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Probabilistic Modeling of a Three-Stage Human Landing System Architecture

Space Policy Directive-1 has led to NASA partnerships with commercial entities on procurement which includes the development of the Human Landing System (HLS) [1]. With the goal of delivering human crew to the lunar surface by 2024, system uncertainties become an important obstacle to the maturation of multiple new, driving technologies and mission concepts of the HLS program. As unmitigated uncertainties have previously led to failed development programs, these risks and their impacts must be understood and handled to ensure program success [2]. Sources of uncertainty include novel engine designs and configurations, increased reliance on cryogenic fluid management(CFM), and refueling technologies—which propagate as high-level performance metrics such as overall propellant mass and engine performance. Also, the occurrence of operational uncertainties—e.g. launch conditions or need to abort during the mission—can cause cascading effects on the rest of the mission that are difficult to definitively quantify, and are outside the scope of control. These concrete examples and other occurrences can be categorized as either epistemic or aleatory uncertainties.Epistemic uncertainty arises due to a lack of knowledge and can be alleviated with design and program maturation. Aleatory uncertainty is due to the inherent randomness of the system and cannot be directly reduced, unlike epistemic uncertainty. Robust design and probabilistic methods can compensate for aleatory effects. A taxonomy of uncertainty is referred to for this work [3]. In this paper, a probabilistic methodology to handle uncertainties has been demonstrated on a three-element HLS concept [1, 4], which allows tracking of current best estimates of the concept and assessment of concept design robustness against uncertainties. A sample case has been completed for this abstract, and an expansion on the methodology will be included in the final paper. This methodology has two key parts: first, the creation of a dynamic architecture model of a three-element HLS concept; and second, its use with surrogate modeling and range estimating techniques to capture and propagate uncertainties. This abstract will cover the basics of the approach used, and further details and justifications will be in the final paper.The mission profile associated with this three-element concept (Fig 1) was modeled as a set of mission events that facilitated mass changes, idles, or spacecraft maneuvers. The mission profile scope starts with each element’s NRHO orbit insertion and aggregation and ends at post-sortie rendezvous with Orion. More detail on the mission profile will be in the final paper. The DYnamic Rocket EQuation Tool (DYREQT), a space systems synthesis and sizing framework used by NASA, was used as the physics framework to model the HLS architecture for applying the probabilistic methodology [5, 6]. Specifically, a parametric representation of the lander, ascent, and transfer elements and the mission profile of each element was established, with vehicle and mission parameters available as inputs to allow for a dynamic model. Each vehicle stage was modeled with high-level performance metrics, using Isp and propellant mass fraction (PMF) to remain parametric. For the probabilistic analysis, uncertainties of interest within the HLS concept were enumerated and represented as parameters within the DYREQT model as inputs for vehicle stages or mission profile events. These parameters were frozen at their nominal values for the purposes of baselining architecture performance and sizing the vehicle appropriately based on reference documentation [1]. Range estimating—a probabilistic method that combines Monte Carlo sampling, focus on critical parameters, and heuristics to assess risk and opportunities—is traditionally used with Mass Equipment Lists (MELs), but has been adapted with operational parameters as well as vehicle parameters in theDYREQT model to capture mission uncertainty alongside vehicle uncertainty [7, 3]. This method was selected due to its application and insight on a system from a bottom-up perspective, independence from historical rules of thumb, and ability to generate sensitivities based on design decisions and uncertainties. As a sample case for the abstract, the boiloff rates of the vehicle elements and the loiter times during the mission (simulating launch time variations and changing window of opportunities) were used with range estimating to provide preliminary results. To perform the range estimation portion of this methodology (depicted in Fig. 3, further details in final paper), the DYREQT model was sampled using a Design of Experiments (DoE) to efficiently explore the architecture design space with respect to the sample set of uncertainty parameters; 5,000 cases via Latin Hypercube Sampling were computed on the DYREQT architecture model. Then, the results were used to create surrogate models, multivariate regressions that can visualize hypercube trends in the design space, of the architecture with respect to the uncertainty parameters. Range estimating was applied to the surrogates instead of the actual models, which saves computational expense due to the bulk of cases needed for the Monte Carlo simulation as part of range estimating. Uncertainty parameters were sampled independently from triangular distributions using the DoE ranges as ‘min’ and ‘max’, and the nominal value as ‘most likely’. Based engineering intuition, some uncertainty parameters are correlated—e.g. if the main propellant has a high boil-off rate, the oxidizer should follow suit as both are related to CFM technology.While a Monte Carlo simulation samples all inputs as independent, the results would show model correlations; thus, it is efficient to sample the inputs as correlated. Using a correlation matrix constructed for the uncertainty parameters, previously independent samples were transformed to perform a Correlated Monte Carlo. A table for the DoE ranges and probability distribution parameters is shown in Table 1, and more details on Correlated Monte Carlo Simulations will be discussed in the final paper. The model’s resulting DoE showed that multivariate polynomial equations fit via least squares method captured its behavior accurately for the sample case. For the Correlated Monte Carlo Simulation, a positive correlation between fuel and oxidizer boiloff rates was used as a demonstration. 10,000 cases were computed with the surrogates and the launched masses for each vehicle element was collated. The results can be displayed in a probability density function (PDF), showing the impact of the uncertainty parameters chosen. Integrating the PDFs will yield a cumulative distribution function (CDF) that shows the cumulative probability of a given value on the x-axis. For the sample case, the elements’ launch mass margin was calculated and represented in as CDFs, as a demonstrated representation of figures of merit for the HLS concept. For the lander and ascent elements, the NRHO mass insertion limit is 16t; the transfer element has a limit of 30t [1]. It can be seen with Figure 2 that this probabilistic methodology can provide insight into mass margin with respect to the uncertainties being modeled. Currently, the results show that the lander (descent) vehicle element has the most restrictive design space; it is the only element to show a 10% probability of negative margin. Further analysis on the Monte Carlo results will show sensitivities for driving constraints and parameters for architecture feasibility, which can lead to establishing potential mission rules.The combination of range estimating with a parametric architecture model for HLS demonstrated the capability of this probabilistic methodology in a sample case. As the HLS development progresses, this methodology has the potential for keeping current best estimates of architecture performance for awarded concepts due to the flexibility in DYREQT’s modeling framework and its parametric nature. Concept maturation and increased epistemic knowledge can be injected into the model probabilistic modeling, and thus continue to track probability of mission success.

Stephanie Y Zhu↗

NASA NTRS1998

Comparative Soot Diagnostics: 1 Year Report

Urban, David L.↗

NASA NTRS2024

Flight Mechanics Modeling and Simulation of the Earth Entry System

Introduction: The Mars Sample Return (MSR) Campaign being planned by NASA and ESA has the ambitious goal to return Mars samples back to Earth. This international collaboration had developed a concept of operations that included a ESA-designed Earth Return Orbiter (ERO) and NASA-designed Capture, Containment, and Return System (CCRS). The Earth Entry System (EES), consisting of a protective aeroshell that houses the samples as well as sample containment vessels, would conduct entry, descent, and landing (EDL) on a direct Earth trajectory. The EES would enter on a spin-stabilized ballistic trajectory with the goal to passively achieve aerodynamic stability throughout all regions of flight. The EDL sequence would end with the EES impacting the soft playa soil of the Utah Test and Training Range (UTTR). As of the submission of this abstract, the MSR campaign is undergoing a re-architecture leading to a pause in EES development. However, the novel approaches developed in flight mechanics modeling and simulation can significantly benefit the greater IPPW community in the development of Earth return vehicles. This paper will present the latest state of EES flight mechanics modeling and simulation. The paper will highlight the simulation architecture developed and key lessons learned from understanding of EDL trajectory sensitivities. Modeling and Simulation: Figure 1 provides a high-level concept of operations for the approach, entry, descent, and landing (AEDL) phase of the CCRS-portion of MSR. The objective of EES flight mechanics is to model and simulate the EES trajectory from ERO separation to ground impact at UTTR. A variety of flight mechanics simulation models were utilized to model both exo-atmopsheric and atmospheric portions of flight. 42, a 6-DOF simulation developed at Goddard Space Flight Center, is utilized for propagating the attitude of EES during exo-atmospheric flight. 42 allows for a variety of spin eject mechanism scenarios to be simulated for analysis. 10 minutes prior to entry, the 42 states are handed off to the EDL sims. The prime EDL sim utilized by EES is the Program to Optimize Simulated Trajectories II (POST2), a 6-DOF sim developed at Langley Research Center, and the independent verification and validation EDL sim utilized is DSENDS, a 6-DOF sim developed at Jet Propulsion Laboratory. Figure 2 provides a visualization of the flight mechanics simulation model flow through various points in the AEDL phase. Due to the existence of a variety of sim models, the EES flight mechanics team developed processes for data hand-off. These processes included the development of a centralized coordinate frame document, utilization of a single, centralized simulation input document for all sims to reference, and hand-off files containing both the technical data to be ingested by other flight mechanics sims as well as annotations of modeling assumptions utilized to generate the data. Figure~\ref{fig:post2simarchitecture} provides an overview of the POST2 sim architecture wherein POST2 ingests numerous subsystem models and input files. The dispersed state file generated by MONTE provides the position/velocity state of the trajectory while the 42 Handoff file provides the attitude. The aerodynamics database, delivered by the EES aeroscience team, is utilized to simulate the aerodynamic forces and moments experienced during EDL. A custom atmosphere model, developed by EES atmosphere team, is utilized to simulate the anticipated atmosphere environment around the region of Earth through which the EES trajectory flys. These inputs and subsystem models can be varied depending on the AEDL flight mechanics scenario being simulated. Monte Carlo simulations are utilized to generate statistical AEDL performance metrics in the form of scorecards and violin plots. Furthermore, outputs from the POST2 simulation are utilized for follow-on analyses including aerothermal and landing performance. \section{Flight Mechanics Lessons Learned} Though the EES flight mechanics team uncovered a variety of lessons learned through the analysis conducted to support CCRS through preliminary design review, this paper will highlight the most important lessons. A key AEDL performance goal is to ensure the landing footprint of EES remains on the UTTR south range. A common modeling strategy used in EDL analysis is One-Variable-At-a-Time (OVAT). OVAT analysis provides insight into the key drivers that affect AEDL performance metrics. Figure 3 shows the landing ellipses for single dispersion sources as compared to the baseline aggregate of all dispersions. The figure shows that atmosphere winds alone dominate the size of the footprint ellipse (note: EES does not use a parachute unlike previous Earth-return missions and is in wind-driven free fall for ~5min). The significance of the wind led the EES flight mechanics team to pursue the development of a Custom Atmosphere Model [4], in lieu of EarthGRAM [1], built on actual radiosonde wind measurements around the UTTR-region. This decision was driven by the realism in the generated footprint ellipses and lessons-learned from Stardust [5]. These findings will be invaluable for future Earth-return missions in providing an early understanding of the key drivers affecting footprint size and modeling considerations for which to account. Another lesson learned is tied to the AEDL performance goal of achieving passive stability throughout all regions of flight. It is well understood that blunt-body aeroshells are less stable as they transition from supersonic to subsonic. Eliminating a backshell does help improvestability; however, other phenomena such as roll-induced instability during terminal descent can still arise. The EES flight mechanics team developed stability metrics as tools to better understand the causes of and better predict the onset of dynamic instability. These tools were built upon analytical models developed by Jaffe [3] and Murphy [2]. The tools were shown to both be very accurate in correlation with actual unstable cases and useful in developing stability margin policies based on the vehicle design and simulation considerations (e.g. sphere-cone angle change, mass change, wind turbulence). These tools allowed for the current EES design to demonstrate the ability to achieve passive stability and can be an invaluable tool for consideration in the design of parachute-less Earth-return vehicles.

Rohan Deshmukh↗

NASA NTRS2022

Snow Microphysical Retrieval from the NASA D3R Radar During ICE-POP 2018

A method is developed to use both polarimetric and dual-frequency radar measurements to retrieve microphysical properties of falling snow. It is applied to the Ku- and Ka-band measurements of the NASA dual-polarization, dual-frequency Doppler radar (D3R) obtained during the International Collaborative Experiments for PyeongChang 2018 Olympic and Paralympic winter games (ICE-POP 2018) field campaign and incorporates the Atmospheric Radiative Transfer Simulator (ARTS) microwave singles cattering property database for oriented particles. The retrieval uses optimal estimation to solve for several parameters that describe the particle size distribution (PSD), relative contribution of pristine, aggregate, and rimed ice species, and the orientation distribution along an entire radial simultaneously. Examination of Jacobian matrices and averaging kernels shows that the dual-wavelength ratio (DWR) measurements provide information regarding the characteristic particle size, and to a lesser extent, the rime fraction and shape parameter of the size distribution, whereas the polarimetric measurements provide information regarding the mass fraction of pristine particles and their characteristic size and orientation distribution. Thus, by combining the dual-frequency and polarimetric measurements, some ambiguities can be resolved that should allow a better determination of the PSD and bulk microphysical properties (e.g., snowfall rate) than can be retrieved from single-frequency polarimetric measurements or dual-frequency, single-polarization measurements. The D3R ICE-POP retrievals were validated using Precipitation Imaging Package (PIP) and Pluvio weighing gauge measurements taken nearby at the May Hills ground site. The PIP measures the snow PSD directly, and its measurements can be used to derived the snowfall rate (volumetric and water equivalent), mean volume-weighted particle size, and effective density, as well as particle aspect ratio and orientation. Four retrieval experiments were performed to evaluate the utility of different measurement combinations: Kuonly, DWR-only, Ku-pol, and All-obs. In terms of correlation, the volumetric snowfall rate (r D 0:95) and snow water equivalent rate (r D 0:92) were best retrieved by the Ku-pol method, while the DWR-only method had the lowest magnitude bias for these parameters (-31% and -8 %, respectively). The methods that incorporated DWR also had the best correlation to particle size (r D 0:74 and r D 0:71 for DWR-only and All-obs, respectively), although none of the methods retrieved density particularly well (r D 0:43 for Allobs). The ability of the measurements to retrieve mean aspect ratio was also inconclusive, although the polarimetric methods (Ku-pol and All-obs) had reduced biases and mean absolute error (MAE) relative to the Ku-only and DWR-only methods. The significant biases in particle size and snowfall rate appeared to be related to biases in the measured DWR, emphasizing the need for accurate DWR measurements and frequent calibration in future D3R deployments.

S Joseph Munchak↗

NASA NTRS1997

Comparative Soot Diagnostics: Preliminary Results

The motivation for the Comparative Soot Diagnostics (CSD) experiment lies in the broad practical importance of understanding combustion generated particulate. Depending upon the circumstances, particulate matter can affect the durability and performance of combustion equipment, can be a pollutant, can be used to detect fires and, in the form of soot, can be the dominant source of radiant energy from flames. The nonbuoyant structure of most flames of practical interest makes understanding of soot processes in low gravity flames important to our ability to predict fire behavior on earth. These studies also have direct applications to fire safety in human-crew spacecraft, since smoke is the indicator used for automated detection in current spacecraft. In the earliest missions (Mercury, Gemini and Apollo), the crew quarters were so cramped that it was considered reasonable that the astronauts would rapidly detect any fire. The Skylab module, however, included approximately 20 UV-sensing fire detectors. The Space Shuttle has 9 particle-ionization smoke detectors in the mid-deck and flight deck and Spacelab has six additional particle-ionization smoke detectors. The designated detectors for the ISS are laser-diode, forward-scattering, smoke or particulate detectors. Current plans for the ISS call for two detectors in the open area of the module, and detectors in racks that have both cooling air flow and electrical power. Due to the complete absence of data concerning the nature of particulate and radiant emission from incipient and fully developed low-g fires, all three of these detector systems were designed based upon l-g test data and experience. As planned mission durations and complexity increase and the volume of spacecraft increases, the need for and importance of effective, crew-independent, fire detection grows significantly. To provide this level of protection, more knowledge is needed concerning low-gravity fire phenomena and, in particular, how they might be detected and suppressed. Prior to CSD, no combustion-generated particulate samples had been collected near the flame zone for well-developed microgravity flames. All of the extant data either came from drop tower tests and therefore only corresponded to the early stages of a fire or were collected far from the flame zone. The fuel sources in the drop tower tests were restricted to laminar gas-jet diffusion flames and very rapidly overheated wire insulation. The gas-jet tests indicated, through thermophoretic sampling, (2) that soot primaries and aggregates (groups of primary particles) in low-gravity may be significantly larger than those in normal gravity (1-g). This raises new scientific questions about soot processes as well as practical issues for particulate size sensitivity and detection alarm threshold levels used in on-orbit smoke detectors. Preliminary tests in the 2.2 second drop tower suggest that particulate generated by overheated wire insulation may be larger in low-g than in 1-g. Transmission Electron Microscope (TEM) grids downstream of the fire region in the Wire Insulation Flammability experiment as well as visual observation of long string-like aggregates, further confirm this suggestion. The combined impact of these limited results and theoretical predictions is that, as opposed to extrapolation from l-g data, direct knowledge of low-g combustion particulate is needed for more confident design of smoke detectors for spacecraft. This paper describes the operation and preliminary results of the CSD, a project conceived and developed at NASA Lewis Research Center. The CSD flight experiment was conducted in the Middeck Glovebox Facility (MGBX) on USMP-3. The project is support by NASA Headquarters Microgravity Science and Applications Division and Code Q. The results presented here are from the microgravity portion of the experiment, including the temporal response of the detectors and average sizes of the primary and aggregate particles captured on the thermophoretic probes.

Urban, David L.↗

NASA NTRS2000

Applications of Fractal Analytical Techniques in the Estimation of Operational Scale

The observational scale and the resolution of remotely sensed imagery are essential considerations in the interpretation process. Many atmospheric, hydrologic, and other natural and human-influenced spatial phenomena are inherently scale dependent and are governed by different physical processes at different spatial domains. This spatial and operational heterogeneity constrains the ability to compare interpretations of phenomena and processes observed in higher spatial resolution imagery to similar interpretations obtained from lower resolution imagery. This is a particularly acute problem, since longterm global change investigations will require high spatial resolution Earth Observing System (EOS), Landsat 7, or commercial satellite data to be combined with lower resolution imagery from older sensors such as Landsat TM and MSS. Fractal analysis is a useful technique for identifying the effects of scale changes on remotely sensed imagery. The fractal dimension of an image is a non-integer value between two and three which indicates the degree of complexity in the texture and shapes depicted in the image. A true fractal surface exhibits self-similarity, a property of curves or surfaces where each part is indistinguishable from the whole, or where the form of the curve or surface is invariant with respect to scale. Theoretically, if the digital numbers of a remotely sensed image resemble an ideal fractal surface, then due to the self-similarity property, the fractal dimension of the image will not vary with scale and resolution, and the slope of the fractal dimension-resolution relationship would be zero. Most geographical phenomena, however, are not self-similar at all scales, but they can be modeled by a stochastic fractal in which the scaling properties of the image exhibit patterns that can be described by statistics such as area-perimeter ratios and autocovariances. Stochastic fractal sets relax the self-similarity assumption and measure many scales and resolutions to represent the varying form of a phenomenon as the pixel size is increased in a convolution process. We have observed that for images of homogeneous land covers, the fractal dimension varies linearly with changes in resolution or pixel size over the range of past, current, and planned space-borne sensors. This relationship differs significantly in images of agricultural, urban, and forest land covers, with urban areas retaining the same level of complexity, forested areas growing smoother, and agricultural areas growing more complex as small pixels are aggregated into larger, mixed pixels. Images of scenes having a mixture of land covers have fractal dimensions that exhibit a non-linear, complex relationship to pixel size. Measuring the fractal dimension of a difference image derived from two images of the same area obtained on different dates showed that the fractal dimension increased steadily, then exhibited a sharp decrease at increasing levels of pixel aggregation. This breakpoint of the fractal dimension/resolution plot is related to the spatial domain or operational scale of the phenomenon exhibiting the predominant visible difference between the two images (in this case, mountain snow cover). The degree to which an image departs from a theoretical ideal fractal surface provides clues as to how much information is altered or lost in the processes of rescaling and rectification. The measured fractal dimension of complex, composite land covers such as urban areas also provides a useful textural index that can assist image classification of complex scenes.

Emerson, Charles W.↗