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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.

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At least 397 records · Page 22
All sourcesNASA NTRSDOE OSTI
NASA NTRS1986

On the design of classifiers for crop inventories

Crop proportion estimators that use classifications of satellite data to correct, in an additive way, a given estimate acquired from ground observations are discussed. A linear version of these estimators is optimal, in terms of minimum variance, when the regression of the ground observations onto the satellite observations in linear. When this regression is not linear, but the reverse regression (satellite observations onto ground observations) is linear, the estimator is suboptimal but still has certain appealing variance properties. In this paper expressions are derived for those regressions which relate the intercepts and slopes to conditional classification probabilities. These expressions are then used to discuss the question of classifier designs that can lead to low-variance crop proportion estimates. Variance expressions for these estimates in terms of classifier omission and commission errors are also derived.

Heydorn, R. P.↗
NASA NTRS1987

Propulsion estimation techniques

A brief overview of statistical tools needed to perform post flight/test reconstruction of state variables is given. Linear regression, recursive linear regression, and the exact connection between the Kalman filter and linear regression are discussed. The regression connection is expected to serve as an aid in the application of a recently developed analytical method of flight reconstruction to single engine test firing data.

Temple, Enoch C.↗
NASA NTRS1992

Correlation and prediction of dynamic human isolated joint strength from lean body mass

A relationship between a person's lean body mass and the amount of maximum torque that can be produced with each isolated joint of the upper extremity was investigated. The maximum dynamic isolated joint torque (upper extremity) on 14 subjects was collected using a dynamometer multi-joint testing unit. These data were reduced to a table of coefficients of second degree polynomials, computed using a least squares regression method. All the coefficients were then organized into look-up tables, a compact and convenient storage/retrieval mechanism for the data set. Data from each joint, direction and velocity, were normalized with respect to that joint's average and merged into files (one for each curve for a particular joint). Regression was performed on each one of these files to derive a table of normalized population curve coefficients for each joint axis, direction, and velocity. In addition, a regression table which included all upper extremity joints was built which related average torque to lean body mass for an individual. These two tables are the basis of the regression model which allows the prediction of dynamic isolated joint torques from an individual's lean body mass.

Pandya, Abhilash K.↗
NASA NTRS1990

The use of remotely sensed surface temperature and a spectral vegetation index for evaluating heat fluxes over the Konza Prairie

The relationship between surface temperature T(s) and the normalized difference vegetation index (NDVI) is examined to determine whether it can be used to characterize latent heat fluxes (LEs). The regression of T(s) on NDVI is studied in the context of surface heat fluxes over the prairie with a limited data set for four flux-measurement sites. The 17 flux-measurement stations at the sites provided data that are consistently significant at the 99-percent confidence level for the regression of T(s) on NDVI. Variations in the regression slopes are found to correlate with variations in the ground heat flux but not with LE. Important components of the regression of T(s) on NDVI include fractional vegetation cover and surface-soil moisture conditions. The relationship is important for determining the relative contributions of the soil and vegetation components of an area's total evaporative flux.

Hope, A. S.↗
NASA NTRS1993

Effect of Malmquist bias on correlation studies with IRAS data base

The relationships between galaxy properties in the sample of Trinchieri et al. (1989) are reexamined with corrections for Malmquist bias. The linear correlations are tested and linear regressions are fit for log-log plots of L(FIR), L(H-alpha), and L(B) as well as ratios of these quantities. The linear correlations for Malmquist bias are corrected using the method of Verter (1988), in which each galaxy observation is weighted by the inverse of its sampling volume. The linear regressions are corrected for Malmquist bias by a new method invented here in which each galaxy observation is weighted by its sampling volume. The results of correlation and regressions among the sample are significantly changed in the anticipated sense that the corrected correlation confidences are lower and the corrected slopes of the linear regressions are lower. The elimination of Malmquist bias eliminates the nonlinear rise in luminosity that has caused some authors to hypothesize additional components of FIR emission.

Verter, Frances↗
NASA NTRS1992

A new model for estimating total body water from bioelectrical resistance

Estimation of total body water (T) from bioelectrical resistance (R) is commonly done by stepwise regression models with height squared over R, H(exp 2)/R, age, sex, and weight (W). Polynomials of H(exp 2)/R have not been included in these models. We examined the validity of a model with third order polynomials and W. Methods: T was measured with oxygen-18 labled water in 27 subjects. R at 50 kHz was obtained from electrodes placed on the hand and foot while subjects were in the supine position. A stepwise regression equation was developed with 13 subjects (age 31.5 plus or minus 6.2 years, T 38.2 plus or minus 6.6 L, W 65.2 plus or minus 12.0 kg). Correlations, standard error of estimates and mean differences were computed between T and estimated T's from the new (N) model and other models. Evaluations were completed with the remaining 14 subjects (age 32.4 plus or minus 6.3 years, T 40.3 plus or minus 8 L, W 70.2 plus or minus 12.3 kg) and two of its subgroups (high and low) Results: A regression equation was developed from the model. The only significant mean difference was between T and one of the earlier models. Conclusion: Third order polynomials in regression models may increase the accuracy of estimating total body water. Evaluating the model with a larger population is needed.

Siconolfi, S. F.↗
NASA NTRS1995

A diagnostic analysis of the VVP single-doppler retrieval technique

A diagnostic analysis of the VVP (volume velocity processing) retrieval method is presented, with emphasis on understanding the technique as a linear, multivariate regression. Similarities and differences to the velocity-azimuth display and extended velocity-azimuth display retrieval techniques are discussed, using this framework. Conventional regression diagnostics are then employed to quantitatively determine situations in which the VVP technique is likely to fail. An algorithm for preparation and analysis of a robust VVP retrieval is developed and applied to synthetic and actual datasets with high temporal and spatial resolution. A fundamental (but quantifiable) limitation to some forms of VVP analysis is inadequate sampling dispersion in the n space of the multivariate regression, manifest as a collinearity between the basis functions of some fitted parameters. Such collinearity may be present either in the definition of these basis functions or in their realization in a given sampling configuration. This nonorthogonality may cause numerical instability, variance inflation (decrease in robustness), and increased sensitivity to bias from neglected wind components. It is shown that these effects prevent the application of VVP to small azimuthal sectors of data. The behavior of the VVP regression is further diagnosed over a wide range of sampling constraints, and reasonable sector limits are established.

Boccippio, Dennis J.↗
NASA NTRS1995

Hybrid fuel formulation and technology development

The objective was to develop an improved hybrid fuel with higher regression rate, a regression rate expression exponent close to 0.5, lower cost, and higher density. The approach was to formulate candidate fuels based on promising concepts, perform thermomechanical analyses to select the most promising candidates, develop laboratory processes to fabricate fuel grains as needed, fabricate fuel grains and test in a small lab-scale motor, select the best candidate, and then scale up and validate performance in a 2500 lbf scale, 11-inch diameter motor. The characteristics of a high performance fuel have been verified in 11-inch motor testing. The advanced fuel exhibits a 15% increase in density over an all hydrocarbon formulation accompanied by a 50% increase in regression rate, which when multiplied by the increase in density yields a 70% increase in fuel mass flow rate; has a significantly lower oxidizer-to-fuel (O/F) ratio requirement at 1.5; has a significantly decreased axial regression rate variation making for more uniform propellant flow throughout motor operation; is very clean burning; extinguishes cleanly and quickly; and burns with a high combustion efficiency.

Dean, D. L.↗
NASA NTRS1995

Combustion of solid fuel slabs with gaseous oxygen in a hybrid motor analog

Using a high-pressure, two-dimensional hybrid motor, an experimental investigation was conducted on fundamental processes involved in hybrid rocket combustion. HTPB (Hydroxyl-terminated- Polybutadiene) fuel cross linked with diisocyanate was burned with GOX under various operating conditions. Large amplitude pressure oscillations were encountered in earlier test runs. After identifying the source of instability and decoupling the GOX feed line system and combustion chamber, the pressure oscillations were drastically reduced from +/- 20% of the localized mean pressure to an acceptable range of +/- 1.5%. Embedded fine-wire thermocouples indicated that the surface temperature of the burning fuel was around 1000 K depending upon axial locations and operating conditions. Also, except near the leading-edge region, the subsurface thermal wave profiles in the upstream locations arc thicker than those in the downstream locations since the solid-fuel regression rate, in general, increases with distance along the fuel slab. The recovered solid fuel slabs in the laminar portion of the boundary layer exhibited smooth surfaces, indicating the existence of a liquid melt layer on the burning fuel surface in the upstream region. After the transition section, which displayed distinct transverse striations, the surface roughness pattern became quite random and very pronounced in the downstream turbulent boundary-layer region. Both real time X-ray radiography and ultrasonic pulse-echo techniques were used to determine the instantaneous web thicknesses and instantaneous solid-fuel regression rates over certain portions of the fuel slabs. Globally averaged and axially dependent but time-averaged regression rates were also obtained and presented. Several tests were conducted using, simultaneously, one translucent fuel slab and one fuel slab processed with carbon black powder. The addition of carbon black did not affect the measured regression rates or surface temperatures in comparison to the translucent fuel slabs.

Chiaverini, Martin J.↗
NASA NTRS1996

Combustion Processes in Hybrid Rocket Engines

In recent years, there has been a resurgence of interest in the development of hybrid rocket engines for advanced launch vehicle applications. Hybrid propulsion systems use a solid fuel such as hydroxyl-terminated polybutadiene (HTPB) along with a gaseous/liquid oxidizer. The performance of hybrid combustors depends on the convective and radiative heat fluxes to the fuel surface, the rate of pyrolysis in the solid phase, and the turbulent combustion processes in the gaseous phases. These processes in combination specify the regression rates of the fuel surface and thereby the utilization efficiency of the fuel. In this paper, we employ computational fluid dynamics (CFD) techniques in order to gain a quantitative understanding of the physical trends in hybrid rocket combustors. The computational modeling is tailored to ongoing experiments at Penn State that employ a two dimensional slab burner configuration. The coordinated computational/experimental effort enables model validation while providing an understanding of the experimental observations. Computations to date have included the full length geometry with and with the aft nozzle section as well as shorter length domains for extensive parametric characterization. HTPB is sed as the fuel with 1,3 butadiene being taken as the gaseous product of the pyrolysis. Pure gaseous oxygen is taken as the oxidizer. The fuel regression rate is specified using an Arrhenius rate reaction, which the fuel surface temperature is given by an energy balance involving gas-phase convection and radiation as well as thermal conduction in the solid-phase. For the gas-phase combustion, a two step global reaction is used. The standard kappa - epsilon model is used for turbulence closure. Radiation is presently treated using a simple diffusion approximation which is valid for large optical path lengths, representative of radiation from soot particles. Computational results are obtained to determine the trends in the fuel burning or regression rates as a function of the head-end oxidizer mass flux, G=rho(e)U(e), and the chamber pressure. Furthermore, computation of the full slab burner configuration has also been obtained for various stages of the burn. Comparisons with available experimental data from small scale tests conducted by General Dynamics-Thiokol-Rocketdyne suggest reasonable agreement in the predicted regression rates. Future work will include: (1) a model for soot generation in the flame for more quantitative radiative transfer modelling, (2) a parametric study of combustion efficiency, and (3) transient calculations to help determine the possible mechanisms responsible for combustion instability in hybrid rocket motors.

Venkateswaran,S.↗
NASA NTRS1995

Combustion of solid fuel slabs with gaseous oxygen in a hybrid motor analog

Using a high-pressure, two-dimensional hybrid motor, an experimental investigation was conducted on fundamental processes involved in hybrid rocket combustion. HTPB (Hydroxyl-terminated Polybutadiene) fuel cross-linked with diisocyanate was burned with gaseous oxygen (GOX) under various operating conditions. Large-amplitude pressure oscillations were encountered in earlier test runs. After identifying the source of instability and decoupling the GOX feed-line system and combustion chamber, the pressure oscillations were drastically reduced from plus or minus 20% of the localized mean pressure to an acceptable range of plus or minus 1.5%. Embedded fine--wire thermocouples indicated that the surface temperature of the burning fuel was around 1000 K depending upon axial locations and operating conditions. Also, except near the leading edge region, the subsurface thermal wave profiles in the upstream locations are thicker than those in the downstream locations since the solid-fuel regression rate, in general, increases with distance along the fuel slab. The recovered solid fuel slabs in the laminar portion of the boundary layer exhibited smooth surfaces, indicating the existence of a liquid melt layer on the burning fuel surface in the upstream region. After the transition section, which displayed distinct transverse striations, the surface roughness pattern became quite random and very pronounced in the downstream turbulent boundary-layer region. Both real-time X-ray radiography and ultrasonic pulse echo techniques were used to determine the instantaneous web thicknesses and instantaneous solid-fuel regression rates over certain portions of the fuel slabs. Globally averaged and axially dependent but time-averaged regression rates were also obtained and presented. Several tests were conducted using, simultaneously, one translucent fuel slab and one fuel slab processed with carbon black powder. The addition of carbon black did not affect the measured regression rates or surface temperatures in comparison to the translucent fuel slabs.

Chiaverini, Martin J.↗
NASA NTRS2000

Estimates of Ground Temperature and Atmospheric Moisture from CERES Observations

A method is developed to retrieve surface ground temperature (T(sub g)) and atmospheric moisture using clear sky fluxes (CSF) from CERES-TRMM observations. In general, the clear sky outgoing longwave radiation (CLR) is sensitive to upper level moisture (q(sub l)) over wet regions and (T(sub g)) over dry regions The clear sky window flux from 800 to 1200/cm (RadWn) is sensitive to low level moisture (q(sub t)) and T(sub g). Combining these two measurements (CLR and RadWn), Tg and q(sub h) can be estimated over land, while q(sub h) and q(sub l) can be estimated over the oceans. The approach capitalizes on the availability of satellite estimates of CLR and RadWn and other auxiliary satellite data. The basic methodology employs off-line forward radiative transfer calculations to generate synthetic CSF data from two different global 4-dimensional data assimilation products. Simple linear regression is used to relate discrepancies in CSF to discrepancies in T(sub g), q(sub h) and q(sub l). The slopes of the regression lines define sensitivity parameters that can be exploited to help interpret mismatches between satellite observations and model-based estimates of CSF. For illustration, we analyze the discrepancies in the CSF between an early implementation of the Goddard Earth Observing System Data Assimilation System (GEOS-DAS) and a recent operational version of the European Center for Medium-Range Weather Prediction data assimilation system. In particular, our analysis of synthetic total and window region SCF differences (computed from two different assimilated data sets) shows that simple linear regression employing Delta(T(sub g)) and broad layer Delta(q(sub l) from .500 hPa to surface and Delta(q(sub h)) from 200 to .300 hPa provides a good approximation to the full radiative transfer calculations. typically explaining more than 90% of the 6-hourly variance in the flux differences. These simple regression relations can be inverted to "retrieve" the errors in the geophysical parameters. Uncertainties (normalized by standard deviation) in the monthly mean retrieved parameters range from 7% for Delta(T(sub g)) to about 20% for Delta(q(sub l)). Our initial application of the methodology employed an early CERES-TRMM data set (CLR and Radwn) to assess the quality of the GEOS2 data. The results showed that over the tropical and subtropical oceans GEOS2 is, in general, too wet in the upper troposphere (mean bias of 0.99 mm) and too dry in the lower troposphere (mean bias of -4.7 min). We note that these errors, as well as a cold bias in the T(sub g). have largely been corrected in the current version of GEOS-2 with the introduction of a land surface model, a moist turbulence scheme and the assimilation of SSM/I total precipitable water.

Wu, Man Li C.↗
NASA NTRS2000

Estimates of Ground Temperature and Atmospheric Moisture from CERES Observations

A method is developed to retrieve surface ground temperature (Tg) and atmospheric moisture using clear sky fluxes (CSF) from CERES-TRMM observations. In general, the clear sky outgoing long-wave radiation (CLR) is sensitive to upper level moisture (q(sub h)) over wet regions and Tg over dry regions The clear sky window flux from 800 to 1200 /cm (RadWn) is sensitive to low level moisture (q(sub j)) and Tg. Combining these two measurements (CLR and RadWn), Tg and q(sub h) can be estimated over land, while q(sub h) and q(sub t) can be estimated over the oceans. The approach capitalizes on the availability of satellite estimates of CLR and RadWn and other auxiliary satellite data. The basic methodology employs off-line forward radiative transfer calculations to generate synthetic CSF data from two different global 4-dimensional data assimilation products. Simple linear regression is used to relate discrepancies in CSF to discrepancies in Tg, q(sub h) and q(sub t). The slopes of the regression lines define sensitivity parameters that can be exploited to help interpret mismatches between satellite observations and model-based estimates of CSF. For illustration, we analyze the discrepancies in the CSF between an early implementation of the Goddard Earth Observing System Data Assimilation System (GEOS-DAS) and a recent operational version of the European Center for Medium-Range Weather Prediction data assimilation system. In particular, our analysis of synthetic total and window region SCF differences (computed from two different assimilated data sets) shows that simple linear regression employing (Delta)Tg and broad layer (Delta)q(sub l) from 500 hPa to surface and (Delta)q(sub h) from 200 to 500 hPa provides a good approximation to the full radiative transfer calculations, typically explaining more than 90% of the 6-hourly variance in the flux differences. These simple regression relations can be inverted to "retrieve" the errors in the geophysical parameters. Uncertainties (normalized by standard deviation) in the monthly mean retrieved parameters range from 7% for (Delta)T to about 20% for (Delta)q(sub t). Our initial application of the methodology employed an early CERES-TRMM data set (CLR and Radwn) to assess the quality of the GEOS2 data. The results showed that over the tropical and subtropical oceans GEOS2 is, in general, too wet in the upper troposphere (mean bias of 0.99 mm) and too dry in the lower troposphere (mean bias of -4.7 mm). We note that these errors, as well as a cold bias in the Tg, have largely been corrected in the current version of GEOS-2 with the introduction of a land surface model, a moist turbulence scheme and the assimilation of SSTM/I total precipitable water.

Wu, Man Li C.↗
NASA NTRS2001

Atlantic Tropical Cyclone Monitoring with AMSU-A: Estimation of Maximum Sustained Wind Speeds

The first Advanced Microwave Sounding Unit temperature sounder (AMSU-A) was launched on the NOAA-15 satellite on 13 May 1998. The AMSU-A's higher spatial and radiometric resolutions provide more useful information on the strength of the middle and upper tropospheric warm cores associated with tropical cyclones than have previous microwave temperature sounders. The gradient wind relationship suggests that the temperature gradient near the core of tropical cyclones increases nonlinearly with wind speed. We recast the gradient wind equation to include AMSU-A derived variables. Stepwise regression is used to determine which of these variables is most closely related to maximum sustained winds (V(sub max)). The satellite variables investigated include the radially averaged gradients at two spatial resolutions of AMSU-A channels 1 through 10 T(sub b) data (delta(sub r)T(sub b)), the squares of these gradients, a channel 15 based scattering index (SI-89), and area averaged T(sub b). Calculations of Tb and delta(sub r)T(sub b) from mesoscale model simulations of Andrew reveal the effects of the AMSU spatial sampling on the cyclone warm core presentation. Stepwise regression of 66 AMSU-A terms against National Hurricane Center (NHC) V(sub max) estimates from the 1998 and 1999 Atlantic hurricane season confirms the existence of a nonlinear relationship between wind speed and radially averaged temperature gradients near the cyclone warm core. Of six regression terms, four are dominated by temperature information, and two are interpreted as correcting for hydrometeor contamination. Jackknifed regressions were performed to estimate the algorithm performance on independent data. For the 82 cases that had in situ measurements of V(sub max), the average error standard deviation was 4.7 m/s. For 108 cases without in situ wind data, the average error standard deviation was 7.5 m/s. Operational considerations, including the detection of weak cyclones and false alarm reduction are also discussed.

Spencer, Roy↗
NASA NTRS2001

Atlantic Tropical Cyclone Monitoring with AMSU-A: Estimation of Maximum Sustained Wind Speeds

The first Advanced Microwave Sounding Unit temperature sounder (AMSU-A) was launched on the NOAA-15 satellite on 13 May 1998. The AMSU-A's higher spatial and radiometric resolutions provide more useful information on the strength of the middle- and upper-tropospheric warm cores associated with tropical cyclones than have previous microwave temperature sounders. The gradient wind relationship suggests that the temperature gradient near the core of tropical cyclones increases nonlinearly with wind speed. The gradient wind equation is recast to include AMSU-A-derived variables, Stepwise regression is used to determine which of these variables is most closely related to maximum sustained winds (V(sub max)). The satellite variables investigated include the radially averaged gradients at two spatial resolutions of AMSU-A channels 1-10 T(sub b) data (delta(sub r)T(sub B)), the squares of these gradients, a channel-15-based scattering index (SI(sub 89)), and area-averaged T(sub B). Calculations of T(sub B) and delta(sub r)T(sub B) from mesoscale model simulations of Andrew reveal the effects of the AMSU spatial sampling on the cyclone warm core presentation. Stepwise regression of 66 AMSU-A terms against National Hurricane Center V(sub max) estimates from the 1998 and 1999 Atlantic hurricane season confirms the existence of a nonlinear relationship between wind speed and radially averaged temperature gradients near the cyclone warm core. Of six regression terms, four are dominated by temperature information, and two are interpreted as correcting for hydrometeor contamination. Jackknifed regressions were performed to estimate the algorithm performance on independent data. For the 82 cases that had in situ measurements of V(sub max), the average error standard deviation was 4.7 m/s. For 108 cases without in situ wind data, the average error standard deviation was 7.5 m/s Operational considerations, including the detection of weak cyclones and false alarm reduction, are also discussed.

Spencer, Roy W.↗
NASA NTRS1995

Geostatistical Approaches for Spatial Estimation of Vegetation Quantities Using Ground and Image Data

A major challenge in the study of the earth system is the mapping of vegetation quantities over large regions. Geostatistical methods, such as cokriging and stochastic simulation, have the potential to exploit more fully both remotely sensed data and ground information and improve the spatial estimation of vegetation variables over traditional regression methods. A synthetic example constructed from imaging spectrometer data allows a useful comparison among regression, cokriging and a simple probability-field method. A range of linear relationships between direct (sampled) and ancillary images is used. The lowest root-mean-square-error is achieved with cokriging until the correlation between direct and ancillary data exceeds .89, at which point regression is the superior estimator. Probability-field simulation gives a range of possible realizations, most more precise than those from regression. The relationship between ground measurements and image data is thus demonstrated to be one of the critical factors in the choice of a spatial estimation method.

Dungan, Jennifer L.↗
NASA NTRS1995

Changes in aerobic power of men, ages 25-70 yr

This study quantified and compared the cross-sectional and longitudinal influence of age, self-report physical activity (SR-PA), and body composition (%fat) on the decline of maximal aerobic power (VO2peak). The cross-sectional sample consisted of 1,499 healthy men ages 25-70 yr. The 156 men of the longitudinal sample were from the same population and examined twice, the mean time between tests was 4.1 (+/- 1.2) yr. Peak oxygen uptake was determined by indirect calorimetry during a maximal treadmill exercise test. The zero-order correlations between VO2peak and %fat (r = -0.62) and SR-PA (r = 0.58) were significantly (P < 0.05) higher that the age correlation (r = -0.45). Linear regression defined the cross-sectional age-related decline in VO2peak at 0.46 ml.kg-1.min-1.yr-1. Multiple regression analysis (R = 0.79) showed that nearly 50% of this cross-sectional decline was due to %fat and SR-PA, adding these lifestyle variables to the multiple regression model reduced the age regression weight to -0.26 ml.kg-1.min-1.yr-1. Statistically controlling for time differences between tests, general linear models analysis showed that longitudinal changes in aerobic power were due to independent changes in %fat and SR-PA, confirming the cross-sectional results.

Oxygen Consumption/physiology↗
NASA NTRS2007

A Method for Calculating the Probability of Successfully Completing a Rocket Propulsion Ground Test

Propulsion ground test facilities face the daily challenge of scheduling multiple customers into limited facility space and successfully completing their propulsion test projects. Over the last decade NASA s propulsion test facilities have performed hundreds of tests, collected thousands of seconds of test data, and exceeded the capabilities of numerous test facility and test article components. A logistic regression mathematical modeling technique has been developed to predict the probability of successfully completing a rocket propulsion test. A logistic regression model is a mathematical modeling approach that can be used to describe the relationship of several independent predictor variables X(sub 1), X(sub 2),.., X(sub k) to a binary or dichotomous dependent variable Y, where Y can only be one of two possible outcomes, in this case Success or Failure of accomplishing a full duration test. The use of logistic regression modeling is not new; however, modeling propulsion ground test facilities using logistic regression is both a new and unique application of the statistical technique. Results from this type of model provide project managers with insight and confidence into the effectiveness of rocket propulsion ground testing.

Messer, Bradley↗