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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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All sourcesNASA NTRSDOE OSTI
NASA NTRS2012

Bootstrap Prediction Intervals in Non-Parametric Regression with Applications to Anomaly Detection

Prediction intervals provide a measure of the probable interval in which the outputs of a regression model can be expected to occur. Subsequently, these prediction intervals can be used to determine if the observed output is anomalous or not, conditioned on the input. In this paper, a procedure for determining prediction intervals for outputs of nonparametric regression models using bootstrap methods is proposed. Bootstrap methods allow for a non-parametric approach to computing prediction intervals with no specific assumptions about the sampling distribution of the noise or the data. The asymptotic fidelity of the proposed prediction intervals is theoretically proved. Subsequently, the validity of the bootstrap based prediction intervals is illustrated via simulations. Finally, the bootstrap prediction intervals are applied to the problem of anomaly detection on aviation data.

Kumar, Sricharan↗
NASA NTRS1992

Interval prediction in structural dynamic analysis

Methods for assessing the predictive accuracy of structural dynamic models are examined with attention given to the effects of modal mass, stiffness, and damping uncertainties. The methods are based on a nondeterministic analysis called 'interval prediction' in which interval variables are used to describe parameters and responses that are unknown. Statistical databases for generic modeling uncertainties are derived from experimental data and incorporated analytically to evaluate responses. Covariance matrices of modal mass, stiffness, and damping parameters are propagated numerically in models of large space structures by means of three methods. The test data tend to fall within the predicted intervals of uncertainty determined by the statistical databases. The present findings demonstrate the suitability of using data from previously analyzed and tested space structures for assessing the predictive accuracy of an analytical model.

Hasselman, Timothy K.↗
NASA NTRS2014

Prediction Interval Development for Wind-Tunnel Balance Check-Loading

Results from the Facility Analysis Verification and Operational Reliability project revealed a critical gap in capability in ground-based aeronautics research applications. Without a standardized process for check-loading the wind-tunnel balance or the model system, the quality of the aerodynamic force data collected varied significantly between facilities. A prediction interval is required in order to confirm a check-loading. The prediction interval provides an expected upper and lower bound on balance load prediction at a given confidence level. A method has been developed which accounts for sources of variability due to calibration and check-load application. The prediction interval method of calculation and a case study demonstrating its use is provided. Validation of the methods is demonstrated for the case study based on the probability of capture of confirmation points.

Landman, Drew↗
NASA NTRS2017

Predicted Weather Display and Decision Support Interface for Flight Deck

A system and method for providing visual depictions of a predictive weather forecast for in-route vehicle trajectory planning. The method includes displaying weather information on a graphical display, displaying vehicle position information on the graphical display, selecting a predictive interval, displaying predictive weather information for the predictive interval on the graphical display, and displaying predictive vehicle position information for the predictive interval on the graphical display, such that the predictive vehicle position information is displayed relative to the predictive weather information, for in-route trajectory planning.

Johnson, Walter W.↗
NASA NTRSDate not supplied

Comparison of Entry Descent and Landing Aerodynamic Databases with Uncertainty Quantification Developed Using Machine Learning Techniques

When developing the aerodynamic databases for use in trajectory simulations, it is important to develop a system of metrics to qualify which aerodynamic models are best to use. Since aerodynamics are just one input into trajectory simulations, the results of these simulations do not reflect on the quality of the aerodynamic database used. This means that aerodynamic database comparisons must be done offline. While traditional metrics that focus on mean/nominal predictions are a good first step, more robust estimates of the prediction interval become important as more focused uncertainty models are developed. We explore the limitations of evaluating aerodynamic models based purely on nominal-centered response surfaces. Before elaborating and evaluating metrics based on distributed models, the value of evaluating prediction interval and confidence interval are discussed to conclude that prediction intervals are more relevant to the use of trajectory analysis. Several metrics to evaluate the prediction interval are introduced with a focus on the standard calibration metric. Finally, we compare candidate models using both mean and distributed metrics. A finalized candidate model developed using state of the art machine learning methods is compared to a baseline model developed using traditional aerodynamic database modeling techniques.

Aerodynamic Database↗
NASA NTRS1983

Statistical summaries of fatigue data for design purposes

Two methods are discussed for constructing a design curve on the safe side of fatigue data. Both the tolerance interval and equivalent prediction interval (EPI) concepts provide such a curve while accounting for both the distribution of the estimators in small samples and the data scatter. The EPI is also useful as a mechanism for providing necessary statistics on S-N data for a full reliability analysis which includes uncertainty in all fatigue design factors. Examples of statistical analyses of the general strain life relationship are presented. The tolerance limit and EPI techniques for defining a design curve are demonstrated. Examples usng WASPALOY B and RQC-100 data demonstrate that a reliability model could be constructed by considering the fatigue strength and fatigue ductility coefficients as two independent random variables. A technique given for establishing the fatigue strength for high cycle lives relies on an extrapolation technique and also accounts for "runners." A reliability model or design value can be specified.

Wirsching, P. H.↗
NASA NTRSDate not supplied

Comparisons of Performance Metrics and Machine Learning Methods on an Entry Descent and Landing Database

This work focuses on evaluating machine learning methods and their applicability to the generation of an aerodynamic database, particularly for trajectory analysis of a capsule during entry, descent, and landing with a focus on uncertainty quantification. The source data to be used is the wind tunnel and computational data for the Integrated Design Assessment Team (IDAT) configuration of the Orion project, which has been publicly released. The methods used to generate the proposed databases are designed to naturally include a prediction interval, which will be evaluated both for their mean response as well as how well the prediction interval performs. These machine learning methods are compared to a traditionally generated database used by the Orion team as a baseline. It is found that while these machine learning methods perform well, the Orion database tends to still outperform them showing that engineering experience is still needed to make the best database possible. However, these methods still provide comparable results with significantly less effort.

Orion↗
NASA NTRSDate not supplied

Comparisons of Performance Metrics and Machine Learning Methods on an Entry, Descent, and Landing Database

This work focuses on evaluating machine learning methods and their applicability to the generation of an aerodynamic database, particularly for trajectory analysis of a capsule during entry, descent, and landing with a focus on uncertainty quantification. The source data to be used is the wind tunnel and computational data for the Integrated Design Assessment Team (IDAT) configuration of the Orion project, which has been publicly released. The methods used to generate the proposed databases are designed to naturally include a prediction interval, which will be evaluated both for their mean response as well as how well the prediction interval performs. These machine learning methods are compared to a traditionally generated database used by the Orion team as a baseline. It is found that while these machine learning methods perform well, the Orion database tends to still outperform them showing that engineering experience is still needed to make the best database possible. However, these methods still provide comparable results with significantly less effort.

Orion↗
NASA NTRS2016

A Comparison of Metamodeling Techniques via Numerical Experiments

This paper presents a comparative analysis of a few metamodeling techniques using numerical experiments for the single input-single output case. These experiments enable comparing the models' predictions with the phenomenon they are aiming to describe as more data is made available. These techniques include (i) prediction intervals associated with a least squares parameter estimate, (ii) Bayesian credible intervals, (iii) Gaussian process models, and (iv) interval predictor models. Aspects being compared are computational complexity, accuracy (i.e., the degree to which the resulting prediction conforms to the actual Data Generating Mechanism), reliability (i.e., the probability that new observations will fall inside the predicted interval), sensitivity to outliers, extrapolation properties, ease of use, and asymptotic behavior. The numerical experiments describe typical application scenarios that challenge the underlying assumptions supporting most metamodeling techniques.

Crespo, Luis G.↗
NASA NTRS2010

Predicting the Size and Timing of Sunspot Maximum for Cycle 24

For cycle 24, the minimum value of the 12-month moving average (12-mma) of the AA-geomagnetic index in the vicinity of sunspot minimum (AAm) appears to have occurred in September 2009, measuring about 8.4 nT and following sunspot minimum by 9 months. This is the lowest value of AAm ever recorded, falling below that of 8.9 nT, previously attributed to cycle 14, which also is the smallest maximum amplitude (RM) cycle of the modern era (RM = 64.2). Based on the method of Ohl (the preferential association between RM and AAm for an ongoing cycle), one expects cycle 24 to have RM = 55+/-17 (the +/-1 - sigma prediction interval). Instead, using a variation of Ohl's method, one based on using 2-cycle moving averages (2-cma), one expects cycle 23's 2-cma of RM to be about 115.5+/-8.7 (the +/-1 - sigma prediction interval), inferring an RM of about 62+/-35 for cycle 24. Hence, it seems clear that cycle 24 will be smaller in size than was seen in cycle 23 (RM = 120.8) and, likely, will be comparable in size to that of cycle 14. From the Waldmeier effect (the preferential association between the ascent duration (ASC) and RM for an ongoing cycle), one expects cycle 24 to be a slow-rising cycle (ASC > or equal to 48 months), having RM occurrence after December 2012, unless it turns out to be a statistical outlier.

Wilson, Robert M.↗
NASA NTRS2008

On the Period-Amplitude and Amplitude-Period Relationships

Examined are Period-Amplitude and Amplitude-Period relationships based on the cyclic behavior of the 12-month moving averages of monthly mean sunspot numbers for cycles 0.23, both in terms of Fisher's exact tests for 2x2 contingency tables and linear regression analyses. Concerning the Period-Amplitude relationship (same cycle), because cycle 23's maximum amplitude is known to be 120.8, the inferred regressions (90-percent prediction intervals) suggest that its period will be 131 +/- 24 months (using all cycles) or 131 +/- 18 months (ignoring cycles 2 and 4, which have the extremes of period, 108 and 164 months, respectively). Because cycle 23 has already persisted for 142 months (May 1996 through February 2008), based on the latter prediction, it should end before September 2008. Concerning the Amplitude-Period relationship (following cycle maximum amplitude versus preceding cycle period), because cycle 23's period is known to be at least 142 months, the inferred regressions (90-percent prediction intervals) suggest that cycle 24's maximum amplitude will be about less than or equal to 96.1 +/- 55.0 (using all cycle pairs) or less than or equal to 91.0 +/- 36.7 (ignoring statistical outlier cycle pairs). Hence, cycle 24's maximum amplitude is expected to be less than 151, perhaps even less than 128, unless cycle pair 23/24 proves to be a statistical outlier.

Wilson, Robert M.↗
NASA NTRS1999

Precision Interval Estimation of the Response Surface by Means of an Integrated Algorithm of Neural Network and Linear Regression

The integration of Radial Basis Function Networks and Back Propagation Neural Networks with the Multiple Linear Regression has been accomplished to map nonlinear response surfaces over a wide range of independent variables in the process of the Modem Design of Experiments. The integrated method is capable to estimate the precision intervals including confidence and predicted intervals. The power of the innovative method has been demonstrated by applying to a set of wind tunnel test data in construction of response surface and estimation of precision interval.

Lo, Ching F.↗
NASA NTRS2004

Characterization and Uncertainty Analysis of a Reference Pressure Measurement System for Wind Tunnels

This paper presents the calibration results and uncertainty analysis of a high-precision reference pressure measurement system currently used in wind tunnels at the NASA Langley Research Center (LaRC). Sensors, calibration standards, and measurement instruments are subject to errors due to aging, drift with time, environment effects, transportation, the mathematical model, the calibration experimental design, and other factors. Errors occur at every link in the chain of measurements and data reduction from the sensor to the final computed results. At each link of the chain, bias and precision uncertainties must be separately estimated for facility use, and are combined to produce overall calibration and prediction confidence intervals for the instrument, typically at a 95% confidence level. The uncertainty analysis and calibration experimental designs used herein, based on techniques developed at LaRC, employ replicated experimental designs for efficiency, separate estimation of bias and precision uncertainties, and detection of significant parameter drift with time. Final results, including calibration confidence intervals and prediction intervals given as functions of the applied inputs, not as a fixed percentage of the full-scale value are presented. System uncertainties are propagated beginning with the initial reference pressure standard, to the calibrated instrument as a working standard in the facility. Among the several parameters that can affect the overall results are operating temperature, atmospheric pressure, humidity, and facility vibration. Effects of factors such as initial zeroing and temperature are investigated. The effects of the identified parameters on system performance and accuracy are discussed.

Amer, Tahani↗
NASA NTRS2008

Using the Modified Precursor Method to Estimate the Size of Cycle 24

Modified geomagnetic precursor techniques for predicting the size of the following sunspot cycle are developed, where these techniques use the 12-month moving averages of the number of disturbed days (when Ap greater than or equals 25), the Ap index, the aa index, and the aaI index at about 4 yr during the declining portion of the preceding sunspot cycle. For cycle 24, these techniques suggest that its RM will measure about 130 +/- 14, a value outside the consensus prediction interval of the low prediction (90 +/- 10) given by the NOAA Solar Cycle 24 Prediction Panel. Furthermore, cycle 24 is predicted to be a fast-rising cycle (ASC = 44 +/- 5 months), peaking before April 2012, presuming the official start of cycle 24 in March 2008. Also discussed are the variation of solar cycle lengths and Hale cycle effects, as related to cycles 23 and 24.

Wilson, Robert M.↗
NASA NTRS2009

Predicting the Size of Sunspot Cycle 24 on the Basis of Single- and Bi-Variate Geomagnetic Precursor Methods

Examined are single- and bi-variate geomagnetic precursors for predicting the maximum amplitude (RM) of a sunspot cycle several years in advance. The best single-variate fit is one based on the average of the ap index 36 mo prior to cycle minimum occurrence (E(Rm)), having a coefficient of correlation (r) equal to 0.97 and a standard error of estimate (se) equal to 9.3. Presuming cycle 24 not to be a statistical outlier and its minimum in March 2008, the fit suggests cycle 24 s RM to be about 69 +/- 20 (the 90% prediction interval). The weighted mean prediction of 11 statistically important single-variate fits is 116 +/- 34. The best bi-variate fit is one based on the maximum and minimum values of the 12-mma of the ap index; i.e., APM# and APm*, where # means the value post-E(RM) for the preceding cycle and * means the value in the vicinity of cycle minimum, having r = 0.98 and se = 8.2. It predicts cycle 24 s RM to be about 92 +/- 27. The weighted mean prediction of 22 statistically important bi-variate fits is 112 32. Thus, cycle 24's RM is expected to lie somewhere within the range of about 82 to 144. Also examined are the late-cycle 23 behaviors of geomagnetic indices and solar wind velocity in comparison to the mean behaviors of cycles 2023 and the geomagnetic indices of cycle 14 (RM = 64.2), the weakest sunspot cycle of the modern era.

Wilson, Robert M.↗
NASA NTRS1974

Prediction and identification of some forbidden lines in the Ne I sequence

A magnetic quadrupole transition which according to a prediction by Garstang (1969) is to have an appreciable transition probability in the higher ions of the Ne I sequence has recently been observed in Fe XVII with high resolution by Parkinson (1973), at 17.086 A. Values of an interval predicted by calculations of Crance (1973) are plotted in a graph. Interval values obtained from the curve are used to predict the values of certain transition wavelengths in the ions Si V Cr XV.

Kastner, S. O.↗
NASA NTRS1976

Attenuation of propagation through rain for an earth-satellite path correlated with predicted values using radar

During the summer of 1974 and spring of 1975, measurements of attenuation of propagation through rain were made at Wallops Island, VA, using 13 and 18 GHz transmitters operating in the uplink mode toward the ATS-6 satellite. Simultaneously, rain reflectivity levels were measured along the earth-satellite path using a high resolution (0.4 deg beamwidth) S-band radar having a scanning antenna. Four rain-gages and two disdrometers were also located in the vicinity of the transmitters. The radar and disdrometer data were used in a modelling program to predict attenuation levels which were subsequently compared to the directly measured fades over nearly simultaneous time intervals. Predicted attenuation levels were obtained for three drop size distributions. Comparisons between predicted and measured attenuation levels showed the APL dropsize distribution gave the smallest rms difference of 1.3 dB at 13 and 18 GHz although the rms difference corresponding to Marshall-Palmer was close to this value. The good agreement suggests the validity of using radar to model path attenuation to obtain attenuation statistics.

Goldhirsh, J.↗
NASA NTRS2011

An Estimate of the Size and Shape of Sunspot Cycle 24 Based on its Early Cycle Behavior using the Hathaway-Wilson-Reichmann Shape-Fitting Function

On the basis of 12-month moving averages (12-mma) of monthly mean sunspot number (R), sunspot cycle 24 had its minimum amplitude (Rm = 1.7) in December 2008. At 12 mo past minimum, R measured 8.3, and at 18 mo past minimum, it measured 16.4. Thus far, the maximum month-to-month rate of rise in 12-mma values of monthly mean sunspot number (AR(t) max) has been 1.7, having occurred at elapsed times past minimum amplitude (t) of 14 and 15 mo. Compared to other sunspot cycles of the modern era, cycle 24?s Rm and AR(t) max (as observed so far) are the smallest on record, suggesting that it likely will be a slow-rising, long-period sunspot cycle of below average maximum amplitude (RM). Supporting this view is the now observed relative strength of cycle 24?s geomagnetic minimum amplitude as measured using the 12-mma value of the aa-geomagnetic index (aam = 8.4), which also is the smallest on record, having occurred at t equals 8 and 9 mo. From the method of Ohl (the inferred preferential association between RM and aam), one predicts RM = 55 +/- 17 (the ?1 se prediction interval) for cycle 24. Furthermore, from the Waldmeier effect (the inferred preferential association between the ascent duration (ASC) and RM) one predicts an ASC longer than 48 mo for cycle 24; hence, maximum amplitude occurrence should be after December 2012. Application of the Hathaway-Wilson-Reichmann shape-fitting function, using an RM = 70 and ASC = 56 mo, is found to adequately fit the early sunspot number growth of cycle 24.

Wilson, Robert M.↗