Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “Random variables”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 307 records · Page 17

Extended Kalman Filter Performance on the Artemis-1 Mission

The Artemis Program is NASA’s campaign to explore the Moon and beyond. Artemis-1, the uncrewed exoLEO test flight of the Orion spacecraft, was completed in 2022. There were four navigation Extended Kalman Filters (EKFs) that are part of the Orion navigation system. The Atmospheric Extended Kalman Filter (ATMEKF) estimates the vehicle position, velocity, and attitude (referred to as the vehicle state) during the ascent and entry phases of flight. Once Orion is outside of Earths atmosphere, the Earth Orbit Extended Kalman Filter (EOEKF) and CisLunar Extended Kalman Filter (CLEKF) estimate the translational states, depending on the phase of flight, while the Attitude Extended Kalman Filter (ATTEKF) estimates the rotational state of the vehicle. The Kalman filters propagate the vehicle state forward in time using a combination of dynamics models and the output data from the Inertial Measurement Unit (IMU). The filters update the vehicle states and associated uncertainties, in the form of the covariance matrix, using pseudorange measurements from GPS (in ATMEKF/EOEKF), optical navigation measurements of the Earth or Moon (in CLEKF), and star tracker measurements (in ATTEKF). Simultaneously, the Kalman filters estimate error sources in the sensors, which are included in the state vectors as Exponentially Correlated Random Variables (ECRVs). This paper will summarize the performance of these filters during the Artemis-1 mission.

Artemis-1↗

Romie: A Domain-Independent Tool for Computer-Aided Robust Operations Management

Romie is a decision support tool based on AI's latest advances in the domain of robust scheduling. Unlike all its predecessors, the tool allows to (i) visually model the operational problem and context entirely (ii) optimize to find near-optimal schedules while taking uncertainty into account and deals with (iii) a combination of various {key performance indicators (KPIs). It comes with a web user interface. Part or all of the modelled activities may be associated to random variables describing their stochastic durations, in order to produce schedules that are robust w.r.t. temporal uncertainty. Hence, depending on the pursued KPIs, the schedules maximize a combination of the following terms: the probability of satisfying the problem constraints, the expected return/efficiency, the expected outcome quality, and even the operators' wellness by minimizing its expected extra-hours. Initially developed for spatial exploration and demonstration in the context of Mars analog missions, this versatile tool is here applied to operations management in both biotechnology manufacturing and robots parametrization in a cave exploration context.

Chien, Steve A.↗

Lila: Optimal Dispatching in Probabilistic Temporal Networks using Monte Carlo Tree Search

Executing a Probabilistic Simple Temporal Network (PSTN) amounts at scheduling, i.e. \textit{dispatch}, a set of events under time uncertainty. This constitutes a NP-hard online optimization problem. The right execution time must be dynamically assigned to each event of the PSTN such that the temporal constraints are met, whereas activity durations are progressively observed as the execution unfolds. We propose a dispatching algorithm based on Monte Carlo Tree Search, called Lila, with the following characteristics: (i) it is an anytime algorithm, both offline and online, proven asymptotically optimal; (ii) it returns the current probability of success, either before or at any moment during operations; (iii) it handles any possible continuous or discrete, even non-parametric, probability distributions, as well as inter-dependencies between random variables, exogenous and endogenous uncertainty; and (iv) can be easily extended to handle probabilistic external events, PSTNs with resources, PSTNs with cutoff times and precondition chains, etc. Lila is universal in the sense that it can handle any dispatching protocol, simply by specifying it to the algorithm. It has the unlimited flexibility offered by the simulation paradigm, whilst it asymptotically converges to optimal decisions and/or robustness approximations.

Chien, Steve A.↗

Higher-Order Statistical Moments of Predicted Sonic Boom Waveforms Through Turbulence

Sonic booms generated by supersonic aircraft are affected by turbulence in the atmospheric boundary layer through which they propagate. Turbulence effects lead to random variability of the sonic boom waveforms measured on the ground, complicating the prediction of such waveforms. As an initial effort to predict the waveform variability, the solution of the coherent or mean sonic boom waveform has previously been formulated by the author. The current paper extends the formulation to derive an expression of the second-order statistical moment necessary to calculate the variance of the spectral amplitudes. Since the derivation uses a full wave equation, results using the derived expression will be compared with those obtained using a parabolic approximation. In order to fully quantify the uncertainty of our predictions, the higher order statistical moments are also formulated and are shown to be approximately zero. Consequently, the probability density function (pdf) of the spectral amplitudes is predicted to be Gaussian. The formulation is further extended to determine the pdf of the loudness of sonic booms and quantify the uncertainties associated with the loudness prediction. Results from the formulation are compared with available flight test data.

sonic booms↗

Evaluation of Finite Impulse Response Filters for Turbulence Effects on Sonic Booms

Turbulence effects on sonic booms lead to random variability of sonic boom waveforms measured on the ground, complicating the prediction of such waveforms using sonic boom propagation codes that do not account for turbulence effects. The NASA PCBoom software is one such code shown to accurately predict sonic booms above the atmospheric boundary layer but not those on the ground. Analyses of measured sonic booms show that, on average, the turbulence effects result in sonic boom loudness reduction, on average, that increases with propagation distance and turbulence strength. To efficiently account for such effects, a signal processing-based approach has been developed at NASA using finite impulse response filters derived from predicted waveforms by solving a nonlinear parabolic equation. Analyses indicate that the mean loudness reduction obtained using the filters does not increase with propagation distance or with increasing turbulence strength, in disagreement with flight test data. An alternative approach to the filters is currently under development employing the multiple scattering theory (MST) of wave propagation. Available results from the physics-based MST approach are used to evaluate the predictive capability of the filters, suggesting that the filters can severely underestimate the prediction of the MST approach.

sonic booms↗

Evaluation of Finite Impulse Response Filters for Turbulence Effects on Sonic Booms

Turbulence effects on sonic booms lead to random variability of sonic boom waveforms measured on the ground, complicating the prediction of such waveforms using sonic boom propagation codes that do not account for turbulence effects. The NASA PCBoom software is one such code shown to accurately predict sonic booms above the atmospheric boundary layer but not those on the ground. Analyses of measured sonic booms show that, on average, the turbulence effects result in sonic boom loudness reduction, on average, that increases with propagation distance and turbulence strength. To efficiently account for such effects, a signal processing-based approach has been developed at NASA using finite impulse response filters derived from predicted waveforms by solving a nonlinear parabolic equation. Analyses indicate that the mean loudness reduction obtained using the filters does not increase with propagation distance or with increasing turbulence strength, in disagreement with flight test data. An alternative approach to the filters is currently under development employing the multiple scattering theory (MST) of wave propagation. Available results from the physics-based MST approach are used to evaluate the predictive capability of the filters, suggesting that the filters can severely underestimate the prediction of the MST approach.

sonic booms↗

The effect of material heterogeneity and random loading on the mechanics of fatigue crack growth

This paper reviews experimental work on the influence of variable amplitude or random loads on the mechanics and micromechanisms of fatigue crack growth. Implications are discussed in terms of the crack driving force, local plasticity, crack closure, crack blunting, and microstructure. Due to heterogeneity in the material's microstructure, the crack growth rate varies with crack tip position. Using the weakest link theory, an expression for crack growth rate is obtained as the expectation of a random variable. This expression is used to predict the crack growth rates for aluminum alloys, a titanium alloy, and a nickel steel in the mid-range region. It is observed, using the present theory, that the crack growth rate obeys the power law for small stress intensity factor range, and that the power is a function of a material constant.

Srivatsan, T. S.↗

Climatology, Natural Cycles, and Modes of Interannual Variability of the Great Plains Low-Level Jet as Assimilated by the GEOS-1 Data Analysis System

Despite the fact that the low-level jet of the southern Great Plains (the GPLLJ) of the U.S. is primarily a nocturnal phenomenon that virtually vanishes during the daylight hours, it is one of the most persistent and stable features of the low-level continental flow during the warm-season months, May through August. We have first used significant-level data to validate the skill of the GEOS-1 Data Assimilation System (DAS) in realistically detecting this jet and inferring its structure and evolution. We have then carried out a 15-year reanalysis with the GEOS-1 DAS to determine and validate its climatology and mean diurnal cycle and to study its interannual variability. Interannual variability of the GPLLJ is much smaller than mean diurnal and random intraseasonal variability and comparable in magnitude, but not location, to mean seasonal variability. There are three maxima of interannual low-level meridional flow variability of the GPLLJ over the upper Great Plains, southeastern Texas, and the western Gulf of Mexico. Cross-sectional profiles of mean southerly wind through the Texas maximum remain relatively stable and recognizable from year to year with only its eastward flank showing significant variability. This variability, however, exhibits a distinct, biennial oscillation during the first six years of the reanalysis period and only then. Each of the three variability maxima corresponds to a spatially coherent, jet-like pattern of low-level flow interannual variability. There are three prominent modes of interannual. variability. These include the intermittent biennial oscillation (IBO), local to the Texas maximum. Its signal is evident in surface pressure, surface temperature, ground wetness and upper air flow, as well. A larger-scale continental convergence pattern (CCP) of covariance, exhibiting strong anti-correlation between the flow near the Texas and the upper Great Plains variability maxima, is revealed only when the IBO is removed from the interannual time series. A third, subtropical mode of covariance is associated with the Gulf of Mexico variability maximum. Significant interannual anti-correlations of the southeasterly flow over the Arizona/New Mexico region with the CCP and the subtropical mode are enhanced when restricted to the month of July. These anti-correlations may relate to an observed out-of-phase precipitation relationship between the Great Plains and the southwestern U.S.. The typical duration of interannual low-level meridional wind anomalies within a given season increases over the continent with decreasing latitude from two to three weeks over the upper Great Plains to six to seven weeks over eastern Texas.

Helfand, H. M.↗

A Multivariate Randomization Text of Association Applied to Cognitive Test Results

Randomization tests provide a conceptually simple, distribution-free way to implement significance testing. We have applied this method to the problem of evaluating the significance of the association among a number (k) of variables. The randomization method was the random re-ordering of k-1 of the variables. The criterion variable was the value of the largest eigenvalue of the correlation matrix.

Ahumada, Albert↗

Probabilistic Structural Analysis of SSME Turbopump Blades: Probabilistic Geometry Effects

A probabilistic study was initiated to evaluate the precisions of the geometric and material properties tolerances on the structural response of turbopump blades. To complete this study, a number of important probabilistic variables were identified which are conceived to affect the structural response of the blade. In addition, a methodology was developed to statistically quantify the influence of these probabilistic variables in an optimized way. The identified variables include random geometric and material properties perturbations, different loadings and a probabilistic combination of these loadings. Influences of these probabilistic variables are planned to be quantified by evaluating the blade structural response. Studies of the geometric perturbations were conducted for a flat plate geometry as well as for a space shuttle main engine blade geometry using a special purpose code which uses the finite element approach. Analyses indicate that the variances of the perturbations about given mean values have significant influence on the response.

Nagpal, V. K.↗

Automatic variable selection in ecological niche modeling: A case study using Cassin’s Sparrow (Peucaea cassinii)

MERRA/Max provides a feature selection approach to dimensionality reduction that enables direct use of global climate model outputs in ecological niche modeling. The system accomplishes this reduction through a Monte Carlo optimization in which many independent MaxEnt runs, operating on a species occurrence file and a small set of randomly selected variables in a large collection of variables, converge on an estimate of the top contributing predictors in the larger collection. These top predictors can be viewed as potential candidates in the variable selection step of the ecological niche modeling process. MERRA/Max’s Monte Carlo algorithm operates on files stored in the underlying filesystem, making it scalable to large data sets. Its software components can run as parallel processes in a high-performance cloud computing environment to yield near real-time performance. In tests using Cassin’s Sparrow (Peucaea cassinii) as the target species, MERRA/Max selected a set of predictors from Worldclim’s Bioclim collection of 19 environmental variables that have been shown to be important determinants of the species’ bioclimatic niche. It also selected biologically and ecologically plausible predictors from a more diverse set of 86 environmental variables derived from NASA’s Modern-Era Retrospective Analysis for Research and Applications Version 2 (MERRA-2) reanalysis, an output product of the Goddard Earth Observing System Version 5 (GEOS-5) modeling system. We believe these results point to a technological approach that could expand the use global climate model outputs in ecological niche modeling, foster exploratory experimentation with otherwise difficult-to-use climate data sets, streamline the modeling process, and, eventually, enable automated bioclimatic modeling as a practical, readily accessible, low-cost, commercial cloud service.

John L. Schnase↗