Probability Density Function Distribution Research Articles

Parallel Kalman filter group integrated particle filter method for the train nonlinear operational status high-precision estimation under non-Gaussian environment

For the problem of multi-mode state estimation in actual train operation, this paper proposes a nonlinear non-gaussian high-precision parallel Kalman filter group (NN-HEKFG) integrated Particle Filter. A multi-model Gaussian decomposition of the probability density function for state equations and measurement equations is performed, and each local state model is represented by a multi-dimensional high-order polynomial to establish the expanded dimensional state model. Then, by updating the mean and variance of the local state expanded dimensional model and in turn solving the particle filtering posterior probability density distribution function, the global estimation results are obtained. In reducing the number of Gaussian terms, a new parameter reduction criterion is established, which can effectively carry out the re-identification of parameters such as weights and means, so as to avoid the problem of parameter explosion. The superiority of NN-HEKFG over particle filters and Gaussian sum filters and its effectiveness for train running state estimation are verified by simulating the multi-model running state of trains.

Investigation of the Static Performance of Hydrostatic Thrust Bearings Considering Non-Gaussian Surface Topography

The dynamic and static characteristics of hydrostatic thrust bearings are significantly affected by the bearing surface topography. Previous studies on hydrostatic thrust bearings have focused on Gaussian distribution models of bearing surface topography. However, based on actual measurements, the non-Gaussianity of the distribution characteristics of bearing surface topography is clear. To accurately characterize the non-Gaussian distribution of bearing surface topography, the traditional probability density function of Gaussian distribution was modified by introducing Edgeworth expansion. The non-Gaussian surface was then reflected by two parameters: kurtosis and skewness. This had an effect on the static characteristics of hydrostatic thrust bearings with both circumferential and radial surface topographies. The comparison between the Gaussian distribution results and those of the non-Gaussian model showed that errors between the two models could reach more than 10%. Therefore, it is important to take into account the non-Gaussianity of bearing surface when discussing static characteristics of hydrostatic thrust bearings considering the surface topography.

Performance Analysis of a Drone-Assisted FSO Communication System over Málaga Turbulence under AoA Fluctuations

Future wireless communications have been envisaged to benefit from integrating drones and free space optical (FSO) communications, which would provide links with line-of-sight propagation and large communication capacity. The theoretical performance analysis for a drone-assisted downlink FSO system is investigated. Furthermore, this paper utilizes the Málaga distribution to characterize the effect of atmospheric turbulence on the optical signal for the drone–terrestrial user link, taking into account atmospheric attenuation, pointing errors, and angle-of-arrival fluctuations. The probability density function and cumulative distribution function are then expressed in closed-form using the heterodyne detection and indirect modulation/direct detection techniques, respectively. Thereafter, the analytical expressions including the average bit error rate (BER) and the ergodic capacity are given. Particularly, the asymptotic behavior of the average BER of the considered system is presented using heterodyne detection at high optical power. The Monte Carlo simulation results certify the theoretical analytical results. Correspondingly, the field-of-view of the receiver is analyzed for optimal communication performance.

Response prediction and fatigue life estimation of thin-walled structures under random excitation using the modified equivalent linearization method

This paper proposes a fast estimation method for the high-cycle fatigue of geometrically nonlinear thin-walled structures under random loading. The core idea of this method is utilizing a modified equivalent linearization method to obtain the statistical properties of the modal displacement response of the thin-walled structures, which is used to generate samples and then transform them into stress samples to determine the peak probability density function of the von Mises stress for fatigue life estimation. There are three critical issues addressed in implementing the method: (1) Using the implicit condensation technique to introduce the membrane softening effect in the regulated equivalent linearization method to improve the computational accuracy of the displacement statistical properties and convert the higher order moments into easily computable second order moments by separating the displacement mean values, so the regulated equations of motion for non-zero mean systems are derived, and fix the problem that the regulated equivalent linearization method does not apply to the prediction of the dynamic response of general thin-walled structures. (2) A nonlinear relationship between modal displacement and stress is derived with the implicit condensation and expansion method to transform the generated displacement samples to stress samples, which are used to determine probability density functions of stress and their derivatives. (3) Simplifying the probability density function of the three-dimensional joint distribution to the probability density function of the two-dimensional joint distribution by taking advantage of the Bayes rule, thus deriving a fast formula for the probability density function of the peak Mises stress.

Multilognormal density structure in Cygnus-X molecular clouds: a fitting for N-PDF without power law

ABSTRACT We studied the H2 column density probability distribution function (N-PDF) based on molecular emission lines using the Nobeyama 45-m Cygnus X CO survey data. Using the DENDROGRAM and SCIMES algorithms, we identified 124 molecular clouds in the 13CO data. From these identified molecular clouds, an N-PDF was constructed for 11 molecular clouds with an extent of more than 0.4 deg2. From the fitting of the N-PDF, we found that the N-PDF could be well fitted with one or two lognormal distributions. These fitting results provided an alternative density structure for molecular clouds from a conventional picture. We investigated the column density, dense molecular cloud cores, and radio continuum source distributions in each cloud and found that the N-PDF shape was less correlated with the star-forming activity over a whole cloud. Furthermore, we found that the lognormal N-PDF parameters obtained from the fitting showed two impressive features. First, the lognormal distribution at the low-density part had the same mean column density (∼1021.5 cm−2) for almost all the molecular clouds. Second, the width of the lognormal distribution tended to decrease with an increasing mean density of the structures. These correlations suggest that the shape of the N-PDF reflects the relationship between the density and turbulent structure of the whole molecular cloud but is less affected by star-forming activities.

On the Performance of STAR-RIS-Aided NOMA at Finite Blocklength

Simultaneous refracting/transmitting and reflecting reconfigurable intelligent surface (STAR-RIS) has emerged as a potential technology for future-generation wireless communication that enhances the signal quality and provides 360∘ coverage area. In this letter, we provide a finite blocklength (FBL) analysis of a STAR-RIS-aided downlink communication system with non-orthogonal multiple access (NOMA), where the base station (BS) transmits a superimposed signal to two users with the aid of a STAR-RIS. First, we derive the probability density function (PDF) and cumulative distribution function (CDF) of the signal-to-interference-plus-noise ratio (SINR) of each user, and then we analyze the system performance by deriving analytical expressions for their block error rate (BLER) and goodput. Finally, using Monte-Carlo simulations, we validate the accuracy of the derived analytical expressions, and highlight the impact of key system parameters such as blocklength, and the number of refracting and reflecting elements on the system performance.

On Bivariate Nadarajah-Haghighi Distribution derived from Farlie-Gumbel-Morgenstern copula in the Presence of Covariates

An important alternative distribution to the Weibull, generalized exponen-tial and gamma distributions that is used in survival analysis is the Nadarajah-Haghighi exponential distribution. Similar to the Weibull, generalized exponen-tial and gamma distributions, the Nadarajah-Haghighi exponential distributionis an extension of the well known exponential distribution. In this paper, a copulafunction commonly used to model very weak linear dependence was used to intro-duced a bivariate Nadarajah-Haghighi distribution. The joint survival function,joint probability density function and joint cumulative distribution were givenin closed form. Bayesian method of estimation was used to estimate the modelparameters considering the presence of right censoring and covariates. Posteriorsummaries of interest were obtained via standard Markov Monte Carlo (MCMC )technique. Two real data sets were used to illustrate the importance and flexi-bility of the bivariate model in comparison with some competing models. It wasobserved that, the bivariate Nadarajah-Haghighi distribution provides a better fltthan bivariate exponential, bivariate Weibull, bivariate generalized exponentialand bivariate modified Weibull distributions.

An Age-Dependent Prognostic Model for Nonlinear Degrading Devices Based on Diffusion Process

Degradation modeling based remaining useful life (RUL) predicting has become a significant basis of prognotics and system health management (PHM), and has drawn much favor of both scholars and engineers in the field of reliability. Based on a purely time-dependent diffusion process, this paper presents a nonlinear degradation model with special focus on the proportional relationship between the age-dependent expectation and variance of the degradation processes of the concerned devices. Exact probability density function (PDF) and cumulative distribution function (CDF) of life time and RUL in explicit forms are derived under the concept of first hitting time (FHT), incorporating the item-to-item variability. An framework of maximizing the likelihood function has been proposed to estimate the unknown parameters utilizing condition monitoring data of the devices. Case studies of fatigue crack length data of alloy and capacity data of electrolytic capacitors have been presented to illustrate the proposed prognostics model. The results show that the proposed degradation model can be well fitted to the nonlinear degradation data and provide an accurate prediction of RUL, and thus demonstrate the effectiveness of the proposed model.

Normal-tangent-logarithm-(G_1,G_2 ): a class of probabilistic distributions depending on two baselines

Based on the normal distribution, a new generator of continuous distributions is presented using the monotonic functions and , such that and are the baselines. A study of identifiability of the proposed class is exhibited as well as the series expansions for its cumulative distribution function and probability density function. Additionally, some mathematical properties of the class are discussed, namely, the raw moments, the central moments, the moment generating function, the characteristic function, the derivatives of the log-likelihood function, and a study of the support. A numerical analysis comprising a simulation study and an application to real data is presented. Comparisons between the proposed model and other well-known models evince its potentialities and modeling benefits.

Effects of fracturing parameters on fracture network evolution during multicluster fracturing in a heterogeneous reservoir

There are some major problems in the study of fracture network evolution during multicluster fracturing, such as the simple assumption that the reservoir is homogeneous, without considering the heterogeneity of rock mineral particles. In addition, different viscosities used in fracturing fluid and fluid injection methods can affect fracture propagation. As reservoir stimulation enters the 2.0 era, it is important to study the evolution of multicluster fracture networks based on reservoir heterogeneity to improve the stimulated reservoir volume. For this purpose, a 2D, coupled stress-seepage-damage field multicluster fracturing numerical model was developed in this study, and a globally embedded 0-thickness cohesive element was used to simulate the random propagation of hydraulic fractures. Moreover, the elastic modulus, tensile strength and mixed fracture energy of the cohesive element mesh were randomly assigned using the Weibull distribution probability density function to simulate the reservoir heterogeneity. In addition, the dynamic distribution of the injected fluid rate during multicluster fracturing was implemented based on the Bernoulli equation. The capability of the model was validated with analytical solutions of the Khristianovich-Geertsma-de Klerk (KGD) problem and similar numerical modeling criteria of multicluster fracturing and was used to investigate the geological and engineering factors that influence the evolution of the fracture network. The results show that the fracture network formed by hydraulic fracturing is more complex when the reservoir has significant heterogeneity and the injection pressure has a larger extreme value. As the reservoir becomes increasingly homogeneous, using low-viscosity fracturing fluid does not significantly contribute to fracture network complexity or effectively reduce the extreme value of the injection pressure. Shortening the pad fluid injection time can significantly increase the fracture network complexity, but it increases the extreme value of the injection pressure, which requires a higher pressure tolerance for fracturing equipment. The results of this study have important significance for the parameter optimization of multicluster fracturing.

DDOFM: Dynamic malicious domain detection method based on feature mining

The domain name system is an essential part of the network, and target hosts are often attacked by malicious domain names to steal resources. Some traditional detection methods have low accuracy, poor generalization ability, and high resource overhead on model construction to deal with complex and variable malicious domain names. A three-level dynamic malicious domain detection method (DDOFM) is proposed in this paper. DDOFM only needs to combine a few high-order statistical features of benign domains with some DNS features, without flagging malicious samples and involving them in training. Firstly, the boundary recognition of passive DNS (PDNS) features extracted from DNS traffic is carried out to conduct an early- warning for some domains. Second, the Hidden Markov Model (HMM) forward algorithm and normal distribution probability density function are used to calculate the formation probabilities of the warned domains and their probability density values. Then the probabilities of every character in the warned domain name and the standard deviation between these probabilities are counted. Further, the probability density values and the standard deviations of these warned domain names are compared with their respective thresholds to identify the attribution of the warned domain names. Finally, if the domain name is not warned, the Jensen–Shannon divergence (JS divergence) between it and the previous domain name will be calculated. Then the local iterative threshold finding algorithm (LLTFA) proposed in this paper will be combined to determine its attribution and identify whether the host is connected to the command and control (C&C) server. Experiments show that the detection indexes of this method exceed 99% for multiple types of malicious domain names. The C&C servers can also be identified by DDOFM faster than similar methods.

CMR Exploration. I. Filament Structure with Synthetic Observations

In this paper, we carry out a pilot parameter exploration for the collision-induced magnetic reconnection (CMR) mechanism that forms filamentary molecular clouds. Following Kong et al., we utilize Athena++ to model CMR in the context of resistive magnetohydrodynamics (MHD), considering the effect from seven physical conditions, including the ohmic resistivity (η), the magnetic field (B), the cloud density (ρ), the cloud radius R, the isothermal temperature T, the collision velocity v x , and the shear velocity v z . Compared to their fiducial model, we consider a higher and a lower value for each one of the seven parameters. We quantify the exploration results with five metrics, including the density probability distribution function (ρ-PDF), the filament morphology (250 μm dust emission), the B–ρ relation, the dominant fiber width, and the ringiness that describes the significance of the ringlike substructures. The exploration forms straight and curved CMR filaments with rich substructures that are highly variable in space and time. The variation translates to fluctuation in all five metrics, reflecting the chaotic nature of magnetic reconnection in CMR. A temporary B ∝ ρ relation is noticeable during the first 0.6 Myr. Overall, the exploration provides useful initial insights into the CMR mechanism.

Wind Energy Resource Potential Evaluation based on Statistical Distribution Models at Four Selected Locations in Amhara Region, Ethiopia

In Ethiopia, and particularly in the Amhara region, the government as well as the concerned organization would not give special attention to establishing wind energy plants. Lack of scientific research inputs about potential assessment can be one of the reasons behind it. In this paper, a wind energy potential assessment for Debel, Malawa, Enwari, and Ayba Eyesus sites in the Amhara region has been investigated. Five statistical distribution methods namely Weibull 3P, Weibull 2P, Rayleigh 2P, Normal, and Lognormal are used to fit the data to the probability density function and cumulative distribution function. The proposed parameter estimation method, to precisely predict the values of the shape parameter, scale parameter, and location parameter, was the Maximum Likelihood Estimation Method (MLE). To analyze the goodness of fit of the models, Kolmogorov, Andersen Darling, and Chi-Square have been used. The test indicated that Weibull 3P is the best fitting method, except for Ayba Eyesus, which is suited to Weibull 2P. For Debel, Malawa, Enwari, and Ayba Eyesus, the maximum annual average wind power density was found to be 74.291 W/m2, 19.183 W/m2, 68.972 W/m2, and 49.221 W/m2 correspondingly. The evaluations show that VENSYS 87 turbine model has better performance in all three sites except Enwari, where Inox Wind DF 100 is favored. With their best performance turbine, the capacity factor of the sites is determined as 14%, 7%, 12%, and 14% for Debel, Malawa, Enwari, and Ayba Eyesus respectively. Furthermore, Economical analysis by initial cost, lifetime, operation, and maintenance cost, has been carried out to estimate the cost of energy. With VENSYS 87 turbine model, the three sites' present value costs are $5,479,586, while it costs $7,306,115 in Enwari with Inox Wind DF 100 turbine. The cost of electricity per kWh is estimated to be $0.00231, $0.00455, $0.00391, and $0.00312 for Debel, Malawa, Enwari, and Ayba Eyesus respectively, and it is significantly lower than the cost from Ethiopian electric utility (EEU), which is around 0.009$/kwh. Access to electricity in Ethiopia was reported at 45% in 2019. This indicates there is a shortage of energy in the country. This kind of study can help authorities and policymakers in taking into account wind power to mitigate energy poverty in the country.

Elevation Angle Characterization for LEO Satellites: First and Second Order Statistics

The elevation angle θ is relevant for the Low Earth orbit (LEO) satellite communications since it is always changing its relative position with respect to fixed Earth stations (ES’s), and this affects the link length and received power, PR. This article provides a new methodology to compute the probability density function (PDF) and cumulative distribution function (CDF) of the elevation angle, θ, for diverse ES locations. This methodology requires as input parameters an ES latitude, ϕ, an orbit inclination value, i, and an orbit altitude, h. The elevation angle is characterized through a well known random variable, which facilitates the computation of the first and second-order statistics, and helps to determine the expected value and measures of dispersion of the angle θ for a particular ES location. The proposed methodology allows an easy and quick calculation of the elevation angle’s CDF, facilitating comparisons against CDF’s of more ES’s located at different latitudes, and longitudes, λ; as well as the comparisons of CDF’s of the elevation angle produced by different orbits. Extensive simulation results are summarized in a small table, which allows computation of the elevation angle’s CDF and PDF for multiple ES locations without requiring of simulations and statistical fitting. Finally, the proposed methodology is validated through an extensive error analysis that show the suitability of the obtained results to characterize the elevation angle.

Experimental Study of Turbulent Wake Flow Around Trapezoidal Cylinders With Varying Streamwise Aspect Ratios

AbstractThe effects of streamwise aspect ratio (AR) on the asymmetric wake flow over and behind right-angled trapezoidal cylinders with AR (= upper cylinder length to height ratio) = 1, 2, 3, 4, and 5 were investigated using particle image velocimetry. The Reynolds number based on the freestream velocity and cylinder height was 14700. The flow characteristics are examined in terms of the mean velocity flow, Reynolds stresses, probability density function (PDF), and two-point correlations. The results show that the primary vortex in the AR1 and AR2 trapezoidal cases extends into the wake region but is confined to the surface of the longer cases and two asymmetrical wake vortexes are only observed in the longer cases. Dual peaks of elevated streamwise Reynolds stresses are observed in the wake region, regardless of the aspect ratios. The magnitudes of the Reynolds stresses and turbulent kinetic energy are higher in the shorter cases (AR1, AR2, and AR3 cases) compared to the longer cases. The PDF distributions show a bimodal asymmetrical shape in the shorter cases but a nearly Gaussian distribution in the AR5 case. Two-point autocorrelations of the streamwise and vertical velocity fluctuations revealed that the spatial coherency of the turbulent structures is highly sensitive to the streamwise aspect ratio and reference locations. Systematic comparison between the present asymmetric results and symmetric wakes generated by rectangular cylinders with similar aspect ratios and Reynolds number shows significant differences between the asymmetric and symmetric wakes, especially at smaller aspect ratios.

Evaluation and Analysis of Wind Speed with the Weibull and Rayleigh Distribution Models for Energy Potential Using Three Models

Medan has a tropical climate and has the potential to support additional renewable energy, one of which is wind energy. Analysis of wind speed in Medan in particular has not been conducted to determine the potential for renewable energy. Research on wind speed in Medan, which ranges from 3.5m/s to 7.5m/s, has been carried out, but its potential has not been analyzed and evaluated. This study was conducted to analyze the shape factor and scale for wind speed using the Weibull and Rayleigh distribution, and three evaluation models were proposed, namely the correlation coefficient (R2), Chi-Square (ꭓ2), and Root mean square error (RMSE). Wind speed data that is used to analyze and evaluate obtained from the Meteorology, Climatology, and Geophysics Agency for a period of three years, 2017 to 2019 in Medan. The probability density distribution function (Pdf) is described based on the shape (k) and scale (c) parameters obtained from the above data analysis. These two parameters are very important to be observed related to the potential of electrical energy produced in a place or area. The analysis result shows that Weibull is better than Rayleigh distribution based on Pdf. Meanwhile statistical analysis, Weibull distribution is better than Rayleigh distribution based on R2. But on the other hand, the Rayleigh distribution is better than the Weibull distribution based on Chi-Square and RMSE. In addition to the analysis and evaluation, the potential for wind energy to be obtained is around 79.5 Watt/m2.

Self-Consistent Study of the Superconducting Gap in the Strontium-doped Lanthanum Cuprate

This work is aimed at numerically investigating the behavior of the Fermi energy in Strontium-doped Lanthanum Cuprate, using a numerical zero temperature elastic scattering cross-section procedure in the unitary collision regime. The main task is to vary the zero temperature superconducting energy gap from its zero value in the normal state, to the highest value of 60 meV. We find that there are two different reduced phase space regimes for the first harmonic line node's order parameter. The first one, represented by a Fermi energy with a value of - 0.4 meV, where the rest of the material parameters, and the degrees of freedom of the normal to the superconducting phase transition are not sensitive to the self-consistent variation of the zero temperature superconducting energy gap. A different case is found when in the self-consistent numerical procedure, the Fermi energy takes a value of - 0.04 meV, indicating that the fermion-dressed quasiparticles have material parameters strongly sensitive to the numerical changes in the zero temperature gap, resulting in a reduced phase space, where the input and output zero superconducting energy values, and the degrees of freedom are separated by the self-consistent numerical analysis. The first scenario considers that when the Fermi energy and the nearest hopping terms have the same order of magnitude, the physics can be described by a picture given by nonequilibrium statistical mechanics. A second scenario indicates, that when the Fermi energy parameter and the hopping term have different order of magnitude; the physical picture tends to be related to the nonrelativistic quantum mechanical degrees of freedom coming from quasi-stationary quantum energy levels, with a damping term seen in the probability density distribution function, that is described in the configuration space. Henceforth, it is concluded that the use of the zero temperature elastic scattering cross-section links the phase and configuration spaces through the inverse scattering lifetime, and helps to clarify the role of the degrees of freedom in Strontium-doped Lanthanum Cuprate. Finally, we think that the self-consistent numerical procedure with the reduced phase space, induces nonlocality in the inverse scattering lifetime.

SOFIA Observations of 30 Doradus. II. Magnetic Fields and Large-scale Gas Kinematics

The heart of the Large Magellanic Cloud, 30 Doradus, is a complex region with a clear core-halo structure. Feedback from the stellar cluster R136 has been shown to be the main source of energy creating multiple parsec-scale expanding-shells in the outer region, and carving a nebula core in the proximity of the ionization source. We present the morphology and strength of the magnetic fields (B-fields) of 30 Doradus inferred from the far-infrared polarimetric observations by SOFIA/HAWC+ at 89, 154, and 214 μm. The B-field morphology is complex, showing bending structures around R136. In addition, we use high spectral and angular resolution [C ii] observations from SOFIA/GREAT and CO(2-1) from APEX. The kinematic structure of the region correlates with the B-field morphology and shows evidence of multiple expanding-shells. Our B-field strength maps, estimated using the Davis–Chandrasekhar–Fermi method and structure-function, show variations across the cloud within a maximum of 600, 450, and 350 μG at 89, 154, and 214 μm, respectively. We estimated that the majority of the 30 Doradus clouds are subcritical and sub-Alfvénic. The probability distribution function of the gas density shows that the turbulence is mainly compressively driven, while the plasma beta parameter indicates supersonic turbulence. We show that the B-field is sufficient to hold the cloud structure integrity under feedback from R136. We suggest that supersonic compressive turbulence enables the local gravitational collapse and triggers a new generation of stars to form. The velocity gradient technique using [C ii] and CO(2-1) is likely to confirm these suggestions.

Secrecy Rate of TAS in AF-Relay Systems With Multi-Antenna Relay and User Over Non-Identical Channel Estimation Error

This work evaluates the secrecy rate of transmit antenna selection (TAS) in the amplify and forward (AF)-relay system with multi-antenna relay and user. This paper considers that the receiver of relays, users, and an eavesdropper have non-identical channel estimation error. To assess the secrecy rate, this work derives new analytical expressions for the cumulative distribution function (CDF) and probability density function (PDF) of the received signal to noise ratio (SNR) using infinite series for maximal-ratio combining (MRC) and selection combining (SC) receivers. Using the CDF for the received SNR, we derive new exact analytical expressions for the secrecy rate with non-identical channel estimation error for four scenarios. Further, using the PDF for the received SNR, we derive the asymptotic analytical expressions for the secrecy rate and quantify the high SNR slope and the high SNR power offset for four scenarios. From the numerical results, we observe that the relay and user selection has the high SNR power offset gain compared to the non-selection. The secrecy rate of the proposed system can be improved according to legitimate receiver's parameters such as the number of receive antennas and channel correlation coefficient and can be degraded according to eavesdropper's parameters. The superiority of the secrecy rate of the MRC receiver and the SC receiver depends on the channel estimation accuracy of the MRC receiver.

Channel Modeling and Performance Analysis of Directional THz Links Under Pointing Errors and α-μ Distribution

This letter focuses on providing an analytical framework for the quantification and evaluation of high-directional terahertz communication links under pointing errors in terms of outage probability (OP), channel capacity, and symbol error rate (SER). To this end, the probability density function and cumulative distribution function of the end-to-end channel are derived in the presence of pointing errors and small-scale fading. Then, closed-form expressions are derived for the OP, average channel capacity, and SER along with the asymptotic expressions for all the aforementioned performance metrics. Using numerical integral results, the accuracy of the analytical derivations are confirmed. Finally, we use the provided analytical expressions to evaluate the effect of the channel parameters on the system performance in terms of OP, channel capacity, and SER.