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At least 721 records · Page 40

Statistical Symbolic Execution with Informed Sampling

Symbolic execution techniques have been proposed recently for the probabilistic analysis of programs. These techniques seek to quantify the likelihood of reaching program events of interest, e.g., assert violations. They have many promising applications but have scalability issues due to high computational demand. To address this challenge, we propose a statistical symbolic execution technique that performs Monte Carlo sampling of the symbolic program paths and uses the obtained information for Bayesian estimation and hypothesis testing with respect to the probability of reaching the target events. To speed up the convergence of the statistical analysis, we propose Informed Sampling, an iterative symbolic execution that first explores the paths that have high statistical significance, prunes them from the state space and guides the execution towards less likely paths. The technique combines Bayesian estimation with a partial exact analysis for the pruned paths leading to provably improved convergence of the statistical analysis. We have implemented statistical symbolic execution with in- formed sampling in the Symbolic PathFinder tool. We show experimentally that the informed sampling obtains more precise results and converges faster than a purely statistical analysis and may also be more efficient than an exact symbolic analysis. When the latter does not terminate symbolic execution with informed sampling can give meaningful results under the same time and memory limits.

Reliability↗

Clutter Identification based on sparse recovery with dynamically changing dictionary sizes for cognitive radar

Existing radar algorithms assume stationary statistical characteristics for environment/clutter. In practical scenarios, the statistical characteristics of the clutter can dynamically change depending on where the radar is operating. Non-stationarity in the statistical characteristics of the clutter may negatively affect the radar performance. Cognitive radar that can sense the changes in the clutter statistics, learn the new statistical characteristics, and adapt to these changes has been proposed to overcome these shortcomings. We have recently developed techniques for detection of statistical changes and learning the new clutter distribution for cognitive radar. In this work, we will extend the learning component. More specifically, in our previous work, we have developed a sparse recovery based clutter distribution identification to learn the distribution of the new clutter characteristics after the detected change in the statistics of the clutter. In our method, we have built a dictionary of clutter distributions and used this dictionary in orthogonal matching pursuit to perform sparse recovery of the clutter distribution assuming that the dictionary includes the new distribution. In this work, we propose a hypothesis testing based approach to detect whether the new distribution of the clutter is included in the dictionary or not, and suggest a method to dynamically update the dictionary. We envision that the successful outcomes of this work will be of high relevance to the adaptive learning and cognitive augmentation of the radar systems that are used in remotely piloted vehicles for surveillance and reconnaissance operations.

Zhu, Yuansheng↗

Statistical Measurement of Longitudinal Beam Halo in Fermilab Recycler

The formation of non-Gaussian halo in both the transverse and longitudinal dimensions of beam bunches has been notoriously difficult both the model and to measure. We present a technique to measure the longitudinal halo of 2.5 MHz bunches in the Fermilab Recycler, which have been formed for the g-2 anomalous magnetic moment experiment. While out of time beam is not a particular concern to this experiment, it is a key issue for the subsequent Mu2e rare muon decay experiment, which will use the same bunch formation procedure. Our measurement relies on a statistical technique, in which a small fraction of the beam is scattered from the primary collimation foil in the recycler, and then is detected by a charge telescope consisting of quartz Cherenkov radiators and photomultiplier tubes. By integrating over many revolutions, the time profile of longitudinal halo (out-of-time beam) can be measured down to less than a 10⁻⁵ fractional level, relative to in-time beam. These results can then be compared to simulations.

43 PARTICLE ACCELERATORS↗

Hierarchical Modeling and Robust Synthesis for the Preliminary Design of Large Scale Complex Systems

Large-scale complex systems are characterized by multiple interacting subsystems and the analysis of multiple disciplines. The design and development of such systems inevitably requires the resolution of multiple conflicting objectives. The size of complex systems, however, prohibits the development of comprehensive system models, and thus these systems must be partitioned into their constituent parts. Because simultaneous solution of individual subsystem models is often not manageable iteration is inevitable and often excessive. In this dissertation these issues are addressed through the development of a method for hierarchical robust preliminary design exploration to facilitate concurrent system and subsystem design exploration, for the concurrent generation of robust system and subsystem specifications for the preliminary design of multi-level, multi-objective, large-scale complex systems. This method is developed through the integration and expansion of current design techniques: Hierarchical partitioning and modeling techniques for partitioning large-scale complex systems into more tractable parts, and allowing integration of subproblems for system synthesis; Statistical experimentation and approximation techniques for increasing both the efficiency and the comprehensiveness of preliminary design exploration; and Noise modeling techniques for implementing robust preliminary design when approximate models are employed. Hierarchical partitioning and modeling techniques including intermediate responses, linking variables, and compatibility constraints are incorporated within a hierarchical compromise decision support problem formulation for synthesizing subproblem solutions for a partitioned system. Experimentation and approximation techniques are employed for concurrent investigations and modeling of partitioned subproblems. A modified composite experiment is introduced for fitting better predictive models across the ranges of the factors, and an approach for constructing partitioned response surfaces is developed to reduce the computational expense of experimentation for fitting models in a large number of factors. Noise modeling techniques are compared and recommendations are offered for the implementation of robust design when approximate models are sought. These techniques, approaches, and recommendations are incorporated within the method developed for hierarchical robust preliminary design exploration. This method as well as the associated approaches are illustrated through their application to the preliminary design of a commercial turbofan turbine propulsion system. The case study is developed in collaboration with Allison Engine Company, Rolls Royce Aerospace, and is based on the Allison AE3007 existing engine designed for midsize commercial, regional business jets. For this case study, the turbofan system-level problem is partitioned into engine cycle design and configuration design and a compressor modules integrated for more detailed subsystem-level design exploration, improving system evaluation. The fan and low pressure turbine subsystems are also modeled, but in less detail. Given the defined partitioning, these subproblems are investigated independently and concurrently, and response surface models are constructed to approximate the responses of each. These response models are then incorporated within a commercial turbofan hierarchical compromise decision support problem formulation. Five design scenarios are investigated, and robust solutions are identified. The method and solutions identified are verified by comparison with the AE3007 engine. The solutions obtained are similar to the AE3007 cycle and configuration, but are better with respect to many of the requirements.

Koch, Patrick N.↗

GEO Population Estimates using Optical Survey Data

Optical survey data taken using the NASA Michigan Orbital Debris Survey Telescope (MODEST) gives us an opportunity to statistically sample faint object population in the Geosynchronous (GEO) and near-GEO environment. This paper will summarize the MODEST survey work that has been conducted by NASA since 2002, and will outline the techniques employed to arrive at the current population estimates in the GEO environment for dim objects difficult to detect and track using current systems in the Space Surveillance Network (SSN). Some types of orbits have a higher detection rate based on what parts of the GEO belt is being observed, a straightforward statistical technique is used to debias these observations to arrive at an estimate of the total population potentially visible to the telescope. The size and magnitude distributions of these fainter debris objects are markedly different from the catalogued population. GEO debris consists of at least two different populations, one which follows the standard breakup power law and one which has anomalously high Area-to-Mass Ratios (1 to approx. 30 square meters per kilogram; a sheet of paper = approx. 13 square meters per kilogram). The Inter-Agency Space Debris Coordination Committee (IADC) is investigating objects in GEO orbits with anomalously high Area-to-Mass Ratios (AMRs). The ESA Space Debris Telescope discovered this population and has and its properties of inclinations (0 to 30 degrees), changing eccentricities (0 and 0.6), and mean motions (approx. 1 rev), will be presented. The accepted interpretation of this orbital behavior is that solar radiation pressure drives the perturbations causing time varying inclinations and eccentricities. The orbital parameters are unstable for this population and thus difficult to predict. Their dim visual magnitudes and photometric variability make observations a challenge. The IADC has enlisted a series of observatories (participating institutions: University of Michigan/CTIO, Astronomical Institute University of Bern, Boeing LTS / AMOS, Keldysh Institute of Applied Mathematics) at different longitudes. Complete observational coverage over periods of days to months will provide a better understanding of the properties, such as solar radiation pressure effects on orbital elements, size, shape, attitude, color variations, and spectral characteristics. Results from recent observational programs will be summarized, and includes a description of the orbit elements prediction processes, a summary of the metric tracking performance, and some photometric characteristics of this class of debris.

Barker, Edwin S.↗

A comparison of Landsat point and rectangular field training sets for land-use classification

Rectangular training fields of homogeneous spectroreflectance are commonly used in supervised pattern recognition efforts. Trial image classification with manually selected training sets gives irregular and misleading results due to statistical bias. A self-verifying, grid-sampled training point approach is proposed as a more statistically valid feature extraction technique. A systematic pixel sampling network of every ninth row and ninth column efficiently replaced the full image scene with smaller statistical vectors which preserved the necessary characteristics for classification. The composite second- and third-order average classification accuracy of 50.1 percent for 331,776 pixels in the full image substantially agreed with the 51 percent value predicted by the grid-sampled, 4,100-point training set.

Tom, C. H.↗

Advanced techniques and technology for efficient data storage, access, and transfer

Advanced techniques for efficiently representing most forms of data are being implemented in practical hardware and software form through the joint efforts of three NASA centers. These techniques adapt to local statistical variations to continually provide near optimum code efficiency when representing data without error. Demonstrated in several earlier space applications, these techniques are the basis of initial NASA data compression standards specifications. Since the techniques clearly apply to most NASA science data, NASA invested in the development of both hardware and software implementations for general use. This investment includes high-speed single-chip very large scale integration (VLSI) coding and decoding modules as well as machine-transferrable software routines. The hardware chips were tested in the laboratory at data rates as high as 700 Mbits/s. A coding module's definition includes a predictive preprocessing stage and a powerful adaptive coding stage. The function of the preprocessor is to optimally process incoming data into a standard form data source that the second stage can handle.The built-in preprocessor of the VLSI coder chips is ideal for high-speed sampled data applications such as imaging and high-quality audio, but additionally, the second stage adaptive coder can be used separately with any source that can be externally preprocessed into the 'standard form'. This generic functionality assures that the applicability of these techniques and their recent high-speed implementations should be equally broad outside of NASA.

Rice, Robert F.↗

Instrumental Response Model and Detrending for the Dark Energy Camera

We describe the model for mapping from sky brightness to the digital output of the Dark Energy Camera (DECam) and the algorithms adopted by the Dark Energy Survey (DES) for inverting this model to obtain photometric measures of celestial objects from the raw camera output. This calibration aims for fluxes that are uniform across the camera field of view and across the full angular and temporal span of the DES observations, approaching the accuracy limits set by shot noise for the full dynamic range of DES observations. The DES pipeline incorporates several substantive advances over standard detrending techniques, including principal-components-based sky and fringe subtraction; correction of the "brighter-fatter" nonlinearity; use of internal consistency in on-sky observations to disentangle the influences of quantum efficiency, pixel-size variations, and scattered light in the dome flats; and pixel-by-pixel characterization of instrument spectral response, through combination of internal-consistency constraints with auxiliary calibration data. This article provides conceptual derivations of the detrending/calibration steps, and the procedures for obtaining the necessary calibration data. Other publications will describe the implementation of these concepts for the DES operational pipeline, the detailed methods, and the validation that the techniques can bring DECam photometry and astrometry within $\approx 2$ mmag and $\approx 3$ mas, respectively, of fundamental atmospheric and statistical limits. In conclusion, the DES techniques should be broadly applicable to wide-field imagers.

79 ASTRONOMY AND ASTROPHYSICS↗

On the Use of Statistics in Design and the Implications for Deterministic Computer Experiments

Perhaps the most prevalent use of statistics in engineering design is through Taguchi's parameter and robust design -- using orthogonal arrays to compute signal-to-noise ratios in a process of design improvement. In our view, however, there is an equally exciting use of statistics in design that could become just as prevalent: it is the concept of metamodeling whereby statistical models are built to approximate detailed computer analysis codes. Although computers continue to get faster, analysis codes always seem to keep pace so that their computational time remains non-trivial. Through metamodeling, approximations of these codes are built that are orders of magnitude cheaper to run. These metamodels can then be linked to optimization routines for fast analysis, or they can serve as a bridge for integrating analysis codes across different domains. In this paper we first review metamodeling techniques that encompass design of experiments, response surface methodology, Taguchi methods, neural networks, inductive learning, and kriging. We discuss their existing applications in engineering design and then address the dangers of applying traditional statistical techniques to approximate deterministic computer analysis codes. We conclude with recommendations for the appropriate use of metamodeling techniques in given situations and how common pitfalls can be avoided.

Simpson, Timothy W.↗

Cost-of-Service Segmentation of Energy Consumers

Uncertainty in consumption is a key challenge at energy utility companies, which are faced with balancing highly stochastic demand with increasingly volatile supply characterized by significant penetration rates of intermittent renewable sources. This paper proposes a methodology to quantify uncertainty in consumption that highlights the dependence of the cost-of-service with volatility in demand. We use a large and rich dataset of consumption time series to provide evidence that there is a substantial degree of high-level structure in the statistics of consumption across users which may be partially explained by certain characteristics of the users. To uncover this structure, we propose a new technique for extracting typical statistical signatures of consumption-energy demand distributions (EDDs)-that is based on clustering distributions using a fast, approximated algorithm. We next study the factors influencing the choice of consumption signature and identify certain types of appliances and behaviors related to appliance operation that are most predictive. Finally, we comment on how structure in consumption statistics may be used to target residential energy efficiency programs to achieve greatest impact in curtailing cost of service.

Albert, A↗

Enhancing statistical moment calculations for stochastic Galerkin solutions with Monte Carlo techniques

Here, we provide a method for enhancing stochastic Galerkin moment calculations to the linear elliptic equation with random diffusivity using an ensemble of Monte Carlo solutions. This hybrid approach combines the accuracy of low-order stochastic Galerkin and the computational efficiency of Monte Carlo methods to provide statistical moment estimates which are significantly more accurate than performing each method individually. The hybrid approach involves computing a low-order stochastic Galerkin solution, after which Monte Carlo techniques are used to estimate the residual. We show that the combined stochastic Galerkin solution and residual is superior in both time and accuracy for a one-dimensional test problem and a more computational intensive two-dimensional linear elliptic problem for both the mean and variance quantities.

97 MATHEMATICS AND COMPUTING↗

Significant DBSCAN+: Statistically Robust Density-based Clustering

Cluster detection is important and widely used in a variety of applications, including public health, public safety, transportation, and so on. Given a collection of data points, we aim to detect density-connected spatial clusters with varying geometric shapes and densities, under the constraint that the clusters are statistically significant. The problem is challenging, because many societal applications and domain science studies have low tolerance for spurious results, and clusters may have arbitrary shapes and varying densities. As a classical topic in data mining and learning, a myriad of techniques have been developed to detect clusters with both varying shapes and densities (e.g., density-based, hierarchical, spectral, or deep clustering methods). However, the vast majority of these techniques do not consider statistical rigor and are susceptible to detecting spurious clusters formed as a result of natural randomness. On the other hand, scan statistic approaches explicitly control the rate of spurious results, but they typically assume a single “hotspot” of over-density and many rely on further assumptions such as a tessellated input space. To unite the strengths of both lines of work, we propose a statistically robust formulation of a multi-scale DBSCAN, namely Significant DBSCAN+, to identify significant clusters that are density connected. As we will show, incorporation of statistical rigor is a powerful mechanism that allows the new Significant DBSCAN+ to outperform state-of-the-art clustering techniques in various scenarios. We also propose computational enhancements to speed-up the proposed approach. Experiment results show that Significant DBSCAN+ can simultaneously improve the success rate of true cluster detection (e.g., 10–20% increases in absolute F1 scores) and substantially reduce the rate of spurious results (e.g., from thousands/hundreds of spurious detections to none or just a few across 100 datasets), and the acceleration methods can improve the efficiency for both clustered and non-clustered data.

Computer Science↗

Assessing Regional Scale Variability in Extreme Value Statistics Under Altered Climate Scenarios

Recent studies have suggested that low-frequency modes of climate variability can significantly influence regional climate. The climatology associated with extreme events has been shown to be particularly sensitive. This has profound implications for droughts, heat waves, and food production. We propose to examine regional climate simulations conducted over the continental United States by applying a recently developed technique which combines wavelet multi–resolution analysis with information theory metrics. This research is motivated by two fundamental questions concerning the spatial and temporal structure of extreme events. These questions are 1) what temporal scales of the extreme value distributions are most sensitive to alteration by low-frequency climate forcings and 2) what is the nature of the spatial structure of variation in these timescales? The primary objective is to assess to what extent information theory metrics can be useful in characterizing the nature of extreme weather phenomena. Specifically, we hypothesize that (1) changes in the nature of extreme events will impact the temporal probability density functions and that information theory metrics will be sensitive these changes and (2) via a wavelet multi–resolution analysis, we will be able to characterize the relative contribution of different timescales on the stochastic nature of extreme events. In order to address these hypotheses, we propose a unique combination of an established regional climate modeling approach and advanced statistical techniques to assess the effects of low-frequency modes on climate extremes over North America. The behavior of climate extremes in RCM simulations for the 20th century will be compared with statistics calculated from the United States Historical Climatology Network (USHCN) and simulations from the North American Regional Climate Change Assessment Program (NARCCAP). This effort will serve to establish the baseline behavior of climate extremes, the validity of an innovative multi–resolution information theory approach, and the ability of the RCM modeling framework to represent the low-frequency modulation of extreme climate events. Once the skill of the modeling and analysis methodology has been established, we will apply the same approach for the AR5 (IPCC Fifth Assessment Report) climate change scenarios in order to assess how climate extremes and the the influence of lowfrequency variability on climate extremes might vary under changing climate. The research specifically addresses the DOE focus area 2. Simulation of climate extremes under a changing climate. Specific results will include (1) a better understanding of the spatial and temporal structure of extreme events, (2) a thorough quantification of how extreme values are impacted by low-frequency climate teleconnections, (3) increased knowledge of current regional climate models ability to ascertain these influences, and (4) a detailed examination of the how the distribution of extreme events are likely to change under different climate change scenarios. In addition, this research will assess the ability of the innovative wavelet information theory approach to characterize extreme events. Any and all of these results will greatly enhance society’s ability to understand and mitigate the regional ramifications of future global climate change.

54 ENVIRONMENTAL SCIENCES↗

Thinking Bayesian for plasma physicists

Bayesian statistics offers a powerful technique for plasma physicists to infer knowledge from the heterogeneous data types encountered. To explain this power, a simple example, Gaussian Process Regression, and the application of Bayesian statistics to inverse problems are explained. The likelihood is the key distribution because it contains the data model, or theoretic predictions, of the desired quantities. By using prior knowledge, the distribution of the inferred quantities of interest based on the data given can be inferred. Because it is a distribution of inferred quantities given the data and not a single prediction, uncertainty quantification is a natural consequence of Bayesian statistics. The benefits of machine learning in developing surrogate models for solving inverse problems are discussed, as well as progress in quantitatively understanding the errors that such a model introduces.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Evaluation of SLAR and thematic mapper MSS data for forest cover mapping using computer-aided analysis techniques

A set of training statistics for the 30 meter resolution simulated thematic mapper MSS data was generated based on land use/land cover classes. In addition to this supervised data set, a nonsupervised multicluster block of training statistics is being defined in order to compare the classification results and evaluate the effect of the different training selection methods on classification performance. Two test data sets, defined using a stratified sampling procedure incorporating a grid system with dimensions of 50 lines by 50 columns, and another set based on an analyst supervised set of test fields were used to evaluate the classifications of the TMS data. The supervised training data set generated training statistics, and a per point Gaussian maximum likelihood classification of the 1979 TMS data was obtained. The August 1980 MSS data was radiometrically adjusted. The SAR data was redigitized and the SAR imagery was qualitatively analyzed.

Hoffer, R. M.↗

Analysis of multispectral data using an unsupervised classification technique: Application to VAS

A statistical classification method based on clustering of multidimensional histograms was applied to several channels of the VAS multispectral imagery. The method automatically discriminates and classifies atmospheric ground features such as cloud types, atmospheric moisture patterns, ocean, or ground. Such a clustering method has the advantage of forming natural data groupings, without a priori classification. Clusters are not limited by straight lines or plane surfaces as is the case in threshold methods. The method was applied to simultaneous full resolution images from channels 8 (11.2 micron), 10 (6.7 micron), and 12 (3.9 micron). Twenty image segments of 64 by 64, 12 image segments of 128 by 128, and 4 image segments of 254 by 254 picture elements were analyzed. In addition, normal VISSR mode images at 1800, 1830, and 2000 GMT were used to identify the classes. The gray levels measured along a scan line and the result of the classification scheme (dashed curves) for the three channels investigated are shown. Each point of the image is affected to a class. Each class is identified by a center of gravity that is represented by a vector in the three dimensional space of gray levels.

Szejwach, G.↗