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At least 19 records

Computing Sensitivities in Evolutionary Systems: A Real-time Reduced Order Modeling Strategy

We present a new methodology for computing sensitivities in evolutionary systems using a model-driven low-rank approximation. To this end, we formulate a variational principle that seeks to minimize the distance between the time derivative of the reduced approximation and sensitivity dynamics. The first order optimality condition of the variational principle leads to a system of closed form evolution equations for an orthonormal basis and corresponding sensitivity coefficients. This approach allows for the computation of sensitivities with respect to a large number of parameters in an accurate and tractable manner by extracting correlations between different sensitivities on the fly. The presented method requires solving forward evolution equations, sidestepping the restrictions imposed by the forward/backward workflow of adjoint sensitivities. For example, the presented method, unlike the adjoint equation, does not impose any input/output load and can be used in applications in which real-time sensitivities are of interest. We demonstrate the utility of the method for three test cases: (1) computing sensitivity with respect to model parameters in the Rössler system, (2) computing sensitivity with respect to an infinite-dimensional forcing parameter in the chaotic Kuramoto--Sivashinsky equation, and (3) computing sensitivity with respect to reaction parameters for species transport in a turbulent reacting flow.

Reduced order model↗

A forward model-based validation of cardiovascular system identification

We present a theoretical evaluation of a cardiovascular system identification method that we previously developed for the analysis of beat-to-beat fluctuations in noninvasively measured heart rate, arterial blood pressure, and instantaneous lung volume. The method provides a dynamical characterization of the important autonomic and mechanical mechanisms responsible for coupling the fluctuations (inverse modeling). To carry out the evaluation, we developed a computational model of the cardiovascular system capable of generating realistic beat-to-beat variability (forward modeling). We applied the method to data generated from the forward model and compared the resulting estimated dynamics with the actual dynamics of the forward model, which were either precisely known or easily determined. We found that the estimated dynamics corresponded to the actual dynamics and that this correspondence was robust to forward model uncertainty. We also demonstrated the sensitivity of the method in detecting small changes in parameters characterizing autonomic function in the forward model. These results provide confidence in the performance of the cardiovascular system identification method when applied to experimental data.

NASA Discipline Cardiopulmonary↗

Adjoint-Based Methodology for Time-Dependent Optimization

This paper presents a discrete adjoint method for a broad class of time-dependent optimization problems. The time-dependent adjoint equations are derived in terms of the discrete residual of an arbitrary finite volume scheme which approximates unsteady conservation law equations. Although only the 2-D unsteady Euler equations are considered in the present analysis, this time-dependent adjoint method is applicable to the 3-D unsteady Reynolds-averaged Navier-Stokes equations with minor modifications. The discrete adjoint operators involving the derivatives of the discrete residual and the cost functional with respect to the flow variables are computed using a complex-variable approach, which provides discrete consistency and drastically reduces the implementation and debugging cycle. The implementation of the time-dependent adjoint method is validated by comparing the sensitivity derivative with that obtained by forward mode differentiation. Our numerical results show that O(10) optimization iterations of the steepest descent method are needed to reduce the objective functional by 3-6 orders of magnitude for test problems considered.

Yamaleev, N. K.↗

Realistic Covariance Generation for the GPM Spacecraft

We present several different methods for generating realistic predictive covariance, including Monte-Carlo simulations and more direct linear methods which require the addition of process noise. The Monte-Carlo simulation starts with an epoch uncertainty sample basis and propagates each trial to a time of interest in the future. The variance-covariance of the state elements as well as other higher order sample statistics can be readily computed from the propagated sample. While this method preserves the nonlinear effects on the propagated uncertainty, it is computationally intensive as a statistically significant sample size must be considered in the propagation process. Moreover, if the epoch covariance is optimistic, this can result in an underestimation of the prediction error. Another method is to propagate a state sensitivity matrix simultaneously with the satellite state, which allows the epoch covariances to be propagated forward in a linear fashion. This method does not preserve the non-linearity of the satellite state uncertainty but is much less computationally intensive. The propagated state covariance is the scaled to represent the realistic level of GPM state uncertainty via a "e-tuning process." The tuning process generates an inflation factor based on the observed error statistics of the predictive satellite trajectories when compared to the definitive ones. Difference tuning strategies are considered and compared via Goodness-of-Fit method testing for the Gaussian properties of the scaled covariance.

prediction error↗

Iterative methods for design sensitivity analysis

A numerical method is presented for design sensitivity analysis, using an iterative-method reanalysis of the structure generated by a small perturbation in the design variable; a forward-difference scheme is then employed to obtain the approximate sensitivity. Algorithms are developed for displacement and stress sensitivity, as well as for eignevalues and eigenvector sensitivity, and the iterative schemes are modified so that the coefficient matrices are constant and therefore decomposed only once.

Belegundu, A. D.↗

Some Advanced Concepts in Discrete Aerodynamic Sensitivity Analysis

An efficient incremental-iterative approach for differentiating advanced flow codes is successfully demonstrated on a 2D inviscid model problem. The method employs the reverse-mode capability of the automatic- differentiation software tool ADIFOR 3.0, and is proven to yield accurate first-order aerodynamic sensitivity derivatives. A substantial reduction in CPU time and computer memory is demonstrated in comparison with results from a straight-forward, black-box reverse- mode application of ADIFOR 3.0 to the same flow code. An ADIFOR-assisted procedure for accurate second-order aerodynamic sensitivity derivatives is successfully verified on an inviscid transonic lifting airfoil example problem. The method requires that first-order derivatives are calculated first using both the forward (direct) and reverse (adjoint) procedures; then, a very efficient non-iterative calculation of all second-order derivatives can be accomplished. Accurate second derivatives (i.e., the complete Hessian matrices) of lift, wave-drag, and pitching-moment coefficients are calculated with respect to geometric- shape, angle-of-attack, and freestream Mach number

Taylor, Arthur C., III↗

Backscattering by nonspherical particles - A review of methods and suggested new approaches

Scattering of electromagnetic radiation near the backward direction is more sensitive to particle shape than scattering near the forward direction. Mie theory is therefore of dubious applicability to predicting backscattering by atmospheric particles known to be irregular or to inverting measurements on such particles. An irregular particle is one with an uncertain shape. In the face of uncertainty one must adopt a statistical approach in which scattering properties of ensembles are determined. To obtain ensemble averages, a basis is needed for averaging over a set of electromagnetic microstates. Ensemble averages based on the Rayleigh theory for small ellipsoids and on the T matrix method for spheroids agree better with measurements than Mie theory does. The coupled-dipole method also provides a basis for ensemble averaging. This method also leads to a simple physical interpretation of why backscattering is so sensitive to particle shape and can be used to calculate scattering by one- and two-dimensional analogs to three-dimensional irregular particles.

Bohren, Craig F.↗

Three-dimensional trajectory analyses of two drop sizing instruments - PMS OAP and PMS FSSP

Flow-induced distortions of water drop fluxes and speeds as seen by the PMS optical array probe (OAP) and the PMS forward scattering spectrometer probe (FSSP) are estimated via three-dimensional flow and trajectory calculation methods. The sensitivities of the instruments to water drop diameter, angle of attack, and free stream air speed are determined. The instruments are first placed in isolation and then mounted under the wing of a Twin Otter airplane. For the wing-mounted OAP at 4-deg angle of attack, partial flow stagnation under the uptilted wing causes a significant decrease in both the flux and speed for small water drops. For the wing-mounted FSSP, sensitivity is found to both angle of attack and free stream air speed.

Norment, H. G.↗

An easily implemented static condensation method for structural sensitivity analysis

A black-box approach to static condensation for sensitivity analysis is presented with illustrative examples of a cube and a car structure. The sensitivity of the structural response with respect to joint stiffness parameter is calculated using the direct method, forward-difference, and central-difference schemes. The efficiency of the various methods for identifying joint stiffness parameters from measured static deflections of these structures is compared. The results indicate that the use of static condensation can reduce computation times significantly and the black-box approach is only slightly less efficient than the standard implementation of static condensation. The ease of implementation of the black-box approach recommends it for use with general-purpose finite element codes that do not have a built-in facility for static condensation.

Gangadharan, S. N.↗

On Study of Air/Space-borne Dual-Wavelength Radar for Estimates of Rain Profiles

In this study, a framework is discussed to apply air/space-borne dual-wavelength radar for the estimation of characteristic parameters of hydrometeors. The focus of our study is on the Global Precipitation Measurements (GPM) precipitation radar, a dual-wavelength radar that operates at Ku (13.8 GHz) and Ka (35 GHz) bands. As the droplet size distributions (DSD) of rain are expressed as the Gamma function, a procedure is described to derive the median volume diameter (D(sub 0)) and particle number concentration (N(sub T)) of rain. The correspondences of an important quantity of dual-wavelength radar, defined as deferential frequency ratio (DFR), to the D(sub 0) in the melting region are given as a function of the distance from the 0 C isotherm. A self-consistent iterative algorithm that shows a promising to account for rain attenuation of radar and infer the DSD without use of surface reference technique (SRT) is examined by applying it to the apparent radar reflectivity profiles simulated from the DSD model and then comparing the estimates with the model (true) results. For light to moderate rain the self-consistent rain profiling approach converges to unique and correct solutions only if the same shape factors of Gamma functions are used both to generate and retrieve the rain profiles, but does not converges to the true solutions if the DSD form is not chosen correctly. To further examine the dual-wavelength techniques, the self-consistent algorithm, along with forward and backward rain profiling algorithms, is then applied to the measurements taken from the 2nd generation Precipitation Radar (PR-2) built by Jet Propulsion Laboratory. It is found that rain profiles estimated from the forward and backward approaches are not sensitive to shape factor of DSD Gamma distribution, but the self-consistent method is.

Liao, Liang↗

Sensitivity of rotor blade vibration characteristics to torsional oscillations.

A theoretical investigation of dynamic response characteristics of helicopter rotor blades in forward flight was carried out with special emphasis on the torsional degrees-of-freedom. The finite element method was applied in the formulation of the coupled equations of motion for flapwise bending and torsion for blades with non-collinear elastic, mass and aerodynamic axes. The sensitivity of blade vibration characteristics with respect to structural, geometric and aerodynamic properties as well as flight conditions was evaluated. Numerical results for sample blades were plotted to show the variation of the coupling between bending and torsional components of the response.

Bratanow, T.↗

Stability sensitivity analysis for the aeroelastic optimization of a helicopter rotor

A sensitivity study of blade stability in forward flight for a hingeless rotor with respect to structural design variables is carried out using a direct analytical method. Structural design variables include nonstructural mass distribution (spanwise and chordwise), chordwise offset of center of gravity, and blade bending stiffnesses (flap, lag and torsion). The formulation for blade steady response is based on a finite element method in space and time. The vehicle trim and blade steady response are calculated iteratively as one coupled solution using a modified Newton method. Eigenvalues corresponding to different blade modes are calculated using Floquet transition matrix theory. The formulation for derivatives of the eigenvalues with respect to design variables is implemented using a direct analytical approach (chain rule differentiation), and constitutes an integral part of the regular stability analysis. The stability sensitivity derivatives were obtained at a fraction of computation time compared to the frequently adopted finite difference method. A parametric study showed that nonstructural mass and chordwise cg offset of outboarad elements, and lag bending stiffness of inboard elements, have powerful influence on blade stability.

Lim, Joon W.↗

PMA-PhyloChip DNA Microarray to Elucidate Viable Microbial Community Structure

Since the Viking missions in the mid-1970s, traditional culture-based methods have been used for microbial enumeration by various NASA programs. Viable microbes are of particular concern for spacecraft cleanliness, for forward contamination of extraterrestrial bodies (proliferation of microbes), and for crew health/safety (viable pathogenic microbes). However, a "true" estimation of viable microbial population and differentiation from their dead cells using the most sensitive molecular methods is a challenge, because of the stability of DNA from dead cells. The goal of this research is to evaluate a rapid and sensitive microbial detection concept that will selectively estimate viable microbes. Nucleic acid amplification approaches such as the polymerase chain reaction (PCR) have shown promise for reducing time to detection for a wide range of applications. The proposed method is based on the use of a fluorescent DNA intercalating agent, propidium monoazide (PMA), which can only penetrate the membrane of dead cells. The PMA-quenched reaction mixtures can be screened, where only the DNA from live cells will be available for subsequent PCR reaction and microarray detection, and be identified as part of the viable microbial community. An additional advantage of the proposed rapid method is that it will detect viable microbes and differentiate from dead cells in only a few hours, as opposed to less comprehensive culture-based assays, which take days to complete. This novel combination approach is called the PMA-Microarray method. DNA intercalating agents such as PMA have previously been used to selectively distinguish between viable and dead bacterial cells. Once in the cell, the dye intercalates with the DNA and, upon photolysis under visible light, produces stable DNA adducts. DNA cross-linked in this way is unavailable for PCR. Environmental samples suspected of containing a mixture of live and dead microbial cells/spores will be treated with PMA, and then incubated in the dark. Thereafter, the sample is exposed to visible light for five minutes, so that the DNA from dead cells will be cross-linked. Following this PMA treatment step, the sample is concentrated by centrifugation and washed (to remove excessive PMA) before DNA is extracted. The 16S rRNA gene fragments will be amplified by PCR to screen the total microbial community using PhyloChip DNA microarray analysis. This approach will detect only the viable microbial community since the PMA intercalated DNA from dead cells would be unavailable for PCR amplification. The total detection time including PCR reaction for low biomass samples will be a few hours. Numerous markets may use this technology. The food industry uses spore detection to validate new alternative food processing technologies, sterility, and quality. Pharmaceutical and medical equipment companies also detect spores as a marker for sterility. This system can be used for validating sterilization processes, water treatment systems, and in various public health and homeland security applications.

Venkateswaran, Kasthuri J.↗

Retrieving the Vertical Structure of the Effective Aerosol Complex Index of Refraction from a Combination of Aerosol in Situ and Remote Sensing Measurements During TARFOX

The largest uncertainty in estimates of the effects of atmospheric aerosols on climate stems from uncertainties in the determination of their microphysical properties, including the aerosol complex index of refraction, which in turn determines their optical properties. A novel technique is used to estimate the aerosol complex index of refraction in distinct vertical layers from a combination of aerosol in situ size distribution and remote sensing measurements during the Tropospheric Aerosol Radiative Forcing Observational Experiment (TARFOX). In particular, aerosol backscatter measurements using the NASA Langley LASE (Lidar Atmospheric Sensing Experiment) instrument and in situ aerosol size distribution data are utilized to derive vertical profiles of the "effective" aerosol complex index of refraction at 815 nm (i.e., the refractive index that would provide the same backscatter signal in a forward calculation on the basis of the measured in situ particle size distributions for homogeneous, spherical aerosols). A sensitivity study shows that this method yields small errors in the retrieved aerosol refractive indices, provided the errors in the lidar-derived aerosol backscatter are less than 30% and random in nature. Absolute errors in the estimated aerosol refractive indices are generally less than 0.04 for the real part and can be as much as 0.042 for the imaginary part in the case of a 30% error in the lidar-derived aerosol backscatter. The measurements of aerosol optical depth from the NASA Ames Airborne Tracking Sunphotometer (AATS-6) are successfully incorporated into the new technique and help constrain the retrieved aerosol refractive indices. An application of the technique to two TARFOX case studies yields the occurrence of vertical layers of distinct aerosol refractive indices. Values of the estimated complex aerosol refractive index range from 1.33 to 1.45 for the real part and 0.001 to 0.008 for the imaginary part. The methodology devised in this study provides, for the first time, a complete set of vertically resolved aerosol size distribution and refractive index data. yielding the vertical distribution of aerosol optical properties required for the determination of aerosol-induced radiative flux changes.

Redemann, J.↗

Retrieving the Vertical Structure of the Effective Aerosol Complex Index of Refraction from a Combination of Aerosol in Situ and Remote Sensing Measurements During TARFOX

The largest uncertainty in estimates of the effects of atmospheric aerosols on climate stems from uncertainties in the determination of their microphysical properties, including the aerosol complex index of refraction, which in turn determines their optical properties. A novel technique is used to estimate the aerosol complex index of refraction in distinct vertical layers from a combination of aerosol in situ size distribution and remote sensing measurements during the Tropospheric Aerosol Radiative Forcing Observational Experiment (TARFOX). In particular, aerosol backscatter measurements using the NASA Langley LASE (Lidar Atmospheric Sensing Experiment) instrument and in situ aerosol size distribution data are utilized to derive vertical profiles of the 'effective' aerosol complex index of refraction at 815 nm (i.e., the refractive index that would provide the same backscatter signal in a forward calculation on the basis of the measured in situ particle size distributions for homogeneous, spherical aerosols). A sensitivity study shows that this method yields small errors in the retrieved aerosol refractive indices, provided the errors in the lidar derived aerosol backscatter are less than 30% and random in nature. Absolute errors in the estimated aerosol refractive indices are generally less than 0.04 for the real part and can be as much as 0.042 for the imaginary part in the case of a 30% error in the lidar-derived aerosol backscatter. The measurements of aerosol optical depth from the NASA Ames Airborne Tracking Sunphotometer (AATS-6) are successfully incorporated into the new technique and help constrain the retrieved aerosol refractive indices. An application of the technique to two TARFOX case studies yields the occurrence of vertical layers of distinct aerosol refractive indices. Values of the estimated complex aerosol refractive index range from 1.33 to 1.45 for the real part and 0.001 to 0.008 for the imaginary part. The methodology devised in this study provides, for the first time a complete set of vertically resolved aerosol size distribution and refractive index data, yielding the vertical distribution of aerosol optical properties required for the determination of aersol-induced radiative flux changes

Redemann, J.↗

Integrated aerodynamic-structural-control wing design

The aerodynamic-structural-control design of a forward-swept composite wing for a high subsonic transport aircraft is considered. The structural analysis is based on a finite-element method. The aerodynamic calculations are based on a vortex-lattice method, and the control calculations are based on an output feedback control. The wing is designed for minimum weight subject to structural, performance/aerodynamic and control constraints. Efficient methods are used to calculate the control-deflection and control-effectiveness sensitivities which appear as second-order derivatives in the control constraint equations. To suppress the aeroelastic divergence of the forward-swept wing, and to reduce the gross weight of the design aircraft, two separate cases are studied: (1) combined application of aeroelastic tailoring and active controls; and (2) aeroelastic tailoring alone. The results of this study indicated that, for this particular example, aeroelastic tailoring is sufficient for suppressing the aeroelastic divergence, and the use of active controls was not necessary.

Rais-Rohani, M.↗

NASA/American Cancer Society High-Resolution Flow Cytometry Project-I

BACKGROUND: The NASA/American Cancer Society (ACS) flow cytometer can simultaneously analyze the electronic nuclear volume (ENV) and DNA content of cells. This study describes the schematics, resolution, reproducibility, and sensitivity of biological standards analyzed on this unit. METHODS: Calibrated beads and biological standards (lymphocytes, trout erythrocytes [TRBC], calf thymocytes, and tumor cells) were analyzed for ENV versus DNA content. Parallel data (forward scatter versus DNA) from a conventional flow cytometer were obtained. RESULTS: ENV linearity studies yielded an R value of 0.999. TRBC had a coefficient of variation (CV) of 1.18 +/- 0.13. DNA indexes as low as 1.02 were detectable. DNA content of lymphocytes from 42 females was 1.9% greater than that for 60 males, with a noninstrumental variability in total DNA content of 0.5%. The ENV/DNA ratio was constant in 15 normal human tissue samples, but differed in the four animal species tested. The ENV/DNA ratio for a hypodiploid breast carcinoma was 2.3 times greater than that for normal breast tissue. CONCLUSIONS: The high-resolution ENV versus DNA analyses are highly reliable, sensitive, and can be used for the detection of near-diploid tumor cells that are difficult to identify with conventional cytometers. ENV/DNA ratio may be a useful parameter for detection of aneuploid populations.

NASA Center JSC↗

Some Advanced Concepts in Discrete Aerodynamic Sensitivity Analysis

An efficient incremental iterative approach for differentiating advanced flow codes is successfully demonstrated on a two-dimensional inviscid model problem. The method employs the reverse-mode capability of the automatic differentiation software tool ADIFOR 3.0 and is proven to yield accurate first-order aerodynamic sensitivity derivatives. A substantial reduction in CPU time and computer memory is demonstrated in comparison with results from a straightforward, black-box reverse-mode applicaiton of ADIFOR 3.0 to the same flow code. An ADIFOR-assisted procedure for accurate second-rder aerodynamic sensitivity derivatives is successfully verified on an inviscid transonic lifting airfoil example problem. The method requires that first-order derivatives are calculated first using both the forward (direct) and reverse (adjoinct) procedures; then, a very efficient noniterative calculation of all second-order derivatives can be accomplished. Accurate second derivatives (i.e., the complete Hesian matrices) of lift, wave drag, and pitching-moment coefficients are calculated with respect to geometric shape, angle of attack, and freestream Mach number.

Taylor, Arthur C., III↗