Probability Density Function Model Research Articles

Graphics processing unit/artificial neural network-accelerated large-eddy simulation of swirling premixed flames

Within the scope of reacting flow simulations, the real-time direct integration (DI) of stiff ordinary differential equations for the computation of chemical kinetics stands as the primary demand on computational resources. Meanwhile, as the number of transport equations that need to be solved increases, the computational cost grows more substantially, particularly for those combustion models involving direct coupling of chemistry and flow such as the transported probability density function model. In the current study, an integrated graphics processing unit-artificial neural network (GPU-ANN) framework is introduced to comply with heavy computational costs while maintaining high fidelity. Within this framework, a GPU-based solver is employed to solve partial differential equations and compute thermal and transport properties, and an ANN is utilized to replace the calculation of reaction rates. Large eddy simulations of two swirling flames provide a robust validation, affirming and extending the GPU-ANN approach's applicability to challenging scenarios. The simulation results demonstrate a strong correlation in the macro flame structure and statistical characteristics between the GPU-ANN approach and the traditional central processing unit (CPU)-based solver with DI. This comparison indicates that the GPU-ANN approach is capable of attaining the same degree of precision as the conventional CPU-DI solver, even in more complex scenarios. In addition, the overall speed-up factor for the GPU-ANN approach is over two orders of magnitude. This study establishes the potential groundwork for widespread application of the proposed GPU-ANN approach in combustion simulations, addressing various and complex scenarios based on detailed chemistry, while significantly reducing computational costs.

Statistical analysis of magnetic divertor configuration influence on H-mode transitions

DIII-D plasmas are compared for two upper divertor configurations: with the outer strike point on the small angle slot (SAS) divertor target and with the outer strike point on the horizontal divertor target (HT). Scanning the vertical distance between the magnetic null point and the divertor target over a range 0.10–0.16 m is shown to increase the threshold power, Pth , and edge plasma power, PLoss , for the low-to-high confinement (L–H) and H–L transitions respectively, by up to a factor of 1.4. The X-point height scans were performed at three L-mode core plasma line average electron densities, n¯e= 1.2, 2.2 and 3.6 ×1019m−3 , to investigate the density dependence of divertor magnetic configuration influence on Pth . The X-point height, Zx-pt , was further extended across the range 0.16–0.22 m with the more open HT divertor configuration, for which a clear decrease in Pth with increasing Zx-pt is observed. The dependence of Pth on divertor magnetic geometry is further investigated using a time-dependent probability density function (PDF) model and information geometry to elucidate the roles played by pedestal plasma turbulence and perpendicular velocity flows. The degree of stochasticity of the plasma turbulence is observed to be sensitive to the plasma heating rate. The calculated square of the information rate shows changes in the relative density fluctuations and perpendicular velocity PDFs begin 2–5 ms prior to the L–H transition for three plasmas; providing a crucial measurement of the dynamic timescale of external transport barrier formation. Additionally, both information length and rate provide potential predictors of the L–H transition for these plasmas.

Elaboration of a Generalized Mixed Model for the wind speed distribution and an assessment of wind energy in Algerian Coastal regions and at the Capes

Understanding and evaluating wind energy involves various steps, including the observed temporal and directional variations in wind speed, choosing a suitable Probability Density Function (PDF) to describe wind regimes, and selecting an appropriate location for building wind farms. The wind speed data archived from nine meteorological stations along the northern coast of Algeria from 2017 to 2021 was used as a dataset to achieve these purposes. Zero-inflated mixed model (ZIMM) has been elaborated to model the wind speed regimes that combine two processes. The first process consists of mixing two PDFs that generate the counts data. The second process generates the residual zero-counts data. The estimation of ZIMM parameters is obtained with the Expectation–Maximization algorithm. ZIMM performances were evaluated at the selected sites using the commonly used goodness of fit (GOF) metrics: coefficient of determination (R2), root mean square error (RMSE), sum of square error (SSE), Kolmogorov–Smirnov (KS), Akaike information criterion (AIK), Bayesian Information Criterion (BIC), and compared with the widespread single PDFs: the two parameters Weibull, generalized extreme value (GEV) and Normal–Weibull mixed model. The datasets are used as input for assessing wind power and the feasibility of wind power plants in 24 Algerian Capes where the data is unavailable, using the Wind Atlas Analyses and Application Program (WAsP) and three different wind turbines, namely Nordex N50, Bonus B54, and Nordex N60. The results show significant variations in diurnal, monthly, and seasonal mean wind speed and power density. According to all GOF, the ZIMM PDF model outperforms conventional PDFs and the mixed model at the nine meteorological stations. The Bonus B54 wind turbine has the best capacity factor (Cp) with the lowest electrical production cost of all Algerian Capes, and the Cp exceeds 0.3 at 15 Capes from the 24 analyzed Capes. The highest Cp, about 0.467 with an annual electric production that reaches 4.09 GWh/year, is obtained at Cape Takouch with the lowest electrical production cost of 0.0414 $/kWh and 2.032 Kton/year of CO2 emission avoided.

Improving paragraph segmentation using BERT with additional information from probability density function modeling of segmentation distances

Paragraphs play a key role in writing and reading texts. Therefore, studies about dividing texts into appropriate paragraphs, or paragraph segmentation have gathered academic attention for a long time. Recent advancements in pre-trained language models have achieved state-of-the-art performances in various natural language processing fields, including paragraph segmentation. However, pre-trained language model based paragraph segmentation methods had a problem in that they could not consider statistical metadata such as how far each paragraph segmentation point should be apart from each other. Therefore we focused on combining paragraph segmentation distance and pre-trained language models so that both statistical metadata and state-of-the-art representation ability could be considered at the same time. We propose a novel model by modifying BERT, a state-of-the-art pre-trained language model, by adding segmentation distance information via probability density function modeling. Our model was trained and tested on the domain of the novel, and showed improved performance compared to baseline BERT and previous study, acquiring a mean of 0.8877 F1-score and 0.8708 MCC. Furthermore, our model showed robust performance regardless of the authors of the novels.

Phase Noise Analysis of Time Transfer over White Rabbit-Network Based Optical Fibre Links.

White Rabbit (WR) is an optical fibre-based time-frequency synchronization technology typically used in timekeeping laboratories for distributing time-frequency signals from a reference clock to distant locations. The accuracy of the received signals at the user end can be affected by random noise processes present in the WR network due to the internal electronic components of WR devices. In this paper, we investigate the presence of random noise processes in the WR network. We then study their statistical properties and model the distribution based on experimentally recorded measurements. According to our study, the probability density function (PDF) follows a Gaussian mixture model (GMM) with varying distribution parameters, and the correlation analysis indicates a strong correlation of the phase noise process over the temporal samples. Furthermore, the developed phase noise models have also been verified by comparing them against additional experimental data. Finally, we present the methodology to generate the phase noise process using computer simulations with the PDF and correlation models developed in this work to help algorithm developers and equipment manufacturers make use of our results.

Probability density function modelling and credible region construction for multivariate, asymmetric, and multimodal distributions of geotechnical data

Geotechnical data are typically Multivariate, Uncertain, and Irregular (MUI), so the probability distribution of geotechnical data is Multivariate, Asymmetric, and Multimodal (MAM). Probability Density Function (PDF) modelling and Credible Region (CR) construction are two key issues for a MAM distribution. There are two fundamental difficulties in characterizing a MAM distribution. The first is on joint PDF modelling as many traditional approaches collapse for a MAM distribution. Copula theory has attracted special attention for this purpose but very few works attempted to tackle the critical problem of probabilistic prediction on target variables using available information of remaining variables based on the copula-based joint PDF. The second is on CR construction of a MAM distribution as it cannot find a unique CR of a MAM distribution given an exceedance probability only. There is still a lack of a unified approach for CR construction for a MAM distribution of geotechnical data. Aiming to resolve these two fundamental difficulties, we propose the BAyeSIan Copula-based Highest density region/contour (BASIC-H) for providing a systematic framework of PDF modelling and CR construction of a MAM distribution. This framework contains Stage-PDF and Stage-CR. Stage-PDF fuses the copula theory and Bayesian inference to develop optimal, robust, and hyper-robust predictions on the posterior distribution and posterior predictive distribution. Stage-CR adopts the constraint for the CR that the probability density of every point inside the CR is at least as large as the probability density of any point outside, which is the same as the idea of the HDR (Highest Density Region). The Monte Carlo Simulation (MCS), based on the developed optimal, robust, and hyper-robust posterior distributions and posterior predictive distributions, is performed for estimation of the probability density boundary, which is a key parameter for constructing the HDR. Examples using simulated data and Quaternary clay data are presented to illustrate the capabilities of the BASIC-H in PDF modelling and CR construction of MAM distributions of geotechnical data.

PDF Comparison based on Various FSO Channel Models under Different Atmospheric Turbulence

Recently, wireless communication environments with high speeds and low complexity have become increasingly essential. Free-space optics (FSO) has emerged as a promising solution for providing direct connections between devices in such high-spectrum wireless setups. However, FSO communications are susceptible to weather-induced signal fluctuations, leading to fading and signal weakness at the receiver. To mitigate the effects of these challenges, several mathematical models have been proposed to describe the transition from weak to strong atmospheric turbulence, including Rayleigh, lognormal, Málaga, Nakagami-m, K-distribution, Weibull, Negative-Exponential, Inverse-Gaussian, G-G, and Fisher-Snedecor F distributions. This paper extensively studies and analyses different probability density functions (PDFs) that govern the FSO channel, considering various channel models. This paper aims to comprehensively understand how FSO channels can be effectively modeled using different PDFs. Accurate modeling is crucial for designing FSO systems that can operate optimally under potential environmental conditions. Selecting the appropriate PDF model plays a crucial role in determining the FSO channel's performance during system design. With a multitude of PDF models available, this study aims to identify the most effective PDF model to be employed in FSO channel modeling.

Critical Sample-Size Analysis for Uncertainty Aerodynamic Evaluation of Compressor Blades with Stagger-Angle Errors

Many probability-based uncertainty quantification (UQ) schemes require a large amount of sampled data to build credible probability density function (PDF) models for uncertain parameters. Unfortunately, the amounts of data collected as to compressor blades of aero-engines are mostly limited due to the expensive and time-consuming tests. In this paper, we develop a preconditioner-based data-driven polynomial chaos (PDDPC) method that can efficiently deal with uncertainty propagation of limited amounts of sampled data. The calculation accuracy of a PDDPC method is closely related to the sample size of collected data. Therefore, the influence of sample size on this PDDPC method is investigated using a nonlinear test function. Subsequently, we consider the real manufacturing errors in stagger angles for compressor blades. Under three different operating conditions, the PDDPC method is applied to investigate the effect of stagger-angle error on UQ results of multiple aerodynamic parameters of a two-dimensional compressor blade. The results show that as the sample-size of measured data increases, UQ results regarding aerodynamic performance obtained by the PDDPC method gradually converge. There exists a critical sample size that ensures accurate UQ analysis of compressor blades. The probability information contained in the machining error data is analyzed through Kullback–Leibler divergence, and the critical sample size is determined. The research results can serve as a valuable reference for the fast and cheap UQ analysis of compressor blades in practical engineering.

Analysis of wall-modelled particle/mesh PDF methods for turbulent parietal flows

Abstract Lagrangian stochastic methods are widely used to model turbulent flows. Scarce consideration has, however, been devoted to the treatment of the near-wall region and to the formulation of a proper wall-boundary condition. With respect to this issue, the main purpose of this paper is to present an in-depth analysis of such flows when relying on particle/mesh formulations of the probability density function (PDF) model. This is translated into three objectives. The first objective is to assess the existing an-elastic wall-boundary condition and present new validation results. The second objective is to analyse the impact of the interpolation of the mean fields at particle positions on their dynamics. The third objective is to investigate the spatial error affecting covariance estimators when they are extracted on coarse volumes. All these developments allow to ascertain that the key dynamical statistics of wall-bounded flows are properly captured even for coarse spatial resolutions.

Influence of the chemical kinetics on the prediction of turbulent non-premixed jet CH_4 flames

The present work focuses on the five different chemical mechanisms coupled with probability density function (PDF) model to represent the local extinction and re-ignition flame characteristics of the well-known Sandia Flames D–F. These five mechanisms span from the Foundational Fuel Chemistry Model (FFCM) mechanism involving 38 species to the Glarborg mechanism involving 150 species. The coupled computational fluid dynamics (CFD) and transported-PDF method are used for the turbulence modeling, and the reaction–diffusion manifolds (REDIMs) are used as an advanced technique for the simplification of chemical kinetics and to speed up the numerical computation. It is demonstrated that these chemical mechanisms have an ability to represent the degree of local extinction and re-ignition accurately. Furthermore, the sensitivity analysis shows that the degree of local extinction is very sensitive to only several key elementary reactions, and an analysis on the turbulence–chemistry interaction investigates the influence of these elementary reactions.

CFD Simulation of oxy-fuel combustion using turbulent non-premixed combustion with medium-rank coal from Kalimantan Indonesia

Carbon capture technology connected with oxy-fuel combustion has a high potential for reducing CO2 emissions, particularly in coal-fired power plants. However, the distinct characteristics of each coal depend on its origin. This study analyzes coal combustion from Kalimantan using a drop tube furnace and varying the volume of oxygen: Coal (21 vol.% O2), OF25 (coal with 25 vol.% O2), OF30 (coal with 30 vol.% O2), the non-premixed combustion model and a structured grid. Probability Density Function (PDF) models were used for combustion chemistry. The overall combustion temperature distribution and the amounts of O2, H2O, C, and CO2 in combustion products were visualized. The numerical results show that increasing the volume of oxygen leads to an increase in temperature distribution for OF25 and OF30, but the flame is shorter than for Coal. During combustion, the mass fraction of oxygen remains in the furnace and H2O increases. Carbon burns quickly and is depleted, whereas the CO2 content increases along with the volume of oxygen, making the CO2 capture process easier. The results obtained from the numerical analysis can offer valuable insights for enhancing the design of combustion chambers in oxy-fuel boilers for better modeling of pulverized coal especially using Kalimantan coal.

Numerical Study of the Influence of the Geometric Parameters of a Radial Crystalizer Using a Multiscale CFD Model

This work investigates how the configuration of the geometric parameters of a radial crystallizer influences the results of the crystallization of lovastatin by antisolvent and using a multi-scale computational fluid dynamics (CFD) model. The OPENFOAM open-source software uses macro and micromixing expressions for flow, and complete energy and population equilibrium equations during nucleation and crystal growth. The model is based on the Reynolds-Averaged-Navier-Stokes (RANS) equation, along with a multi-environment probability density function (PDF) model and the spatially semi-discretized population equilibrium equation, operating a high-resolution finite volume method. The variation crystallizer construction parameters provided another crystallizer design, and analyses demonstrated improved performance and effects on crystal distribution.

Simulation of turbulent non-premixed combustion in pulverized coal from Kalimantan Indonesia

A computational simulation was created to investigate pollutants during coal combustion in a Drop Tube Furnace using Kalimantan coal. Previous research has explored Drop Tube Furnace combustion with Kalimantan coal, but lacked an understanding of combustion phenomena and pollutants, which are challenging to observe experimentally. This study utilized three samples of Kalimantan coal, namely RP, MB, and KC, acquired from various mining sources. This research is new study of simulation combustion coal in Drop Tube Furnace using non-premixed turbulent combustion and the Probability Density Function model with structured grid. The study reports on the temperatures and mass fractions of pollutants, including NOX, SO2, and CO2, along the centerline of the domain. The findings show that RP coal produced the highest combustion temperature, while KC coal produced the lowest. MB coal had the highest CO2 mass fraction, KC coal had the highest NOx value, and RP coal had the highest SO2 value.

On composite length-biased exponential-Pareto distribution: Properties, simulation, and application in actuarial science

The composite length-biased exponential-Pareto (CLBEP) distribution is a new composite distribution that is introduced in this article. This model's probability density function, moments, and quantiles, among other statistical characteristics, are determined mathematically. The parameters' maximum-likelihood estimation and stochastic ordering are discussed. A comparison study with other new composite and conventional distributions is also included. Specifically, using two actual fire insurance data sets, the goodness of fit of this new model is contrasted with the composite exponential-Pareto, composite lognormal-Pareto, and composite Rayleigh-Pareto distributions (Algerian and Danish fire insurance losses).2010 AMS subject classifications62E10; 60E05.

Probability Density Function Models for Float Glass under Mechanical Loading with Varying Parameters

Glass as a construction material has become indispensable and is still on the rise in the building industry. However, there is still a need for numerical models that can predict the strength of structural glass in different configurations. The complexity lies in the failure of glass elements largely driven by pre-existing microscopic surface flaws. These flaws are present over the entire glass surface, and the properties of each flaw vary. Therefore, the fracture strength of glass is described by a probability function and will depend on the size of the panels, the loading conditions and the flaw size distribution. This paper extends the strength prediction model of Osnes et al. with the model selection by the Akaike information criterion. This allows us to determine the most appropriate probability density function describing the glass panel strength. The analyses indicate that the most appropriate model is mainly affected by the number of flaws subjected to the maximum tensile stresses. When many flaws are loaded, the strength is better described by a normal or Weibull distribution. When few flaws are loaded, the distribution tends more towards a Gumbel distribution. A parameter study is performed to examine the most important and influencing parameters in the strength prediction model.

Pressure effects on soot formation and evolution in turbulent jet flames

In this study, two series of pressurized turbulent jet sooting flames at 1, 3, and 5 bar with either fixed jet velocity or fixed Reynolds number are simulated to study the pressure effects on soot formation and evolution. Through a radiation flamelet progress variable approach with a conditional soot subfilter probability density function (PDF) model to consider the turbulence–chemistry–soot interactions, quantitatively good agreements are achieved for soot volume fraction (SVF) predictions compared with the experimental data, regardless different turbulent intensities and residence times. SVF source terms are then discussed to show the pressure effects on nucleation, condensation, surface growth, and oxidation at different axial positions in these flames. It is found that surface growth and oxidation increase by about three orders of magnitude from 1 to 5 bar, while nucleation and condensation only increase within one order of magnitude. The stronger SVF scaling on pressure than measured data is found to be attributed to the inaccurate surface growth and oxidation scaling on pressure. Further analysis indicates that (i) the uncertainty of C2H2 prediction at elevated pressures is likely a major reason for the too strong surface growth scaling; and (ii) taking account of pressure effects in the conditional subfilter PDF modeling for turbulence–soot–chemistry interactions is likely a key to improve oxidation prediction. The results in this study open up the possibilities for improving future turbulent sooting flame modeling by improving C2H2 chemistry and turbulence–chemistry–soot modeling at elevated pressures.

An indirect approach to optimize the reaction rates of thermal NO formation for diesel engines

With stringent emission regulations, it has become more important for modern diesel engine manufacturers to accurately predict engine-out nitrogen oxide (NOx) emissions across a wide range of operating conditions. Thermal NO is the major source of engine-out NOx in modern diesel engines. For thermal NO formation, several earlier studies have recommended the forward and reverse reaction rate coefficients of the rate-limiting reaction (O + N2⇌ NO + N). However, due to deficiencies in sub-models and inadequacies of reduced chemical mechanisms to represent diesel combustion, these recommended values more often than not need to be adjusted in reduced order combustion models to accurately predict engine-out NOx. Hence, in this work a systematic and computationally efficient approach has been proposed to streamline the process of determining the optimum reaction rate coefficients. To develop the optimization approach, four different production diesel engines with different operating conditions in terms of speed, load, and exhaust-gas recirculation have been considered. Numerical simulations have been performed using a detailed zero-dimensional velocity-composition-frequency transported probability density function (0D-VCF-tPDF) model that uses hundreds of notional particles to capture in-cylinder stratification. Four different combinations of hydrocarbon and NOx chemical mechanisms were used to represent chemistry. It was found that for the rate-limiting reaction, the pre-exponent factors (Af1,Ar1) and activation energies (EA,f1,EA,r1) of the forward and reverse reaction rates follow a linear band in Af1−EA,f1 and Ar1−EA,r1 space where predicted engine-out NOx match the measured values closely. By encompassing such bands from different engines and considering constraints on activation energies, a reduced search domain of pre-exponent factors and activation energies was constructed that is expected to be applicable to any diesel engine. Eventually, computationally efficient three-line and one-line search approaches were proposed to determine the optimum values of the pre-exponent factors and activation energies that led to a minimum error between measured and predicted engine-out NOx. Finally, these three-line and one-line NOx optimization approaches were applied to a fifth production diesel engine for which the 0D-VCF-tPDF model showed a very good predictive performance in terms of predicting peak pressure, 50% burn rate, and engine-out NOx when compared to measured and 3D-CFD values.

Composition and Evolution of Continental Crust at Orogenic Belts: Constraints From a 3‐D Crustal Model of Southeast China

AbstractThe chemical composition of continental crust is fundamental and crucial to understanding its origin and evolution. Orogenic belts make up about 30% of the global continental crust, yet their chemical compositions are still poorly constrained. In this study, we report an overall estimate for the continental crust composition of a collisional orogenic belt terrane: the Southeast China. The estimate is obtained through a 3‐D crustal model combining a lithology proportion model and probability density function models for element concentrations of various lithologies. Based on our model, the Southeast China crust is amongst one of the most evolved continental crust composition estimates (71.0% SiO2 content for the upper crust and 64.7% SiO2 for the bulk crust). A strong correlation between SiO2 and the chemical index of alteration (CIA) of different composition models for upper continental crust (UCC) indicates that chemical weathering is a controlling factor for the development of a felsic UCC. In contrast, weak correlations of SiO2 with Ninorm (15.9*Ni/Al2O3) and CIA suggest that igneous differentiation and chemical weathering act together to modify the composition of the bulk continental crust. Orogenic belt terranes like the Southeast China can develop a highly evolved crustal composition, especially for the upper crust, due to extensive intracrustal reworking and differentiation, enhanced chemical weathering, and potential subsequent delamination and removal of thickened crust root. Therefore, an overall estimation of the average composition of continental crust should take into account the more evolved composition of orogenic belts.

On the effect of flow regime and pore structure on the flow signatures in porous media

In this study, lattice Boltzmann method (LBM) is utilized for three-dimensional simulation of fluid flow through two porous structures, consisting of grains with the same diameter: (i) a homogeneous porous domain, in which the grains are placed with a simple cubic packing configuration, and (ii) a randomly packed porous domain. An ultra-fine mesh size is considered to perform the simulations in three orders of magnitude of Reynolds number (Re), covering laminar to turbulent flow regimes, and capture different flow signatures. Pore velocity fields are derived, and their sample probability density functions (PDF) are analyzed vs time to investigate the dynamics of the flow. The analysis of the PDFs clearly shows that stagnant zones play a significant role in the formation of the pore flow fields, manifested by multimodal PDFs, and the distribution of the velocities in porous media at various Re cannot be characterized by a single PDF model regardless of the pore structure. While the velocities at the stagnant regions and in the vicinity of the solid boundaries are primarily affected by the viscous forces and exhibit a power-law PDF at different Re, the velocities in the main (preferential) flow pathways away from the boundaries are shown to be influenced by the inertial forces, hence having an exponential PDF when Re is low. At high Re, however, depending on the tortuosity of the porous structure, the velocities may exhibit an exponential or even Laplace PDF.

Exploring short-term optical variability of blazars using TESS

ABSTRACT We present a first systematic time series study of a sample of blazars observed by the Transiting Exoplanet Survey Satellite (TESS). By cross matching the positions of the sources in the TESS observations with those from Roma-BZCAT, 29 blazars including both BL Lacerate objects and flat-spectrum radio quasars were identified. The observation lengths of the 79 light curves of the sources, across all sectors on which the targets of interest have been observed by TESS, range between 21.25 and 28.2 d. The light curves were analysed using various methods of time series analysis. The results show that the sources exhibit significant variability with fractional variability spanning between 1.41 per cent and 53.84 per cent. The blazar flux distributions were studied by applying normal and log-normal probability density function models. The results indicate that optical flux histogram of the sources are consistent with normal probability density function with most of them following bimodal distribution as opposed to unimodal distribution. This suggests that the days-time-scale optical variability is contributed either by two different emission zones or two distinct states of short-term activity in blazars. Power spectral density analysis was performed by using the power spectral response method and the true power spectra of unevenly sampled light curves were estimated. The power spectral slopes of the light curves ranged from 1.7 to 3.2.