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At least 163 records · Page 9

Are the 1986-1988 changes in solar free-oscillation frequency splitting significant?

The solar normal-mode splitting coefficients deduced from Big Bear Solar Observatory (BBSO) data differ between 1986 and 1988; inversions for equatorial rotation are slower at depth and faster near the surface in 1988 than in 1986. The significance of the change has been disputed. The data sets overlap for five splitting coefficients (a(j))super 5 sub j = 1 associated with 710 multiplets. On the assumption that rotation rate varies smoothly with radius, both data sets are satisfied by the same rotation model at all colatitudes except near 30-40 deg and near 70 deg (and at their southern hemisphere reflections 140-150 deg and 110 deg). The evidence for equatorial change is weak. Nonparametric tests show a significant offset in the magnitudes of a(1), a(2), and a(4), and of linear combinations sensitive to rotation at colatitudes of 60-80 deg (and 120 deg). Nonparametric tests show significant radial trends in the changes to a(2), a(4), and (less significantly) a(5). There is strong anticorrelation between a(2) and a(4), a(1) and a(3), and a(3) and a(5), suggesting that the estimates are not independent. Individual coefficients a(j) show more evidence for change than do 'physical' linear combinations, adding weight to this hypothesis. Some of the changes in splitting might be related to solar activity, which changed most near colatitude 70 deg from 1986 to 1988.

Gough, Douglas↗

Hidden Markov models and neural networks for fault detection in dynamic systems

Neural networks plus hidden Markov models (HMM) can provide excellent detection and false alarm rate performance in fault detection applications, as shown in this viewgraph presentation. Modified models allow for novelty detection. Key contributions of neural network models are: (1) excellent nonparametric discrimination capability; (2) a good estimator of posterior state probabilities, even in high dimensions, and thus can be embedded within overall probabilistic model (HMM); and (3) simple to implement compared to other nonparametric models. Neural network/HMM monitoring model is currently being integrated with the new Deep Space Network (DSN) antenna controller software and will be on-line monitoring a new DSN 34-m antenna (DSS-24) by July, 1994.

Smyth, Padhraic↗

Wavelet Filtering to Reduce Conservatism in Aeroservoelastic Robust Stability Margins

Wavelet analysis for filtering and system identification was used to improve the estimation of aeroservoelastic stability margins. The conservatism of the robust stability margins was reduced with parametric and nonparametric time-frequency analysis of flight data in the model validation process. Nonparametric wavelet processing of data was used to reduce the effects of external desirableness and unmodeled dynamics. Parametric estimates of modal stability were also extracted using the wavelet transform. Computation of robust stability margins for stability boundary prediction depends on uncertainty descriptions derived from the data for model validation. F-18 high Alpha Research Vehicle aeroservoelastic flight test data demonstrated improved robust stability prediction by extension of the stability boundary beyond the flight regime.

Brenner, Marty↗

On-Line Robust Modal Stability Prediction using Wavelet Processing

Wavelet analysis for filtering and system identification has been used to improve the estimation of aeroservoelastic stability margins. The conservatism of the robust stability margins is reduced with parametric and nonparametric time- frequency analysis of flight data in the model validation process. Nonparametric wavelet processing of data is used to reduce the effects of external disturbances and unmodeled dynamics. Parametric estimates of modal stability are also extracted using the wavelet transform. Computation of robust stability margins for stability boundary prediction depends on uncertainty descriptions derived from the data for model validation. The F-18 High Alpha Research Vehicle aeroservoelastic flight test data demonstrates improved robust stability prediction by extension of the stability boundary beyond the flight regime. Guidelines and computation times are presented to show the efficiency and practical aspects of these procedures for on-line implementation. Feasibility of the method is shown for processing flight data from time- varying nonstationary test points.

Brenner, Martin J.↗

A Globally Optimal Minimax Solution for Spectral Overbounding and Factorization

In this paper, an algorithm is introduced to find a minimum phase transfer function of specified order whose magnitude "tightly" overbounds a specified real-valued nonparametric function of frequency. This method has direct application to transforming nonparametric uncertainty bounds (available from system identification experiments and/or plant modeling) into parametric representations required for modern robust control design software (i.e., a minimum-phase transfer function multiplied by a norm-bounded perturbation).

Scheid, Robert E.↗

The Statistical Consulting Center for Astronomy (SCCA)

The process by which raw astronomical data acquisition is transformed into scientifically meaningful results and interpretation typically involves many statistical steps. Traditional astronomy limits itself to a narrow range of old and familiar statistical methods: means and standard deviations; least-squares methods like chi(sup 2) minimization; and simple nonparametric procedures such as the Kolmogorov-Smirnov tests. These tools are often inadequate for the complex problems and datasets under investigations, and recent years have witnessed an increased usage of maximum-likelihood, survival analysis, multivariate analysis, wavelet and advanced time-series methods. The Statistical Consulting Center for Astronomy (SCCA) assisted astronomers with the use of sophisticated tools, and to match these tools with specific problems. The SCCA operated with two professors of statistics and a professor of astronomy working together. Questions were received by e-mail, and were discussed in detail with the questioner. Summaries of those questions and answers leading to new approaches were posted on the Web (www.state.psu.edu/ mga/SCCA). In addition to serving individual astronomers, the SCCA established a Web site for general use that provides hypertext links to selected on-line public-domain statistical software and services. The StatCodes site (www.astro.psu.edu/statcodes) provides over 200 links in the areas of: Bayesian statistics; censored and truncated data; correlation and regression, density estimation and smoothing, general statistics packages and information; image analysis; interactive Web tools; multivariate analysis; multivariate clustering and classification; nonparametric analysis; software written by astronomers; spatial statistics; statistical distributions; time series analysis; and visualization tools. StatCodes has received a remarkable high and constant hit rate of 250 hits/week (over 10,000/year) since its inception in mid-1997. It is of interest to scientists both within and outside of astronomy. The most popular sections are multivariate techniques, image analysis, and time series analysis. Hundreds of copies of the ASURV, SLOPES and CENS-TAU codes developed by SCCA scientists were also downloaded from the StatCodes site. In addition to formal SCCA duties, SCCA scientists continued a variety of related activities in astrostatistics, including refereeing of statistically oriented papers submitted to the Astrophysical Journal, talks in meetings including Feigelson's talk to science journalists entitled "The reemergence of astrostatistics" at the American Association for the Advancement of Science meeting, and published papers of astrostatistical content.

Akritas, Michael↗

Kernel PLS Estimation of Single-trial Event-related Potentials

Nonlinear kernel partial least squaes (KPLS) regressior, is a novel smoothing approach to nonparametric regression curve fitting. We have developed a KPLS approach to the estimation of single-trial event related potentials (ERPs). For improved accuracy of estimation, we also developed a local KPLS method for situations in which there exists prior knowledge about the approximate latency of individual ERP components. To assess the utility of the KPLS approach, we compared non-local KPLS and local KPLS smoothing with other nonparametric signal processing and smoothing methods. In particular, we examined wavelet denoising, smoothing splines, and localized smoothing splines. We applied these methods to the estimation of simulated mixtures of human ERPs and ongoing electroencephalogram (EEG) activity using a dipole simulator (BESA). In this scenario we considered ongoing EEG to represent spatially and temporally correlated noise added to the ERPs. This simulation provided a reasonable but simplified model of real-world ERP measurements. For estimation of the simulated single-trial ERPs, local KPLS provided a level of accuracy that was comparable with or better than the other methods. We also applied the local KPLS method to the estimation of human ERPs recorded in an experiment on co,onitive fatigue. For these data, the local KPLS method provided a clear improvement in visualization of single-trial ERPs as well as their averages. The local KPLS method may serve as a new alternative to the estimation of single-trial ERPs and improvement of ERP averages.

Rosipal, Roman↗

Parametric Covariance Model for Horizon-Based Optical Navigation

This Note presents an entirely parametric version of the covariance for horizon-based optical navigation measurements. The covariance can be written as a function of only the spacecraft position, two sensor design parameters, the illumination direction, the size of the observed planet, the size of the lit arc to be used, and the total number of observed horizon points. As a result, one may now more clearly understand the sensitivity of horizon-based optical navigation performance as a function of these key design parameters, which is insight that was obscured in previous (and nonparametric) versions of the covariance. Finally, the new parametric covariance is shown to agree with both the nonparametric analytic covariance and results from a Monte Carlo analysis.

Optical Navigatio↗

Advances in Hyperspectral Image Classification Methods for Vegetation and Agricultural Cropland Studies

Hyperspectral data are becoming more widely available via sensors on airborne and unmanned aerial vehicle (UAV) platforms, as well as proximal platforms. While space-based hyperspectral data continue to be limited in availability, multiple spaceborne Earth-observing missions on traditional platforms are scheduled for launch, and companies are experimenting with small satellites for constellations to observe the Earth, as well as for planetary missions. Land cover mapping via classification is one of the most important applications of hyperspectral remote sensing and will increase in significance as time series of imagery are more readily available. However, while the narrow bands of hyperspectral data provide new opportunities for chemistry-based modeling and mapping, challenges remain. Hyperspectral data are high dimensional, and many bands are highly correlated or irrelevant for a given classification problem. For supervised classification methods, the quantity of training data is typically limited relative to the dimension of the input space. The resulting Hughes phenomenon, often referred to as the curse of dimensionality, increases potential for unstable parameter estimates, overfitting, and poor generalization of classifiers. This is particularly problematic for parametric approaches such as Gaussian maximum likelihood–based classifiers that have been the backbone of pixel-based multispectral classification methods. This issue has motivated investigation of alternatives, including regularization of the class covariance matrices, ensembles of weak classifiers, development of feature selection and extraction methods, adoption of nonparametric classifiers, and exploration of methods to exploit unlabeled samples via semi-supervised and active learning. Data sets are also quite large, motivating computationally efficient algorithms and implementations. This chapter provides an overview of the recent advances in classification methods for mapping vegetation using hyperspectral data. Three data sets that are used in the hyperspectral classification literature (e.g., Botswana Hyperion satellite data and AVIRIS airborne data over both Kennedy Space Center and Indian Pines) are described in Section 3.2 and used to illustrate methods described in the chapter. An additional high-resolution hyperspectral data set acquired by a SpecTIR sensor on an airborne platform over the Indian Pines area is included to exemplify the use of new deep learning approaches, and a multiplatform example of airborne hyperspectral data is provided to demonstrate transfer learning in hyperspectral image classification. Classical approaches for supervised and unsupervised feature selection and extraction are reviewed in Section 3.3. In particular, nonlinearities exhibited in hyperspectral imagery have motivated development of nonlinear feature extraction methods in manifold learning, which are outlined in Section 3.3.1.4. Spatial context is also important in classification of both natural vegetation with complex textural patterns and large agricultural fields with significant local variability within fields. Approaches to exploit spatial features at both the pixel level (e.g., co-occurrence–based texture and extended morphological attribute profiles [EMAPs]) and integration of segmentation approaches (e.g., HSeg) are discussed in this context in Section 3.3.2. Recently, classification methods that leverage nonparametric methods originating in the machine learning community have grown in popularity. An overview of both widely used and newly emerging approaches, including support vector machines (SVMs), Gaussian mixture models, and deep learning based on convolutional neural networks is provided in Section 3.4. Strategies to exploit unlabeled samples, including active learning and metric learning, which combine feature extraction and augmentation of the pool of training samples in an active learning framework, are outlined in Section 3.5. Integration of image segmentation with classification to accommodate spatial coherence typically observed in vegetation is also explored, including as an integrated active learning system. Exploitation of multisensor strategies for augmenting the pool of training samples is investigated via a transfer learning framework in Section 3.5.1.2. Finally, we look to the future, considering opportunities soon to be provided by new paradigms, as hyperspectral sensing is becoming common at multiple scales from ground-based and airborne autonomous vehicles to manned aircraft and space-based platforms.

Pasolli, Edoardo↗

Variational Coupled Loads Analysis using the Hybrid Parametric Variation Method

Time-domain coupled loads analysis (CLA)is used to determine the response of a launch vehicle and payload system to transient forces, such as liftoff, engine ignitions and shutdowns, jettison events, and atmospheric flight loads, such as buffet. CLA, using Hurty/Craig-Bampton (HCB)component models, is the accepted method for the establishment of design-level loads for launch systems. However, uncertainty in the component models flows into uncertainty in predicted system results. Uncertainty in the structural responses during launch is a significant concern because small variations in launch vehicle and payload mode shapes and their interactions can result in significant variations in system loads. Uncertainty quantification (UQ)is used to determine statistical bounds on prediction accuracy based on model uncertainty. In this paper uncertainty is treated at the HCB component-model level. In an effort to account for model uncertainties and statistically bound their effect on CLA predictions, this work combines CLA with UQ in a process termed variational coupled loads analysis (VCLA). The modeling of uncertainty using a parametric approach, in which input parameters are represented by random variables, is common, but its major drawback is the resulting uncertainty is limited to the form of the nominal model. Uncertainty in model form is one of the biggest contributors to uncertainty in complex built-up structures. Model-form uncertainty can be represented using a nonparametric approach based on random matrix theory (RMT). In this work, UQ is performed using the hybrid parametric variation (HPV)method, which combines parametric with nonparametric uncertainty at the HCB component model level. The HPV method requires the selection of dispersion values for the HCB fixed-interface (FI)eigenvalues, and the HCB mass and stiffness matrices. The dispersions are based upon component test-analysis modal correlation results. During VCLA, random component models are assembled into an ensemble of random systems using a Monte Carlo (MC)approach. CLA is applied to each of the ensemble members to produce an ensemble of system-level responses for statistical analysis. The proposed methodology is demonstrated through its application to a buffet loads analysis of NASA’s Space Launch System (SLS)during the transonic regime fifty seconds after liftoff. Core stage (CS)section shears and moments are recovered, and statistics are computed.

Uncertainty Quantification↗

SLS Integrated Modal Test Uncertainty Quantification using the Hybrid Parametric Variation Method

Uncertainty in structural loading during launch is a significant concern in the development of spacecraft and launch vehicles. Small variations in launch vehicle and payload mode shapes and their interaction can result in significant variation in system loads. In many cases involving large aerospace systems it is difficult, not economical, or impossible to perform a system modal test. However, it is still vital to obtain test results that can be compared with analytical predictions to validate models. Instead, the “Building Block Approach” is used in which system components are tested individually. Component models are correlated and updated to agree as best they can with test results. The Space Launch System consists of a number of components that are assembled into a launch vehicle. Finite element models of the components are developed, reduced to Hurty/Craig-Bampton models and assembled to represent different phases of flight. The only opportunity to obtain modal test data from an assembled Space Launch System will be during the Integrated Modal Test. There is always uncertainty in every model, which flows into uncertainty in predicted system results. Uncertainty Quantification is used to determine statistical bounds on prediction accuracy based on model uncertainty. For the Space Launch System, model uncertainty is at the Hurty/Craig-Bampton component level. Uncertainty in the Hurty/Craig-Bampton components is quantified using the hybrid parametric variation approach that combines parametric and nonparametric uncertainty. Uncertainty in model form is one of the biggest contributors to uncertainty in complex built-up structures. This type of uncertainty cannot be represented by variations infinite element model input parameters and thus cannot be included in a parametric approach. However, model-form uncertainty can be modeled using a nonparametric approach based on random matrix theory. The hybrid parametric variation method requires the selection of dispersion values for the Hurty/Craig-Bampton fixed-interface eigenvalues, and the Hurty/Craig-Bampton stiffness matrices. Component test/analysis frequency error is used to identify the fixed-interface eigenvalue dispersions, while test/analysis cross-orthogonality is used to identify stiffness dispersion values. The hybrid parametric variation uncertainty quantification approach is applied to the Space Launch System Integrated Modal Test configuration. Monte Carlo analysis is performed, and statistics are determined for modal correlation metrics, frequency response from Integrated Modal Test shakers to selected accelerometers, as well as other metrics for determining how well target modes are excited and identified. If the predicted uncertainty envelopes future Integrated Modal Test results, then there will be increased confidence in the utility of the component-based hybrid parametric variation uncertainty quantification approach.

Uncertainty Quantification↗

Asymptotic inconsistency of the cumulative algorithm for laser-induced damage probability analysis

The “cumulative algorithm” is a data analysis method that has been proposed to provide an objective, nonparametric determination of laser-induced damage probability as a function of fluence from experimental data that contain both damaged sites and undamaged sites (i.e., 1-on-1 or S-on-1 testing protocols). In this work, the limitations of this approach are explored by considering the asymptotic limit of a large number of test sites. It is shown that the cumulative algorithm does not converge to the true probability distribution and significantly underestimates the damage probability near the damage onset. Here, based on the results of this work, the cumulative algorithm is not recommended for accurate estimation of damage probability.

Computational methods↗

A Bayesian Measurment Error Model for Misaligned Radiographic Data

An understanding of the inherent variability in micro-computed tomography (micro-CT) data is essential to tasks such as statistical process control and the validation of radiographic simulation tools. The data present unique challenges to variability analysis due to the relatively low resolution of radiographs, and also due to minor variations from run to run which can result in misalignment or magnification changes between repeated measurements of a sample. Positioning changes artificially inflate the variability of the data in ways that mask true physical phenomena. We present a novel Bayesian nonparametric regression model that incorporates both additive and multiplicative measurement error in addition to heteroscedasticity to address this problem. We also use this model to assess the effects of sample thickness and sample position on measurement variability for an aluminum specimen. Supplementary materials for this article are available online.

97 MATHEMATICS AND COMPUTING↗

Spatially Dependent Multiple Testing Under Model Misspecification, With Application to Detection of Anthropogenic Influence on Extreme Climate Events

The Weather Risk Attribution Forecast (WRAF) is a forecasting tool that uses output from global climate models to make simultaneous attribution statements about whether and how greenhouse gas emissions have contributed to extreme weather across the globe. However, in conducting a large number of simultaneous hypothesis tests, the WRAF is prone to identifying false “discoveries.” A common technique for addressing this multiple testing problem is to adjust the procedure in a way that controls the proportion of true null hypotheses that are incorrectly rejected, or the false discovery rate (FDR). Unfortunately, generic FDR procedures suffer from low power when the hypotheses are dependent, and techniques designed to account for dependence are sensitive to misspecification of the underlying statistical model. In this paper, we develop a Bayesian decision-theoretical approach for dependent multiple testing and a nonparametric hierarchical statistical model that flexibly controls false discovery and is robust to model misspecification. We illustrate the robustness of our procedure to model error with a simulation study, using a framework that accounts for generic spatial dependence and allows the practitioner to flexibly specify the decision criteria. Finally, we apply our procedure to several seasonal forecasts and discuss implementation for the WRAF workflow. Lastly, supplementary materials for this article, including a standardized description of the materials available for reproducing the work, are available as an online supplement.

54 ENVIRONMENTAL SCIENCES↗

BASS: An R Package for Fitting and Performing Sensitivity Analysis of Bayesian Adaptive Spline Surfaces

In this work, we present the R package BASS as a tool for nonparametric regression. The primary focus of the package is fitting fully Bayesian adaptive spline surface (BASS) models and performing global sensitivity analyses of these models. The BASS framework is similar to that of Bayesian multivariate adaptive regression splines (BMARS) from Denison, Mallick, and Smith (1998), but with many added features. The software is built to efficiently handle significant amounts of data with many continuous or categorical predictors and with functional response. Under our Bayesian framework, most priors are automatic but these can be modified by the user to focus on parsimony and the avoidance of overfitting. If directed to do so, the software uses parallel tempering to improve the reversible jump Markov chain Monte Carlo (RJMCMC) methods used to perform inference. We discuss the implementation of these features and present the performance of BASS in a number of analyses of simulated and real data.

97 MATHEMATICS AND COMPUTING↗

Deep Neural Networks are Adaptive to Function Regularity and Data Distribution in Approximation and Estimation

Deep learning has exhibited remarkable results across diverse areas. To understand its success, substantial research has been directed towards its theoretical foundations. Nev- ertheless, the majority of these studies examine how well deep neural networks can model functions with uniform regularities. In this paper, we explore a different angle: how deep neural networks can adapt to varying degrees of smoothness in functions and nonuni- form data distributions across different locations and scales. More precisely, we focus on a broad class of functions defined by nonlinear tree-based approximation methods. This class encompasses a range of function types, such as functions with uniform regularities and discontinuous functions. We develop nonparametric approximation and estimation theories for this class using deep ReLU networks. Our results show that deep neural networks are adaptive to the nonuniform smoothness of functions and nonuniform data distributions at different locations and scales. We apply our results to several function classes, and derive the corresponding approximation and generalization errors. The validity of our results is demonstrated through numerical experiments.

97 MATHEMATICS AND COMPUTING↗

Comparisons of Wilks’ and Monte Carlo Methods in Response to the 10CFR50.46(c) Proposed Rulemaking

The Nuclear Regulatory Commission (NRC) is proposing a new rulemaking on emergency core system/loss-of-coolant accident (LOCA) performance analysis. In the proposed rulemaking, designated as 10CFR50.46(c), the US NRC put forward an equivalent cladding oxidation criterion as a function of cladding pre-transient hydrogen content. The proposed rulemaking imposes more restrictive and burnup-dependent cladding embrittlement criteria; consequently nearly all the fuel rods in a reactor core need to be analyzed under LOCA conditions to demonstrate compliance to the safety limits. New analysis methods are required to provide a thorough characterization of the reactor core in order to identify the locations of the limiting rods as well as to quantify the safety margins under LOCA conditions. With the new analysis method presented in this work, the limiting transient case and the limiting rods can be easily identified to quantify the safety margins in response to the proposed new rulemaking. In this work, the best-estimate plus uncertainty (BEPU) analysis capability for large break LOCA with the new cladding embrittlement criteria using the RELAP5-3D code is established and demonstrated with a reduced set of uncertainty parameters. Both the direct Monte Carlo method and the Wilks’ nonparametric statistical method can be used to perform uncertainty quantification. Wilks’ method has become the de-facto industry standard to perform uncertainty quantification in BEPU LOCA analyses. Despite its widespread adoption by the industry, the use of small sample sizes to infer statement of compliance to the existing 10CFR50.46 rule, has been a major cause of unrealized operational margin in today’s BEPU methods. Moreover the debate on the proper interpretation of the Wilks’ theorem in the context of safety analyses is not fully resolved yet, even more than two decades after its introduction in the frame of safety analyses in the nuclear industry. This represents both a regulatory and application risk in rolling out new methods. With the 10CFR50.46(c) proposed rulemaking, the deficiencies of the Wilks’ approach are further exacerbated. The direct Monte Carlo approach offers a robust alternative to perform uncertainty quantification within the context of BEPU analyses. In this work, the Monte Carlo method is compared with the Wilks’ method in response to the NRC 10CFR50.46(c) proposed rulemaking.

10CFR50.46(c)↗

Uncertainty quantification and global sensitivity analysis of the Los Alamos sea ice model

Changes in the high-latitude climate system have the potential to affect global climate through feedbacks with the atmosphere and connections with midlatitudes. Sea ice and climate models used to understand these changes have uncertainties that need to be characterized and quantified. We present a quantitative way to assess uncertainty in complex computer models, which is a new approach in the analysis of sea ice models. We characterize parametric uncertainty in the Los Alamos sea ice model (CICE) in a standalone configuration and quantify the sensitivity of sea ice area, extent, and volume with respect to uncertainty in 39 individual model parameters. Unlike common sensitivity analyses conducted in previous studies where parameters are varied one at a time, this study uses a global variance-based approach in which Sobol' sequences are used to efficiently sample the full 39-dimensional parameter space. We implement a fast emulator of the sea ice model whose predictions of sea ice extent, area, and volume are used to compute the Sobol' sensitivity indices of the 39 parameters. Main effects and interactions among the most influential parameters are also estimated by a nonparametric regression technique based on generalized additive models. A ranking based on the sensitivity indices indicates that model predictions are most sensitive to snow parameters such as snow conductivity and grain size, and the drainage of melt ponds. Lastly, it is recommended that research be prioritized toward more accurately determining these most influential parameter values by observational studies or by improving parameterizations in the sea ice model.

54 ENVIRONMENTAL SCIENCES↗