Inherit variability characterization considering piezocone test data: Application to bauxite tailings

In order to assess the availability of wind potential energy in a given place, a fundamental part is to investigate the behavior of the wind during a certain period. A standard way to characterize wind data is by using statistical models such as the Weibull distribution. To define the parameters of the Weibull probability density function (PDF) which best describes the input data, the estimation of two parameters is needed. Rather than testing different estimation methods for the Weibull distribution parameters and choosing the one with greater fitting level, we propose a iterative method aiming to maximize the suitability of the PDF into the raw data histogram. The method is based on the Newton-Raphson algorithm and uses as initial guess the parameters yielded by a Maximum Likelihood estimation. We also assess the performance of the hybrid Weibull distribution proposed by Tackle and Brown for different types of data and compare it to the standard Weibull PDF. The results show that, for every set of data analyzed, the proposed method outperformed the state-of-the-art Maximum Likelihood method. Also the hybrid Weibull PDF model yielded better fit than the standard Weibull PDF in all cases.

Presented are novel theoretical probability density functions (PDF) for the magnitude and phase of electromagnetic fields inside reverberation chambers (RC) operating in a ‘good-but-imperfect regime’. The derivation is based on considering two Gaussian random variables with mean values, variances and correlation between them that depart from the ideal assumptions. A multivariate approach using a complete joint Gaussian distribution of these variables is defined. Marginal distributions obtained by integration of this two-dimensional joint PDF are compared with theoretical PDFs for ideal situations, and significantly lower rejection rates are experienced for field data measured in real RCs. Additionally, these novel marginal PDFs are highly general since they are able to describe both ideal and non-ideal stirred fields.

Probability density functions of the involved random variables are essential for the reliability-based design of offshore structures. The objective of present research was the derivation of probability density function (PDF) for the local joint flexibility (LJF) factor, fLJF, in two-planar tubular DK-joints commonly found in jacket-type offshore structures. A total of 162 finite element (FE) analyses were carried out on 81 FE models of DK-joints subjected to two types of axial loading. Generated FE models were validated using available experimental data, FE results, and design formulas. Based on the results of parametric FE study, a sample database was prepared for the fLJF values and density histograms were generated for respective samples based on the Freedman-Diaconis rule. Nine theoretical PDFs were fitted to the developed histograms and the maximum likelihood (ML) method was applied to evaluate the parameters of fitted PDFs. In each case, the Kolmogorov-Smirnov and chi-squared tests were used to evaluate the goodness of fit. Finally, the Inverse Gaussian model was proposed as the governing probability distribution function for the fLJF. After substituting the values of estimated parameters, two fully defined PDFs were presented for the fLJF in tubular DK-joints subjected to two types of axial loading.

The polarisation ratio (PR) of an electromagnetic wave can provide information on the scattering from natural targets or on the emission from radio sources. In this study, a dual-polarisation radar operating at simultaneous reception mode is taken into account. Statistical properties of the PR of the radar signals on the basis of complex Gaussian models with zero and non-zero means are derived, respectively. Especially for the non-zero-mean case, the probability density functions (PDFs) and moments of the amplitude distribution in a single polarimetric channel are expressed in closed forms. PDFs of the amplitude ratio and the phase difference between orthogonal polarimetric channels are also derived. Comparisons of statistical properties are presented between theoretical PDFs and simulated data, as well as real polarimetric radar data. The well fitted results demonstrate the advantages of the PR models.

11 - Are my results significant?

In this paper we analyze wind measurements using the Weibull probability density function (PDF). We estimate the shape factor (k) and the scale factor (c) of a Weibull PDF using maximum likelihood estimators (MLE) and the least squares estimation (LSE) method. We then compare the energy production results that would be obtained when using the parameters estimated with each method. An economical analysis is performed to show the effects of overestimating or underestimating energy production caused by an erroneous estimation of the Weibull PDF parameters. Finally a Monte Carlo simulation is performed to asses the economical risk that the shape and scale parameters represent to the outcome of the project.

Indirect approaches to estimation of biomass factors are often applied to measure carbon flux in the forestry sector. An assumption underlying a country-level carbon stock estimate is the representativeness of these factors. Although intensive studies have been conducted to quantify biomass factors, each study typically covers a limited geographic area. The goal of this study was to employ a meta-analysis approach to develop regional biomass factors for Quercus mongolica forests in South Korea. The biomass factors of interest were biomass conversion and expansion factor (BCEF), biomass expansion factor (BEF) and root-to-shoot ratio (RSR). Our objectives were to select probability density functions (PDFs) that best fitted the three biomass factors and to quantify their means and uncertainties. A total of 12 scientific publications were selected as data sources based on a set of criteria. From these publications we chose 52 study sites spread out across South Korea. The statistical model for the meta-analysis was a multilevel model with publication (data source) as the nesting factor specified under the Bayesian framework. Gamma, Log-normal and Weibull PDFs were evaluated. The Log-normal PDF yielded the best quantitative and qualitative fit for the three biomass factors. However, a poor fit of the PDF to the long right tail of observed BEF and RSR distributions was apparent. The median posterior estimates for means and 95 % credible intervals for BCEF, BEF and RSR across all 12 publications were 1.016 (0.800–1.299), 1.414 (1.304–1.560) and 0.260 (0.200–0.335), respectively. The Log-normal PDF proved useful for estimating carbon stock of Q. mongolica forests on a regional scale and for uncertainty analysis based on Monte Carlo simulation.

We analyzed the probability density function (PDF) of velocity and temperature differences in the canopy sublayer of Amazonia based on Tsallis' generalized thermostatistics theory. We show that such a theory provides an accurate framework for modeling the statistical behavior of the inertial subrange above and below the canopy. For this, we compared the experimental PDFs with the theoretically predicted ones. The data were measured during the wet season of the Large‐Scale Biosphere‐Atmosphere Experiment in Amazonia (LBA), which was carried out during the months of January–March 1999 in the southwestern part of Amazonia region. Measurements were made simultaneously at different heights in a 60 m micrometeorological tower located in the Biological Reserve of Jaru (10°04′S, 61°56′W), Brazil. The fast response wind speed measurements, sampled at 60 Hz rate, were made using three‐dimensional sonic anemometers at the heights of 66 m (above the canopy) and 21 m (below the canopy). The results showed good agreement between experimental data measured above the canopy forest and Tsallis' generalized thermostatistics theory. For below canopy data, the agreement between experimental and theoretical PDFs was fairly good, but some distortion was observed. This is probably due to some peculiar characteristics of turbulent momentum transfer process inside the forest crown. Discussion is presented to explain these results. Conclusions regarding the absence of “universal scaling” in the inertial subrange are also presented in the context of the entropic parameter of Tsallis' theory.

The boresight and atmospheric jitter errors in a satellite tracking experiment are currently estimated by matching the probability density function (PDF) of the received signal counts with a set of PDFs of the signal for several combinations of jitter and boresight errors and then the best choice of jitter and boresight error is accepted via the chi-square test. Here a technique that can estimate atmospheric beam jitter and boresight error directly in a satellite active tracking experiment using the moments of the returns off the satellites is proposed. That is, we use the theoretical PDF for the signal return from a small target and compute the corresponding theoretical PDF moments. We can then form a few equations from these moments with only two unknowns, namely, the jitter and boresight. Solving for the unknowns is then unambiguous and very rapid. The method is valid for small physical cross-section targets and has been verified by using simulation and experimental data. Extending the case to asymmetric jitter and asymmetric boresight is possible.

Recent climate change has significantly affected the magnitude and frequency of rainfall, which critically affects the safety of levees and leads to severe flooding damage when levees fail. This study aimed to analyze the impact of the shape of flood hydrographs on levee failure characteristics using numerical analysis. Three types of flood hydrographs derived from lognormal, beta, and Weibull probability density functions (PDFs) were utilized, with each showing differences in the timing and magnitude of the peak flows. Levee overtopping and failure phenomena were simulated using a three-dimensional numerical analysis model, namely, FLOW-3D. The simulation results indicate that the failure patterns of levees vary, depending on the PDF used, with the lognormal PDF showing significant levee failure, owing to relatively high initial flows. These results suggest that a rapid increase in the flow at the onset is a direct factor that causes levee failure. These numerical analysis results highlight the importance of understanding the characteristics of each probability density function to accurately predict and effectively respond to levee failure risk. Future research should focus on a more precise analysis of levee failure mechanisms as well as the propagation and impacts of flood waves resulting from such failures.

In order to study the power patrol technology of unmanned aerial vehicle, the tracking algorithm was applied. The automatic patrolling of power lines was discussed in terms of algorithms. An unmanned aerial vehicle transmission line inspection method based on machine vision was proposed. The image and video of the unmanned aerial vehicle inspection of the power line had a complex background. By Wiener filtering de-noising and probability density functions, the image clarity was improved. According to the existing tracking techniques and algorithms, a Camshaft target tracking algorithm based on lossless Kalman filter was proposed. The method of non-destructive Kalman filter was adopted to predict the region of interest of power line identification. Using the Camshaft algorithm, the prediction of the window was searched and the size of the window was adjusted. Transmission lines were tracked in real time. The results showed that the restoration effect of the algorithm was obvious. The clarity of the image was improved. It prepared for the extraction and tracking of the future transmission lines. Therefore, the proposed method provides a feasible way for the UAV power line inspection technology based on machine vision.

The Discrete Moment Method for the numerical integration of piecewise higher order convex functions

A method to compute several scalar quantities of Cosmic Microwave Background maps on the sphere is presented. We consider here four type of scalars: the Hessian matrix scalars, the distortion scalars, the gradient related scalars and the curvature scalars. Such quantities are obtained directly from the spherical harmonic coefficients (alm) of the map. We also study the probability density function of these quantities for the case of a homogeneous and isotropic Gaussian field, which are functions of the power spectrum of the initial field. From these scalars it is posible to construct a new set of scalars which are independent of the power spectrum of the field. We test our results using simulations and find a good agreement between the theoretical probability density functions and those obtained from simulations. Therefore, these quantities are proposed to investigate the presence of non-Gaussian features in CMB maps. Finally, we show how to compute the scalars in presence of anisotropic noise and realistic masks.

For the wind energy assessment, it is important to know the probability density distribution of the wind speed in order to calculate the mean power of a wind. In this study wind data, for the period from January 2000 to December 2002, hourly records of speed and direction at Alexandria coast are analyzed as random monthly observations. Statistical methods are used for determination of best fit random distributions of wind speed and direction using statistical standard software that helps in evaluation of wind speed energy potential in a study area. In the present paper, different theoretical Probability Density Functions (PDF) have been tried to determine the appropriate models, including Weibull distribution and their parameters. The minimum wind power density at Alexandria found in July and August (2000-2002) were 20.41 and 21.34 w/m² and the maximum was in December and January (110.81 and 123.34 w/m²). The most important distributions of the wind speed were Weibull and Dagum and the direction followed mostly the Johnson SB model.

Generalized thermostatistics and wavelet analysis of solar wind and proton density variability