study

The world-wide aviation system is one of the most complex dynamical systems ever developed and is generating data at an extremely rapid rate. Most modern commercial aircraft record several hundred flight parameters including information from the guidance, navigation, and control systems, the avionics and propulsion systems, and the pilot inputs into the aircraft. These parameters may be continuous measurements or binary or categorical measurements recorded in one second intervals for the duration of the flight. Currently, most approaches to aviation safety are reactive, meaning that they are designed to react to an aviation safety incident or accident. In this paper, we discuss a novel approach based on the theory of multiple kernel learning to detect potential safety anomalies in very large data bases of discrete and continuous data from world-wide operations of commercial fleets. We pose a general anomaly detection problem which includes both discrete and continuous data streams, where we assume that the discrete streams have a causal influence on the continuous streams. We also assume that atypical sequence of events in the discrete streams can lead to off-nominal system performance. We discuss the application domain, novel algorithms, and also discuss results on real-world data sets. Our algorithm uncovers operationally significant events in high dimensional data streams in the aviation industry which are not detectable using state of the art methods

Das, Santanu↗

NASA NTRS1961

A General Computer Program for Ionospheric Ray-Tracing

The study of the ionosphere using the Faraday rotation effect has been undertaken recently by means of rocket, satellite, and moon echo experiments. Different approximations have been used by different authors, resulting in methods with different degrees of complexity, and it is possible to say that the more accurate a method is, the more difficult its application becomes. However, the use of modern high-speed digital computers offers the possibility of using more complex methods in the solution of this problem, The program described in this report was written for the ILLIAC, the digital computer of the University of Illinois. Only the general features common to most digital computers will be mentioned. This program was prepared having in mind the analysis of the Faraday rotation effect, as recorded from artificial satellites. It is intended to be as general as possible in the conditions imposed on the assumed propagating medium: specifically there are no restrictions on the models of the electron density distribution and the earth's magnetic fields. long as the ray theory Ls valid. The program will trace separately the ordinary and the extraordinary mode, and it will find the virtual phase path length of a ray of each mode between the transmitter (satellite) and a receiver (station). The difference between respective phase path-lengths is related to the Faraday rotation through a constant which depends on the frequency.

Gonzales, Victor H.↗

NASA NTRS1996

Dynamic Smagorinsky model on anisotropic grids

Large Eddy Simulation (LES) of complex-geometry flows often involves highly anisotropic meshes. To examine the performance of the dynamic Smagorinsky model in a controlled fashion on such grids, simulations of forced isotropic turbulence are performed using highly anisotropic discretizations. The resulting model coefficients are compared with a theoretical prediction (Scotti et al., 1993). Two extreme cases are considered: pancake-like grids, for which two directions are poorly resolved compared to the third, and pencil-like grids, where one direction is poorly resolved when compared to the other two. For pancake-like grids the dynamic model yields the results expected from the theory (increasing coefficient with increasing aspect ratio), whereas for pencil-like grids the dynamic model does not agree with the theoretical prediction (with detrimental effects only on smallest resolved scales). A possible explanation of the departure is attempted, and it is shown that the problem may be circumvented by using an isotropic test-filter at larger scales. Overall, all models considered give good large-scale results, confirming the general robustness of the dynamic and eddy-viscosity models. But in all cases, the predictions were poor for scales smaller than that of the worst resolved direction.

Scotti, A.↗

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 NTRS2014

Static Aeroelastic Analysis with an Inviscid Cartesian Method

An embedded-boundary, Cartesian-mesh flow solver is coupled with a three degree-of-freedom structural model to perform static, aeroelastic analysis of complex aircraft geometries. The approach solves a nonlinear, aerostructural system of equations using a loosely-coupled strategy. An open-source, 3-D discrete-geometry engine is utilized to deform a triangulated surface geometry according to the shape predicted by the structural model under the computed aerodynamic loads. The deformation scheme is capable of modeling large deflections and is applicable to the design of modern, very-flexible transport wings. The coupling interface is modular so that aerodynamic or structural analysis methods can be easily swapped or enhanced. After verifying the structural model with comparisons to Euler beam theory, two applications of the analysis method are presented as validation. The first is a relatively stiff, transport wing model which was a subject of a recent workshop on aeroelasticity. The second is a very flexible model recently tested in a low speed wind tunnel. Both cases show that the aeroelastic analysis method produces results in excellent agreement with experimental data.

Aeroelastic↗

NASA NTRS1997

An Algorithm for Integrated Subsystem Embodiment and System Synthesis

Consider the statement,'A system has two coupled subsystems, one of which dominates the design process. Each subsystem consists of discrete and continuous variables, and is solved using sequential analysis and solution.' To address this type of statement in the design of complex systems, three steps are required, namely, the embodiment of the statement in terms of entities on a computer, the mathematical formulation of subsystem models, and the resulting solution and system synthesis. In complex system decomposition, the subsystems are not isolated, self-supporting entities. Information such as constraints, goals, and design variables may be shared between entities. But many times in engineering problems, full communication and cooperation does not exist, information is incomplete, or one subsystem may dominate the design. Additionally, these engineering problems give rise to mathematical models involving nonlinear functions of both discrete and continuous design variables. In this dissertation an algorithm is developed to handle these types of scenarios for the domain-independent integration of subsystem embodiment, coordination, and system synthesis using constructs from Decision-Based Design, Game Theory, and Multidisciplinary Design Optimization. Implementation of the concept in this dissertation involves testing of the hypotheses using example problems and a motivating case study involving the design of a subsonic passenger aircraft.

Lewis, Kemper↗

NASA NTRS1996

Recent Developments in Gun Operating Techniques at the NASA Ames Ballistic Ranges

This paper describes recent developments in gun operating techniques at the Ames ballistic range complex. This range complex has been in operation since the early 1960s. Behavior of sabots during separation and projectile-target impact phenomena have long been observed by means of short-duration flash X-rays: new versions allow operation in the lower-energy ("soft") X-ray range and have been found to be more effective than the earlier designs. The dynamics of sabot separation is investigated in some depth from X-ray photographs of sabots launched in the Ames 1.0 in and 1.5 in guns; the sabot separation dynamics appears to be in reasonably good agreement with standard aerodynamic theory. Certain sabot packages appear to suffer no erosion or plastic deformation on traversing the gun barrel, contrary to what would be expected. Gun erosion data from the Ames 0.5 in, 1.0 in, and 1.5 in guns is examined in detail and can be correlated with a particular non- dimensionalized powder mass parameter. The gun erosion increases very rapidly as this parameter is increased. Representative shapes of eroded gun barrels are given. Guided by a computational fluid dynamics (CFD) code, the operating conditions of the Ames 0.5 in and 1.5 in guns were modified. These changes involved: (1) reduction in the piston mass, powder mass and hydrogen fill pressure and (2) reduction in pump tube volume, while maintaining hydrogen mass. These changes resulted in muzzle velocity increases of 0.5-0.8 km/sec, achieved simultaneously with 30-50 percent reductions in gun erosion.

Bogdanoff, D. W.↗

NASA NTRS2001

The 3D Recognition, Generation, Fusion, Update and Refinement (RG4) Concept

This paper describes an active (real time) recognition strategy whereby information is inferred iteratively across several viewpoints in descent imagery. We will show how we use inverse theory within the context of parametric model generation, namely height and spectral reflection functions, to generate model assertions. Using this strategy in an active context implies that, from every viewpoint, the proposed system must refine its hypotheses taking into account the image and the effect of uncertainties as well. The proposed system employs probabilistic solutions to the problem of iteratively merging information (images) from several viewpoints. This involves feeding the posterior distribution from all previous images as a prior for the next view. Novel approaches will be developed to accelerate the inversion search using novel statistic implementations and reducing the model complexity using foveated vision. Foveated vision refers to imagery where the resolution varies across the image. In this paper, we allow the model to be foveated where the highest resolution region is called the foveation region. Typically, the images will have dynamic control of the location of the foveation region. For descent imagery in the Entry, Descent, and Landing (EDL) process, it is possible to have more than one foveation region. This research initiative is directed towards descent imagery in connection with NASA's EDL applications. Three-Dimensional Model Recognition, Generation, Fusion, Update, and Refinement (RGFUR or RG4) for height and the spectral reflection characteristics are in focus for various reasons, one of which is the prospect that their interpretation will provide for real time active vision for automated EDL.

Maluf, David A.↗

NASA NTRS2012

Causal Correlation Functions and Fourier Transforms: Application in Calculating Pressure Induced Shifts

By adopting a concept from signal processing, instead of starting from the correlation functions which are even, one considers the causal correlation functions whose Fourier transforms become complex. Their real and imaginary parts multiplied by 2 are the Fourier transforms of the original correlations and the subsequent Hilbert transforms, respectively. Thus, by taking this step one can complete the two previously needed transforms. However, to obviate performing the Cauchy principal integrations required in the Hilbert transforms is the greatest advantage. Meanwhile, because the causal correlations are well-bounded within the time domain and band limited in the frequency domain, one can replace their Fourier transforms by the discrete Fourier transforms and the latter can be carried out with the FFT algorithm. This replacement is justified by sampling theory because the Fourier transforms can be derived from the discrete Fourier transforms with the Nyquis rate without any distortions. We apply this method in calculating pressure induced shifts of H2O lines and obtain more reliable values. By comparing the calculated shifts with those in HITRAN 2008 and by screening both of them with the pair identity and the smooth variation rules, one can conclude many of shift values in HITRAN are not correct.

correlation function↗

NASA NTRS2007

Comparing Consider-Covariance Analysis with Sigma-Point Consider Filter and Linear-Theory Consider Filter Formulations

Recent literature in applied estimation theory reflects growing interest in the sigma-point (also called unscented ) formulation for optimal sequential state estimation, often describing performance comparisons with extended Kalman filters as applied to specific dynamical problems [c.f. 1, 2, 3]. Favorable attributes of sigma-point filters are described as including a lower expected error for nonlinear even non-differentiable dynamical systems, and a straightforward formulation not requiring derivation or implementation of any partial derivative Jacobian matrices. These attributes are particularly attractive, e.g. in terms of enabling simplified code architecture and streamlined testing, in the formulation of estimators for nonlinear spaceflight mechanics systems, such as filter software onboard deep-space robotic spacecraft. As presented in [4], the Sigma-Point Consider Filter (SPCF) algorithm extends the sigma-point filter algorithm to the problem of consider covariance analysis. Considering parameters in a dynamical system, while estimating its state, provides an upper bound on the estimated state covariance, which is viewed as a conservative approach to designing estimators for problems of general guidance, navigation and control. This is because, whether a parameter in the system model is observable or not, error in the knowledge of the value of a non-estimated parameter will increase the actual uncertainty of the estimated state of the system beyond the level formally indicated by the covariance of an estimator that neglects errors or uncertainty in that parameter. The equations for SPCF covariance evolution are obtained in a fashion similar to the derivation approach taken with standard (i.e. linearized or extended) consider parameterized Kalman filters (c.f. [5]). While in [4] the SPCF and linear-theory consider filter (LTCF) were applied to an illustrative linear dynamics/linear measurement problem, in the present work examines the SPCF as applied to nonlinear sequential consider covariance analysis, i.e. in the presence of nonlinear dynamics and nonlinear measurements. A simple SPCF for orbit determination, exemplifying an algorithm hosted in the guidance, navigation and control (GN&C) computer processor of a hypothetical robotic spacecraft, was implemented, and compared with an identically-parameterized (standard) extended, consider-parameterized Kalman filter. The onboard filtering scenario examined is a hypothetical spacecraft orbit about a small natural body with imperfectly-known mass. The formulations, relative complexities, and performances of the filters are compared and discussed.

Lisano, Michael E.↗