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Relative values assigned to double mistakes and changed iteratively. Method for statistical analysis of threshold detection saves experimental time by enabling use of same set of measurements with respect to two thresholds. Accounts for double mistakes, unresolvable by threshold-detection technique.
Wind turbine design standards recommend the use of statistical modeling coupled with extrapolation of the short-term load data to long-term periods for fatigue reliability assessment. However, statistical error and computational expense can limit the accuracy of such approaches. In the case of wind turbine blades, the errors are more significant because of the high material fatigue exponent that makes the damage estimations more sensitive to variations. In addition, due to different excitation sources, the flapwise load range histogram is not unimodal, and thus its statistical modeling is complex. In the present work, we provide three methods for statistical modeling of the flapwise bending moment ranges including a novel approach based on frequency-based separation of the modes. The first two methods are simplified approaches for modeling the most crucial load ranges using unimodal distributions and the third method involves multimodal distribution fitting. The research is based on 3600 10-minute aeroelastic simulations of DTU 10MW case study wind turbine from which a benchmark damage equivalent load (DEL) is calculated. The DEL calculated by each of the three proposed methods is compared to this reference. The results show that the conventional approach based on using 6 seeds as well as using mixture models fitted on the limited data lead to under-conservative results with errors up to 23%. On the other hand, the simplified unimodal approaches provided in this work can provide conservative estimations of the fatigue damage with mean values 5% and 12% higher than the benchmark. However, the variability of the DEL estimates is higher when using unimodal extrapolation of the load ranges, and the data can be conservative by 17.5%. The proposed unimodal fits suggested for modeling and extrapolation of the blade's load ranges provide less errors relatively and most importantly conservative DEL estimations while maintaining computational efficiency.
The GEANT4 toolkit is used extensively in high energy physics to simulate the passage of particles through matter and to predict effects such as detector efficiencies and smearing. GEANT4 uses many underlying models to predict particle interaction kinematics, and uncertainty in these models leads to uncertainty in high energy physics measurements. The GEANT4 collaboration recently made free parameters in some models accessible through partnership with GEANT4 developers. We present a study of the impact of varying parameters in three GEANT4 hadronic physics models on agreement with thin target datasets and describe fits to these datasets using the Professor model tuning framework [1]. We find that varying parameters produces substantially better agreement with some datasets, but that more degrees of freedom are required for full agreement. This work is a first step towards a common framework for propagating uncertainties in GEANT4 models to high energy physics measurements, and we outline future work required to complete that goal.
Comparison of monte carlo, percus-yevick integral equations and convolution-hypernetted-chain methods for computing radial distribution functions of gaussian model
Although the common genetic origin of the Kreutz family of sun-grazing comets has generally been accepted, there remains uncertainty with regard to genetic identity among other groups of comets whose orbital elements are nearly alike. Porter (1952) has listed a number of such groups, and Opik (1971) has made a statistical study of the orbits of 472 comets with aphelion distances beyond Saturn. Opik lists 97 groups that show similarities among their three angular elements, calculates an overall probability of some 10 to the -39th power that these similarities could have occurred by chance, and thus concludes that 60% or more of such comets fall into genetic groups containing from two to seven members. This paper explores the statistical reality of Opik's groups utilizing the Monte Carlo method of statistics as well as ordinary probability theory. The conclusion is reached that except for a few pairs, the similarity among orbital elements within the groups is no greater than random expectation.
Cloud observation and cloud modeling data can be presented in histograms for each characteristic to be measured. Combining information from single-cloud histograms yields a summary histogram. Summary histograms can be compared to each other to reach conclusions about the behavior of an ensemble of clouds in different places at different times or about the accuracy of a particular cloud model. As in any scientific comparison, it is necessary to decide whether any apparent differences are statistically significant. The usual methods of deciding statistical significance when comparing histograms do not apply in this case because they assume independent data. Thus, a new method is necessary. The proposed method uses the Euclidean distance metric and bootstrapping to calculate the significance level.
Optimization of atomic coordinates and lattice parameters remains a significant challenge to the wide use of stochastic electronic structure methods such as quantum Monte Carlo (QMC). Measurements of the forces and stress tensor by these methods contain statistical errors, challenging conventional gradient-based numerical optimization methods that assume deterministic results. Additionally, forces are not yet available for some methods, wavefunctions, and basis sets and when available may be expensive to compute to sufficiently high statistical accuracy near energy minima, where the energy surfaces are flat. Here, we explore the use of Gaussian process based techniques to sample the energy surfaces and reduce sensitivity to the statistical nature of the problem. We utilize Latin hypercube sampling, with the number of sampled energy points scaling quadratically with the number of optimized parameters. Furthermore, we show these techniques may be successfully applied to systems consisting of tens of parameters, demonstrating QMC optimization of a benzene molecule starting from a randomly perturbed, broken symmetry geometry.
We propose a stellar locus outlier (SLOT) method to determine the binary fraction of main-sequence stars statistically. The method is sensitive to neither the period nor mass ratio distributions of binaries and is able to provide model-free estimates of binary fraction for large numbers of stars of different populations in large survey volumes. We have applied the SLOT method to two samples of stars from the Sloan Digital Sky Survey (SDSS) Stripe 82, constructed by combining the recalibrated SDSS photometric data with the spectroscopic information from the SDSS and LAMOST surveys. For the SDSS spectroscopic sample, we find an average binary fraction for field FGK stars of 41% ± 2%. The fractions decrease toward late spectral types and are 44% ± 5%, 43% ± 3%, 35% ± 5%, and 28% ± 6% for stars with g – i colors in the range 0.3-0.6 mag, 0.6-0.9 mag, 0.9-1.2 mag, and 1.2-1.6 mag, respectively. A modest metallicity dependence is also found. The fraction decreases with increasing metallicity. For stars with [Fe/H] between –0.5 and 0.0 dex, –1.0 and –0.5 dex, –1.5 and –1.0 dex, and –2.0 and –1.5 dex, the inferred binary fractions are 37% ± 3%, 39% ± 3%, 50% ± 9%, and 53% ± 20%, respectively. We have further divided the sample into stars from the thin disk, the thick disk, the transition zone between them, and the halo. The results suggest that the Galactic thin and thick disks have comparable binary fractions, whereas the Galactic halo contains a significantly larger fraction of binaries. Applying the method to the LAMOST spectroscopic sample yields consistent results. Finally, other potential applications and future work with the method are discussed.
Abstract Gaussian process regression is a Bayesian method for inferring profiles based on input data. The technique is increasing in popularity in the fusion community due to its many advantages over traditional fitting techniques including intrinsic uncertainty quantification and robustness to over-fitting. This work investigates the use of a new method, the change-point method, for handling the varying length scales found in different tokamak regimes. The use of the Student’s t-distribution for the Bayesian likelihood probability is also investigated and shown to be advantageous in providing good fits in profiles with many outliers. To compare different methods, synthetic data generated from analytic profiles is used to create a database enabling a quantitative statistical comparison of which methods perform the best. Using a full Bayesian approach with the change-point method, Matérn kernel for the prior probability, and Student’s t-distribution for the likelihood is shown to give the best results.
Here, we report a simple and pure data-driven method to find new energy levels of quantum many-body systems only from observed line wavelengths. In our method, all the possible combinations are computed from known energy levels and wavelengths of unidentified lines. As each excited state exhibits many transition lines to different lower levels, the true levels should be reconstructed coincidentally from many level-line combinations, while the wrong combinations distribute randomly. Such a coincidence can be easily detected statistically. We demonstrate this statistical method by finding new levels for various atomic and nuclear systems from unidentified line lists available online.
Continuum methods require the additional development of solids stress closures for polydisperse powders based on complex kinetic theories that are non-trivial to develop, code, and numerically converge for the wide range of fluidization regimes from very dilute to dense/frictional flow limit. On the other hand, it is straightforward to model the flow of polydisperse granular materials by treating particles as discrete rigid bodies that are tracked following simple physical laws of motion. The coarsening of these discrete methods by lumping several particles in a parcel alleviates the significant computational cost associated with these discrete methods while introducing some inaccuracies in the numerical results. In this research, we explore two different coarse graining methods that can be applied to polydisperse powders, namely the same statistic weight method (SSW) and the same size parcel method (SSP), and assess their accuracy by comparison with the finest simulation results obtained with a discrete element method (DEM). For Geldart group B powders fluidized at a relative low superficial velocity, the numerical results indicate that the SSW is more accurate than the SSP method. For type A powders fluidized at relatively high velocity, these two methods predict similar results. Interestingly, up to four times increase in the speed of simulation of the SSP method was obtained because the original polydisperse powder is scaled to a mono-disperse system in terms of particle-particle collision. Lastly, these results suggest that the SSP method is more favorable for the simulation of fluidized beds due to its accuracy and efficiency while the SSW method may be used for granular flow and dense fluidized bed systems where capturing the size segregation of particles due to collision is important.
ABSTRACT We present an extended validation of semi-analytical, semi-empirical covariance matrices for the two-point correlation function (2PCF) on simulated catalogs representative of luminous red galaxies (LRGs) data collected during the initial 2 months of operations of the Stage-IV ground-based Dark Energy Spectroscopic Instrument (DESI). We run the pipeline on multiple effective Zel’dovich (EZ) mock galaxy catalogs with the corresponding cuts applied and compare the results with the mock sample covariance to assess the accuracy and its fluctuations. We propose an extension of the previously developed formalism for catalogs processed with standard reconstruction algorithms. We consider methods for comparing covariance matrices in detail, highlighting their interpretation and statistical properties caused by sample variance, in particular, non-trivial expectation values of certain metrics even when the external covariance estimate is perfect. With improved mocks and validation techniques, we confirm a good agreement between our predictions and sample covariance. This allows one to generate covariance matrices for comparable data sets without the need to create numerous mock galaxy catalogs with matching clustering, only requiring 2PCF measurements from the data itself. The code used in this paper is publicly available at https://github.com/oliverphilcox/RascalC.
Feature extraction and classification algorithms for high dimensional data are investigated. Developments with regard to sensors for Earth observation are moving in the direction of providing much higher dimensional multispectral imagery than is now possible. In analyzing such high dimensional data, processing time becomes an important factor. With large increases in dimensionality and the number of classes, processing time will increase significantly. To address this problem, a multistage classification scheme is proposed which reduces the processing time substantially by eliminating unlikely classes from further consideration at each stage. Several truncation criteria are developed and the relationship between thresholds and the error caused by the truncation is investigated. Next an approach to feature extraction for classification is proposed based directly on the decision boundaries. It is shown that all the features needed for classification can be extracted from decision boundaries. A characteristic of the proposed method arises by noting that only a portion of the decision boundary is effective in discriminating between classes, and the concept of the effective decision boundary is introduced. The proposed feature extraction algorithm has several desirable properties: it predicts the minimum number of features necessary to achieve the same classification accuracy as in the original space for a given pattern recognition problem; and it finds the necessary feature vectors. The proposed algorithm does not deteriorate under the circumstances of equal means or equal covariances as some previous algorithms do. In addition, the decision boundary feature extraction algorithm can be used both for parametric and non-parametric classifiers. Finally, some problems encountered in analyzing high dimensional data are studied and possible solutions are proposed. First, the increased importance of the second order statistics in analyzing high dimensional data is recognized. By investigating the characteristics of high dimensional data, the reason why the second order statistics must be taken into account in high dimensional data is suggested. Recognizing the importance of the second order statistics, there is a need to represent the second order statistics. A method to visualize statistics using a color code is proposed. By representing statistics using color coding, one can easily extract and compare the first and the second statistics.
Structures in many environments experience both random and harmonic excitation. A variety of closed-form techniques has been used in the aerospace industry to combine the loads resulting from the two sources. The resulting combined loads are then used to design for both yield/ultimate strength and high- cycle fatigue capability. This Technical Publication examines the cumulative distribution percentiles obtained using each method by integrating the joint probability density function of the sine and random components. A new Microsoft Excel spreadsheet macro that links with the software program Mathematica to calculate the combined value corresponding to any desired percentile is then presented along with a curve tit to this value. Another Excel macro that calculates the combination using Monte Carlo simulation is shown. Unlike the traditional techniques. these methods quantify the calculated load value with a consistent percentile. Using either of the presented methods can be extremely valuable in probabilistic design, which requires a statistical characterization of the loading. Additionally, since the CDF at high probability levels is very flat, the design value is extremely sensitive to the predetermined percentile; therefore, applying the new techniques can substantially lower the design loading without losing any of the identified structural reliability.
Structures in many environments experience both random and harmonic excitation. A variety of closed-form techniques has been used in the aerospace industry to combine the loads resulting from the two sources. The resulting combined loads are then used to design for both yield ultimate strength and high cycle fatigue capability. This paper examines the cumulative distribution function (CDF) percentiles obtained using each method by integrating the joint probability density function of the sine and random components. A new Microsoft Excel spreadsheet macro that links with the software program Mathematics is then used to calculate the combined value corresponding to any desired percentile along with a curve fit to this value. Another Excel macro is used to calculate the combination using a Monte Carlo simulation. Unlike the traditional techniques, these methods quantify the calculated load value with a Consistent percentile. Using either of the presented methods can be extremely valuable in probabilistic design, which requires a statistical characterization of the loading. Also, since the CDF at high probability levels is very flat, the design value is extremely sensitive to the predetermined percentile; therefore, applying the new techniques can lower the design loading substantially without losing any of the identified structural reliability.
Nonlinear system under random excitation, discussing analytic solution method and statistical properties
The new method of statistical studying of cosmic gamma-ray bursts is presented based on the averaging of time profiles. The comparison is done between bright and dim events: while no differences were found between average flux curves, the hardness ratios pointed out the effect of hardness/brightness correlation.
Physical theories that depend on many parameters or are tested against data from many different experiments pose unique challenges to statistical inference. Many models in particle physics, astrophysics and cosmology fall into one or both of these categories. These issues are often sidestepped with statistically unsound ad hoc methods, involving intersection of parameter intervals estimated by multiple experiments, and random or grid sampling of model parameters. Whilst these methods are easy to apply, they exhibit pathologies even in low-dimensional parameter spaces, and quickly become problematic to use and interpret in higher dimensions. In this article we give clear guidance for going beyond these procedures, suggesting where possible simple methods for performing statistically sound inference, and recommendations of readily-available software tools and standards that can assist in doing so. Our aim is to provide any physicists lacking comprehensive statistical training with recommendations for reaching correct scientific conclusions, with only a modest increase in analysis burden. Furthermore, our examples can be reproduced with the code publicly available at Zenodo.