Uniform Probability Density Function Research Articles

Integral inequalities of h‐superquadratic functions and their fractional perspective with applications

The purpose of this article is to provide a number of Hermite–Hadamard and Fejér type integral inequalities for a class of ‐superquadratic functions. We then develop the fractional perspective of inequalities of Hermite–Hadamard and Fejér types by use of the Riemann–Liouville fractional integral operators and bring up with few particular cases. Numerical estimations based on specific relevant cases and graphical representations validate the results. Another motivating component of the study is that it is enriched with applications of modified Bessel function of first type, special means, and moment of random variables by defining some new functions in terms of modified Bessel function and considering uniform probability density function. The results in this paper have not been initiated before in the frame of ‐superquadraticity. We are optimistic that this effort will greatly stimulate and encourage additional research.

The Overall Collection Efficiency of Catching‐Type Precipitation Gauges in Windy Conditions

AbstractThe wind‐induced bias of catching‐type precipitation measurement instruments is quantified using Computational Fluid Dynamics with embedded liquid (raindrops) and solid (snowflakes) particle tracking. The performance of six common commercial gauges having different outer geometry is compared under a range of Precipitation Intensity (PI) and wind speed conditions by means of the numerically calculated catch ratios. Validation of the simulated aerodynamic behavior and its effect on water drop trajectories is provided by previous wind tunnel experiments. The functional dependence of the overall collection efficiency on the PI is derived as a quantitative measure of the instrument performance under a wind climatology with a uniform probability density function. Instruments with aerodynamic design produce a less pronounced diversion of hydrometeor trajectories—at any given size—than those having more traditional geometry. For liquid precipitation measurements, chimney‐shaped instruments rank low, while inverted conical and Nipher shielded instruments are quite performant solutions. The investigated quasi‐cylindrical gauges have intermediate behavior depending on their detailed aerodynamic features. For solid precipitation, all instruments rank low at light to moderate PI, except the Nipher shielded gauge. Results allow selecting the appropriate instrument for the local precipitation climatology at the measurement site and can be used to apply suitable adjustments to the measured precipitation.

R] Inferential Statistics IV: Uniform and (Standard) Normal Probability (Density) Functions

R] Inferential Statistics IV: Uniform and (Standard) Normal Probability (Density) Functions

Effect of porosity and pore size distribution on elastic modulus of foams

In this study, we investigate the impact of pore distribution and size on the mechanical response of elastic porous materials. Two-dimensional porous media with convex porosity are considered (e.g., foams and sponges). These structures are numerically generated by subtracting randomly dispersed circular holes from a solid square domain. The in-plane position vector of pore centers is given by a uniform probability density function (PDF). The pore diameters are, instead, drawn from a non-uniform two-parameter continuous probability distribution. The influence of the void ratio, i.e., the volume fraction of voids, and the parameters of the diameter PDF are studied over a wide range of values, including the percolation threshold, where the effective elastic modulus of the material abruptly drops to zero. This transition takes place at a critical value of the void ratio, which turns out to be unaffected by the parameters of the pore size distribution. Our results demonstrate that the elastic response of these structures is primarily governed by the void ratio, with the correlation length playing a secondary role. While the pore size distribution may affect the correlation length, it has a minimal impact on the foam’s overall behavior.

Probabilistic Transition-Based Optimal Energy Transaction of a Non-Convex CHP-Microgrid during Generation and Load Uncertainty

Combined heat power dispatch with improved operation remains a popular preference in microgrid having uncertain and non-convex nature of the system. This research work deploys an efficient energy management system driven by a novel stochastic transitions tuned unscented Gaussian distribution (ST-UnGD) for optimal energy transaction. The proposed scheme has been introduced with uncertainty modeling of available generations and load using probabilistic transition-based timed petri net. Echo algorithm has been used to influence prioritized transition for appropriate number of token distribution. The control over the process during transition has been supervised with UnGD. A uniform probability density function has been created using Gaussian distribution to characterize random variables for effective time series scenario generation. The mean and variance which helps in sorting ten competent scenarios from one thousand scenarios, has been computed with the proposed strategy and compared with other methods. The improvement has been noticed with standard deviation of 0.0162% after 40 trials run with average operational cost of 254.211€ when token distribution was updated by 100, 200, 300, 400, and 500 firings. A statistical analysis by parametric and non-parametric test confirmed the effectiveness of the proposed algorithm showing appropriate confidence level in the mentioned case study.

On the properties of residential rooftop azimuth and tilt uncertainties for photovoltaic power generation modeling and hosting capacity analysis

One of the essential epistemic uncertainties that has not yet been studied enough for distributed photovoltaic systems is the azimuth and tilt of rooftop photovoltaic panels, as previous studies of grid impacts and hosting capacity have tended to assume uniform and optimal roof facet conditions. In this study, rooftop facet orientation distributions are presented and analyzed for all single-family buildings in the Swedish city of Uppsala, based on LiDAR-based data that consist of every roof facet from the around 13,500 single-family buildings in the city. From these distributions, novel methods to proportionally include less suitable roofs for every penetration level are proposed using a simple method based on normal and uniform probability density functions, and are tested for both time-series and stochastic hosting capacity analysis. The results show that under the assumption that the best roof facets are utilized first, a uniform distribution for rooftop facet azimuth and a normal distribution for rooftop facet tilt with parameters that depend linearly on the penetration level were shown to be accurate. The hosting capacity simulations demonstrate how the proposed methods perform significantly better in estimating the photovoltaic hosting capacity than the more common simplified methods for both time-series and stochastic hosting capacity analysis. The proposed model could help distribution system operators as well as researchers in this area to model the rooftop facet orientation uncertainty better and improve the quality of aggregated photovoltaic generation models and hosting capacity analyses.

Singularity Behaviour of the Density, Information, and Entropy Functions Defining a Uniform Non-stationary Stochastic Process

Precise definitions and derivatives of the time-dependent continuous and discrete uniform probability density functions and related information and entropy functions are investigated. A stochastic system is formed that can represent a uniform noise source having a time-dependent variance and forming a uniform non-stationary stochastic process. The information and entropy function of the system are defined, and their properties are investigated in the time domain, including the limit cases defined for infinite and zero values of the time-dependent variance. In particular, the singularity properties of the entropy function will be investigated when the time-dependent variance reaches infinity. Like in thermodynamics, where the physical entropy of a system increases all the time, the information entropy of the stochastic system in information theory is also expected to increase towards infinity when the variance increases. All investigations are conducted for both the continuous and discrete random variables and their density functions. The presented theory is of particular interest in analyzing the Gaussian density function having infinite variance and tending to a uniform density function.

Custom distribution for sampling-based motion planning

Sampling-based motion planning algorithms are widely used in robotics because they are very effective in high-dimensional spaces. However, the success rate and quality of the solutions are determined by an adequate selection of their parameters such as the distance between states, the local planner, and the sampling distribution. For robots with large configuration spaces or dynamic restrictions, selecting these parameters is a challenging task. This paper proposes a method for improving the performance to a set of the most popular sampling-based algorithms, the Rapidly-exploring Random Trees (RRTs) by adjusting the sampling method. The idea is to replace the uniform probability density function (U-PDF) with a custom distribution (C-PDF) learned from previously successful queries in similar tasks. With a few samples, our method builds a custom distribution that allows the RRT to grow to promising states that will lead to a solution. We tested our method in several autonomous driving tasks such as parking maneuvers, obstacle clearance and under narrow passages scenarios. The results show that the proposed method outperforms the original RRT and several improved versions in terms of success rate, tree density and computation time. In addition, the proposed method requires a relatively small set of examples, unlike current deep learning techniques that require a vast amount of examples.

A uniform compact genetic algorithm for matching bibliographic ontologies

Digital Library (DL) is a source of inspiration for the standards and technologies on Semantic Web (SW), which is usually implemented by using bibliographic data. To address DL’s data heterogeneity problem, it is necessary to annotate the bibliographic data with semantic information, which requires the utilization of the bibliographic ontologies. In particular, a bibliographic ontology provides the domain knowledge by specifying the domain concepts and their relationships. However, due to human subjectivity, a concept in different bibliographic ontologies might be defined in different names, causing the data heterogeneity problem. To address this issue, it is necessary to find the mappings between bibliographic ontologies’ concepts, which is the so-called bibliographic ontology matching. In this paper, a Uniform Compact Genetic Algorithm (UCGA) is proposed to match the bibliographic ontologies, which employs the real-valued compact encoding mechanism to improve the algorithm’s performance, the Linearly Decreasing Virtual Population (LDVP) to trade-off the exploration and exploitation of the algorithm, and the local perturbation to enhance the convergence speed and avoid the algorithm’s premature convergence. In addition, by using the Uniform Probability Density Function (UPDF) and Uniform Cumulative Distribution Function (UCDF), the UCGA can greatly reduce the evolutionary time and memory consumption. The experiment uses the Biblio testing cases provided by the Ontology Alignment Evaluation Initiative (OAEI) to evaluate UCGA’s performance and the experimental results show that UCGA is both effective and efficient.

Turbulent fuel-air mixing study of jet in crossflow at different velocity ratios using LES

In order to study the mixing mechanism of fuel and air in gas turbine, large eddy simulation has been used to investigate the methane jet-in-crossflow with the velocity ratio (R) of 1.5 and 4. This study aims to explore the formation mechanism of vortices such as the hairpin vortices, hovering vortices and horseshoe vortices, the relationship between the fuel–air mixing and flow characteristics at different velocity ratios. The numerical methods in the present work are firstly validated with the experimental data in terms of mean and root mean square values of velocity. For R = 4, the shear layer vortices, horseshoe vortices, counter-rotating vortices pairs (CVP) and wake vortices can be observed, while the jet shear layer cannot be observed for R = 1.5. The hairpin vortices originating from the vortice-ring are lifted and shed from the downstream of the jet-outlet due to Kutta-Joukowski lift. The hairpin vortices are similar to CVP. The horseshoe vortices in R = 1.5 and 4 are formed due to the blockage of the jet (CH4) and the crossflow (air) respectively, and its evolution is associated with the hovering vortices which only exist for R = 1.5. The uniform index and pr-obability density function are used for quantitative analysis of the mixing performance. The uniform index at X/D = 0 (fuel-inlet) and at X/D = 25 (outlet) are 0.033 and 0.335 for R = 1.5 and 0.130 and 0.047 for R = 4. For R = 4, the jet penetration is higher and the deflection angle of jet is smaller than that in case of R = 1.5. Higher R will provide more region for mixing, therefore uniform index is higher and the mixing is more uniform in the downstream.

Surface rupture in stochastic slip models

SUMMARYAs an alternative to spectral methods, stochastic self-similar slip can be produced through a composite source model by placing a power-law scaling size-frequency distribution of circular slip dislocations on a fault surface. However these models do not accurately account for observed surface rupture behaviour. We propose a modification to the composite source model that corrects this issue. The advantage of this technique is that it accommodates the use of fractal slip distributions on non-planar fault surfaces. However to mimic a surface rupture using this technique, releasing the boundary condition at the top of the fault, we observed a systematic decrease in slip at shallow depths. We propose a new strategy whereby the surface is treated like a reflector with the slip being folded back onto the fault. Two different techniques based on this principal are presented: the first is the method of images. It requires a small change to pre-existing codes and works for planar faults. The second involves the use of a multistage trilateration technique. It is applied to non-planar faults described by an unstructured mesh. The reflected slip calculated using the two techniques is near identical on a planar fault, suggesting they are equivalent. Applying this correction, where reflected slip is accounted for in the composite source model, the lack of slip at shallow depths is not observed any more and there is no systematic trend with depth. However, there are other parameters which may affect the spatial distribution of slip across the fault plane. For example, the type of probability density function used in the placement of the subevent is also important. In the case where the location of maximum slip is known to a first order, a Gaussian may be appropriate to describe the probability function. For hazard assessment studies a uniform probability density function is more suitable as it provides no underlying systematic spatial trend.

PoCET: a Polynomial Chaos Expansion Toolbox for Matlab

We introduce PoCET: a free and open-scource Polynomial Chaos Expansion Toolbox for Matlab, featuring the automatic generation of polynomial chaos expansion (PCE) for linear and nonlinear dynamic systems with time-invariant stochastic parameters or initial conditions, as well as several simulation tools. It offers a built-in handling of Gaussian, uniform, and beta probability density functions, projection and collocation-based calculation of PCE coefficients, and the calculation of stochastic moments from a PCE. Efficient algorithms for the calculation of the involved integrals have been designed in order to increase its applicability. PoCET comes with a variety of introductory and instructive examples. Throughout the paper we show how to perform a polynomial chaos expansion on a simple ordinary differential equation using PoCET, as well as how it can be used to solve the more complex task of optimal experimental design.

Optimal estimation of matter-field coupling strength in the dipole approximation

This paper is devoted to the study of the Bayesian-inference approach in the context of estimating the dipole coupling strength in matter-field interactions. In particular, we consider the simplest model of a two-level system interacting with a single mode of the radiation field. Our estimation strategy is based on the emerging state of the two-level system, whereas we determine both the minimum mean-square error and maximum likelihood estimators for uniform and Gaussian prior probability density functions. In the case of the maximum likelihood estimator, we develop a mathematical method which extends the already existing approaches to the variational problem of the average cost function. We demonstrate that long interaction times, large initial mean photon numbers, and nonzero detuning between two-level system transition and the frequency of the electromagnetic field mode have a deleterious effect on the optimality of the estimation scenario. We also present several cases where the estimation process is inconclusive, despite many ideal conditions being met.

Seismic fragility of structures isolated by single concave sliding devices for different soil conditions

This study deals with the seismic fragility of elastic structural systems equipped with single concave sliding (friction pendulum system (FPS)) isolators considering different soil conditions. The behavior of these systems is analyzed by employing a two-degree-of-freedom model, whereas the FPS response is described by means of a velocity-dependent model. The uncertainty in the seismic inputs is taken into account by considering artificial seismic excitations modelled as timemodulated filtered Gaussian white noise random processes of different intensity within the power spectral density method. In particular, the filter parameters, which control the frequency content of the random excitations, are calibrated to describe stiff, medium and soft soil conditions. The sliding friction coefficient at large velocity is also considered as a random variable modelled through a uniform probability density function. Incremental dynamic analyses are developed in order to evaluate the probabilities of exceeding different limit states related to both the reinforced concrete (RC) superstructure and isolation level, defining the seismic fragility curves within an extensive parametric study carried out for different structural system properties and soil conditions. The abovementioned seismic fragility curves are useful to evaluate the seismic reliability of base-isolated elastic systems equipped with FPS and located in any site for any soil condition.

Discrete time domain analysis of chaos-based wireless communication systems with imperfect sequence synchronization

Abstract Problem of sequence synchronization in chaos-based direct sequence spread-spectrum (DS-SS) systems and code division multiple access systems (CDMA) has been widely investigated. However, no mathematical expressions have been derived in closed form for the bit error probability in these systems when they operate with the imperfect time synchronization (represented by a delay between the received and reference spreading sequence generated in the receiver). Precise derivatives for this bit error probability are necessary to quantify the effect of imperfect synchronization on the overall properties of the system. To implement a random delay between the received and the receiver reference sequence, all signals in this paper are represented in the discrete time domain. To represent finite and random discrete delays between the sequences (which occur in a limited interval) the Gaussian and uniform probability density functions are expressed in discrete form. Furthermore, due to the finite value of possible random discrete delays, the expressions of related truncated density functions are expressed in closed form. Following this approach, the expressions for the bit error probability in closed form for chaotic and random spreading sequences have been derived.

Subgrid-scale variability in clear-sky relative humidity and forcing by aerosol–radiation interactions in an atmosphere model

Abstract. Atmosphere models with resolutions of several tens of kilometres take subgrid-scale variability in the total specific humidity qt into account by using a uniform probability density function (PDF) to predict fractional cloud cover. However, usually only mean relative humidity, RH, or mean clear-sky relative humidity, RHcls, is used to compute hygroscopic growth of soluble aerosol particles. While previous studies based on limited-area models and also a global model suggest that subgrid-scale variability in RH should be taken into account for estimating radiative forcing due to aerosol–radiation interactions (RFari), here we present the first estimate of RFari using a global atmospheric model with a parameterization for subgrid-scale variability in RH that is consistent with the assumptions in the model. For this, we sample the subsaturated part of the uniform RH-PDF from the cloud cover scheme for its application in the hygroscopic growth parameterization in the ECHAM6-HAM2 atmosphere model. Due to the non-linear dependence of the hygroscopic growth on RH, this causes an increase in aerosol hygroscopic growth. Aerosol optical depth (AOD) increases by a global mean of 0.009 ( ∼ 7.8 % in comparison to the control run). Especially over the tropics AOD is enhanced with a mean of about 0.013. Due to the increase in AOD, net top of the atmosphere clear-sky solar radiation, SWnet, cls, decreases by −0.22 W m−2 ( ∼ −0.08 %). Finally, the RFari changes from −0.15 to −0.19 W m−2 by about 31 %. The reason for this very disproportionate effect is that anthropogenic aerosols are disproportionally hygroscopic.

A Proposal of a Novel Method for Generating Discrete Analog Uniform Noise

This paper presents a proposal of a new way to generate analog noise, discrete in time, with uniform probability density function. Instead of the usual way of generating discrete ana ...

A computational model for biosonar echoes from foliage.

Since many bat species thrive in densely vegetated habitats, echoes from foliage are likely to be of prime importance to the animals’ sensory ecology, be it as clutter that masks prey echoes or as sources of information about the environment. To better understand the characteristics of foliage echoes, a new model for the process that generates these signals has been developed. This model takes leaf size and orientation into account by representing the leaves as circular disks of varying diameter. The two added leaf parameters are of potential importance to the sensory ecology of bats, e.g., with respect to landmark recognition and flight guidance along vegetation contours. The full model is specified by a total of three parameters: leaf density, average leaf size, and average leaf orientation. It assumes that all leaf parameters are independently and identically distributed. Leaf positions were drawn from a uniform probability density function, sizes and orientations each from a Gaussian probability function. The model was found to reproduce the first-order amplitude statistics of measured example echoes and showed time-variant echo properties that depended on foliage parameters. Parameter estimation experiments using lasso regression have demonstrated that a single foliage parameter can be estimated with high accuracy if the other two parameters are known a priori. If only one parameter is known a priori, the other two can still be estimated, but with a reduced accuracy. Lasso regression did not support simultaneous estimation of all three parameters. Nevertheless, these results demonstrate that foliage echoes contain accessible information on foliage type and orientation that could play a role in supporting sensory tasks such as landmark identification and contour following in echolocating bats.

Distortion of magnetic field lines caused by radial displacements of ITER toroidal field coils

An assessment of distortions of ideal (circle) field lines caused by random radial displacements of the TF coils by |∆R|≤5mm has been performed from the statistical analysis assuming a uniform probability density function for displacements.

How to Compute the Information Content of 3-FR, 3-DP Decoupled Designs with Uniform Probability Density Functions for Their FRs

The computation of the information content of decoupled designs implies the use of conditional probability, because the existing design parameters must be adjusted in a certain order, as to fulfil all the existing functional requirements at the first trial. Nevertheless, the computation of the information content is hard to perform when the system range of the functional requirements is denoted by probability density functions. In their works, Suh and Park proposed a graphical method to compute the information content of 2-FR, 2-DP decoupled designs when the probability density functions of the FRs are uniform. This paper introduces an extension to the Suh and Park's previous findings. It presents a method that uses analytical and descriptive geometry techniques to compute the information content of 3-FR, 3-DP decoupled designs with uniform probability density distributions of their FRs, and an illustrative example is presented as well.