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All sourcesNASA NTRSDOE OSTI
NASA NTRS1992

Design of an essentially non-oscillatory reconstruction procedure in finite-element type meshes

An essentially non oscillatory reconstruction for functions defined on finite element type meshes is designed. Two related problems are studied: the interpolation of possibly unsmooth multivariate functions on arbitary meshes and the reconstruction of a function from its averages in the control volumes surrounding the nodes of the mesh. Concerning the first problem, the behavior of the highest coefficients of two polynomial interpolations of a function that may admit discontinuities of locally regular curves is studied: the Lagrange interpolation and an approximation such that the mean of the polynomial on any control volume is equal to that of the function to be approximated. This enables the best stencil for the approximation to be chosen. The choice of the smallest possible number of stencils is addressed. Concerning the reconstruction problem, two methods were studied: one based on an adaptation of the so called reconstruction via deconvolution method to irregular meshes and one that lies on the approximation on the mean as defined above. The first method is conservative up to a quadrature formula and the second one is exactly conservative. The two methods have the expected order of accuracy, but the second one is much less expensive than the first one. Some numerical examples are given which demonstrate the efficiency of the reconstruction.

Abgrall, Remi↗
NASA NTRS1993

Bayesian image reconstruction - The pixon and optimal image modeling

In this paper we describe the optimal image model, maximum residual likelihood method (OptMRL) for image reconstruction. OptMRL is a Bayesian image reconstruction technique for removing point-spread function blurring. OptMRL uses both a goodness-of-fit criterion (GOF) and an 'image prior', i.e., a function which quantifies the a priori probability of the image. Unlike standard maximum entropy methods, which typically reconstruct the image on the data pixel grid, OptMRL varies the image model in order to find the optimal functional basis with which to represent the image. We show how an optimal basis for image representation can be selected and in doing so, develop the concept of the 'pixon' which is a generalized image cell from which this basis is constructed. By allowing both the image and the image representation to be variable, the OptMRL method greatly increases the volume of solution space over which the image is optimized. Hence the likelihood of the final reconstructed image is greatly increased. For the goodness-of-fit criterion, OptMRL uses the maximum residual likelihood probability distribution introduced previously by Pina and Puetter (1992). This GOF probability distribution, which is based on the spatial autocorrelation of the residuals, has the advantage that it ensures spatially uncorrelated image reconstruction residuals.

Pina, R. K.↗
NASA NTRS2006

Semi-Analytic Reconstruction of Flux in Finite Volume Formulations

Semi-analytic reconstruction uses the analytic solution to a second-order, steady, ordinary differential equation (ODE) to simultaneously evaluate the convective and diffusive flux at all interfaces of a finite volume formulation. The second-order ODE is itself a linearized approximation to the governing first- and second- order partial differential equation conservation laws. Thus, semi-analytic reconstruction defines a family of formulations for finite volume interface fluxes using analytic solutions to approximating equations. Limiters are not applied in a conventional sense; rather, diffusivity is adjusted in the vicinity of changes in sign of eigenvalues in order to achieve a sufficiently small cell Reynolds number in the analytic formulation across critical points. Several approaches for application of semi-analytic reconstruction for the solution of one-dimensional scalar equations are introduced. Results are compared with exact analytic solutions to Burger s Equation as well as a conventional, upwind discretization using Roe s method. One approach, the end-point wave speed (EPWS) approximation, is further developed for more complex applications. One-dimensional vector equations are tested on a quasi one-dimensional nozzle application. The EPWS algorithm has a more compact difference stencil than Roe s algorithm but reconstruction time is approximately a factor of four larger than for Roe. Though both are second-order accurate schemes, Roe s method approaches a grid converged solution with fewer grid points. Reconstruction of flux in the context of multi-dimensional, vector conservation laws including effects of thermochemical nonequilibrium in the Navier-Stokes equations is developed.

Gnoffo, Peter A.↗
NASA NTRS2009

The Reconstruction and Failure Analysis of the Space Shuttle Columbia

Several days following the Columbia accident a team formed and began planning for the reconstruction of Columbia. A hangar at the Kennedy Space Center was selected for this effort due to it's size, available technical workforce and materials science laboratories and access to the vehicle ground processing infrastructure. The Reconstruction team established processes for receiving, handling, decontamination, tracking, identifying, cleaning and assessment of the debris. Initially, a 2-dimensional reconstruction of the Orbiter outer mold line was developed. As the investigation progressed fixtures which allowed a 3-dimensional reconstruction of the forward portions of the left wing's leading edge was developed. To support the reconstructions and forensic analyses a Materials and Processes (M&P) 'team was formed. This M&P team established processes for recording factual observations, debris cleaning, and engineering analysis. Fracture surfaces and thermal effects of selected airframe debris were assessed, and process flows for both nondestructive and destructive sampling and evaluation of debris were developed. The Team also assessed left hand airframe components that were believed to be associated with a structural breach of Columbia. A major portion of this analysis was evaluation of metallic deposits were prevalent on left wing leading edge components. Extensive evaluation of the visual, metallurgical and chemical nature of the deposits provided conclusions that were consistent with the visual assessments and interpretations of the NASA lead teams and the findings of the Columbia Accident Investigation Board. Analytical data collected by the M&P Team showed that a significant thermal event occurred at the left wing leading edge in the proximity of LH RCC Panels 8-9, and a correlation was formed between the deposits and overheating in these areas to the wing leading edge components. The analysis of deposits also showed exposure to temperatures in excess of 1649 C (3200 F), which would severely degrade support structure, tiles, and RCC panel materials. The integrated failure analysis of wing leading edge debris and deposits strongly supported the hypothesis that a breach occurred at LH RCC Panel 8.

Russell, Richard↗
NASA NTRS2013

Mars Entry Atmospheric Data System Trajectory Reconstruction Algorithms and Flight Results

The Mars Entry Atmospheric Data System is a part of the Mars Science Laboratory, Entry, Descent, and Landing Instrumentation project. These sensors are a system of seven pressure transducers linked to ports on the entry vehicle forebody to record the pressure distribution during atmospheric entry. These measured surface pressures are used to generate estimates of atmospheric quantities based on modeled surface pressure distributions. Specifically, angle of attack, angle of sideslip, dynamic pressure, Mach number, and freestream atmospheric properties are reconstructed from the measured pressures. Such data allows for the aerodynamics to become decoupled from the assumed atmospheric properties, allowing for enhanced trajectory reconstruction and performance analysis as well as an aerodynamic reconstruction, which has not been possible in past Mars entry reconstructions. This paper provides details of the data processing algorithms that are utilized for this purpose. The data processing algorithms include two approaches that have commonly been utilized in past planetary entry trajectory reconstruction, and a new approach for this application that makes use of the pressure measurements. The paper describes assessments of data quality and preprocessing, and results of the flight data reduction from atmospheric entry, which occurred on August 5th, 2012.

Karlgaard, Christopher D.↗
NASA NTRS2016

Exploration Flight Test 1 Afterbody Aerothermal Environment Reconstruction

The Exploration Flight Test 1 vehicle included roughly 100 near surface thermocouples on the after body of the vehicle. The temperature traces at each of these instruments have been used to perform inverse environment reconstruction to determine the aerothermal environment experienced during re-entry of the vehicle. This paper provides an overview of the reconstructed environments and identifies critical aspects of the environment. These critical aspects include transition and reaction control system jet influence. A blind test of the process and reconstruction tool was also performed to build confidence in the reconstructed environments. Finally, an uncertainty quantification analysis was also performed to identify the impact of each of the uncertainties on the reconstructed environments.

Hyatt, Andrew J.↗
NASA NTRS2016

The PRISM4 (mid-Piacenzian) Palaeoenvironmental Reconstruction

The mid-Piacenzian is known as a period of relative warmth when compared to the present day. A comprehensive understanding of conditions during the Piacenzian serves as both a conceptual model and a source for boundary conditions as well as means of verification of global climate model experiments. In this paper we present the PRISM4 reconstruction, a paleoenvironmental reconstruction of the mid-Piacenzian (approximately 3 Ma) containing data for paleogeography, land and sea ice, sea-surface temperature, vegetation, soils, and lakes. Our retrodicted paleogeography takes into account glacial isostatic adjustments and changes in dynamic topography. Soils and lakes, both significant as land surface features, are introduced to the PRISM reconstruction for the first time. Sea-surface temperature and vegetation reconstructions are unchanged but now have confidence assessments. The PRISM4 reconstruction is being used as boundary condition data for the Pliocene Model Intercomparison Project Phase 2 (PlioMIP2) experiments.

soils↗
NASA NTRS2002

Sparse matrix wavefront reconstruction: simulations and experiments

Adaptive optics systems with Shack-Hartmann wavefront sensors require reconstruction of the atmospheric phase error from slope measurements, with every sensor in the array being used in the computation of each actuator command. This fully populated reconstruction matrix can result in a significant computational burden for adaptive optics systems with large numbers of actuators. A method for generating sparse wavefront reconstruction matrices for adaptive optics isproposed. The method exploits the relevance of nearby slope measurements for control of an individual actuator, and relies upon the limited extent of the influence function for a zonal deformable mirror. Relying only on nearby sensor information can significantly reduce the calculation time for wavefront reconstruction. In addition, a hierarchic controller is proposed to recover some of the global wavefront information. The performance of these sparse wavefront reconstruction matrices was evaluated in simulation, and tested on the Palomar Adaptive Optics System. This paper will present some initial results from the simulations and experiments.

space↗
NASA NTRSDate not supplied

Mars 2020 Reconstructed Aerothermal Environments and Design Margins

The Mars 2020 aeroshell's thermal protection system was nearly identical to the Mars Science Laboratory system that successfully completed its mission for the Curiosity rover's landing in 2012. It was predicted that, like Mars Science Laboratory, the Mars 2020 heatshield would experience boundary layer transition and that the thermal protection system would provide sufficient material thickness margins against the aerothermal environments, even after adding radiative heating that was not included for Mars Science Laboratory. The Mars 2020 flight instrumentation suite included heatshield sensors similar to Mars Science Laboratory and new backshell measurements. A full set of surface pressure and in-depth temperature data were collected during atmospheric entry. This paper provides an initial analysis of the flight data and focuses on the reconstructed total surface heat flux inferred from the measured temperatures. Turbulent boundary layer conditions again were observed on the Mars 2020 heatshield, and the temperatures at all eleven heatshield and six backshell thermocouple in-depth sensor locations were well within system capabilities due to favorable entry conditions and conservative uncertainties. New computational fluid dynamics results on the reconstructed entry trajectory are compared to the measured surface pressures and reconstructed total heat fluxes. The predicted heatshield surface pressures at six locations match the data qualitatively and quantitatively well, as expected. Smooth-wall laminar heating predictions prior to boundary layer transition fall above the reconstructed heating on the heatshield. After the observed boundary layer transition time, total heat flux based on algebraic turbulence model calculations generally match the heat flux trends relative to one another. The convective heat flux was predicted to constitute the majority of the total heating. On the backshell, smooth-wall laminar total heat flux predictions generally exceed the reconstructed total heating at six locations. At each of these locations, it is estimated that radiative heating provided almost all of the total heating. The Mars 2020 as-flown aerothermal environments were well below the design levels for all measurement locations due to conservative design assumptions and a stressing design trajectory.

Mars 2020↗
NASA NTRSDate not supplied

Mars 2020 Reconstructed Aerothermal Environments and Design Margins

The Mars 2020 aeroshell's thermal protection system was nearly identical to the Mars Science Laboratory system that successfully completed its mission for the Curiosity rover's landing in 2012. It was predicted that, like Mars Science Laboratory, the Mars 2020 heatshield would experience boundary layer transition and that the thermal protection system would provide sufficient material thickness margins against the aerothermal environments, even after adding radiative heating that was not included for Mars Science Laboratory. The Mars 2020 flight instrumentation suite included heatshield sensors similar to Mars Science Laboratory and new backshell measurements. A full set of surface pressure and in-depth temperature data were collected during atmospheric entry. This paper provides an initial analysis of the flight data and focuses on the reconstructed total surface heat flux inferred from the measured temperatures. Turbulent boundary layer conditions again were observed on the Mars 2020 heatshield, and the temperatures at all eleven heatshield and six backshell thermocouple in-depth sensor locations were well within system capabilities due to favorable entry conditions and conservative uncertainties. New computational fluid dynamics results on the reconstructed entry trajectory are compared to the measured surface pressures and reconstructed total heat fluxes. The predicted heatshield surface pressures at six locations match the data qualitatively and quantitatively well, as expected. Smooth-wall laminar heating predictions prior to boundary layer transition fall above the reconstructed heating on the heatshield. After the observed boundary layer transition time, total heat flux based on algebraic turbulence model calculations generally match the heat flux trends relative to one another. The convective heat flux was predicted to constitute the majority of the total heating. On the backshell, smooth-wall laminar total heat flux predictions generally exceed the reconstructed total heating at six locations. At each of these locations, it is estimated that radiative heating provided almost all of the total heating. The Mars 2020 as-flown aerothermal environments were well below the design levels for all measurement locations due to conservative design assumptions and a stressing design trajectory.

Mars 2020↗
NASA NTRSDate not supplied

Space Launch System Artemis I Ascent Loads Reconstruction Summary

On November 16, 2022, NASA successfully launched the Space Launch System (SLS) rocket and Orion spacecraft for the first SLS mission, Artemis 1. This first flight was outfitted with Developmental Flight Instrumentation (DFI) such as accelerometers, pressure sensors, and strain gauges. The DFI supports many post-flight activities, one of which is the ascent loads reconstruction effort. The integrated vehicle ascent loads spans both boost phase and Core phase and often produces the largest loads experienced by the vehicle during flight. One of the primary goals of the ascent loads reconstruction is to evaluate applicable Coupled Loads Analysis (CLA) design math models, assumptions, and analysis methodologies. To achieve this goal, all significant ascent subevents have been reconstructed through the use of flight data, reconstructed inputs, and existing CLA simulations. Resulting responses have been compared to available flight measurements. Additionally, reconstructed subevent loads were combined and compared to appropriate flight data and pre-flight predictions.

SLS↗
NASA NTRS2024

High-Order/Low-Dissipation Chain-Rule Flux Solution Reconstruction Schemes in FUN3D

In this paper, we report progress in the development of economically high-order flux-solution-reconstruction (FSR) schemes, which are second-order accurate on general unstructured grids but achieve high-order accuracy when a grid is regular, i.e., has the same stencil (with the same spacing) throughout the domain. Two variants of the FSR schemes are discussed: chain-rule-flux-solution reconstruction (CFSR) and quadratic-form-flux-solution reconstruction (QFSR), where the former is based on the chain rule and the latter on the flux reconstruction expressed as a function of solution variables. These schemes are tested for flows with shock waves with a limiter incorporated in the flux and solution reconstructions. Improved results, compared with second-order methods are demonstrated for inviscid and viscous flows with smooth grids.

high-order↗
NASA NTRS2019

InSight's Reconstructed Aerothermal Environments

The InSight spacecraft was proposed to be a build-to-print copy of the Phoenix vehicle due to the knowledge that the lander payload would be similar and the trajectory would be similar. However, the InSight aerothermal analysts, based on tests performed in CO2 during the Mars Science Laboratory mission (MSL) and completion of Russian databases, considered radiative heat flux to the aftbody from the wake for the first time for a US Mars mission. The combined convective and radiative heat flux was used to determine if the as-flown Phoenix thermal protection system (TPS) design would be sufficient for InSight. All analyses showed that the design would be adequate. Once the InSight lander was successfully delivered to Mars on November 26, 2018, work began to reconstruct the atmosphere and trajectory in order to evaluate the aerothermal environments that were actually encountered by the spacecraft and to compare them to the design environments.The best estimated trajectory (BET) reconstructed for the InSight atmospheric entry fell between the two trajectories considered for the design, when looking at the velocity versus altitude values. The maximum heat rate design trajectory (MHR) flew at a higher velocity and the maximum heat load design trajectory (MHL) flew at a lower velocity than the BET. For TPS sizing, the MHL trajectory drove the design. Reconstruction has shown that the BET flew for a shorter time than either of the design environments, hence total heat load on the vehicle should have been less than used in design. Utilizing the BET, both DPLR and LAURA were first run to analyze the convective heating on the vehicle with no angle of attack. Both codes were run with axisymmetric, laminar flow in radiative equilibrium and vibrational non-equilibrium with a surface emissivity of 0.8. Eight species Mitcheltree chemistry was assumed with CO2, CO, N2, O2, NO, C, N, and O. Both codes agreed within 1% on the forebody and had the expected differences on the aftbody. The NEQAIR and HARA codes were used to analyze the radiative heating on the vehicle using full spherical ray-tracing. The codes agreed within 5% on most aftbody points of interest.The LAURA code was then used to evaluate the conditions at angle of attack at the peak heating and peak pressure times. Boundary layer properties were investigated to confirm that the flow over the forebody was laminar for the flight.Comparisons of the aerothermal heating determined for the reconstructed trajectory to the design trajectories showed that the as-flown conditions were less severe than design

radiation↗
NASA NTRS1979

Effects of asymmetric passband filtering on the phase of the Costas loop's reconstructed carrier

The reconstructed carrier of a telemetry return signal is used in deriving the Doppler and range information in the radiometric systems. When suppressed carrier BPSK signalling with Costas loop demodulation is used, there are concerns on the amount of shift in the reconstructed carrier phase, when the received signal suffers asymmetric bandpass filtering through the various stages of the receiver. It is concluded that the phase shifts due to asymmetric bandpass filtering on the Costas loop's reconstructed carrier can be slightly worse than those suffered by the residual carrier loop's reconstructed carrier. However, they are well within the error budgets of the radiometric system.

Woo, K. T.↗
NASA NTRS1982

Reconstruction of atmospheric pollutant concentrations from remote sensing data - An application of distributed parameter observer theory

The reconstruction of a concentration distribution from spatially averaged and noise-corrupted data is a central problem in processing atmospheric remote sensing data. Distributed parameter observer theory is used to develop reconstructibility conditions for distributed parameter systems having measurements typical of those in remote sensing. The relation of the reconstructibility condition to the stability of the distributed parameter observer is demonstrated. The theory is applied to a variety of remote sensing situations, and it is found that those in which concentrations are measured as a function of altitude satisfy the conditions of distributed state reconstructibility.

Koda, M.↗
NASA NTRS1985

Formulation and implementation of nonstationary adaptive estimation algorithm with applications to air-data reconstruction

The dynamics model and data sources used to perform air-data reconstruction are discussed, as well as the Kalman filter. The need for adaptive determination of the noise statistics of the process is indicated. The filter innovations are presented as a means of developing the adaptive criterion, which is based on the true mean and covariance of the filter innovations. A method for the numerical approximation of the mean and covariance of the filter innovations is presented. The algorithm as developed is applied to air-data reconstruction for the space shuttle, and data obtained from the third landing are presented. To verify the performance of the adaptive algorithm, the reconstruction is also performed using a constant covariance Kalman filter. The results of the reconstructions are compared, and the adaptive algorithm exhibits better performance.

Whitmore, S. A.↗
NASA NTRS1985

Formulation and implementation of nonstationary adaptive estimation algorithm with applications to air-data reconstruction

The dynamics model and data sources used to perform air-data reconstruction are discussed, as well as the Kalman filter. The need for adaptive determination of the noise statistics of the process is indicated. The filter innovations are presented as a means of developing the adaptive criterion, which is based on the true mean and covariance of the filter innovations. A method for the numerical approximation of the mean and covariance of the filter innovations is presented. The algorithm as developed is applied to air-data reconstruction for the Space Shuttle, and data obtained from the third landing are presented. To verify the performance of the adaptive algorithm, the reconstruction is also performed using a constant covariance Kalman filter. The results of the reconstructions are compared, and the adaptive algorithm exhibits better performance.

Whitmore, S. A.↗
NASA NTRS1987

Quantitative analysis of the reconstruction performance of interpolants

The analysis presented provides a quantitative measure of the reconstruction or interpolation performance of linear, shift-invariant interpolants. The performance criterion is the mean square error of the difference between the sampled and reconstructed functions. The analysis is applicable to reconstruction algorithms used in image processing and to many types of splines used in numerical analysis and computer graphics. When formulated in the frequency domain, the mean square error clearly separates the contribution of the interpolation method from the contribution of the sampled data. The equations provide a rational basis for selecting an optimal interpolant; that is, one which minimizes the mean square error. The analysis has been applied to a selection of frequently used data splines and reconstruction algorithms: parametric cubic and quintic Hermite splines, exponential and nu splines (including the special case of the cubic spline), parametric cubic convolution, Keys' fourth-order cubic, and a cubic with a discontinuous first derivative. The emphasis in this paper is on the image-dependent case in which no a priori knowledge of the frequency spectrum of the sampled function is assumed.

Lansing, Donald L.↗