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This paper describes a simple empirical stategy for computing manuever times and magnitudes autonomously for Earth orbiting spacecraft with a ground track repeat requirement.
The Deep Space Network (DSN) currently makes use of the technique of Multiple Spacecraft per Antenna (MSPA) where a single antenna is used to track multiple spacecraft downlinks within its beam, such as in the case of multiple spacecraft orbiting Mars at 8.4 GHz (X-band). It is desired to extend this technique to the uplink where a single station is used to send a signal to multiple spacecraft in order to make more efficient use of ground resources. This would be applicable to numerous smallsat constellations being considered for future missions or to future spacecraft at Venus, Mars, or more distant destinations that are all within the half-power beamwidth of a single 34-m diameter antenna. In one scheme, each spacecraft’s command sequences would be time multiplexed onto a single uplink frequency. Each spacecraft would lock onto the uplink signal and would accept only commands intended for it via special identifier codes. Each spacecraft would also emit a downlink signal to the ground that is coherent with the uplink signal but would have its own allocated frequency channel and identifier information. A couple of key challenges associated with using this technique need to be addressed. Because of the single uplink frequency, coherent turnaround for two-way Doppler and ranging would not conform to established ratios, thus the radios employed by the spacecraft would need to be capable of variable turnaround ratios. In addition, because of the different orbits or spacecraft trajectories, the relative Doppler shifts and rates can be large with respect to the common uplink signal whose frequency would lie at the centroid of the frequencies of the expected received signals of the constellation. This would be problematic with standard analog spacecraft radios whose acquisition bandwidths are relatively small (~1.7 kHz) relative to the large frequency offsets (~100 kHz) expected using the single frequency uplink technique. With the advent of software defined radios (SDRs), signal frequency search algorithms can be utilized within the flight software and/or programmable hardware (e.g., FPGAs) that can easily acquire and track signals with large frequency offsets and varying dynamics. Such techniques could include FFT search algorithms, step-and-sweep search algorithms, or onboard frequency steering making use of trajectory vectors uplinked to each member spacecraft. Other challenges include mitigation of potential interference between received signals. We have identified several software defined radios that are in different stages of development and whose key parameters have been tabulated. We have examined each radio’s capabilities with respect to acquiring and tracking signals with large frequency offsets. Such analyses made use of previous studies supplemented with specially designed tests using both simulation tools and/or existing testbeds. We have compared signal acquisition times computed from provided algorithms along with measured values derived from tests using existing hardware and simulation tools for the purpose of conducting tradeoff studies between the various radio designs and software/firmware programming approaches.
An analytic transfer inverse model for Earth Polychromatic Imaging Camera (EPIC) observations is proposed to retrieve the cloud-top pressure (CTP) with the consideration of in-cloud photon penetration. In this model, an analytic equation was developed to represent the reflection at the top of the atmosphere from above cloud, in cloud, and below cloud. The coefficients of this analytic equation can be derived from a series of EPIC simulations under different atmospheric conditions using a nonlinear regression algorithm. With estimated cloud pressure thickness, the CTP can be retrieved from EPIC observation data by solving the analytic equation. To simulate the EPIC measurements, a program package using the double-k approach was developed. Compared to line-by-line calculation, this approach can calculate high-accuracy results with a 100-fold computation time reduction. During the retrieval processes, two kinds of retrieval results, i.e., baseline CTP and retrieved CTP, are provided. The baseline CTP is derived without considering in-cloud photon penetration, and the retrieved CTP is derived by solving the analytic equation, taking into consideration in-cloud and below-cloud interactions. The retrieved CTPs for the oxygen A and B bands are smaller than their related baseline CTP. At the same time, both baseline CTP and retrieved CTP at the oxygen B band are larger than those at the oxygen A band. Compared to the difference in baseline CTP between the B band and A band, the difference in retrieved CTP between these two bands is generally reduced. Out of around 10 000 cases, in retrieved CTP between the A and B bands we found an average bias of 93 mb with a standard deviation of 81 mb. The cloud layer top pressure from Cloud–Aerosol Lidar and Infrared Pathfinder Satellite Observations (CALIPSO) measurements is used for validation. Under single-layer cloud situations, the retrieved CTPs for the oxygen A band agree well with the CTPs from CALIPSO, the mean difference of which within 5 mb in the case study. Under multiple-layer cloud situations, the CTPs derived from EPIC measurements may be larger than the CTPs of high-level thin clouds due to the effect of photon penetration.
As part of the Game Changing Development (GCD) Program, funded by NASA’s Space Technology Mission Directorate (STMD), the development of simulation capability for the prediction of extra-terrestrial Plume Surface Interaction (PSI) environments has been undertaken by the Fluid Dynamics Branch at NASA/MSFC. The GCD PSI Project, planned to be accomplished over a four year period, contains a Predictive Simulation Capability (PSC) Element focused on creating simulation capability for the reliable and accurate prediction of PSI in Martian (~650 Pa) and Lunar (vacuum) ambient environments. In addition to the PSC Element, the PSI Project also contains a companion Ground Testing Element for development of focused datasets for validation of predictive capability as well as a Flight-focused Instrumentation Element. This paper describes the activities and accomplishments in the past year for the Prediction of Plume Flow in low pressure environments component of the PSI Project. While the Loci/Chem Computational fluid dynamics (CFD) application has been validated and used extensively for simulating launch environments in atmospheric conditions, use of this tool for simulating supersonic plumes at Mars-like ambient pressure requires further validation. CFD simulations of underexpanded jets have been performed using Loci/Chem for Mars-like conditions to predict several metrics for steady laminar, turbulent, and impinging plumes. The CFD results are compared with an experimental data set for low Reynolds number plumes at these conditions in order to evaluate the current capability of the Loci/Chem tool for these types of environments. The CFD validation results to date show reasonable agreement with the experimental data across all of the metrics of interest for the configurations considered. The Loci/Chem-Boltzmann CFD application is a hybrid continuum/rarefied flow solver which extends modeling capabilities to very low pressure environments such as those on the Moon. The Loci/Chem-Boltzmann solver uses a gradient-based continuum breakdown criterion to restrict solution of the computationally expensive Boltzmann equation to only a subset of the domain, while using the Navier-Stokes equations elsewhere. This CFD application is under active development, and current efforts toward establishing production ready capability for evaluating Lunar plume surface interactions are well under way. Initial simulations of an Apollo LEM indicate that several regions of the flow require solving the Boltzmann equations due to extreme rarefaction. Early simulations are promising, indicating reasonable overall computational time for a full 3D human scale lander simulation.
The buckling response of thin-walled cylindrical structures have long been shown to be sensitive to various imperfections. That is, imperfections related to load introduction, boundary conditions, material property variation, and geometric deviations can all contribute to experimentally obtained buckling loads being lower than the buckling loads predicted for perfect representations of the same thin-walled cylindrical structure. To account for the influence of geometry-based imperfections of a thin-walled cylindrical structure on buckling response, a design factor (also known as a buckling knockdown factor) is used during the design phase. Guidelines for buckling knockdown factors are readily available in NASA SP-8007, Buckling of Thin Walled Circular Cylinders, which was updated in 2020. Prior to this recent update, NASA SP-8007 had not been updated since 1969, and since that time, computational analysis, experimental testing, and manufacturing methods have significantly improved. The NASA Engineering and Safety Center (NESC) Shell Buckling Knockdown Factor Project (SBKF, NESC Assessment 07-010-E) had the goal of developing buckling design recommendations for select classes of metallic and composite launch-vehicle structures [3]. Specifically, the test and analysis results from the fourth SBKF composite test article SBKF-P3-CYL-CTA8.2B, which is referred to as CTA8.2B, are described in this paper. This test was the fourth in a series of four tests on sandwich composite cylinders that will be used to experimentally validate analysis methods, which in turn can be used to develop new analysis-based shell buckling design guidelines for typical sandwich composite launch vehicle cylindrical structures. Publications describing previous test validation with analysis are available in Refs. CTA8.2B was designed to occupy one corner of the design space with approximately equal bending stiffnesses in the axial and transverse directions and have a larger ratio of radius to effective shell thickness. Each test article had a unique design and was designed to occupy a specific region of the design space. CTA8.2B was an 8-foot diameter honeycomb-core sandwich cylinder that was fabricated and tested at the NASA Marshall Space Flight Center (MSFC). The primary objectives of this test were to interrogate the structural capability of a composite test article, and to verify the test article design and analysis approach for cylinders subjected to axial compression and combined axial and bending loads. First, descriptions of the test article design and test are given in Section 2.0, and modeling and analysis methods used in support of the test article design and testing activities are described briefly in Section 3.0. Then, select test results are presented and compared to predicted results in Section 4.0, and concluding remarks are presented in Section 5.0. Finally, drawings of CTA8.2B and references used to support the test and analysis are provided in the Appendix.
This paper discusses the Dynamic Mode Decomposition (DMD) of the Unsteady Pressure-Sensitive Paint (uPSP) measurements, which were collected with four Phantom high-speed cameras at a constant sample frequency in the Ascent Transient Aerodynamics Test (ATAT) of the Space Launch System (SLS) Block 1 cargo vehicle with the Unitary Plan Wind Tunnel (UPWT) 11-by-11-foot Transonic Wind Tunnel in September 2019 at NASA Ames Research Center. The conventional DMD algorithm is based on the Singular Value Decomposition (SVD). For the data with zero mean, the DMD is equivalent to the Discrete Fourier Transform (DFT). Since the uPSP is mainly used to determine the unsteady property of the aerodynamic flow, the DMD of the uPSP measurements is implemented in two steps: (1) subtract the mean value from the uPSP measurement; (2) apply the Fast Fourier Transform (FFT) on the resulting data with zero mean. The DMD of the uPSP measurements with FFT has two advantages: (1) the FFT algorithm is well known for its computational efficiency, therefore, compared to the SVD-based DMD algorithm, the DMD with FFT reduces the computation time; (2) the DMD with FFT can be easily implemented in parallel processing. The DMD outputs were generated with the execution in parallel of a code in C, with libraries of FFTW for FFT and MPI/OpenMP for parallel processing, on the NASA Pleiades supercomputer. In this paper, the results of DMD of the uPSP measurements in the tests of Mach sweep runs of the SLS ATAT are presented, and the effectiveness of the DMD of the uPSP measurements in the diagnosis of the unsteady, aerodynamic phenomena is demonstrated. The work described in this paper is a part of NASA’s development of a new state-of-the-art uPSP capability in production wind tunnels. Funding for this research was provided by the NASA Aeroscience Evaluation and Test Capabilities Project.
While the Loci/Chem Computational fluid dynamics (CFD) application has been validated and used extensively for simulating launch environments in atmospheric conditions, use of this tool for simulating supersonic plumes at much lower ambient pressure requires further validation. Simulations of underexpanded plumes have been performed using Loci/Chem at Martian pressure to predict several metrics for laminar, turbulent, and impinging plumes. The CFD results are compared with an experimental data set for low Reynolds number plumes at these conditions in order to evaluate the current capability of the Loci/Chem tool for these types of environments. The CFD validation results to date show reasonable agreement with the experimental data across all the metrics of interest for the configurations considered. The Loci/Chem-Boltzmann tool is a hybrid continuum/rarefied flow solver which extends modeling capabilities to very low-pressure environments such as those on the Moon. The Loci/Chem-Boltzmann solver uses a gradient-based continuum breakdown criterion to restrict solution of the computationally expensive Boltzmann equation to only a subset of the domain, while using the Navier-Stokes equations elsewhere. This CFD application is under active development, and current efforts toward establishing production ready capability for evaluating Lunar plume surface interactions are well under way. Initial simulations of an Apollo Lunar excursion module indicate that several regions of the flow require solving the Boltzmann equations due to extreme rarefaction. Early simulations are promising, indicating reasonable overall computational time for a full 3D human scale lander simulation.
This work presents a probabilistic operational intent model for vehicles operating in upper Class E airspace. A hybrid method is developed to calculate the intent conflict probability leveraging and extending past works on probabilistic conflict computation. Simulation results verify that the probabilistic intent model can accurately encompass the uncertain positions of each vehicle type, that are a result of wind prediction errors and vehicle performance. A comparison with past methods showed that the proposed hybrid method captures the intent conflict probability with better accuracy, especially for a larger look-ahead horizon, and computational time is reasonable for real-time applications. An example is presented to illustrate the use of the intent conflict probability in strategic planning applications.
This work presents a probabilistic operational intent model for vehicles operating in upper Class E airspace. A hybrid method is developed to calculate the intent conflict probability leveraging and extending past works on probabilistic conflict computation. Simulation results verify that the probabilistic intent model can accurately encompass the uncertain positions of each vehicle type, that are a result of wind prediction errors and vehicle performance. A comparison with past methods showed that the proposed hybrid method captures the intent conflict probability with better accuracy, especially for a larger look-ahead horizon, and computational time is reasonable for real-time applications. An example is presented to illustrate the use of the intent conflict probability in strategic planning applications.
When performing symbolic regression using genetic programming, overfitting and bloat can negatively impact generalizability and interpretability of the resulting equations as well as increase computation times. A Bayesian fitness metric is introduced and its impact on bloat and overfitting during population evolution is studied and compared to common alternatives in the literature. The proposed approach was found to be more robust to noise and data sparsity in numerical experiments, guiding evolution to a level of complexity appropriate to the dataset. Further evolution of the population resulted not in overfitting or bloat, but rather in slight simplifications in model form. The ability to identify an equation of complexity appropriate to the scale of noise in the training data was also demonstrated. In general, the Bayesian model selection algorithm was shown to be an effective means of regularization which resulted in less bloat and overfitting when any amount of noise was present in the training data.
Widely used to calculate illumination geometry forestimates of solar and emitted longwave radiation, and forcorrecting remotely sensed data for topographic effects, digitalelevation models (DEMs) are now extensive globally at 10–30-mspatial resolution and locally at spatial resolutions down to afew centimeters. Globally, regionally, or locally, elevation datasetshave many grid points. Many software packages calculate gradi-ents over every grid cell or point, but in the mountains, shadingby nearby terrain must also be assessed. Terrain may obscure aslope that would otherwise face the Sun. Four decadesago, a fastmethod to calculate topographic horizons at every point in anelevation grid required computations related only linearly to thesize of the grid, but grids now have so many points that parallelcomputing still provides an advantage. Exploiting parallelismover terrain grids can use alternative strategies: among columnsof a rotated grid, or simultaneously at multiple rotation angles,or on different tiles of a grid. On a multi-processor machine, theimprovement in computing time approaches 2/3 the number ofprocessors deployed,
Hologram reconstruction via the angular spectrum method utilizes fast Fourier transforms which quickly but inefficiently shift between image and pupil planes. We demonstrate hologram reconstruction using discrete transforms over limited regions, decreasing computation time 10x.
The objective of this work is to optimize scramjet inlet designs under uncertainty at multiple fidelity levels. Optimizations are performed for both deterministic and stochastic conditions. For stochastic conditions, robust design is used to minimize the variance in system performance in addition to optimizing mean system performance. Uncertainty quantification is performed using non-intrusive polynomial chaos. Comparisons are made between low-fidelity analysis and high-fidelity analysis, as well as deterministic optimization and robust optimization. Results indicate that the general design trend of previous inlet optimization techniques is recovered for the external compression portion of an inlet. For the internal compression portion of an inlet, when viscous effects become more significant and boundary layer separation becomes more likely, the optimal trend departs from previous results. Multifidelity uncertainty quantification methods are found to substantially reduce the computation time of robust design while obtaining results that nearly match those of high-fidelity analysis. Robust optimization is found to decrease the standard deviation of throat Mach number by up to 40% compared to deterministic optimization. Changes in the design variables and total turning that lead to robust scramjet inlets are identified and linked back to fundamental physical principles through the theta-beta-Mach function.
Data collection using unsteady pressure-sensitive paint (uPSP) has been greatly increased in recent large-scale demonstrations. With this significant increase comes challenges to process this magnitude of data. Techniques designed for several thousands of images collected in a lab do not necessarily scale to millions collected in a production-level system. Novel techniques are needed to meet the tighter requirements imposed on computation time, robustness, and accuracy. This paper outlines a number of such techniques and improvements in regards to the camera calibration process.
In supersonic and hypersonic flow computations, well-resolved boundary layers are essential for accurate quantification of surface heating and transition prediction, particularly via linear stability analysis. Grid design for hypersonic flows with shocks, boundary-layer separation, and/or complex mean flow features incorporating spanwise/azimuthal inhomogeneities is a difficult issue. In comparison to a manual grid adaptation procedure, an autonomous grid adaptation technique offers significant improvements in computing time and solution quality. The VULCAN-CFD solver already includes a validated procedure for automatic adaption of structured grids to the bow shock. The present focus is on implementing an automatic boundary-layer adaptation capability in VULCAN-CFD that adapts structured, multiblock grids to both the bow shock and the boundary layer at the same time. The boundary-layer adaptation algorithm allows the user to specify the number of cells within the boundary layer, along with the input parameters used for detecting the edge of the boundary layer, namely, the variable used in the edge detection criterion,the edge detection method, the detection direction, and the relaxation factor used during the morphing of the grid. The algorithm automatically distributes grid points along the wall-normal direction to achieve a smooth variation in grid spacing from the edge of the boundary layer to a"junction" location within the outer part of the grid. Illustrative results are presented for three different high-speed configurations: the two-dimensional flow over a cylinder at Mach 17.6 and unit Reynolds number of Re=0.38x10^6 m^-1, the axisymmetric flow over a cone-cylinder-flare model at Mach 6.0 and Re = 10.5×10^6 m^-1, and the three-dimensional flow over a blunt, 7-degree half-angle cone at 5-degree angle of attack in a Mach 9.79 flow with Re = 17.1×10^6 m^-1. The automated boundary-layer adaptation is shown to provide an adequate grid topology that is aligned with the bow shock in the outer part of the grid and also resolves the viscous boundary-layer region close to the surface.
When performing symbolic regression using genetic programming, overfitting and bloat can negatively impact generalizability and interpretability of the resulting equations as well as increase computation times. A Bayesian fitness metric is introduced and its impact on bloat and overfitting during population evolution is studied and compared to common alternatives in the literature. The proposed approach was found to be more robust to noise and data sparsity in numerical experiments, guiding evolution to a level of complexity appropriate to the dataset. Further evolution of the population resulted not in overfitting or bloat, but rather in slight simplifications in model form. The ability to identify an equation of complexity appropriate to the scale of noise in the training data was also demonstrated. In general, the Bayesian model selection algorithm was shown to be an effective means of regularization which resulted in less bloat and overfitting when any amount of noise was present in the training data.
This paper presents an efficient approach for tuning finite element models to match the measured ground vibrationtest and proof test data. Frequencies, mode shapes, total weight, location of the center of gravity, and staticdeformation computed from the finite element model are matched to the measured data. The model tuningprocedure used in this work is based on solving an optimization problem in which the errors for the consideredmetrics, between the finite element prediction and the measured data, are minimized. Analytical sensitivity values ofperformance indices are computed using the NASTRAN-generated sensitivity values together with the in-housecomputer programs, which allow for faster computational time and the use of gradient-based optimizers. The methodis applied to the Aerostructures Test Wing 4 model. The study shows that the military standard and the NASAstandard for comparing analytical and experimental modal data are all satisfied. The final finite element modelcorrelates well with the test data. The flutter speed decreases by 8.91% after model tuning compared with the original Aerostructures Test Wing 4 design.
This report presents an efficient approach for tuning finite element models to match the measured ground vibration test and static test data. Frequencies, mode shapes, total weight, location of the center of gravity, and static deformation computed from the finite element model are matched to the measured data. The model tuning procedure used in this work is based on solving an optimization problem in which the errors for the considered metrics, between the finite element prediction and the measured data, are minimized. Analytical sensitivity values of performance indices are computed using the NASTRAN-generated sensitivity values together with the in-house computer codes, which allow for faster computational time and the use of gradient-based optimizers. The method is applied to the Aerostructures Test Wing IV model. The study shows that the military standard and the National Aeronautics and Space Administration standard for comparing analytical and experimental modal data are all satisfied. The final finite element model correlates well with the test data. The flutter speed decreases by 8.91 percent after model tuning compared with the original Aerostructures Test Wing IV design.