Cosine Distribution Research Articles

Oversampling-Based Imbalanced Signal Modulation Classification via Cosine Distance and Distribution

Oversampling-Based Imbalanced Signal Modulation Classification via Cosine Distance and Distribution

Sampling Distribution and Point and Interval Estimation of Kelley’s Percentile Coefficient of Kurtosis

There is a robust measure for estimating kurtosis based on quantiles, developed by the American psychologist Truman Lee Kelley, but it is seldom used. This underutilization is likely because it is not available in any statistical package, including R program. Additionally, Kelley reported its standard error when the random variable is drawn from a normal distribution but did not establish its sampling distribution. The objective of this study is to determine its asymptotic sampling distribution and to develop an R script to provide point and interval estimates for this measure. The R program was chosen because it is freely available, developed by the mathematical community, and considered one of the most comprehensive statistical packages currently available. To determine the asymptotic sampling distribution, samples of 100, 500, 1000, 5000, 10000, and 20000 data points were generated from three symmetric distributions: uniform (platykurtic), normal (mesokurtic), and Laplace (leptokurtic). From these 18 source samples, 1000 samples were drawn by resampling with replacement to obtain 18 bootstrap sampling distributions. Normality was then determined using Grubbs (outliers), D’Agostino (symmetry), Anscombe-Glynn (mesokurtosis), and Anderson-Darling, Lilliefors, Shapiro-Francia, and D’Agostino-Belanger-D’Agostino (normality) tests. The script included tests for several assumptions to decide which confidence interval to use: Wald type (normal asymptotic) or bootstrap (Gaussian, percentile, and percentile bias-corrected and accelerated). As an example, the script was applied to a random sample drawn from the raised cosine distribution on waiting time in a social service. It was concluded that the asymptotic sampling distribution of Kelley’s kurtosis measure is normal and that this measure appears less specific than classical Pearson and Fisher measures in the presence of a distribution very close to normal. It is suggested to use this script, which may have practical and academic utility.

A Design Proposal Using Coherently Radiating Periodic Structures (CORPSs) for 2-D Phased Arrays of Limited Scanning

New configurations of 2-D phased arrays are proposed in this paper for reducing the number of phase shifters. This design methodology is based on the use of a novel coherently radiating periodic structures (CORPSs) block for 2-D phased arrays. Two new antenna systems for 2-D phased arrays are studied and analyzed utilizing the CORPSs blocks of four inputs and nine outputs. These CORPSs feeding blocks are applied in a smart way to feed the planar antenna arrays by generating the required phase plane and reducing the number of control ports. Interesting results are provided based on the experimental measurements and full-wave simulations. These results illustrate a great reduction of the active devices (phase shifters), providing a good design compromise in terms of the scanning range and side lobe level performance. Furthermore, the provided results illustrate a maximum reduction capability in the number of phase shifters of 81%, considering a scanning range of ±30° in azimuth and ±30° in elevation. A raised cosine distribution is applied to reach side lobe levels of −19 dB for ±18° and −17 dB for ±30° in elevation. These benefits could be of interest to designers of phased antenna systems.

Investigating an Asymmetric Ratio Cosine Distribution

Most real-world data have asymmetric features, slight or pronounced, that cannot be analyzed in depth using classical symmetric distributions. This is especially true when the underlying phenomena take their values in bounded support. Examples include data with support (−1, 1), which may correspond to daily temperature anomalies, stock market returns and satisfaction ratings, among others. Motivated by this last point, this article introduces a novel asymmetric cosine distribution of the ratio type. It aims to extend the functionalities of the classical cosine distribution by incorporating two adjustable parameters that allow for flexible levels of asymmetry. The main functions and theoretical properties such as moments, quantiles and distributional properties are studied. Some derived distributions are also established, extending the scope of the Cauchy and half-Cauchy distributions. Applications to simulated data in hypothetical environmental, financial and sentiment analysis scenarios demonstrate the practical utility of the asymmetric cosine distribution in capturing nuanced behavior.

The kinetic theory of prompt redeposition in the case of thin Debye sheath

Prompt redeposition is a process in which a neutral atom sputtered from a divertor target or the first wall of a tokamak returns on the surface right after ionization, before experiencing any collisions with the background plasma. This paper presents analytical solutions of kinetic equations for sputtered neutrals and resulting ions. Using obtained distribution functions, the redeposition coefficient and average impact angle are derived under assumptions of thin Debye sheath. Our expression for the prompt redeposition coefficient explicitly depends on the angular and energy distributions of sputtered atoms and, therefore, is more universal than often used Fussmann equation valid only for cosine distribution. The effect of the angular distributions of sputtered particles on the prompt redeposition efficiency and parameters of redeposited ions is analyzed.

An analytical method for free vibration analysis of multi‐directional functionally graded porous doubly‐curved shells in thermal environment with various boundary conditions

This paper uses the analytical method with arbitrary boundary conditions to model and analyze the free vibrations of multi‐directionally functionally graded porous (MFGP) doubly‐curved shallow shells resting on the Pasternak foundation in a temperature environment. It is anticipated that all mechanical parameters, except Poisson's ratio, will change in the direction of length, width, and thickness. To comprehensively describe the shell's displacement, strain, and stress fields, a modified first‐order shear deformation theory (FSDT) with an assumption of cosine distribution shear stresses has been developed. The fact that the enhanced FSDT theory does not require the use of shear correction and that the shear stress at the two free faces of the shells is zero are two of the theory's most significant advantages. Using Hamilton's principle and improved FSDT, one may get the governing equation for free vibration analysis of MFGP doubly‐curved shallow shells. The Galerkin approach is proposed to solve the governing equation of MFGP doubly‐curved shallow shells with various boundary conditions. The trustworthiness of the article is evaluated via its publication in the article model's several special cases. From this point on, a collection of findings about the natural frequency of MFGP doubly‐curved shallow shells is identified and shown in the form of tables and graphs. The results provided in this manuscript can be used as a benchmark solution for further studies as far as the vibration behavior of the MFGP doubly‐curved shallow shells is concerned.

Large-eddy simulation of upwind-hill effects on wind-turbine wakes and power performance

The present study utilizes high-fidelity large-eddy simulation (LES) to examine the upwind-hill impacts on wind-turbine wakes and power performance. Both the LES and Reynolds-Averaged Navier–Stokes (RANS) show good agreement with the experimental results of average velocity, whereas the LES exhibits great improvements in predicting turbulence characteristics. In turbine simulations, the wake half-width shows different behaviors in the hill and flat cases. The Gaussian and cosine distributions are good representations of the unskewed profiles of velocity deficit, although some discrepancies are seen around the wake edges. However, the spanwise profiles of velocity deficit become skewed in some hill cases. The non-zero pressure gradient (NZPG) model is employed to predict the velocity deficit in the wakes of a hilltop-sited turbine, and a generalized condition is proposed so that the NZPG model can work in the scenario where the pressure gradients at the turbine location or in its near wakes are not zero. Appropriately assigning initial values for the NZPG model is important for its successful use. The presence of the upwind hill has an adverse influence on the power output of the hilltop-sited turbine. The installation of wind turbines in the valley region near upwind hills is not recommended due to the limited wind-energy resources and intense turbulence levels.

A minimum entropy criterion for distribution selection for measurement uncertainty analysis

This paper presents a minimum entropy criterion for selecting the best probability distribution among a set of candidate distributions based on available information for measurement uncertainty analysis. We consider two cases that are most commonly encountered in practice: A and B. In Case A, the available information is a series of observations. In Case B, the available information is the maximum permissible error according to manufacturer’s specification. Three candidate distributions are considered in Case A: the scaled and shifted z-distribution (i.e. normal distribution), the scaled and shifted t-distribution, and the Laplace distribution. Five candidate distributions are considered in Case B: rectangular, triangular, quadratic, raised cosine, and half-cosine. According to the proposed minimum entropy criterion, the scaled and shifted z-distribution is the best distribution in Case A, and the raised cosine distribution is the best distribution in Case B. A case study is presented to demonstrate the effectiveness of the proposed minimum entropy criterion.

Evolution mechanism of flip-fold removal behaviour through crossed scratching of glass-ceramics

In this study, a novel flip-fold removal model was established to reveal the ductile–brittle mixed removal phenomenon in the grinding process of glass-ceramics. This flip-fold model proposed for the ductile–brittle mixed removal mode differs from conventional brittle or ductile removal mechanisms. Using the theoretical exploration method, a theoretical model of flip-fold removal is established based on the analysis of different scenarios of the relationship between the depth of the stagnation region and pile-up height of the interference zone. Through an experimental verification method, the approach of crossing double scratches with a continuously variable scratch distance is proposed to observe the evolution progression and verify the flip-fold removal model. Using the analytical analysis method, the amplitude and direction cosine distributions of the interference stress field were analysed to reveal the internal mechanism of the flip-fold removal model. The results of the three scientific research methods were in good agreement with those of the proposed model. The flip-fold material removal model supports the comprehension of the ductile–brittle mixed removal mode during the grinding of hard-brittle materials. This model provides an approach to controlling the material removal mode from the perspective of regulating the flip-fold behaviour by adjusting the scratch distance.

Simulating phenomena with exponentiated trigonometric distributions: a comparative study of estimation methods and real-world applications

Recent research has highlighted the statistical significance and usefulness of trigonometric distribution models for simulating a variety of phenomena. A new set of distributions generated by exponentiated cosine and tangent functions has been introduced. Consequently, two families of distributions called the exponentiated cosine and tan Stacy distributions are derived. Some vital statistical and reliability characteristics are studied. The finite sample characteristics of parameter estimations are compared to the exponentiated cosine and tan distribution generated by four estimation methods: maximum likelihood, ordinary least squares, weighted least squares, and Cramer–von Mises. The methodologies are evaluated using simulation studies. Finally, the practical applications of the proposed trigonometric versions of the Stacy model are examined and applied on two lifetime reliability engineering datasets and another lifetime medical dataset concerning bladder cancer data. These real applications serve to highlight the effectiveness and adaptability of this innovative families within the respective fields compared with other lifetime well-known distribution models.

EXCEL-oriented procedures for determining the entropy of a distribution function and its relative parametric sensitivity (elasticity) under the conditions of two-sided restrictions on the range of values of a continuous random variable

The goal of the work. Development of an EXCEL-oriented calculator for calculating entropy and its elasticity for distribution functions under the condition of a limited domain of definition of a continuous random variable. Subject of study. Probability density functions and their entropy under the condition of bilateral restrictions on the domain of possible values of random variables. Research methods. Algorithmic and numerical analysis of procedures for obtaining numerical values of entropy of density functions of continuous random variables under the condition of two-way restrictions on the area of its definition. The obtained results. The work proposes an EXCEL-oriented calculator for calculating entropy and its elasticity for distribution functions under the condition of a limited area of definition of a continuous random variable. All distribution functions used in the work are divided into three categories depending on the form in which entropy and its elasticity are presented. The first category includes distribution functions for which entropy and its elasticity can be determined analytically, namely: Simpson distribution, Right-angled and negatively skew version distribution, Right-angled and positively skew version distribution, Sine Wave Distribution, Ark – Sine Distribution Type I, Ark – Sine Distribution Type IІ, Ordinary Cosine Distribution, Raised Cosine Distribution, U-shaped parabolic distribution Type I, Semi-elliptical distribution, Ark – Sine Distribution Type II. Another category includes distribution functions for which entropy can be defined in the analytical group, its elasticity can be defined in the tabular part, namely: Truncated Normal Distribution, Kumaraswamy Distribution, Beta Distribution, Generalized Beta Distribution, Uniformly increasing distribution density, Ark-Sine Distribution Type III. The third category includes distribution functions for which entropy and its elasticity can be determined in tabular form. Basic information about the structure of the proposed calculator and examples of its application are provided. The method of determining the confidence interval of the point estimate of entropy is described. An example of using the calculator proposed in this message for planning an experiment related to entropy data analysis is given.

Stress Characteristics of Horizontal-Axis Wind Turbine Blades under Dynamic Yaw

The dynamic yaw significantly affects the aerodynamic load distribution of wind turbines, and the aerodynamic load is one of the main influencing factors of wind turbine structural stress variation. Taking the NACA4415 horizontal axis wind turbine designed by the research group as the research object, the numerical simulation was used to analyze the distribution characteristics of blade stress, surface thrust coefficient, and the wind turbine power output under periodic dynamic yaw conditions. The results show that the blade stress, blade axial thrust, and wind turbine output power were presented as a cosine distribution with yaw fluctuations. The distribution trend of blade stress showed an increase followed by a decrease from the inside out along the span direction. In addition, due to the influence of dynamic yaw and aerodynamic loads, the stress values near the blade root exhibited significant fluctuations. With the increase in tip speed ratio, the stress values of dynamic windward yaw gradually exceeded those of leeward yaw. Within the range of a 10° to 30° yaw variation period, the stress value with positive yaw was larger than that with negative yaw, and the highest stress value occurred in the range of −5° to 15°. The results can be provided as a theoretical basis for the structural design and yaw control strategies of wind turbines, considering dynamic yaw operation.

Simplified Method for Determining Thermal Stresses during the Construction of Massive Monolithic Foundation Slabs

For massive monolithic foundation slabs, the problem of early cracking due to the intense heat release of concrete during the hardening process is relevant. The purpose of this article is to develop a simplified method for determining thermal stresses during the construction of massive monolithic foundation slabs. The proposed technique is based on the hypothesis of parabolic temperature distribution over the thickness of the structure at each moment of time. In addition to the parabolic distribution, the half-wave cosine distribution is also used. A hypothesis is also introduced about the same conditions of heat exchange with the environment on the lower and upper surfaces of the foundation. As a result, formulas are obtained that establish a direct relationship between thermal stresses and the temperature difference between the center and the surface. The solution to the test problem for the foundation slab is presented and compared with an alternative technique that does not use the hypothesis about the character of the temperature distribution over the thickness. Also, the inverse problem of determining the allowable temperature drop between the center and the surface of the structure is solved, at which the stresses on the upper surface at each moment of time will not exceed the tensile strength of concrete.

Probability propagation for faster and efficient point cloud segmentation using a neural network

Neural networks (NN) have shown promising performance in point cloud segmentation (PCS). However, the measured points are too numerous to be used as model input at once. It results in a long inference time and high computational cost due to iterative sampling and inference. This study proposes Probability Propagation (PP) as a stochastic upsampling method. PP propagates the predicted probability of a sampled part of a point cloud into the other unpredicted points by considering proximity. By replacing the iterative inference of NN with PP, large point clouds can be dealt with quickly and efficiently. We investigated the effectiveness of PP using the ShapeNet benchmark on various settings: sampling methods (random, farthest point, and Poisson disk sampling) with sampling ratios (5%, 10%, 20%, 39%, and 78%) for NN and the stochastic mapping conditions (uniform, linear, cosine, Gaussian, and exponential distributions) for PP. Using NN with PP achieved higher performance and faster inference speed than when using NN alone. For the farthest point sampling method of 5% sampling ratio, NN+PP improved the instance mIoU by 2.457%p with 102 times faster speed compared to that when using NN alone. The result indicates that PP can significantly contribute to the improvement of performance and efficiency in PCS when used in edge AI systems.

Influence of Target-Substrate Distance on the Transport Process of Sputtered Atoms: MC-MD Multiscale Coupling Simulation.

A Monte Carlo (MC) and molecular dynamics (MD) coupling simulation scheme for sputtered particle transport was first proposed in this work. In this scheme, the MC method was utilized to model the free-flight process of sputtered atoms, while the MD model was adopted to simulate the collision between the sputtered atom and background gas atom so as to self-consistently calculate the post-collision velocity of the sputtered atom. The reliability of the MD collision model has been verified by comparing the computation results of the MD model and of an analytical model. This MC-MD coupling simulation scheme was used to investigate the influence of target-substrate distance on the transport characteristic parameters of sputtered Cu atoms during magnetron sputtering discharge. As the target-substrate distance increased from 30 to 150 mm, the peak energy of the incident energy distribution of deposited Cu atoms decreased from 2 to 1 eV due to the gradual thermalization of sputtered atoms. The distribution of differential deposition rate in unit solid angle firstly became more forward-peaked and then reversely approached the cosine distribution, which was agreed with the existing experimental observations. This work is expected to provide a more realistic simulation scheme for sputtered particle transport, which can be further combined with the MD simulation of sputtered film growth to explore the influence mechanism of process parameters on the properties of sputtered film.

Novel Design Techniques for the Fermat Spiral in Antenna Arrays, for Maximum SLL Reduction.

This paper presents novel design techniques for the Fermat spiral, considering a maximum side lobe level (SLL) reduction. The array system based on a Fermat spiral configuration considers techniques based on uniform and non-uniform amplitude excitation. The cases of uniform amplitude excitation are the golden angle and the optimization of the angular separations. The cases of non-uniform amplitude excitations consider a raised cosine distribution and the optimization of the amplitude excitations through the Fermat spiral array. In this study, the method of genetic algorithms (GA) was used in the cases to find the values of the angular separations and the amplitude excitations of the Fermat spiral array. A performance evaluation was conducted for all these design cases, considering the Fermat spiral geometry. These design cases were validated using electromagnetic simulation to take mutual coupling into account and consider the effect of the antenna element pattern in each proposed design case.

A boundary layer solution for the post-critical thermo-electro-mechanical stability of nonlocal-strain gradient Functionally Graded Piezoelectric cylindrical shells

Continuum mechanics is extended to the Nonlocal (NL) and the Strain Gradient (SG) theories by incorporating the long-range molecular interactions. Nanostructures are often made of smart materials (e.g. Piezoelectric) for multifunctional attributes. The NL-SG theory based analysis/design of nanostructures offers convenience comparing the computationally expensive atomistic simulation. This study investigates the thermal post-buckling of a piezoelectric, NLSG thin cylindrical shell with thickness-wise gradation of elastic properties. The governing equations are derived following the Donnell's approach including the pre-buckling nonlinearity, large post-critical deflection and geometric imperfections. A thickness-wise cosine distribution of the electric potential is employed following the Maxwell equation. The Boundary Layer (BL) concept is employed to solve the nonlinear equations using asymptotic expansions of the regular and the BL field variables. The solution is illustrated on moderately short shells to show the prominent SG but nominal NL effects. The interactions result in conservative critical temperature but non-conservative post-critical path in contrast with the classical shell. The influence of functional gradation and the electric fields are illustrated. Increasingly sharper displacement gradient around the BL of the SG shell suggests the increasing relevance of the BL theory. The proposed solution may be useful for analysis, design and active instability control by adaptive feedback voltage.

Total and Differential Sputtering Yields Explored by SRIM Simulations

Total sputtering yield and spatial distributions of sputtered atoms are important for numerous deposition techniques. We performed SRIM (Stopping and Range of Ions in Matter) simulations to analyze the total sputtering yield and angular distribution of sputtered atoms for a range of single-element target materials. The simulations were conducted for normal argon ion incidence in the 300–1200 eV range and at an oblique angle for selected ion energies. We examined the total and differential sputtering yields for the transition metals in the periods 4–6 and groups 4–6 (Ti, V, Cr; Zr, Nb, Mo; Hf, Ta, and W) and group 11 (Cu, Ag, and Au) of the periodic table, and other materials that are relevant to sputtering (B and C; Al and Si). For the transition metals, the total sputtering yield increases with the group of the periodic table. The elements in group 4 (i.e., Ti, Zr, and Hf) have the lowest sputtering yield, while the elements in group 11 (i.e., Cu, Ag, and Au) exhibit the highest sputtering yield. The angular distribution of the sputtered atoms shows a cosine distribution for the transition metal atoms. The angular distribution of the sputtered atoms for the oblique ion incidence is more asymmetric for the lower ion energies, while for the higher ion energies, the atoms are sputtered more symmetrically. The symmetry also depends on the group of the periodic table and the atomic mass of the target material. The elements in group 11 show the most symmetric distribution, while the elements in group 4 experience the most asymmetric distribution. Furthermore, in an individual group, the distribution becomes more symmetric with heavier target elements. We also examined in detail the influence of the surface binding energy, atomic mass, and ion energy on the total sputtering yield. These parameters were analyzed with regard to the simplified analytical formula for the total sputtering yield, which was derived by Sigmund. This formula was modified by introducing a power fitting parameter, which accounts for the non-linear sputtering yield dependence on the ion energy. The equation provided good estimates for the total sputtering yield of the transition metals that were sputtered by argon ions with energies up to 1200 eV.

Exceedance probability analysis: a practical and effective alternative to t-tests

This paper presents a practical and effective alternative to the traditional t-tests for (1) comparing a sample or sample mean against a known mean (i.e. one-sample test) and (2) comparing two samples or two sample means (i.e. two-sample test). The proposed method is referred to as exceedance probability (EP) analysis. In a one-sample test, EP is defined as the probability that a sample or sample mean is greater than a known mean. In a two-sample test, EP is defined as the probability that the difference between two samples or between two sample means is greater than a specified value (referred to as probabilistic effect size (PES)). This paper also defines a new statistic called relative mean effect size (RMES). RMES provides a true measure of the scientific significance (not the statistical significance) of the difference between two means. A case study of preference between two manufacturers is presented to demonstrate the effectiveness of the proposed EP analysis, compared with four existing methods: t-tests, common language effect size (CL) analysis, signal content index (SCI) analysis, and Bayesian analysis. Unlike these existing methods that require the assumption of normality, the proposed EP analysis can be performed with any type of distributions. The case study example is examined with a normal distribution model and a raised cosine distribution model. The former is solved with an analytical solution and the latter is solved with a numerical method known as probability domain simulation (PDS).

Large-scale shake table testing of pile group-bridge model in inclined liquefiable soils with overlying crusts

Large scale shaking table tests were performed to investigate the failure mechanism of pile group-bridge system subjected to liquefaction-induced lateral spreading. The tests comprised two cases: Case L which refers to a bridge model supported by a 2 × 2 pile group embedded into the inclined liquefiable soils with crusts; and case R which refers to the same bridge model fixed to a rigid foundation. The experimental details are provided and typical test results are elucidated. The failure mechanism of the pile group-bridge system under strong earthquakes is revealed. The results indicate that the lateral peak soil displacement profile has a linear distribution, while the lateral permanent displacement profile has a cosine distribution pattern. It was also found that the pile is prone to damage and bending failure both at its head and at the bottom of saturated sand where it is fixed into bearing stratum. For the pile group-bridge system, the liquefaction-induced lateral spreading causes the failure position to move from the pier bottom to the pile head. In addition, the pier bottom is more likely to experience damage under strong earthquakes in case R than in case L, while the opposite is true during weak earthquake excitation.