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NASA NTRS1985

The effect of sensor and actuator errors on static shape control for large space structures

An analytical study was performed to predict and assess the effect of actuator and sensor errors on the performance of a shape control procedure for flexible space structures using applied temperatures. Approximate formulas were derived for the expected value and variance of the rms distortion ratio (ratio of rms distortions with and without corrections) based on the assumption of zero-mean normally distributed random errors in measured distortions and actuator output temperatures. Studies were carried out for a 55-meter radiometer antenna reflector distorted from its ideal parabolic shape by nonuniform orbital heating. The first study consisted of varying the sensor and actuator errors for the case of 12 actuators and computing the distortion ratio. In the second study, sensor and actuator errors were prescribed and the effect of increasing the number of actuators was evaluated.

Haftka, R. T.↗

NASA NTRS1987

Effect of sensor and actuator errors on static shape control for large space structures

Haftka, Raphael T.↗

NASA NTRS1993

Sampling errors in rainfall estimates by multiple satellites

This paper examines the sampling characteristics of combining data collected by several low-orbiting satellites attempting to estimate the space-time average of rain rates. The several satellites can have different orbital and swath-width parameters. The satellite overpasses are allowed to make partial coverage snapshots of the grid box with each overpass. Such partial visits are considered in an approximate way, letting each intersection area fraction of the grid box by a particular satellite swath be a random variable with mean and variance parameters computed from exact orbit calculations. The derivation procedure is based upon the spectral minimum mean-square error formalism introduced by North and Nakamoto. By using a simple parametric form for the spacetime spectral density, simple formulas are derived for a large number of examples, including the combination of the Tropical Rainfall Measuring Mission with an operational sun-synchronous orbiter. The approximations and results are discussed and directions for future research are summarized.

North, Gerald R.↗

NASA NTRSDate not supplied

Assessing Risk Due to Small Sample Size in Probability of Detection Analysis Using Tolerance Intervals

Small sample size (e.g.6-30) poses risk in results of probability of detection (POD) analysis using tolerance intervals. This method is also called as the limited sample or LS POD. The analysis is performed either during NDE procedure qualification or for assessment of reliability of an NDE procedure. The risk is primarily due to sampling error. Smaller samples are not likely to be random to the population or representative of the population. The small samples are likely to be biased. Biased samples have smaller standard deviation compared to the population. POD analysis with small biased sample can lead to overestimation of POD. Many sampling schemes are available in statistics to mitigate sampling risk. Primary objective of POD analysis is to determine a decision threshold from signal response measurements of a sample such that it is less than or equal to population decision threshold for 90% POD. Sampling error implies that this NDE reliability condition is violated. One of sampling types is called a representative sample. Representative samples reduce variance in POD estimates but also reduce magnitude of the error. Sampling sensitivity analysis for some sampling types is performed here using repetitive random sampling or Monte Carlo method. Six sampling types are considered for comparison. Some of the sampling types are similar to drawing a representative sample. LS POD model assumes random sampling. Therefore, random sampling is used as a basis for comparison with each sampling type. The sampling types used in the analysis are, A. Nominal and worst-case sampling, B. Worst-case sampling, C. Nominal case sampling, D. Random sampling, E. Random target, and sub-target sampling. F. Nominal target and sub-target sampling. Results of Monte Carlo simulation indicate that type F sampling can mitigate sampling risk and is also more practical to implement. Type A sampling may also mitigate the sampling risk, but it may be less practical to implement.

Ajay M Koshti↗

NASA NTRSDate not supplied

Use of three-cornered hat error estimates in MERRA-2 to guide an improved reanalysis-Part 1

The three-cornered hat (3CH) method estimates the uncertainties of three different co-located model or observational data sets (Anthes and Rieckh, 2018; Sjoberg et al., 2021). Rieckh et al. (2021) used the 3CH method to compare the random error statistics of different global forecast and reanalysis models, as well as radio occultation (RO) and radiosonde observations. That study showed that the MERRA-2 reanalysis, while having smaller errors in the stratosphere than its predecessor MERRA, had larger errors in the troposphere than many of the other data sets analyzed. The MERRA-2 errors were particularly large in the tropics. In a collaborative effort between UCAR’s COSMIC (Constellation Observing System for Meteorology, Ionosphere and Meteorology) program and NASA’s Global Modeling and Assimilation Office (GMAO), we carried out further 3CH error diagnostics to help isolate the causes of these larger errors and help guide the development of an improved reanalysis. This presentation summarizes random error statistics associated with MERRA-2, ECMWF’s ERA5 reanalysis, and COSMIC-2 (C2) RO observations. We compute 3CH error variance estimates of refractivity, as well as temperature and specific humidity using UCAR’s COSMIC Data Analysis and Archive Center (CDAAC) improved 1D-variational (1D-Var) retrieval (wetPf2) over 15 latitude bands from 45S to 45N. The 1D-Var retrievals of specific humidity and temperature for C2 use NCEP’s Global Forecast System (GFS) as the background. Anthes et al. (2021) showed that it gives accurate estimates of temperature and specific humidity in the tropics and subtropics, even in the challenging environment of intense Hurricane Dorian (2019). This presentation confirms the previous results that MERRA-2 has significantly larger errors in the tropics and subtropics than either C2 or ERA5. Its errors are larger between 30S and 30N compared to 30-45 N-S latitudes, and are also larger over land compared to oceans. Most of the MERRA-2 refractivity errors come from specific humidity, except over land below 3 km where temperature errors are large. These results suggest that moist convection and atmospheric boundary layer physics in MERRA-2 may be responsible for a significant part of the higher uncertainties. These results are being used to guide GMAO in developing an improved next-generation reanalysis, as shown in a companion presentation submitted to this conference (El Akkraoui et al., 2021), which extends this study and describes improvements to MERRA-2 leading to the next GMAO reanalysis.

Jeremiah Sjoberg↗

NASA NTRS1994

Non-sea-salt sulfate and methanesulfonate at American Samoa

High-volume bulk aerosol samples have been collected at American Samoa (14.25 deg S, 170.58 deg W) on a semicontinuous basis since the system was erected as part of the Sea/Air Exchange Program (SEAREX) in March 1983. In this report we consider those samples collected through May 6, 1992. For most of this period the sample filters were changed once a week. However, during November 1989 and from May 10 to June 10, 1990, in conjunction with the aircraft missions of the NASA Global Backscatter Experiment (GLOBE), the filters were changed daily. All of the samples were analyzed for nonsea-salt (nss) SO4(2-) and NO3(-). Analyses for methanesulfonate (MSA) include all of the 53 daily samples, 22 weekly samples from March 19, 1983, through April 12, 1984, and 96 weekly samples from January 3, 1990, through May 6, 1992. The mean concentrations (in micrograms per cubic meter) were 0.37 for nss SO4(2-), 0.0229 for MSA, 0.114 for NO3(-), and 5.1 for Na(+). Nss SO4(2-) and MSA are strongly linearly correlated in these 171 samples (r(exp 2) = 0.66) and the regression intercept does not differ significantly from zero. The geometric mean (GM) nss SO4(2-)/MSA ratio, 18.1 +/- 0.9 (where +/- indicates the 95% confidence interval of the GM) is about 7% higher than had previously been reported for this station. The ratio exhibits no significant seasonal variation. Although the ratio appeared to be significantly lower in the May - June 1990 daily samples (GM = 15.3 +/- 1.2), a further examination of the results indicated that the variance of the measured ratios from 18.1 (the GM for the whole data set) was attributable almost exclusively to the typical random errors in the analyses as determined from the 1 sigma analytical uncertainties of 5% for MSA and SO4(2-) and 2% for Na(+).

Savoie, Dennis L.↗

NASA NTRS2016

Estimating Model Prediction Error: Should You Treat Predictions as Fixed or Random?

Crop models are important tools for impact assessment of climate change, as well as for exploring management options under current climate. It is essential to evaluate the uncertainty associated with predictions of these models. We compare two criteria of prediction error; MSEP fixed, which evaluates mean squared error of prediction for a model with fixed structure, parameters and inputs, and MSEP uncertain( X), which evaluates mean squared error averaged over the distributions of model structure, inputs and parameters. Comparison of model outputs with data can be used to estimate the former. The latter has a squared bias term, which can be estimated using hindcasts, and a model variance term, which can be estimated from a simulation experiment. The separate contributions to MSEP uncertain (X) can be estimated using a random effects ANOVA. It is argued that MSEP uncertain (X) is the more informative uncertainty criterion, because it is specific to each prediction situation.

model structure uncertainty↗

NASA NTRS2006

Estimating Random Errors Due to Shot Noise in Backscatter Lidar Observations

In this paper, we discuss the estimation of random errors due to shot noise in backscatter lidar observations that use either photomultiplier tube (PMT) or avalanche photodiode (APD) detectors. The statistical characteristics of photodetection are reviewed, and photon count distributions of solar background signals and laser backscatter signals are examined using airborne lidar observations at 532 nm using a photon-counting mode APD. Both distributions appear to be Poisson, indicating that the arrival at the photodetector of photons for these signals is a Poisson stochastic process. For Poisson-distributed signals, a proportional, one-to-one relationship is known to exist between the mean of a distribution and its variance. Although the multiplied photocurrent no longer follows a strict Poisson distribution in analog-mode APD and PMT detectors, the proportionality still exists between the mean and the variance of the multiplied photocurrent. We make use of this relationship by introducing the noise scale factor (NSF), which quantifies the constant of proportionality that exists between the root-mean-square of the random noise in a measurement and the square root of the mean signal. Using the NSF to estimate random errors in lidar measurements due to shot noise provides a significant advantage over the conventional error estimation techniques, in that with the NSF uncertainties can be reliably calculated from/for a single data sample. Methods for evaluating the NSF are presented. Algorithms to compute the NSF are developed for the Cloud-Aerosol Lidar and Infrared Pathfinder Satellite Observations (CALIPSO) lidar and tested using data from the Lidar In-space Technology Experiment (LITE). OCIS Codes:

Liu, Zhaoyan↗

NASA NTRS1984

Light Scattered from Polished Optical Surfaces: Wings of the Point Spread Function

Random figure errors from the polishing process plus particles on the main mirrors in a telescope cause an extended point spread function (PSF) declining approximately as the inverse square of the sine of the angle from a star from about 100 micro-rad to a right angle. The decline in at least one case, and probably in general, proceeds as the inverse cube at smaller angles where the usual focal plane aperture radius is chosen. The photometric error due to misalignment by one Airy ring spacing with an aperture of n rings depends on the net variance in the figure. It is approximately 60/(n+1)(3) when using the data of Kormendy (1973). A typical value is 6 x 10 to the -5th power per ring of misalignment with n = 100 rings. The encircled power may be modulated on a time scale of hours by parts per thousand in a wavelength dependent manner due to relative humidity effects on mirror dust. The scattering according to an inverse power law is due to a random walk in aberration height caused by a multitude of facets and slope errors left by the polishing process. A deviation from such a law at grazing emergence may permit monitoring the dust effects.

Kenknight, C. E.↗

NASA NTRS1965

On a priori statistics in minimum-variance estimation problems.

Errors in a priori statistics in minimum variance estimation of regression parameters and effects on a posteriori estimates

REGRESSION ANALYSIS↗

DOE OSTI2023

Evaluating the Interplay between Trajectory Segmentation and Mode Inference Error

Travel behavior changes are essential to transportation decarbonization. Travel diaries, consisting of sequences of trips between places, are typically used to instrument human travel behavior. However, these diaries are only as accurate as the underlying methods used to construct them. Travel diary algorithms have been a popular research topic since the advent of Global Positioning System tracking surveys. These algorithms have typically been validated using prompted recall of presegmented trips, thus disregarding the continuity of mode inference. Phone operating systems have adopted battery-conserving techniques, but the resulting data collection errors have not been studied extensively. We introduce a framework to evaluate the accuracy of trip length computations and mode inference by analyzing continuous mode-segmented trajectories for groups of trips. We then use the framework to identify the input data quality and the impact of postprocessing. Our primary inputs to this evaluation are MobilityNet, a public dataset containing information from three artificial timelines covering 15 different travel modes, and sample open-source travel diary creation algorithms from the OpenPATH project. Our framework concretely shows that the variance of the distance error drops from (0.217, 0.0848) to (o.011, 0.0407) (Android, iOS) after postprocessing. Similarly, the weighted F-scores for mode inference increase from (0.25, 0.29) to (0.60, 0.74) (iOS, Android) between random forest and geographic information system-based models. We hope that this standardized method will be adapted to evaluate other, potentially proprietary, travel diary algorithms. Finally, the results can be used to understand and improve the state of the art in the travel diary creation field.

33 ADVANCED PROPULSION SYSTEMS↗

NASA NTRS1972

Variance reduction in Monte Carlo analysis of rarefied gas diffusion

The present analysis uses the Monte Carlo method to solve the problem of rarefied diffusion between parallel walls. The diffusing molecules are evaporated or emitted from one of two parallel walls and diffused through another molecular species. The analysis treats the diffusing molecule as undergoing a Markov random walk and the local macroscopic properties are found as the expected value of the random variable, the random walk payoff. By biasing the transition probabilities and changing the collision payoffs the expected Markov walk payoff is retained but its variance is reduced so that the M. C. result has a much smaller error.

Perlmutter, M.↗

NASA NTRS1972

Variance reduction in Monte Carlo analysis of rarefied gas diffusion.

The problem of rarefied diffusion between parallel walls is solved using the Monte Carlo method. The diffusing molecules are evaporated or emitted from one of the two parallel walls and diffuse through another molecular species. The Monte Carlo analysis treats the diffusing molecule as undergoing a Markov random walk, and the local macroscopic properties are found as the expected value of the random variable, the random walk payoff. By biasing the transition probabilities and changing the collision payoffs, the expected Markov walk payoff is retained but its variance is reduced so that the Monte Carlo result has a much smaller error.

Perlmutter, M.↗

NASA NTRS1981

Dynamical predictability of monthly means

The concept of predictability which is conditioned by synoptic-scale disturbance instabilities is extended to that of time averages, which are determined by low-frequency planetary wave predictability, in an attempt to determine the theoretical upper limit of dynamical predictability of monthly means for prescribed, nonfluctuating external forcings. Sixty-day integrations of a global general circulation model with nine different initial conditions but identical boundary conditions of sea surface temperatures, snow, sea ice and soil moisture are carried out, where the rms vector wind error between the observed initial conditions is greater than 15 m/sec. It is found that while the variances among the first 30-day means, predicted from mostly different initial conditions, are significantly different from the variances due to random perturbations in the initial conditions, variances for days 31-60 are not so distinguishable. These results suggest that the evolution of long waves remains predictable for between one month and 45 days.

Shukla, J.↗

NASA NTRS2013

Comparison of Force and Moment Coefficients for the Same Test Article in Multiple Wind Tunnels

This paper compares the results of force and moment measurements made on the same test article and with the same balance in three transonic wind tunnels. Comparisons are made for the same combination of Reynolds number, Mach number, sideslip angle, control surface configuration, and angle of attack range. Between-tunnel force and moment differences are quantified. An analysis of variance was performed at four unique sites in the design space to assess the statistical significance of between-tunnel variation and any interaction with angle of attack. Tunnel to tunnel differences too large to attribute to random error were detected were observed for all forces and moments. In some cases these differences were independent of angle of attack and in other cases they changed with angle of attack.

Deloach, Richard↗

NASA NTRS1976

Large Area Crop Inventory Experiment (LACIE). Phase 1: Evaluation report

It appears that the Large Area Crop Inventory Experiment over the Great Plains, can with a reasonable expectation, be a satisfactory component of a 90/90 production estimator. The area estimator produced more accurate area estimates for the total winter wheat region than for the mixed spring and winter wheat region of the northern Great Plains. The accuracy does appear to degrade somewhat in regions of marginal agriculture where there are small fields and abundant confusion crops. However, it would appear that these regions tend also to be marginal with respect to wheat production and thus increased area estimation errors do not greatly influence the overall production estimation accuracy in the United States. The loss of segments resulting from cloud cover appears to be a random phenomenon that introduces no significant bias into the estimates. This loss does increase the variance of the estimates.

Source record↗

NASA NTRS1978

Rain-rate estimates for an attenuating radar

An iterative method has been used to produce rain-rate estimates for an attenuating frequency radar. An infinite number of higher-order estimates are shown to converge in the limit to the Hitschfeld-Bordan solution under certain conditions. An error analysis was performed by a model accounting for the randomness of the radar return power, the k-Z, Z-R relations, and offsets in the radar calibration constant. Since the behavior of the estimates strongly depends on system errors, the choice of the best estimate requires a knowledge of the variance and range of offsets in meteorological data and the calibration constant. As the errors increase, the use of the lower orders avoids significant overpredictions. In order to obtain reliable rain-rate predictions in the presence of realistic errors, an antenna pointing angles away from the horizontal at frequencies in the lower end of the X-band may be used. Such antenna configurations insure low attenuation.

Meneghini, R.↗

NASA NTRSDate not supplied

Comparison Study of Machine Learning Techniques to Predict Flight Energy Consumption for Advanced Air Mobility

This paper addresses the need to predict the flight energy consumption of aerial vehicles in the presence of wind using machine learning techniques. The presented work is critical to achieving sustainable and efficient operations for Advanced Air Mobility (AAM) and to evaluating the readiness of the ground-supporting energy infrastructure, e.g., electric grid and AAM portals. The flight energy consumption is described using the "energy per meter" (EPM) metric. We present a comparison study of influential machine learning techniques in predicting EPM using real-world flight test data. We presented new results of using the Decision Tree, Random Forest, and linear regression techniques, along with our previous results using the Recurrent Neural Network and Feed Forward Neural Network techniques. The comparison results show that the Linear Regression method outperforms other methods on the basis of the Mean Squared Error and error variance.

Machine Learning↗