Estimating a Distribution Function at the Boundary

Estimation of distribution functions has many real-world applications. We study kernel estimation of a distribution function when the density function has compact support. We show that, for densities taking value zero at the endpoints of the support, the kernel distribution estimator does not need boundary correction. Otherwise, boundary correction is necessary. In this paper, we propose a boundary distribution kernel estimator which is free of boundary problem and provides non-negative and non-decreasing distribution estimates between zero and one. Extensive simulation results show that boundary distribution kernel estimator provides better distribution estimates than the existing boundary correction methods. For practical application of the proposed methods, a data-dependent method for choosing the bandwidth is also proposed.

Statistical Simulation of the Probability Distribution Kernel and Its Application to Solve the Quantile Optimization Problem with the Bilinear Loss Function

The article considers a plane quantile optimization problem with a bilinear loss function, which, using suffi cient optimality conditions, is reduced to a linear programming problem. The reduction is based on the use of a polyhedral model of the kernel of the probability distribution of the vector of random parameters. To build this model, an algorithm based on the method of statistical modeling is proposed. A description of the software package for constructing a kernel model for a number of probability distributions of random parameters is given.

CSDK: A Chi-square distribution-Kernel method for image de-noising under the Internet of things big data environment

Nowadays, Internet of things not only brings promising opportunities but also faces a lot of challenges. It attracts a lot of researchers’ attention and has important economic and social values. Internet of things plays a key role in the big data processing, especially in image field. Image de-noising still is a key problem in image pre-processing. Considering a given noisy image, the selection of thresholds should significantly affect the quality of the de-noising image. Although the state-of-the-art wavelet image de-noising methods perform better than other de-noising methods, they are not very effective for de-noising with different noises and with redundancy convergence time, sometimes. To mitigate the poor effect of traditional de-noising methods, this article proposes a new wavelet soft threshold based on the Chi-square distribution-Kernel method under the Internet of things big data environment. The new method alternates three minimization steps. First, the Chi-square distribution-Kernel model is constructed to find the customized threshold that corresponds to the de-noised image. Second, a freedom degree is considered, which is related to the customized wavelet coefficient of the Chi-square distribution-Kernel to be thresholded for image de-noising. Here, noisy image is first decomposed into many levels to obtain different frequency bands and the soft thresholding method based on Chi-square distribution-Kernel method is used to remove the noisy coefficients, by fixing the optimum threshold value using the proposed method. Third, the wavelet soft thresholding based on Chi-square distribution-Kernel method is adopted to handle the image de-noising, and a significant improvement is obtained by a specially developed Chi-square distribution-Kernel method. Finally, the experimental results illustrate that this computationally scalable algorithm achieves state-of-the-art de-noising performance in terms of peak signal-to-noise ratio, normalized mean square error, structural similarity, and subjective visual quality. It also shows a consistent accuracy, edge preservation, and detailed retention improvement compared to the classic de-noising algorithms.

Near-wake analysis of actuator line method immersed in turbulent flow using large-eddy simulations

The interaction between wind turbines through their wakes is an important aspect of the conception and operation of a wind farm. Wakes are characterized by an elevated turbulence level and a noticeable velocity deficit, which causes a decrease in energy output and fatigue on downstream turbines. In order to gain a better understanding of this phenomenon this work uses large-eddy simulations together with an actuator line model and different ambient turbulence imposed as boundary conditions. This is achieved by using the Simulator fOr Wind Farm Applications (SOWFA) framework from the National Renewable Energy Laboratory (NREL) (USA), which is first validated against another popular Computational Fluid Dynamics (CFD) framework for wind energy, EllipSys3D, and then verified against the experimental results from the Model Experiment in Controlled Conditions (MEXICO) and New Model Experiment in Controlled Conditions (NEW MEXICO) wind tunnel experiments. By using the predicted torque as a global indicator, the optimal width of the distribution kernel for the actuator line is determined for different grid resolutions. Then, the rotor is immersed in homogeneous isotropic turbulence and a shear layer turbulence with different turbulence intensities, allowing us to determine how far downstream the effect of the distinct blades is discernible. This can be used as an indicator of the extents of the near wake for different flow conditions.

Near wake analysis of actuator line method immersed in turbulent flow using large-eddy simulations

The interaction between wind turbines through their wakes is an important aspect of the conception and operation of a wind farm. Wakes are characterized by an elevated turbulence level and a noticable velocity deficit which causes a decrease in energy output and fatigue on downstream turbines. In order to gain a better understanding of this phenomenon this works uses large-eddy simulations together with an actuator line model and different ambient turbulences imposed as boundary conditions. This is achieved by using the SOWFA framework from NREL (USA) which is first validated against another popular CFD framework for wind energy, EllipSys3D, and then verified against the experimental results from the MEXICO and NEW MEXICO wind tunnel experiments. By using the predicted torque as a global indicator, the optimal width of the distribution kernel for the actuator line is determined for different grid resolutions. Then the rotor is immersed in homogeneous isotropic turbulence and a shear layer turbulence with different turbulence intensities, allowing to determine how far downstream the effect of the distinct blades is discernible. This can be used as an indicator for the extents of the near wake for different flow conditions