Uncertainty Quantification of Two-phase Flow in Heterogeneous Reservoirs Using a Streamline-based Pdf Formulation

SER performance investigation of a MPPM relay-aided FSO system with three decision thresholds over EW fading channel considering pointing errors

81 8-354-2674 Abstract - Simple models for the patterns as well as their cumulative gain probability and probability density functions of the JPUNASA Deep Space Network (DSN) antennas are developed. These a~ needed for the study and evaluation of interference from unwanted sources such as the emerging terrestrial system, High Density Fixed Service (HDFS), with the Ka-band receiving antenna systems in Goldstone Station of the JPLNASA Deep Space Network. Several different models for the high gain ground antennas of the JPUNASA Deep Space Network @SN) are considered. The model definitions are then used to evaluate cumulative probability functions and probability density functions for the gain values at a receiving antenna randomly located anywhere in the far field of the model antenna. Both two-dimensional models which simulate the pattern in a plane cut through the boresight of the antenna and the range of the angle from boresight to *180 degrees and three- dimensional ones in which the pattem is given anywhere in the half-space above the ground, with the range of angle from zero at boresight to 90 degrees are considered. In both cases, regular as well as smooth interpolated models have been developed. The gain value as seen by a receiver at a random location and exposed to the radiation from a transmitting antenna with a given gain profile, can be thought of as a uniformly distributed random variable. Formulas are derived and various plots are presented for the gain models and their associated cumulative probability functions and probability density functions.

Latin Hypercube Sampling (LHS), unlike other simulation methods such as Monte Carlo Simulation (MCS), has not enjoyed wide applications in determination of reserve despite its capability to realize same accuracy as with the latter even with much fewer simulation trials. The parameters used in these distributions are extracted using software ‘digitizer’ from different plot of values derived from measurements of reservoir and fluid properties. This work dwells on analysis of two depleted gas fields for which the ultimate recovery is known. The distribution of porosity, water saturation, reservoir thickness and reserve size are input to crystalbal software to generate cumulative distribution function (CDF) and Probability density function (PDF) of original gas in place (OGIP) for each of the fields. The accuracy of Latin Hypercube Sampling is analysed by comparing the actual ultimate recovery and the OGIP predicted by LHS. The calculated recovery factors of 68.7% and 93.3%, for water driven and depletion driven gas reservoirs respectively, compare favourably with those of known gas reservoirs. Therefore, LHS is a good estimator of gas reserve. It is recommended that similar study should be carried out on condensate and oil reservoir, particularly on Niger Delta fields.

In this paper, we have derived and studied new probability distributions by extending the 2‐dimensional Rayleigh distribution (RD). First, we extend the RD to 3 dimensions and then generalize it to k dimensions for any positive integer k ≥ 3. The distributions are named the 3‐dimensional Rayleigh distribution (3‐DRD) and k‐dimensional Rayleigh distribution (k‐DRD), respectively. For both 3‐DRD and k‐DRD, detailed mathematical and statistical properties including derivations of the corresponding cumulative distribution, probability density, survival, and hazard functions, moments, moment generating functions, mode, skewness, kurtosis, and differential entropy are obtained in closed forms. Parameter estimation is done for both models using the maximum likelihood estimation method and some statistical properties of the estimator are discussed for each case. Interestingly, the commonly known Normal, Rayleigh, Maxwell–Boltzmann, chi‐square, gamma, and Erlang distributions are related to the newly developed extended RDs as special cases. For the 3‐DRD, plots of cumulative distribution, probability density, survival, and hazard functions are exhibited, a simulation study is carried out, and random samples are generated using the standard accept–reject (AR) algorithm to check the efficiency of the maximum likelihood estimates of the parameter. Moreover, the new 3‐DRD model is fitted to one simulated and three real datasets, revealing good performance compared to four existing Rayleigh‐based distributions. This study will contribute new knowledge to the field of applied statistics and probability, and the findings will be used as a basis for future research in the field.

The use of aerial platforms has recently attracted significant interest in Internet of Things (IoT)-based heterogeneous communication networks to support flexible and efficient network connection. This work investigates the performance of a ground-aerial autonomous aerial vehicle (AAV)-assisted hybrid power line communication (PLC)/free-space optical (FSO) communication system employing both decode-and-forward (DF) and fixed-gain amplify-and-forward (AF) relaying protocols. It is assumed that the PLC channel gain is Log-normally distributed while the Bernoulli-Gaussian random process models the PLC channel noise. The FSO link established between the FSO transmitter and the AAV considers the combined influence of the generalized Málaga distributed atmospheric turbulence (AT), random fog, nonzero boresight pointing errors, and Angle-of-Arrival (AoA) fluctuations of the AAV. Based on this, we evaluate the cumulative distribution function (CDF) and probability density function (PDF) of the end-to-end signal-to-noise ratio (SNR). Further, capitalizing on the statistical characterization of CDF and PDF, we derive series-based expressions for average symbol error rate (ASER), outage probability (OP), and average channel capacity (ACC) utilizing both heterodyne detection (HD) and direct detection (DD) techniques. Additionally, we conduct an asymptotic analysis of ASER in terms of the coding gain and diversity order in a high SNR regime. Likewise, a detailed analysis is carried out to find the optimal value of the field-of-view (FOV) angle and average SNR to achieve minimum ASER under the combined influence of the aforementioned channel conditions using the DF relaying scheme. Furthermore, the impact of all the considered channel parameters and impairments is demonstrated through the numerical results.

Постановка задачi. З розвитком технологiй радiозв’язку, особливо, мобiльного, усе бiльш важливу
\nроль вiдiграє розробка моделей радiоканалiв. У данiй
\nстаттi розглядається одна з популярних нинi моделей,
\nа саме, двопроменевий радiоканал з розсiюванням потужностi сигналу, яку в лiтературi прийнято позначати
\nабревiатурою TWDP (вiд Two-Wave with Diffuse Power).
\nДля цiєї моделi вiдомi як точнi, так i наближенi вирази
\nдля густини розподiлу iмовiрностей (ГРI) i кумулятивної функцiї розподiлу (КФР) обвiдної сигналу. Однак,
\nзагальним їх недолiком є висока складнiсть з точки зору практичного застосування. У зв’язку iз цим у данiй
\nроботi розглядається можливiсть значно бiльш простої
\nапроксимацiї ГРI та КФР обвiдної сигналу на основi
\nметоду Накагами.
\nРозробка методу. Апроксимацiя розподiлiв по методу Накагами зводиться до обчислення другого та
\nчетвертого початкових моментiв обвiдної сигналу на
\nвиходi каналу. Такi обчислення й виконанi в роботi,
\nщо дозволяє представити зазначенi моменти у виглядi
\nфункцiй вiд двох загальноприйнятих параметрiв каналу
\nTWDP: К-фактора та параметра Д, який визначається
\nспiввiдношенням амплiтуд радiо променiв.
\nАналiз похибок апроксимацiї. Похибки оцiнювалися шляхом зiставлення розрахункiв ГРI i КФР за
\nточними формулами та розрахункiв iз використанням
\nапроксимацiї Накагами. Паралельно також проводилися розрахунки вiдповiдно до формул апроксимацiї, що
\nвiдомi у лiтературi. Аналiз показав, що похибка методу
\nНакагами при обчисленнi КФР є цiлком задовiльною
\nдля практичних потреб майже у всьому дiапазонi змiн
\nпараметрiв каналу. У той же час точнiсть апроксимацiї
\nГРI у порiвняннi з iншими вiдомими методами апроксимацiї виявилася не дуже задовiльна.
\nВисновки. Проведенi дослiдження пiдтвердили можливiсть апроксимацiї КФР обвiдної сигналу в каналi TWDP розподiлом Накагами. Результати такої ж
\nапроксимацiї для ГРI виявилися менш задовiльними.
\nТакож вiдзначається кориснiсть отриманих результатiв
\nдля трактування даних натурних експериментiв.

We develop a probabilistic approach to map parametric uncertainty to output state uncertainty in first‐order hyperbolic conservation laws. We analyze this problem for nonlinear immiscible two‐phase transport in heterogeneous porous media in the presence of a stochastic velocity field. The uncertainty in the velocity field can arise from incomplete descriptions of either porosity field, injection flux, or both. This uncertainty leads to spatiotemporal uncertainty in the saturation field. Given information about spatial/temporal statistics of spatially correlated heterogeneity, we leverage the method of distributions to derive deterministic equations that govern the evolution of pointwise cumulative distribution functions (CDFs) of saturation for a vertical reservoir, while handling the manipulation of multiple shocks arising due to buoyancy forces. Unlike the Buckley‐Leverett equation, the equation describing the fine‐grained CDF is linear in space and time. Ensemble averaging of the fine‐grained CDF results in the CDF of saturation. Thus, we give routes to circumventing the computational cost of Monte Carlo simulations (MCS), while obtaining a pointwise description of the saturation field. We conduct a set of numerical experiments for one‐dimensional transport, and compare the obtained saturation CDFs, against those obtained using MCS as our reference solution, and the statistical moment equation method. This comparison demonstrates that the CDF equations remain accurate over a wide range of statistical properties, that is, standard deviation and correlation length of the underlying random fields, whereas the corresponding low‐order statistical moment equations significantly deviate from the MCS results, except for very small values of standard deviation and correlation length.

In this paper, an analytical framework is provided to analyze the energy coverage performance of unmanned aerial vehicle (UAV) energy harvesting networks with clustered user equipments (UEs). Locations of UAVs are modeled as a Poison Point Process (PPP), while locations of UEs are modeled as a Poisson Cluster Process (PCP). Two different models are considered for the line-of-sight (LOS) probability function to compare their effect on the network performance. Moreover, ultra-wideband (UWB) antennas with doughnut-shaped radiation patterns are employed in both UAVs and UEs, and the impact of practical 3D antenna radiation patterns on the network performance is also investigated. Initially, the complementary cumulative distribution function (CCDF) and probability density function (PDF) of path losses for each tier are derived. Subsequently, association probabilities with each tier are obtained. Energy coverage probability is derived for the entire network using tools from stochastic geometry. Via numerical results, we show that UAV height and antenna orientation play crucial roles on the energy coverage performance.

A K-tier heterogeneous downlink millimeter wave (mmWave) cellular network with user-centric small cell deployments is studied in this paper. In particular, we consider a heterogeneous network model with user equipments (UEs) being deployed according to a Poisson Cluster Process (PCP), i.e., Thomas cluster process, where the UEs are clustered around the base stations (BSs) and the distances between UEs and the BS are modeled as Gaussian distributed. In addition, distinguishing features of mmWave communications including directional beamforming and a sophisticated path loss model incorporating both line-of-sight (LOS) and non-line-of-sight (NLOS) transmissions, are taken into account. In this paper, the complementary cumulative distribution function (CCDF) and probability density function (PDF) of the path loss are provided. Also, using tools from stochastic geometry, we derive a general expression of the signal-to-interference-plus-noise ratio (SINR) coverage probability. Our results demonstrate that coverage probability can be improved by decreasing the size of UE clusters around BSs, and interference has noticeable influence on the coverage performance of our model.

Reliability Assessment of Strip Footings on Spatially Varying Sand

Hybrid uncertain static analysis with random and interval fields

The effect of random porosity field on supercritical carbonation of cement-based materials

In this work, the Cumulative Distribution Function (CDF) and the Probability Density Function (PDF) are examined for a data set of finite elements. The CDF and the PDF are valid only for the theoretical asymptotes when the number of elements in the set approaches infinity. The equivalent functions defined for a finite set are currently unknown. In various fields, especially in signal processing, data size is usually statistically limited and more accurate analysis is often required for the validation of new algorithms. In this work, discontinuous CDF (DCDF) is defined and proposed for measuring the ‘statistical distance’ and the ‘statistical error’. These new definitions enable comparisons of different data sets with each other and with the theoretical asymptotic function CDF. The proposed statistical functions are illustrated on Gaussian distributed data.

<p><span>Measurement uncertainty analysis based on combining the state-of-knowledge distributions requires evaluation of the probability density function (PDF), the cumulative distribution function (CDF), and/or the quantile function (QF) of a random variable reasonably associated with the measurand. This can be derived from the characteristic function (CF), which is defined as a Fourier transform of its probability distribution function. Working with CFs provides an alternative and frequently much simpler route than working directly with PDFs and/or CDFs. In particular, derivation of the CF of a weighted sum of independent random variables is a simple and trivial task. However, the analytical derivation of the PDF and/or CDF by using the inverse Fourier transform is available only in special cases. Thus, in most practical situations, a numerical derivation of the PDF/CDF from the CF is an indispensable tool. In metrological applications, such approach can be used to form the probability distribution for the output quantity of a measurement model of additive, linear or generalized linear form. In this paper we propose new original algorithmic implementations of methods for numerical inversion of the characteristic function which are especially suitable for typical metrological applications. The suggested numerical approaches are based on the Gil-Pelaez inverse formulae and on using the approximation by discrete Fourier transform and the fast Fourier transform (FFT) algorithm for computing PDF/CDF of the univariate continuous random variables. As illustrated here, for typical metrological applications based on linear measurement models the suggested methods are an efficient alternative to the standard Monte Carlo methods.</span></p>

In the estimation, using confidence intervals, of quantiles and reliability of the two – parameter exponential distribution based on record data, a pivot is defined and its exact cumulative distribution function and probability density function are computed. Confidence intervals using critical values from the cumulative distribution function of the pivot are obtained. Applications to crushed rock sizes and concentration of Sulfur dioxide from Long Beach, California.