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NASA NTRS1988

Using ridge regression in systematic pointing error corrections

A pointing error model is used in the antenna calibration process. Data from spacecraft or radio star observations are used to determine the parameters in the model. However, the regression variables are not truly independent, displaying a condition known as multicollinearity. Ridge regression, a biased estimation technique, is used to combat the multicollinearity problem. Two data sets pertaining to Voyager 1 spacecraft tracking (days 105 and 106 of 1987) were analyzed using both linear least squares and ridge regression methods. The advantages and limitations of employing the technique are presented. The problem is not yet fully resolved.

Guiar, C. N.↗

NASA NTRS1990

Ridge Regression Signal Processing

The introduction of the Global Positioning System (GPS) into the National Airspace System (NAS) necessitates the development of Receiver Autonomous Integrity Monitoring (RAIM) techniques. In order to guarantee a certain level of integrity, a thorough understanding of modern estimation techniques applied to navigational problems is required. The extended Kalman filter (EKF) is derived and analyzed under poor geometry conditions. It was found that the performance of the EKF is difficult to predict, since the EKF is designed for a Gaussian environment. A novel approach is implemented which incorporates ridge regression to explain the behavior of an EKF in the presence of dynamics under poor geometry conditions. The basic principles of ridge regression theory are presented, followed by the derivation of a linearized recursive ridge estimator. Computer simulations are performed to confirm the underlying theory and to provide a comparative analysis of the EKF and the recursive ridge estimator.

Kuhl, Mark R.↗

NASA NTRS1990

Ridge regression processing

Current navigation requirements depend on a geometric dilution of precision (GDOP) criterion. As long as the GDOP stays below a specific value, navigation requirements are met. The GDOP will exceed the specified value when the measurement geometry becomes too collinear. A new signal processing technique, called Ridge Regression Processing, can reduce the effects of nearly collinear measurement geometry; thereby reducing the inflation of the measurement errors. It is shown that the Ridge signal processor gives a consistently better mean squared error (MSE) in position than the Ordinary Least Mean Squares (OLS) estimator. The applicability of this technique is currently being investigated to improve the following areas: receiver autonomous integrity monitoring (RAIM), coverage requirements, availability requirements, and precision approaches.

Kuhl, Mark R.↗

NASA NTRS1989

Improved effectiveness of GPS RAIM through ridge regression signal processing

A measurement processing method has been developed which markedly improves the GPS Receiver Autonomous Integrity Monitoring (RAIM) software-based algorithm system's effectiveness in detecting satellite signal failures. Detection is via the consistency of a redundant set of pseudorange measurements. When five satellites are in view, five different subsolutions can be calculated; the integrity alarm is triggered on the basis of subsolution comparisons. Because a poor distribution of the satellites also causes RAIM subsolution scattering, a methodology for selecting the covariance matrix is presented which incorporates ridge regression into a Kalman filter.

Kelly, Robert J.↗

NASA NTRSDate not supplied

Open-source Numerical Modeling of Solidification Cracking Susceptibility: Application to Refractory Alloy Systems

Introduction. Alloys such as aluminum, nickel-base, and austenitic stainless steels are susceptible to solidification cracking during welding and 3D printing. Compositional optimization is one method used to effectively mitigate solidification cracking of those alloy systems. With the surge in hypersonic and in-space propulsion activities, refractory metals (Nb, Mo, Ta, W, and Re) and their alloy derivatives are increasing in importance due to their extreme high melting point and retention of high-temperature strength; however, their chemistry was most typically optimized to promote ductility during mechanical operations such as drawing and forming. Welding of such alloys has been a challenge due to a number of issues including solidification cracking, atmospheric contamination (O, C, and N), as well as a shift in ductile-to-brittle transition to higher temperature following grain growth induced by welding. Compositional optimization of refractory alloys for solidification cracking resistance in particular is desirable as their usage increases with the advent of advanced manufacturing methods such as 3D printing. This work evaluates the effect of compositional variation in refractory metal systems on the solidification cracking susceptibility with the goals of optimizing existing alloys and joining process techniques, and formulating new alloys with increased solidification cracking resistance. Experimental Procedures. A python code was developed in a Jupyter notebook environment (Michael and Sowards, 2023) to facilitate the calculation of crack susceptibility index proposed by Kou (2015). Composition is entered as a single point, or as a 1-D or 2-D array. The notebook calls pycalphad (Otis and Liu, 2017 and Bocklund et al, 2020) to calculate the evolution of fraction solid as a function of temperature (under either Scheil or equilibrium assumptions) and then evaluates steepness of the fraction solid curve near the terminal stage of solidification to predict solidification cracking resistance. Open source thermodynamic databases available at online repositories are used (van de Walle). The process is setup in an automated fashion to generate plots that show variation in solidification cracking susceptibility according to composition on 1-D line plots or 2-D contour plots. The Jupyter notebook and crack susceptibility algorithm was also integrated with a widely used commercial CALPHAD code for validation and alloy exploration. Results and Discussion. The crack susceptibility model was first validated against a series of refractory alloy compositions evaluated in past work which utilized a specialized Varestraint test built inside a vacuum chamber environment (Lessman and Gold, 1971). The alloys tested in the Varestraint apparatus included T-111 (Ta-8W-2Hf), ASTAR-811C (Ta-8W-1Re-0.7Hf-0.025C), FS-85 (Nb-27Ta-10W-1Zr), T-222 (Ta-9.6W-2.4Hf-0.01C), Ta-10W, B-66 (Nb-5Mo-5V-1Zr), and SCb-291 (Nb-10W-10Ta). The initial test of the model showed a strong correlation with empirical Varestraint data, i.e., a Spearman rank correlation between model predictions and hot cracking measurements was observed to be greater than 0.8. Following the validation, a set of refractory metal binary mixtures was investigated to evaluate sensitivity of Nb, Mo, W, and Ta to C, N, and O content. A series of plots were produced that suggest ppmw ranges of C, N, and O where solidification cracking increases significantly and reaches a maximum. Also comparative ranking of each primary refractory metal to each interstitial was produced. For example C produces greater cracking response in Mo whereas O produces greater cracking response in Ta and Nb. Such compositional values have utility in setting limits on pickup of these interstitial elements during welding and printing rather than using a one-size-fits-all approach. Furthermore, the results have use in determining additive powder recycling requirements, which is especially pertinent for refractory metal powders due to their high cost compared to conventional alloys. Another application created thousands of hypothetical alloys within the nominal specified composition range of two widely used refractory alloys C103 (Nb-10Hf-1Ti) and TZM (Mo-0.5Ti-0.1Zr). The cracking index was calculated for the alloys and results were fed into machine learning regression techniques including Multiple Linear Regression, Ridge Regression, and Lasso Regression to determine relative potency each alloying element had on computed solidification cracking index. A series of linear equations were produced that relate composition of C103 and TZM to solidification cracking index. The crack susceptibility of C103 for example is described by an equation of the form: cracking index ~ O + 0.667*C + 0.635*N + 0.00037*Ta – 0.0008*Hf (in wt.%) From that equation, it is clear that O has strong propensity to induce solidification cracking. Interestingly, Hf is shown to reduce calculated cracking response. Finally, realizing the potential of this method to discover new refractory alloy formulations across the period table that have low solidification cracking sensitivity, the code was applied to new untested alloy systems including W-Zr-C, W-Ta-C, and others. Conclusions. In summary, an open source numerical method has been developed using Python code to calculate Kou’s crack susceptibility index. The method was applied to refractory metals which are inherently difficult to study from a weldability testing standpoint since inert shielding gas is not sufficient and welding is typically done in vacuum, especially in light of findings presented here where oxygen has profound influence on solidification cracking. This work revealed the effect of compositional variations on a series of refractory metals and showed the framework defined here will be useful in 1) the development of new alloys that have improved weldability and 3D printability, 2) placing compositional limits on existing alloys, and 3) ensuring adequate controls of manufacturing processes such as 3D printing where powder reuse is critical. Keywords. pycalphad; Python; refractory metals; solidification cracking. References. B. Bocklund et. al. (2020) http://doi.org/10.5281/zenodo.3630657. S. Kou. (2015) https://doi.org/10.1016/j.actamat.2015.01.034. G.G. Lessmann and R.E. Gold. Welding Journal, issue 1, pp. 1-s – 8-s (1971). F.N. Michael and J.W. Sowards. NASA/TM-20230002218 (2023). R. Otis and Z.-K. Liu. (2017) http://doi.org/10.5334/jors.140. A. Van de Wallle et. al. (2018) https://doi.org/10.1016/j.calphad.2018.04.003.

pycalphad↗

NASA NTRS2021

Applying Machine Learning to Predict Alaskan Ionospheric Irregularities

In this work several machine-learning (ML) techniques for predicting ionospheric irregularities in the northern auroral zone were tested. The techniques include Ridge Regression, Long Short-Term Memory Neural Network (LSTM), Classification Neural Network (CNN), Autoencoder Classification Neural Network (ACNN), and LSTM Autoencoder Classification Neural Network (LACNN). These techniques were tested with the rate of total electron content (TEC) index (ROTI) data collected during 2008 and 2009 from a geodetic station in Fairbanks, Alaska (64.98°N, 147.50°W), which is in the auroral zone. Using ROTI data with the ML techniques, experiments were conducted to reach two goals: (1) examine what space weather measurements present good correlation with ROTI so that they may be helpful in ML-based prediction of ionospheric irregularities in the polar region; (2) predict ROTI hours and days ahead by training the neural network models with historical ROTI data alone. The Ridge Regression experiments indicate that a combination of measurements of local geomagnetic horizontal components, geomagnetic SYM-H index, 3-hour Kp and ap indices, and F10.7 solar flux index appears to be more correlated to the single-site ROTI measurements than other parameters. The neural network (NN) experiments show that although the LACNN model allows for predictions of non-irregularity and irregularity conditions defined by ROTI levels up to 3 hours in advance, with an overall accuracy ≥ 92%, a number of irregularity events can still be missed. Hence, further development is needed to reduce the number of missed events. In this paper, the models, data processing, model performance, prediction results, and potential applications are presented.

Pi, Xiaoqing↗

NASA NTRS1982

Evaluation of trends in wheat yield models

Trend terms in models for wheat yield in the U.S. Great Plains for the years 1932 to 1976 are evaluated. The subset of meteorological variables yielding the largest adjusted R(2) is selected using the method of leaps and bounds. Latent root regression is used to eliminate multicollinearities, and generalized ridge regression is used to introduce bias to provide stability in the data matrix. The regression model used provides for two trends in each of two models: a dependent model in which the trend line is piece-wise continuous, and an independent model in which the trend line is discontinuous at the year of the slope change. It was found that the trend lines best describing the wheat yields consisted of combinations of increasing, decreasing, and constant trend: four combinations for the dependent model and seven for the independent model.

Ferguson, M. C.↗

NASA NTRS1983

The impact of conventional surface data upon VAS regression retrievals in the lower troposphere

Surface temperature and dewpoint reports are added to the infrared radiances from the VISSR Atmospheric Sounder (VAS) in order to improve the retrieval of temperature and moisture profiles in the lower troposphere. The conventional (airways) surface data are combined with the twelve VAS channels as additional predictors in a ridge regression retrieval scheme, with the aim of using all available data to make high resolution space-time interpolations of the radiosonde network. For one day of VAS observations, retrievals using only VAS radiances are compared with retrievals using VAS radiances plus surface data. Temperature retrieval accuracy evaluated at coincident radiosonde sites shows a significant impact within the boundary layer. Dewpoint retrieval accuracy shows a broader improvement within the lowest tropospheric layers. The most dramatic impact of surface data is observed in the improved relative spatial and temporal continuity of low-level fields retrieved over the Midwestern United States.

Lee, T. H.↗

NASA NTRS1983

The impact of conventional surface data upon VAS regression retrievals in the lower troposphere

Lee, T.-H.↗

NASA NTRS1990

Investigation of Air Transportation Technology at Ohio University, 1989-1990

The activities of the participants in the Joint University Program (JUP) at Ohio University are briefly surveyed. During 1989 to 1990, five topics received emphasis. A spectrum-efficient weather data uplink system was designed, constructed, and flight tested. An integrated Global Positioning System/Inertial Navigation System (GPS/INS) study continued, utilizing the Redundant strapdown Inertial Measurement Unit (IMU) on loan from NASA. The Ridge Regression theory was refined and applied to air navigation scenarios. System Identification theory was applied to GPS data to point the way to better understanding of the effects of Selective Availability on civilian users of this navigation system. An analysis of thought-related (electroencephalographic) signals for application to control of computer systems that could have significance in aiding paraplegics or for hands-off systems control in industrial or air traffic control areas was carried out.

Lilley, Robert W.↗

NASA NTRS1990

Study of the crust and mantle using magnetic surveys by Magsat and other satellites

This article summarizes some of the methodology and results for studies of the earth's mantle and crust. Mantle conductivity studies can be made either by studying signals impressed on the earth from outside, e.g., the ionosphere or magnetosphere, or by studing signals originating in the core and transmitted through the mantle. Crustal field studies begin with a careful selection of the data and subsequent removal of core and external fields by some sort of filtering. Average maps from different local times sometimes differ, presumably due to the remaining presence of fields of external origin. Several techniques for further filtering are discussed. Where large-area aeromagnetic maps are available, crustal maps derived from satellite data can be compared with upward continued data. In general, the comparisons show agreement, with some differences, particularly in and near the auroral belts. The satellite data are further reduced by various methods of inverse and forward modeling, sometimes including reduction to the pole. These techniques are generally unstable at the equator. Common methods of stabilizing the inversions include principle components analysis and ridge regression. Because of the presence of the core field, the entire crustal contribution from the field is not known. Also, there is a basic nonuniqueness to the inverse solutions. Nevertheless, magnetizations that are interpretable can be derived.

Langel, Robert A.↗

NASA NTRSDate not supplied

Variance Decomposition of MEDLI2 Reconstructed Heating Using Neural Networks

The Mars Entry, Descent, and Landing Instrumentation (MEDLI2) sensor suite collected data during entry of the Mars 2020 Perseverance rover into Mars’ atmosphere. This suite included a network of MEDLI2 Instrumented Sensor Plugs (MISPs). Each MISP was comprised of a cylinder made of Thermal Protection System (TPS) material with 1-3 embedded thermocouples (TCs), and it was flush mounted into the heatshield or backshell. Data from these in-depth TCs were used to reconstruct the aeroheating environment of the vehicle throughout entry. Surface heating was posed as an inverse problem, with the goal of estimating the surface heating by minimizing an objective function of the difference between MISP temperature measurements during flight and the temperature predictions derived from the Fully Implicit Ablation and Thermal response (FIAT) program. Given an aerothermal environment, FIAT calculates the material response and provides in-depth temperatures throughout the TPS material. To achieve the reverse, an internal tool called FIAT_Opt runs through multiple different environments until the output temperature at the TC depth closely matches the flight data. 95% confidence intervals on the reconstructed surface heating were obtained using Monte Carlo analysis, in which uncertainties in the thermocouple depth and the TPS material properties (e.g., density, thermal conductivity, heat capacity, emissivity) based on flight-lot material testing were included. A variance decomposition method using Sobol indices was employed to assess the sensitivity of the reconstructed peak heating to the TC placement and material property uncertainties. Variance decomposition was found to require tens of thousands of FIAT_Opt runs in order for the Sobol indices to converge. With a single FIAT_Opt run taking on the order of 40 minutes, the required number of computations would take months to complete, even if using multiple CPUs. To mitigate this problem, three machine learning models (ridge regression with cross-validation, random forest regression, and a deep neural network) were trained and tested using the 2000 Monte Carlo runs that were already completed. A subset of 1600 runs were used to train the model (i.e., training set), while the remaining 400 runs were used as the test set. The predictions from the deep neural network (DNN) on the test set showed nearly perfect agreement to the actual values computed with FIAT_Opt (R2 > 0.99). Using the DNN as a surrogate model, the variance decomposition using 50,000 runs was completed within minutes. The resulting Sobol indices showed that the reconstructed peak surface heating was most sensitive to the uncertainties in the thermal conductivity (ST = 0.37) and heat capacity (ST = 0.26). This method can be leveraged to provide requirements for material property measurements needed to improve the accuracy of surface heating prediction and ultimately lead to the reduction of design margins in the future. This presentation will include background on the MEDLI2 suite; the method used for inverse heating estimation; the way that material property uncertainties were accounted for using Monte Carlo analysis; a brief background on variance decomposition; the motivation for using machine learning in this context; how a neural network was trained on the data to enable variance decomposition in a fraction of the time; and the variance decomposition results for one of the MISPs.

Hannah Alpert↗

NASA NTRS2001

Sedimentation along the Eastern Chenier Plain Coast: Down Drift Impact of a Delta Complex Shift

The Mississippi River Chenier Plain is a shore parallel landform (down-drift from the Atchafalaya distributary of the Mississippi River) consisting of an alternating series of transgressive sand-shell ridges and regressive, progradational mudflats. The late 1940s shift of 1/3 of the flow of the Mississippi to the newly developing Atchafalaya delta complex to the west has resulted in injection of the river waters and suspended sediment into the westward flowing currents of the coastal current system. This has reactivated the dormant processes of mud accumulation along this coast. These environmental circumstances have provided the opportunity to: (1) investigate the depositional processes of the prograding, fine grained, mud flat facies of the open Chenier main coast and (2) to test the hypothesis that the impacts of the frequent cold front passages of fall, winter and spring exceed those of the occasional and more localized hurricane in shaping the coast and powering the dominant sedimentary processes. We conducted field investigations with the benefit of multi - scale, time series environmental surveillance by remote sensing systems, including airborne and satellite sensors. These systems provided invaluable new information on areal geomorphic patterns and the behavior of the coastal waters. This is a classic case of weather impacting inner shelf waters and sediments and causing the development of a new landform. It is clear that mud flats of the eastern chenier plain are prograding seaward, as well as progressively growing in a westerly direction.

Huh, Oscar K.↗

NASA NTRS1975

Comparison of some biased estimation methods (including ordinary subset regression) in the linear model

Ridge, Marquardt's generalized inverse, shrunken, and principal components estimators are discussed in terms of the objectives of point estimation of parameters, estimation of the predictive regression function, and hypothesis testing. It is found that as the normal equations approach singularity, more consideration must be given to estimable functions of the parameters as opposed to estimation of the full parameter vector; that biased estimators all introduce constraints on the parameter space; that adoption of mean squared error as a criterion of goodness should be independent of the degree of singularity; and that ordinary least-squares subset regression is the best overall method.

Sidik, S. M.↗

NASA NTRS1991

Comparison of three atmospheric correction models for a vegetated airborne visible/infrared imaging spectrometer (AVIRIS) scene

Current atmospheric correction models applied to imaging spectroscopy data include such methods as residual or scene average, flat field correction, regression method or empirical line algorithm, the continuum interpolated band ratio (CIBR) derivation and the LOWTRAN 7 method. Due to the limitations of using residual and flat field corrections on vegetated scenes, three methods will be compared: regression, CIBR derivation and LOWTRAN 7. Field-measured bright and dark targets taken at the time of the 13 April, 1989 AVIRIS overflight of Jasper Ridge, California were used to formulate the regression method atmospheric correction. Using this corrected scene as 'ground truth', the CIBR derivation and the LOWTRAN 7 method with both input models are compared on the vegetated Jasper Ridge scene. Although representing a qualitative approach, this is a first approximation and shows the need for more quantitative analysis.

Van Den Bosch, J. M.↗

NASA NTRS1991

Comparison of two atmospheric correction models for a vegetated Airborne Visible/Infrared Imaging Spectrometer (AVIRIS) scene

Current atmospheric correction models applied to imaging spectroscopy data include such methods as residual (scene average) and flat field correction, regression method, and the LOWTRAN 7 method. Due to the limitations of using residual and flat field corrections on vegetated scenes, regression and LOWTRAN 7 are compared. Field measured targets taken at the time of the 13 April, 1989 AVIRIS overflight of Jasper Ridge, California (U.S.) were used to formulate the regression atmospheric correction. Assuming the regressed image represents ground truth, results show that the LOWTRAN 7 method with radiosonde data does not compensate as well for atmospheric water vapor as the regression method, but it may be easier to obtain a posteriori information to perform the LOWTRAN 7 atmospheric correction.

Vandenbosch, Jeannette Marie↗

NASA NTRS1973

Pulsations, interpulsations, and sea-floor spreading.

It is postulated that worldwide transgressions (pulsations) and regressions (interpulsations) through the course of geologic time are related to the elevation and subsidence of oceanic ridge systems and to sea-floor spreading. Two multiple working hypotheses are advanced to explain major transgressions and regressions and the elevation and subsidence of oceanic ridge systems. One hypothesis interrelates the sea-floor spreading hypothesis to the hypothesis of sub-Mohorovicic serpentinization. The second hypothesis relates the sea-floor spreading hypothesis to a hypothesis involving thermal expansion and contraction.

Pessagno, E. A., Jr.↗

NASA NTRS1987

Empirical prediction of the summer monsoon rainfall over India

Forty-six years (1939-1984) of observed data were examined to study synoptic and statistical relationships between the summer monsoon rainfall over India, the Southern Oscillation, and the midtropospheric circulation over India. The change in Darwin pressure from January to April and the latitudinal position of the April 500-mb ridge along 75 deg E are taken as two quasi-independent predictor parameters to develop a regression equation to predict the summer monsoon rainfall. Verification of predictions on independent data shows that the root-mean-square error for predicted rainfall is 36 mm, which is less than half of the standard deviation and only about 4 percent of the mean rainfall (857 mm).

Shukla, J.↗