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NASA NTRS2016

Applicability and Limitations of Reliability Allocation Methods

Reliability allocation process may be described as the process of assigning reliability requirements to individual components within a system to attain the specified system reliability. For large systems, the allocation process is often performed at different stages of system design. The allocation process often begins at the conceptual stage. As the system design develops, more information about components and the operating environment becomes available, different allocation methods can be considered. Reliability allocation methods are usually divided into two categories: weighting factors and optimal reliability allocation. When properly applied, these methods can produce reasonable approximations. Reliability allocation techniques have limitations and implied assumptions that need to be understood by system engineers. Applying reliability allocation techniques without understanding their limitations and assumptions can produce unrealistic results. This report addresses weighting factors, optimal reliability allocation techniques, and identifies the applicability and limitations of each reliability allocation technique.

Reliability allocation↗
NASA NTRS1979

Recent theoretical developments and experimental studies pertinent to vortex flow aerodynamics, with a view towards design

Recent progress in a research program directed toward an improved vortex flow technology base was reviewed. Analysis methods for conical flow and analysis and design methods for nonconical flows are presented. Applications are made for a variety of planar, nonplanar, and interferring lifting surfaces. Several methods are shown to provide reasonable estimates of over-all forces and moments for simple wing planforms with the suction analogy method currently offering the most versatility for arbitrary configuration applications. For the prediction of surface loadings the free vortex sheet method being developed by Boeing is shown to have considerable promise and further development of this type of method is encouraged. A data base for ogee strake-wing configurations is summarized with an emphasis on the requirements for maximizing the interference lift. A strake planform design procedure is discussed and a first solution (gothic in planview) is integrated with a wing body. The data show the strake to exhibit expected stable vortex characteristics. It was found that, apart from increasing sweep, conically cambered delta wings developed drag levels approaching that of attached flow with increasing either the lift or the wing camber height, lastly, an approximate vortex flow design method, based on the suction analogy, is outlined and an example is given.

Lamar, J. E.↗
NASA NTRS1992

Electromagnetic scattering in clouds

Techniques used to explain the nature of the optical effects of clouds on the light produced by lightning include a Monte Carlo simulation, an equivalent medium approach, and methods based on Boltzmann transport theory. A cuboidal cloud has been considered using transform methods and a diffusion approximation. Many simplifying assumptions have been used by authors to make this problem tractable. In this report, the cloud will have a spherical shape and its interior will consist of a uniform distribution of identical spherical water droplets. The source will be modeled as a Hertz dipole, electric or magnetic, inside or outside the cloud. An impulsive source is used. Superposition may be employed to obtain a sinusoid within an envelope which describes a lightning event. The problem is investigated by transforming to the frequency domain, obtaining Green's functions, and then using the Cagniard-DeHoop method to symbolically recover the time domain solution.

Solakiewicz, Richard↗
NASA NTRS1992

A fast operator perturbation method for the solution of the special relativistic equation of radiative transfer in spherical symmetry

A fast method for the solution of the radiative transfer equation in rapidly moving spherical media, based on an approximate Lambda-operator iteration, is described. The method uses the short characteristic method and a tridiagonal approximate Lambda-operator to achieve fast convergence. The convergence properties and the CPU time requirements of the method are discussed for the test problem of a two-level atom with background continuum absorption and Thomson scattering. Details of the actual implementation for fast vector and parallel computers are given. The method is accurate and fast enough to be incorporated in radiation-hydrodynamic calculations.

Hauschildt, P. H.↗
NASA NTRS2015

Improving the Timeliness of Winter Wheat Production Forecast in the United States of America, Ukraine and China Using MODIS Data and NCAR Growing Degree Day Information

Wheat is themost important cereal crop traded on international markets and winter wheat constitutes approximately 80% of global wheat production. Thus, accurate and timely production forecasts are critical for making informed agricultural policies and investments, as well as increasing market efficiency and stability. Becker-Reshef et al. (2010) developed an empirical generalized model for forecasting winter wheat production. Their approach combined BRDF-corrected daily surface reflectance from Moderate resolution Imaging Spectroradiometer (MODIS) Climate Modeling Grid (CMG) with detailed official crop statistics and crop typemasks. It is based on the relationship between the Normalized Difference Vegetation Index (NDVI) at the peak of the growing season, percent wheat within the CMG pixel (area within the CMG pixel occupied by wheat), and the final yields. This method predicts the yield approximately one month to six weeks prior to harvest. In this study, we include Growing Degree Day (GDD) information extracted from NCEP/NCAR reanalysis data in order to improve the winter wheat production forecast by increasing the timeliness of the forecasts while conserving the accuracy of the original model. We apply this modified model to three major wheat-producing countries: the Unites States (US), Ukraine and China from 2001 to 2012. We show that a reliable forecast can be made between one month to a month and a half prior to the peak NDVI (meaning two months to two and a half months prior to harvest), while conserving an accuracy of 10% in the production forecast.

Production↗
NASA NTRS1979

An implicit factored scheme for the compressible Navier-Stokes equations. II - The numerical ODE connection

An attempt is made to establish a connection between linear multistep methods for applications to ordinary differential equations and their extension (by approximate factorization) to alternating direction implicit methods for partial differential equations. An earlier implicit factored scheme for the compressible Navier-Stokes equations is generalized by innovations that (1) increase the class of temporal difference schemes to include all linear multistep methods, (2) optimize the class of unconditionally stable factored schemes by a new choice of unknown variable, and (3) improve the computational efficiency by the introduction of quasi-one-leg methods.

Beam, R. M.↗
NASA NTRS1986

A comparison of the bounded derivative and the normal-mode initialization methods using real data

Application of the bounded-derivative and normal-mode methods to a simple linear barotropic model at a typical middle latitude shows that the two methods lead to identical constraints up to a certain degree of approximation. Beyond this accuracy the two methods may differ from each other. When applied to a global nonlinear barotropic model using real data, again the two methods lead to similar balanced initial states. The gravity oscillations in the unbalanced height field, which have amplitudes of up to 60 m with a dominant periodicity of about 5 to 6 h, are practically eliminated by both initialization methods. The rotational wind component is smooth even for the unbalanced initial state. The small-scale spatial features of the irrotational wind component are drastically reduced by initialization. Both the nonlinear normal-mode and the bounded-derivative initialization methods yield similar divergence fields centered around the areas of highest orography. The comparison shows that there is no significant loss of information in the mass and momentum fields, despite the fact that the bounded-derivative method employs only the original, rotational wind component to construct a balanced initial state compared to the normal-mode method, which, in addition, makes use of the unbalanced divergent wind and height fields.

Semazzi, F. H. M.↗
NASA NTRS1994

Rapid in situ assessment of physiological activities in bacterial biofilms using fluorescent probes

Two rapid in situ enumeration methods using fluorescent probes were used to assess the physiological activities of Klebsiella pneumoniae biofilms on stainless steel. Fluorescent dyes, 5-cyano-2,3-ditolyl tetrazolium chloride (CTC) and rhodamine 123 (Rh 123), were chosen to perform this study. CTC is a soluble redox indicator which can be reduced by respiring bacteria to fluorescent CTC-formazan crystals. Rh 123 is incorporated into bacteria with respect to cellular proton motive force. The intracellular accumulation of these fluorescent dyes can be determined using epifluorescence microscopy. The results obtained with these two fluorescent probes in situ were compared to the plate count (PC) and in situ direct viable count (DVC) methods. Viable cell densities within biofilms determined by the three in situ methods were comparable and always showed approximately 2-fold higher values than those obtained with the PC method. As an additional advantage, the results were observed after 2 h, which was shorter than the 4 h incubation time required for the DVC method and 24 h for colony formation. The results indicate that staining with CTC and Rh 123 provides rapid information regarding cell numbers and physiological activities of bacteria within biofilms.

NASA Discipline Number 04-10↗
NASA NTRS1994

Fast two-stream method for computing diurnal-mean actinic flux in vertically inhomogeneous atmospheres

Based on a derivation of the two-stream daytime-mean equations of radiative flux transfer, a method for computing the daytime-mean actinic fluxes in the absorbing and scattering vertically inhomogeneous atmosphere is suggested. The method applies direct daytime integration of the particular solutions of the two-stream approximations or the source functions. It is valid for any duration of period of averaging. The merit of the method is that the multiple scattering computation is carried out only once for the whole averaging period. It can be implemented with a number of widely used two-stream approximations. The method agrees with the results obtained with 200-point multiple scattering calculations. The method was also tested in runs with a 1-km cloud layer with optical depth of 10, as well as with aerosol background. Comparison of the results obtained for a cloud subdivided into 20 layers with those obtained for a one-layer cloud with the same optical parameters showed that direct integration of particular solutions possesses an 'analytical' accuracy. In the case of the source function interpolation, the actinic fluxes calculated above the one-layer and 20-layer clouds agreed within 1%-1.5%, while below the cloud they may differ up to 5% (in the worst case). The ways of enhancing the accuracy (in a 'two-stream sense') and computational efficiency of the method are discussed.

Filyushkin, V. V.↗
NASA NTRS1975

The determination of orbits using Picard iteration

The determination of orbits by using Picard iteration is reported. This is a direct extension of the classical method of Picard that has been used in finding approximate solutions of nonlinear differential equations for a variety of problems. The application of the Picard method of successive approximations to the initial value and the two point boundary value problems is given.

Mikkilineni, R. P.↗
NASA NTRS1984

Unsteady aerodynamics in time and frequency domains for finite time arbitrary motion of rotary wings in hover and forward flight

Several incompressible finite-time arbitrary-motion airfoil theories suitable for coupled flap-lag-torsional aeroelastic analysis of helicopter rotors in hover and forward flight are derived. These theories include generalized Greenberg's theory, generalized Loewy's theory, and a staggered cascade theory. The generalized Greenberg's and staggered cascade theories were derived directly in Laplace domain considering the finite length of the wake and using operational methods. The load expressions are presented in Laplace, frequency, and time domains. Approximate time domain loads for the various generalized theories, discussed in the paper, are obtained by developing finite state models using the Pade approximant of the appropriate lift deficiency functions. Three different methods for constructing Pade approximants of the lift deficiency functions were considered and the more flexible one was used. Pade approximants of Loewy's lift deficiency function, for various wake spacing and radial location parameters of a helicopter typical rotor blade section, are presented.

Dinyavari, M. A. H.↗
NASA NTRS1975

An approximate closed-form solution for lead lag damping of rotor blades in hover

Simple stability methods are used to derive an approximate, closed-form expression for the lead-lag damping of rotor blades in hover. Destabilizing terms are shown to be a result of two dynamic mechanisms. First, the destabilizing aerodynamic forces that can occur when blade lift is higher than a critical value are maximized when the blade motion is in a straight line equidistant from the blade chord and the average direction of the air flow velocity. This condition occurs when the Coriolis terms vanish and when the elastic coupling terms align the blade motion with this least stable direction. Second, the nonconservative stiffness terms that result from pitch-flap or pitch-lag coupling can add or subtract energy from the system depending upon whether the motion of the blade tip is clockwise or counterclockwise.

Peters, D. A.↗
NASA NTRS1977

Analysis of simple 2-D and 3-D metal structures subjected to fragment impact

Theoretical methods were developed for predicting the large-deflection elastic-plastic transient structural responses of metal containment or deflector (C/D) structures to cope with rotor burst fragment impact attack. For two-dimensional C/D structures both, finite element and finite difference analysis methods were employed to analyze structural response produced by either prescribed transient loads or fragment impact. For the latter category, two time-wise step-by-step analysis procedures were devised to predict the structural responses resulting from a succession of fragment impacts: the collision force method (CFM) which utilizes an approximate prediction of the force applied to the attacked structure during fragment impact, and the collision imparted velocity method (CIVM) in which the impact-induced velocity increment acquired by a region of the impacted structure near the impact point is computed. The merits and limitations of these approaches are discussed. For the analysis of 3-d responses of C/D structures, only the CIVM approach was investigated.

Witmer, E. A.↗
NASA NTRS1984

The prediction of tropopause height from clusters of brightness temperatures and its application in the stratified regression temperature retrievals using microwave and infrared satellite measurements

A total of 1575 radiosondes and the corresponding simulated brightness temperatures were used in an effort to derive a temperature retrieval based on the clusters of brightness temperatures. The 8 simulated channels, namely, 3 MSU and 5 IR of the TIROS-N satellite are used by the GLAS temperature retrieval method. The 3 MSU and 5 IR brightness temperatures were clustered into 17 cluster groups and a regression for the prediction of the tropopause height in mb was generated. The overall r.m.s. for the tropopause prediction is excellent, namely, around 16 mb for the summer and 23 mb for the winter. The correct cluster of brightness temperatures can be identified 98% of the time by the method of discriminatory classification if it is approximately a normal distribution or, in general, by the method of the nearest neighbor.

Munteanu, M. J.↗
NASA NTRS1989

Some comments on global-local analyses

The main theme concerns methods that may be classified as global (approximate) and local (exact). Some specific applications of these methods are found in: fracture and fatigue analysis of structures with 3-D surface flaws; large-deformation, post-buckling analysis of large space trusses and space frames, and their control; and stresses around holes in composite laminates.

Atluri, Satya N.↗
NASA NTRS1990

Non-LTE model calculations for SN 1987A and the extragalactic distance scale

This paper presents model atmospheres for the first week of SN 1987A, based on the luminosity and density/velocity structure from hydrodynamic models of Woosley (1988). The models account for line blanketing, expansion, sphericity, and departures from LTE in hydrogen and helium and differ from previously published efforts because they represent ab initio calculations, i.e., they contain essentially no free parameters. The formation of the UV spectrum is dominated by the effects of line blanketing. In the absorption troughs, the Balmer line profiles were fit well by these models, but the observed emissions are significantly stronger than predicted, perhaps due to clumping. The generally good agreement between the present synthetic spectra and observations provides independent support for the overall accuracy of the hydrodynamic models of Woosley. The question of the accuracy of the Baade-Wesselink method is addressed in a detailed discussion of its approximations. While the application of the standard method produces a distance within an uncertainty of 20 percent in the case of SN 1987A, systematic errors up to a factor of 2 are possible, particularly if the precursor was a red supergiant.

Schmutz, W.↗
NASA NTRS1993

Raman linewidths and rotationally inelastic collision rates in nitrogen

Using the N2-N2 interaction potential of van der Avoird et al. (1986) rotationally inelastic collision cross sections have been computed within the infinite order sudden (IOS) approximation, assuming the molecules are distinguishable. Methods for enforcing detailed balance and correcting for effects of inelasticity, which are ignored in the IOS approximation, are considered, including the energy corrected sudden (ECS) method. Suitably averaged cross sections are compared with experimental Raman Q-branch linewidths for temperatures from 295 to 1500 K and with recently measured room temperature state-to-state rates. Agreement is rather good, especially if ECS corrections are applied.

Green, Sheldon↗
NASA NTRS1994

A Numerical Comparison of Barrier and Modified Barrier Methods for Large-Scale Bound-Constrained Optimization

When a classical barrier method is applied to the solution of a nonlinear programming problem with inequality constraints, the Hessian matrix of the barrier function becomes increasingly ill-conditioned as the solution is approached. As a result, it may be desirable to consider alternative numerical algorithms. We compare the performance of two methods motivated by barrier functions. The first is a stabilized form of the classical barrier method, where a numerically stable approximation to the Newton direction is used when the barrier parameter is small. The second is a modified barrier method where a barrier function is applied to a shifted form of the problem, and the resulting barrier terms are scaled by estimates of the optimal Lagrange multipliers. The condition number of the Hessian matrix of the resulting modified barrier function remains bounded as the solution to the constrained optimization problem is approached. Both of these techniques can be used in the context of a truncated-Newton method, and hence can be applied to large problems, as well as on parallel computers. In this paper, both techniques are applied to problems with bound constraints and we compare their practical behavior.

Nash, Stephen G.↗