Estimating the Probability of Electrical Short Circuits from Tin Whiskers
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Recent popular movies have raised public consciousness of the very real possibility of a comet or asteroid collision with the Earth.
NASA is developing a new capsule-based, crewed vehicle that will land in the ocean, and the space agency desires to reduce the risk of injury from impact during these landings. Because landing impact occurs for each flight and the crew might need to perform egress tasks, current injury assessment reference values (IARV) were deemed insufficient. Because NASCAR occupant restraint systems are more effective than the systems used to determine the current IARVs and are similar to NASA s proposed restraint system, an analysis of NASCAR impacts was performed to develop new IARVs that may be more relevant to NASA s context of vehicle landing operations. Head IARVs associated with race car impacts were investigated by completing a detailed analysis of all of the 2002-2008 NASCAR impact data. Specific inclusion and exclusion criteria were used to select 4071 impacts from the 4015 recorder files provided (each file could contain multiple impact events). Of the 4071 accepted impacts, 274 were selected for numerical simulation using a custom NASCAR restraint system and Humanetics Hybrid-III 50th percentile numerical dummy model in LS-DYNA. Injury had occurred in 32 of the 274 selected impacts, and 27 of those injuries involved the head. A majority of the head injuries were mild concussions with or without brief loss of consciousness. The 242 non-injury impacts were randomly selected and representative of the range of crash dynamics present in the total set of 4071 impacts. Head dynamics data (head translational acceleration, translational change in velocity, rotational acceleration, rotational velocity, HIC-15, HIC-36, and the Head 3ms clip) were filtered according to SAE J211 specifications and then transformed to a log scale. The probability of head injury was estimated using a separate logistic regression analysis for each log-transformed predictor candidate. Using the log transformation constrains the estimated probability of injury to become negligible as IARVs approach zero. For the parameters head translational acceleration, head translational velocity change, head rotational acceleration, HIC-15, and HIC-36, conservative values (in the lower 95% confidence interval) that gave rise to a 5% risk of any injury occurring were estimated as 40.0 G, 7.9 m/s, 2200 rad/s2, 98.4, and 77.4 respectively. Because NASA is interested in the consequence of any particular injury on the ability of the crew to perform egress tasks, the head injuries that occurred in the NASCAR dataset were classified according to a NASA-developed scale (Classes I - III) for operationally relevant injuries, which classifies injuries on the basis of their operational significance. Additional analysis of the data was performed to determine the probability of each injury class occurring, and this was estimated using an ordered probit model. For head translational acceleration, head translational velocity change, head rotational acceleration, head rotational velocity, HIC-36, and head 3ms clip, conservative values of IARVs that produced a 5% risk of Class II injury were estimated as 50.7 G, 9.5 m/s, 2863 rad/s2, 11.0 rad/s, 30.3, and 46.4 G respectively. The results indicate that head IARVs developed from the NASCAR dataset may be useful to protect crews during landing impact.
NASA uses environment models such as ORDEM96 to characterize the long-term orbital debris collision hazard for spacecraft in LEO. Occasionally, however, there are breakups of satellites or rocket bodies that create enhanced collision hazard for a period of time. This enhanced collision hazard can pose increased risks to space operations - especially those involving manned missions where the tolerance for risk is very low. NASA has developed SBRAM to simulate the enhanced debris environment in the days and weeks that follow such a breakup. This simulation provides the kind of risk probabilities that can be used by mission planners to consider if changes are warranted for the mission. Announcements of breakups come to NASA from US Space Command as soon as they are identified. The pre-breakup orbit and time of breakup are used to determine the initial conditions of the explosion. SBRAM uses the latest explosion models developed at NASA to simulate a debris cloud for the breakup. The model uses a Monte Carlo technique to create a random debris cloud from the probability distributions in the breakup model. Each piece of debris randomly created in the cloud is propagated in a deterministic manner to include the effects of drag and other orbital perturbations. The detailed geometry of each simulated close approach to the target spacecraft is noted and logged and the collision probability is computed using an estimated probability density in down-range and cross-range positions of both the target spacecraft and debris object. The collision probability is computed from the overlap of these probability densities for each close-approach geometry and summed over all computed conjunctions. Cloud propagation runs over the desired time interval are then repeated until the scale of the collision risk can be estimated to a desired precision. This paper presents an overview of the SBRAM model and a number of examples, both real and hypothetical, to demonstrate its use. In addition, a number of different examples are shown how the data can be used by decision makers on issues such as spacecraft orientation and timing of EVAs.
NASA is collaborating with private entities for the development of commercial space vehicles. The Space and Clinical Operations Division was tasked to review the oxygen and respiratory support system and recommend what capabilities, if any, the vehicle should have to support the return of an ill or injured crewmember. The Integrated Medical Model (IMM) was utilized as a data source for the development of these recommendations. The Integrated Medical Model (IMM) was used to simulate a six month, six crew, International Space Station (ISS) mission. Three medical system scenarios were considered based on the availability of (1) oxygen only, (2) oxygen and a ventilator, or (3) neither oxygen nor ventilator. The IMM analysis provided probability estimates of medical events that would require either oxygen or ventilator support. It also provided estimates of crew health, the probability of evacuation, and the probability of loss of crew life secondary to medical events for each of the three medical system scenarios. These IMM outputs were used as objective data to enable evidence‐based decisions regarding oxygen and respiratory support system requirements for commercial crew vehicles. The IMM provides data that may be utilized to support informed decisions regarding the development of medical systems for commercial crew vehicles.
A derivation is presented for proton fluence over the duration of the Mariner Venus-Mercury 1973 (MVM73) mission in terms of a relatively constant, low energy component, the solar wind, and a probabilistic high energy component from discrete solar events. An updated correlation of yearly energetic proton fluence with yearly average sunspot number is presented. This correlation and sunspot cycle forecasts for the period of the MVM73 mission (late 1973 through early 1975) form the basis for the high energy proton fluence estimates with various confidence levels. Uncertainties in the probability estimates and in calculation of the scaling with distance from the Sun are discussed. Selection of a particular 95-percentile model as the design constraint is recommended, and reasons are presented for not using the worst-case model. Interior fluences were calculated and expressed in terms useful for spacecraft design.
Maximum probability estimators and conservative confidence interval models for reliability growth problems with debugging phase
The problem of estimating the prior probabilities q sub k of a mixture of known density functions f sub k(X), based on a sequence of N statistically independent observations is considered. It is shown that for very mild restrictions on f sub k(X), the maximum likelihood estimate of Q is asymptotically efficient. A recursive algorithm for estimating Q is proposed, analyzed, and optimized. For the M = 2 case, it is possible for the recursive algorithm to achieve the same performance with the maximum likelihood one. For M 2, slightly inferior performance is the price for having a recursive algorithm. However, the loss is computable and tolerable.
Poisson and normal distribution used to estimate probability tropical cyclone induced winds
An extension of the method of Jaynes, whereby least biased probability estimates are obtained, permits such estimates to be made which account for experimental data on hand as well as prior and posterior knowledge. These estimates can be made for both discrete and continuous sample spaces. The method allows a simple interpretation of Laplace's two rules: the principle of insufficient reason and the rule of succession. Several examples are analyzed by way of illustration.
The NASA Conjunction Assessment Risk Analysis (CARA) team has recently implemented updated software to calculate the probability of collision (P (sub c)) for Earth-orbiting satellites. The algorithm can employ complex dynamical models for orbital motion, and account for the effects of non-linear trajectories as well as both position and velocity uncertainties. This “3D P (sub c)” method entails computing a 3-dimensional numerical integral for each estimated probability. Our analysis indicates that the 3D method provides several new insights over the traditional “2D P (sub c)” method, even when approximating the orbital motion using the relatively simple Keplerian two-body dynamical model. First, the formulation provides the means to estimate variations in the time derivative of the collision probability, or the probability rate, R (sub c). For close-proximity satellites, such as those orbiting in formations or clusters, R (sub c) variations can show multiple peaks that repeat or blend with one another, providing insight into the ongoing temporal distribution of risk. For single, isolated conjunctions, R (sub c) analysis provides the means to identify and bound the times of peak collision risk. Additionally, analysis of multiple actual archived conjunctions demonstrates that the commonly used “2D P (sub c)” approximation can occasionally provide inaccurate estimates. These include cases in which the 2D method yields negligibly small probabilities (e.g., P (sub c)) is greater than 10 (sup -10)), but the 3D estimates are sufficiently large to prompt increased monitoring or collision mitigation (e.g., P (sub c) is greater than or equal to 10 (sup -5)). Finally, the archive analysis indicates that a relatively efficient calculation can be used to identify which conjunctions will have negligibly small probabilities. This small-P (sub c) screening test can significantly speed the overall risk analysis computation for large numbers of conjunctions.
The results of sensitivity studies performed to estimate probable ranges for four key Space Station parameters using the Space Station Freedom's Model for Estimating Space Station Operations Cost (MESSOC) are discussed. The variables examined are grouped into five main categories: logistics, crew, design, space transportation system, and training. The modification of these variables implies programmatic decisions in areas such as orbital replacement unit (ORU) design, investment in repair capabilities, and crew operations policies. The model utilizes a wide range of algorithms and an extensive trial logistics data base to represent Space Station operations. The trial logistics data base consists largely of a collection of the ORUs that comprise the mature station, and their characteristics based on current engineering understanding of the Space Station. A nondimensional approach is used to examine the relative importance of variables on parameters.
A method for finding curves in digital images with speckle noise is described. The solution method differs from standard linear convolutions followed by thresholds in that it explicitly allows curvature in the features. Maximum a posteriori (MAP) estimation is used, together with statistical models for the speckle noise and for the curve-generation process, to find the most probable estimate of the feature, given the image data. The estimation process is first described in general terms. Then, incorporation of the specific neighborhood system and a multiplicative noise model for speckle allows derivation of the solution, using dynamic programming, of the estimation problem. The detection of curvilinear features is considered separately. The detection results allow the determination of the minimal size of detectable feature. Finally, the estimation of linear features, followed by a detection step, is shown for computer-simulated images and for a SAR image of sea ice.
Statistical-mechanical estimate of orbital collision probabilities
This global feasibility study assesses the potential of coarse-scale, gridded soil water estimates for the probabilistic modeling of hydrologically-triggered landslides, using Soil Moisture Ocean Salinity (SMOS), Soil Moisture Active Passive (SMAP) and Gravity Recovery and Climate Experiment (GRACE) remote sensing data, Catchment Land Surface Model (CLSM) simulations and six data products based on the assimilation of SMOS, SMAP, and/or GRACE observations into CLSM. SMOS or SMAP observations (~40-km resolution) are only available for less than 20% of the globally reported landslide events, because they are intermittent and uncertain in regions with complex terrain. GRACE terrestrial water storage estimates include 75% of the reported landslides but have coarse spatial and temporal resolutions (monthly, ~300-km). CLSM soil water simulations have the added advantage of complete spatial and temporal coverage, and are found to be able to distinguish between “stable slope” (no landslide) conditions and landslide-inducing conditions in a probabilistic way. Assimilating SMOS and/or GRACE data increases the landslide probability estimates based on soil water percentiles for the reported landslides, relative to model-only estimates at 36-km resolution for the period 2011-2016, unless the CLSM model-only soil water content is already high (≥ 50th percentile). The SMAP Level 4 data assimilation product (at 9-km resolution, period 2015-2019) more generally updates the soil water conditions towards higher landslide probabilities for the reported landslides, but is similar to model-only estimates for the majority of landslides where SMAP data cannot easily be converted to soil moisture owing to complex terrain.
Complex PRA is the best method and current gold standard, as it allows us to reflect changes (improvements) in individual spacecraft system risks over time. Yet, Bayesian methods – using simple inputs – allowed us to get estimates that are in line with high-complexity PRA. Here Bayesian estimation acts as a “gut check” on PRA (supposing a “reasonable” prior is used). Frequentist calculations can overestimate P(failure), especially when total number of trials are few (e.g., after Challenger). In general, Bayesian probability estimation can be used in any risk assessment situation to integrate what we think we know ahead of time with what we observe over time.
Introduction The Integrated Medical Model (IMM) is a decision support tool that is useful to space flight mission managers and medical system designers in assessing risks and optimizing medical systems. The IMM employs an evidence-based, probabilistic risk assessment (PRA) approach within the operational constraints of space flight. Methods Stochastic computational methods are used to forecast probability distributions of medical events, crew health metrics, medical resource utilization, and probability estimates of medical evacuation and loss of crew life. The IMM can also optimize medical kits within the constraints of mass and volume for specified missions. The IMM was used to forecast medical evacuation and loss of crew life probabilities, as well as crew health metrics for a near-earth asteroid (NEA) mission. An optimized medical kit for this mission was proposed based on the IMM simulation. Discussion The IMM can provide information to the space program regarding medical risks, including crew medical impairment, medical evacuation and loss of crew life. This information is valuable to mission managers and the space medicine community in assessing risk and developing mitigation strategies. Exploration missions such as NEA missions will have significant mass and volume constraints applied to the medical system. Appropriate allocation of medical resources will be critical to mission success. The IMM capability of optimizing medical systems based on specific crew and mission profiles will be advantageous to medical system designers. Conclusion The IMM is a decision support tool that can provide estimates of the impact of medical events on human space flight missions, such as crew impairment, evacuation, and loss of crew life. It can be used to support the development of mitigation strategies and to propose optimized medical systems for specified space flight missions. Learning Objectives The audience will learn how an evidence-based decision support tool can be used to help assess risk, develop mitigation strategies, and optimize medical systems for exploration space flight missions.
Currently, thermal sensors on satellites and other orbital platforms with high spatial resolution designed to monitor the oceans are often insufficient to assess the surface temperature of small bodies of water or within the coastal boundary layer. As the accuracy and sensitivity of remote sensing satellites improve, the demand for more accurate and up-to-date basic data sets for calibration increases. The quality of the thermal data collected by ECOSTRESS on the International Space Station allows the characterization of thermal stress levels in coastal ecosystems with a high spatial resolution of 70 m and a return time from hours to 5 days. This study focused on the calibration of ECOSTRESS estimates with in situ surface temperature data from sensors installed at 3 cm depth in the sediment on the intertidal muddy sandflats of three of the Rías Baixas in Galicia, NW Iberian Peninsula, from 2019 to 2021. A final number of 45 ECOSTRESS temperature images were analyzed. From these, 20% contained substantial georeferencing errors which had to be corrected manually with GIS software tools. We applied the Fourier's law of Heat Conduction to derive surface estimates from loggers sub-surface measurements that could be directly compared with ECOSTRESS data. Overall, a good calibration which explained more than 80% of ECOSTRESS temperature estimates for the whole dataset was obtained, but with an intrinsic cold bias around 1.39 °C. When temperatures at a depth of 3 cm were used, the linear fit became worse and the negative bias increased to 1.49 °C. Closer inspection revealed that night measurements were responsible for this larger deviation, as ECOSTRESS estimates became much colder compared to within sediment measurements because of the combined effect of the instrument intrinsic bias and nocturnal surface cooling. The best calibration was obtained when surface estimates were calculated just for the nighttime, as the cold bias decreased to 0.93 °C. More importantly, during hot daytime conditions in emersion above 20 °C, ECOSTRESS data matched surface temperature estimates, probably because of a better performance of ECOSTRESS algorithm at dry surfaces with lower emissivity. Thus, during the most ecologically relevant periods when high temperatures could drive thermal stress in many commercially-important bivalve species, ECOSTRESS provides accurate surface estimates that can be used to derive sub surface temperatures at the depths at which the different burrowing organisms live. We thus conclude that this instrument constitutes an important global tool to examine thermal stress at an unprecedented spatial scale for complex sea-land boundary systems.