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NASA NTRS1998

First- and Second-Order Sensitivity Analysis of a P-Version Finite Element Equation Via Automatic Differentiation

Sensitivity analysis is a technique for determining derivatives of system responses with respect to design parameters. Among many methods available for sensitivity analysis, automatic differentiation has been proven through many applications in fluid dynamics and structural mechanics to be an accurate and easy method for obtaining derivatives. Nevertheless, the method can be computational expensive and can require a high memory space. This project will apply an automatic differentiation tool, ADIFOR, to a p-version finite element code to obtain first- and second- order then-nal derivatives, respectively. The focus of the study is on the implementation process and the performance of the ADIFOR-enhanced codes for sensitivity analysis in terms of memory requirement, computational efficiency, and accuracy.

Hou, Gene↗

NASA NTRS1994

Analytic Sensitivities for Shape Optimization in Equivalent Plate Structural Wing Models

Equivalent plate modeling techniques based on Ritz analysis with simple polynomials prove to be efficient tools for structural modeling of wings in the preliminary design stage. Accuracy problems are encountered, however, when these models are used to obtain finite difference behavior sensitivities with respect to planform shape. The accuracy problems are associated with the poor numerical conditioning of static and eigenvalue equations. As higher-order polynomials are being used to Improve the analysis itself, the more sensitive is the finite difference derivative to the step size used. This article describes a formulation of wing equivalent plate modeling in which it is simple to obtain analytic, explicit expressions for stiffness and mass matrix elements without the need to perform numerical integration. This formulation leads naturally to analytic expressions for the derivatives of displacements, stresses, and natural frequencies with respect to shape design variables. This article examines the accuracy of finite difference derivatives compared with the analytic derivatives, and shows that In some cases it is impossible to obtain any information of value by finite differences. Analytic sensitivities, in this case, are still sufficiently accurate for design optimization.

Livne, Eli↗

NASA NTRS1995

Analytic Sensitivity and Approximation of Skin Buckling Constraints in Wing-Shape Synthesis

Explicit expressions for terms of the stiffness and geometric stiffness matrices are derived for the buckling analysis of trapezoidal fiber composite wing skin panels. The formulation is based on Ritz analysis using simple polynomials, and leads to explicit expressions for the analytic sensitivities of the stiffness and geometric stiffness matrices with respect to layer thickness, fiber directions, and panel shape. Integration with wing box analysis using either the equivalent plate approach or the finite element method, makes it possible to obtain sensitivities of panel buckling constraints with respect to wing planform shape or locations of internal ribs and spars. The analytic sensitivities are used to construct approximations of panel buckling constraints for integrated wing/panel design synthesis.

Livne, Eli↗

NASA NTRS1998

New Ultra-High Sensitivity, Absolute, Linear, and Rotary Encoders

Several new types of absolute optical encoders of both rotary and linear function are discussed. The means for encoding are complete departures from conventional optical encoders and offer advantages of compact form, immunity to damage-induced dropouts of position information, and about an order of magnitude higher sensitivity over what is commercially available. Rotary versions have sensitivity from 0.02 arcseconds down to 0.003 arcsecond while linear models have sensitivity of 10 nm.

Leviton, Douglas B.↗

NASA NTRS1999

Sensitized Liquid Hydrazine Detonation Studies

Vapor-phase hydrazine (N2H4) is known to be very sensitive to detonation while liquid hydrazine is very insensitive to detonation, theoretically requiring extremely high pressures to induce initiation. A review of literature on solid and liquid explosives shows that when pure explosive substances are infiltrated with gas cavities, voids, and/or different phase contaminants, the energy or shock pressure necessary to induce detonation can decrease by an order of magnitude. Tests were conducted with liquid hydrazine in a modified card-gap configuration. Sensitization was attempted by bubbling helium gas through and/or suspending ceramic microspheres in the liquid. The hydrazine was subjected to the shock pressure from a 2 lb (0.9 kg) Composition C-4 explosive charge. The hydrazine was contained in a 4 in. (10.2 cm) diameter stainless steel cylinder with a 122 in(sup 3) (2 L) volume and sealed with a polyethylene cap. Blast pressures from the events were recorded by 63 high speed pressure transducers located on three radial legs extending from 4 to 115 ft (1.2 to 35.1 in) from ground zero. Comparison of the neat hydrazine and water baseline tests with the "sensitized" hydrazine tests indicates the liquid hydrazine did not detonate under these conditions.

Rathgeber, K. A.↗

NASA NTRS1999

Pressure-Sensitive Paint Measurements on Surfaces with Non-Uniform Temperature

Pressure-sensitive paint (PSP) has become a useful tool to augment conventional pressure taps in measuring the surface pressure distribution of aerodynamic components in wind tunnel testing. While the PSP offers the advantage of a non-intrusive global mapping of the surface pressure, one prominent drawback to the accuracy of this technique is the inherent temperature sensitivity of the coating's luminescent intensity. A typical aerodynamic surface PSP test has relied on the coated surface to be both spatially and temporally isothermal, along with conventional instrumentation for an in situ calibration to generate the highest accuracy pressure mappings. In some tests however, spatial and temporal thermal gradients are generated by the nature of the test as in a blowing jet impinging on a surface. In these cases, the temperature variations on the painted surface must be accounted for in order to yield high accuracy and reliable data. A new temperature correction technique was developed at NASA Lewis to collapse a "family" of PSP calibration curves to a single intensity ratio versus pressure curve. This correction allows a streamlined procedure to be followed whether or not temperature information is used in the data reduction of the PSP. This paper explores the use of conventional instrumentation such as thermocouples and pressure taps along with temperature-sensitive paint (TSP) to correct for the thermal gradients that exist in aeropropulsion PSP tests. Temperature corrected PSP measurements for both a supersonic mixer ejector and jet cavity interaction tests are presented.

Bencic, Timothy J.↗

NASA NTRS2000

LSENS, The NASA Lewis Kinetics and Sensitivity Analysis Code

A general chemical kinetics and sensitivity analysis code for complex, homogeneous, gas-phase reactions is described. The main features of the code, LSENS (the NASA Lewis kinetics and sensitivity analysis code), are its flexibility, efficiency and convenience in treating many different chemical reaction models. The models include: static system; steady, one-dimensional, inviscid flow; incident-shock initiated reaction in a shock tube; and a perfectly stirred reactor. In addition, equilibrium computations can be performed for several assigned states. An implicit numerical integration method (LSODE, the Livermore Solver for Ordinary Differential Equations), which works efficiently for the extremes of very fast and very slow reactions, is used to solve the "stiff" ordinary differential equation systems that arise in chemical kinetics. For static reactions, the code uses the decoupled direct method to calculate sensitivity coefficients of the dependent variables and their temporal derivatives with respect to the initial values of dependent variables and/or the rate coefficient parameters. Solution methods for the equilibrium and post-shock conditions and for perfectly stirred reactor problems are either adapted from or based on the procedures built into the NASA code CEA (Chemical Equilibrium and Applications).

Radhakrishnan, K.↗

NASA NTRS2000

Interactive Soil Dust Aerosol Model in the GISS GCM: Sensitivity of the Soil Dust Cycle to Radiative Properties of Soil Dust Aerosols - Part 1

The sensitivity of the soil dust aerosol cycle to the radiative forcing by soil dust aerosols is studied. Four experiments with the NASA/GISS atmospheric general circulation model, which includes a soil dust aerosol model, are compared, all using a prescribed climatological sea surface temperature as lower boundary condition. In one experiment, dust is included as dynamic tracer only (without interacting with radiation), whereas dust interacts with radiation in the other simulations. Although the single scattering albedo of dust particles is prescribed to be globally uniform in the experiments with radiatively active dust, a different single scattering albedo is used in those experiments to estimate whether regional variations in dust optical properties, corresponding to variations in mineralogical composition among different source regions, are important for the soil dust cycle and the climate state. On a global scale, the radiative forcing by dust generally causes a reduction in the atmospheric dust load corresponding to a decreased dust source flux. That is, there is a negative feedback in the climate system due to the radiative effect of dust. The dust source flux and its changes were analyzed in more detail for the main dust source regions. This analysis shows that the reduction varies both with the season and with the single scattering albedo of the dust particles. By examining the correlation with the surface wind, it was found that the dust emission from the Saharan/Sahelian source region and from the Arabian peninsula, along with the sensitivity of the emission to the single scattering albedo of dust particles, are related to large scale circulation patterns, in particular to the trade winds during Northern Hemisphere winter and to the Indian monsoon circulation during summer. In the other regions, such relations to the large scale circulation were not found. There, the dependence of dust deflation to radiative forcing by dust particles is probably dominated by physical processes with short time scales. The experiments show that dust radiative forcing can lead to significant changes both in the soil dust cycle and in the climate state. To estimate dust concentration and radiative forcing by dust more accurately, dust size distributions and dust single scattering albedo in the model should be a function of the source region, because dust concentration and climate response to dust radiative forcing are sensitive to dust radiative parameters.

Perlwitz, Jan↗

NASA NTRS2000

Actinic Flux Calculations: A Model Sensitivity Study

calculate direct and diffuse surface irradiance and actinic flux (downwelling (2p) and total (4p)) for the reference model. Sensitivity analysis has shown that the accuracy of the radiative transfer flux calculations for a unit ETS (i.e. atmospheric transmittance) together with a numerical interpolation technique for the constituents' vertical profiles is better than 1% for SZA less than 70(sub o) and wavelengths longer than 310 nm. The differences increase for shorter wavelengths and larger SZA, due to the differences in pseudo-spherical correction techniques and vertical discretetization among the codes. Our sensitivity study includes variation of ozone cross-sections, ETS spectra and the effects of wavelength shifts between vacuum and air scales. We also investigate the effects of aerosols on the spectral flux components in the UV and visible spectral regions. The "aerosol correction factors" (ACFs) were calculated at discrete wavelengths and different SZAs for each flux component (direct, diffuse, reflected) and prescribed IPMMI aerosol parameters. Finally, the sensitivity study was extended to calculation of selected photolysis rates coefficients.

Krotkov, Nickolay A.↗

NASA NTRS2001

Inferring Instantaneous, Multivariate and Nonlinear Sensitivities for the Analysis of Feedback Processes in a Dynamical System: Lorenz Model Case Study

A new approach is presented for the analysis of feedback processes in a nonlinear dynamical system by observing its variations. The new methodology consists of statistical estimates of the sensitivities between all pairs of variables in the system based on a neural network modeling of the dynamical system. The model can then be used to estimate the instantaneous, multivariate and nonlinear sensitivities, which are shown to be essential for the analysis of the feedbacks processes involved in the dynamical system. The method is described and tested on synthetic data from the low-order Lorenz circulation model where the correct sensitivities can be evaluated analytically.

Aires, Filipe↗

NASA NTRS2001

Approach for Uncertainty Propagation and Robust Design in CFD Using Sensitivity Derivatives

This paper presents an implementation of the approximate statistical moment method for uncertainty propagation and robust optimization for a quasi 1-D Euler CFD (computational fluid dynamics) code. Given uncertainties in statistically independent, random, normally distributed input variables, a first- and second-order statistical moment matching procedure is performed to approximate the uncertainty in the CFD output. Efficient calculation of both first- and second-order sensitivity derivatives is required. In order to assess the validity of the approximations, the moments are compared with statistical moments generated through Monte Carlo simulations. The uncertainties in the CFD input variables are also incorporated into a robust optimization procedure. For this optimization, statistical moments involving first-order sensitivity derivatives appear in the objective function and system constraints. Second-order sensitivity derivatives are used in a gradient-based search to successfully execute a robust optimization. The approximate methods used throughout the analyses are found to be valid when considering robustness about input parameter mean values.

Putko, Michele M.↗

NASA NTRS2000

Sensitivity of Age-of-Air Calculations to the Choice of Advection Scheme

The age of air has recently emerged as a diagnostic of atmospheric transport unaffected by chemical parameterizations, and the features in the age distributions computed in models have been interpreted in terms of the models' large-scale circulation field. This study shows, however, that in addition to the simulated large-scale circulation, three-dimensional age calculations can also be affected by the choice of advection scheme employed in solving the tracer continuity equation, Specifically, using the 3.0deg latitude X 3.6deg longitude and 40 vertical level version of the Geophysical Fluid Dynamics Laboratory SKYHI GCM and six online transport schemes ranging from Eulerian through semi-Lagrangian to fully Lagrangian, it will be demonstrated that the oldest ages are obtained using the nondiffusive centered-difference schemes while the youngest ages are computed with a semi-Lagrangian transport (SLT) scheme. The centered- difference schemes are capable of producing ages older than 10 years in the mesosphere, thus eliminating the "young bias" found in previous age-of-air calculations. At this stage, only limited intuitive explanations can be advanced for this sensitivity of age-of-air calculations to the choice of advection scheme, In particular, age distributions computed online with the National Center for Atmospheric Research Community Climate Model (MACCM3) using different varieties of the SLT scheme are substantially older than the SKYHI SLT distribution. The different varieties, including a noninterpolating-in-the-vertical version (which is essentially centered-difference in the vertical), also produce a narrower range of age distributions than the suite of advection schemes employed in the SKYHI model. While additional MACCM3 experiments with a wider range of schemes would be necessary to provide more definitive insights, the older and less variable MACCM3 age distributions can plausibly be interpreted as being due to the semi-implicit semi-Lagrangian dynamics employed in the MACCM3. This type of dynamical core (employed with a 60-min time step) is likely to reduce SLT's interpolation errors that are compounded by the short-term variability characteristic of the explicit centered-difference dynamics employed in the SKYHI model (time step of 3 min). In the extreme case of a very slowly varying circulation, the choice of advection scheme has no effect on two-dimensional (latitude-height) age-of-air calculations, owing to the smooth nature of the transport circulation in 2D models. These results suggest that nondiffusive schemes may be the preferred choice for multiyear simulations of tracers not overly sensitive to the requirement of monotonicity (this category includes many greenhouse gases). At the same time, age-of-air calculations offer a simple quantitative diagnostic of a scheme's long-term diffusive properties and may help in the evaluation of dynamical cores in multiyear integrations. On the other hand, the sensitivity of the computed ages to the model numerics calls for caution in using age of air as a diagnostic of a GCM's large-scale circulation field.

Eluszkiewicz, Janusz↗

NASA NTRS2001

Satellite Remote Sensing of the Liquid Water Sensitivity in Water Clouds

In estimation of the aerosol indirect effect, cloud liquid water path is considered either constant (Twomey effect) or increasing with enhanced droplet number concentrations (drizzle-suppression effect, or Albrecht effect) if cloud microphysics is the prevailing mechanism during the aerosol-cloud interactions. On the other hand, if cloud thermodynamics and dynamics are considered, the cloud liquid water path may be decreased with increasing droplet number concentration, which is predicted by model calculations and observed in ship-track and urban influence studies. This study is to examine the different responses of cloud liquid water path to changes of cloud droplet number concentration. Satellite data (January, April, July and October 1987) are used to retrieve the cloud liquid water sensitivity, defined as the changes of liquid water path versus changes of column droplet number concentrations. The results of a global survey reveal that 1) in at least one third of the cases the cloud liquid water sensitivity is negative, and the regional and seasonal variations of the negative liquid water sensitivity are consistent with other observations; 2) cloud droplet sizes are always inversely proportional to column droplet number concentrations. Our results suggest that an increase of cloud droplet number concentration leads to reduced cloud droplet size and enhanced evaporation, which weakens the coupling between water clouds and boundary layer in warm zones, decreases water supply from surface and desiccates cloud liquid water. Our results also suggest that the current evaluations of negative aerosol indirect forcing by global climate models (GCM), which are based on Twomey effect or Albrecht effect, may be overestimated.

Han, Qing-Yuan↗

NASA NTRS2001

Tropospheric Ozone Near-Nadir-Viewing IR Spectral Sensitivity and Ozone Measurements from NAST-I

Infrared ozone spectra from near nadir observations have provided atmospheric ozone information from the sensor to the Earth's surface. Simulations of the NPOESS Airborne Sounder Testbed-Interferometer (NAST-I) from the NASA ER-2 aircraft (approximately 20 km altitude) with a spectral resolution of 0.25/cm were used for sensitivity analysis. The spectral sensitivity of ozone retrievals to uncertainties in atmospheric temperature and water vapor is assessed in order to understand the relationship between the IR emissions and the atmospheric state. In addition, ozone spectral radiance sensitivity to its ozone layer densities and radiance weighting functions reveals the limit of the ozone profile retrieval accuracy from NAST-I measurements. Statistical retrievals of ozone with temperature and moisture retrievals from NAST-I spectra have been investigated and the preliminary results from NAST-I field campaigns are presented.

Zhou, Daniel K.↗

NASA NTRS2001

Tropical Ocean Evaporation/SST Sensitivity and It's Link to Water and Energy Budget Variations During ENSO

The continuing debate over feedback mechanisms governing tropical sea surface temperatures (SSTs) and tropical climate in general has highlighted the diversity of potential checks and balances within the climate system. Competing feedbacks due to changes in surface evaporation, water vapor, and cloud long- and shortwave radiative properties each may serve critical roles in stabilizing or destabilizing the climate system. It is also intriguing that even those climate variations having origins internal to the climate system - changes in ocean heat transport for example, apparently require complementary equilibrating effects by changes in atmospheric energy fluxes. Perhaps the best observational evidence of this is the relatively invariant nature of tropically averaged net radiation exiting the top-of-atmosphere (TOA) as measured by broadband satellite sensors over the past two decades. Thus, analyzing how these feedback mechanisms are operating within the context of current interannual variability may offer considerable insight for anticipating future climate change. In this paper we focus primarily on interannual variations of ocean evaporative fluxes and their significance for coupled water and energy cycles within the tropical climate system. In particular, we use both the da Silva estimates of surface fluxes (based on the Comprehensive Ocean Atmosphere Data Set, COADS) and numerical simulations from several global climate models to examine evaporation sensitivity to perturbations in SST associated with warm and cold ENSO events. The specific questions we address are as follows: (1) What recurring patterns of surface wind and humidity anomalies are present during ENSO and how do they combine to yield systematic evaporation anomalies?, (2) What is the resulting tropical ocean mean evaporation-SST sensitivity associated with this climate perturbation?, and (3) What role does this evaporation play in tropical heat and water balance over tropical oceanic regions? We use the da Silva ocean flux data to identify composite structure of departures of latent heat flux from climatology. We also show how these patterns arise out of associated wind and humidity anomaly distributions. Our preliminary work shows that evaporation sensitivity estimates from the da Silva / COADS data, computed for the tropical oceans (30 degrees N/S) are in the neighborhood of 5 to 6 W/square m K. Model estimates are also quite close to this figure. This rate is only slightly less than a rate corresponding to constant relative humidity; however, substantial regional departures from constant relative humidity are present. These patterns are robust and we relate the associated wind and humidity fluctuations noted in previous investigations to the derived evaporation anomalies. Finally, these results are interpreted with other data from the Earth radiation Budget Experiment (ERBE), Global Precipitation Climatology Project (GPCP) and NASA's Surface Radiation Budget (SRB) data set to characterize the tropical energetics of ENSO-related climate variability.

Robertson, Franklin R.↗

NASA NTRS1995

Kuiper Airborne Observatory's Telescope Stabilization System: Disturbance Sensitivity Reduction Via Velocity Loop Feedback

In July of 1994 the Kuiper Airborne Observatory's (KAO) Telescope Stabilization System (TSS) was upgraded to meet performance goals necessary to view the Shoemaker-Levy 9 comet collision with Jupiter. The KAO is a modified C-141 Aircraft supporting a 36 inch Infrared telescope used to gather and analyze astronomical data. Before the upgrade, the TSS exhibited approximately a 10 arc-second resolution pointing accuracy. The majority of the inaccuracy was attributable to aircraft vibration and wind buffeting entering through the aircraft's telescope door opening; in other words, the TSS was overly sensitive to external disturbances. Because of power limitations and noise requirements, improving the pointing accuracy of the telescope required more sophistication than simply raising the bandwidth as some classical control strategies might suggest. Instead, relationships were developed between the disturbance sensitivity and closed loop transfer functions. These relationships suggested that employing velocity feedback along with an increase in current loop gain would dramatically improve the pointing resolution of the TSS by decreasing the control system's sensitivity to external disturbances. With the implementation of some classical control techniques and the above philosophy, the KAO's TSS's resolution was improved to approximately 2-3 arc-seconds.

Lawrence, David P.↗

NASA NTRS2002

Sensitivity of Middle Atmospheric Analyses to the Representation of Gravity-Wave Drag in the DAO's Data Assimilation System

The damping of mesoscale gravity waves has important effects on the global circulation, structure, and composition of the atmosphere. A number of assimilation and forecast experiments have been conducted to examine the sensitivity of meteorological analyses and forecasts to the representation of gravity wave impacts in a data assimilation system (DAS). The experiments were conducted with the Finite-Volume (FV) DAS developed at NASA's Data Assimilation Office (DAO), The main purpose of this research is to determine the optimal combination of wave number, phase speed, wavelength, etc. for representing gravity-wave drag (GWD) in FVDAS. The GWD included in FVDAS includes a spectrum of waves, as would be forced by topography and transient motions (e.g., convection) in the troposphere. The sensitivity experiments are performed by modifying several parameters, such as the number of waves allowed, their wavelength, the background stress amplitude, etc. The results show that the assimilated fields are very sensitive to the number of gravity waves represented in the system, especially at high latitudes of the middle and upper stratosphere and mesosphere in winter. The analyzed stratopause temperature varies by up to 10K when the GWD scheme is modified from a multiple-wave scheme (using a stationary wave and waves with phase speeds of 10, 20, 30 and 40 m/s in each direction) to a single, stationary wave. Insight into the reality of the various versions of the GWD can be obtained by examining the "Observation minus Forecast" residuals from the FVDAS.

Li, Shuhua↗

NASA NTRS2002

Directionally Sensitive Silicon Radiation Sensor (VCELL)

Sensors are a mission critical element in many NASA programs and require some very unique properties such as small size, low power, high reliability, low weight. Low cost sensors offer the possibility of technology transfer to the public domain for commercial applications. One sensor application that is important to many NASA programs is the ability to point at a radiation source, such as the sun. Such sensors may be an integral part of the guidance and control systems in space platforms and in remote exploratory vehicles. Sun/solar pointing is also important for ground-based systems such as solar arrays. These systems are not required to be small and lightweight. However, if a sensor with a sun pointing capability was developed that is very small, rugged, lightweight and at the same time low cost, it certainly could be used in existing and perhaps many new ground based applications. The objective of the VCELL (Directionally Sensitive Silicon Radiation Sensor) research is to develop a new and very unique silicon based directionally sensitive radiation sensor which can be fabricated using conventional monolithic IC technologies and which will meet the above requirements. The proposed sensor is a novel silicon chip that is directionally sensitive to incident radiation, providing azimuth and elevation information on the incident radiation. The resulting sensor chip will be appropriate for integration into a silicon IC or useful in a hybrid structure to be interfaced with a standard IEEE 1451 bus interface IC to create an Intelligent Sensor. It is presently estimated that it will require about three man-years of effort to complete the VCELL research and development. This includes the optical, electrical, mechanical and silicon fabrication and testing as well as computer simulations and theoretical analysis and modeling including testing in simulated space environments. This report summarizes the sensor research completed this summer as part of the Summer Faculty Fellowship Program. The primary effort was focused on activity necessary to fabricate prototype sensor.

Koy B. Cook↗