Probability Density Function Model Research Articles

Marine target cfar detection method based on superpixel difference degree

Abstract At present, the method based on constant false alarm rate (CFAR) technology is one of the important means of marine target detection. The performance of traditional sliding window CFAR detectors is easy to be affected by speckle noise and multi-target crosstalk, resulting in a low success rate of visual inspection. In this paper, a CFAR detection method based on superpixel difference degree is proposed. This method can effectively distinguish potential target superpixels and background superpixels, and then through the selection of background superpixels, the clutter probability density function model is fitted with the unbounded Johnson distribution model, to carry out CFAR detection. Based on the SAR images of the Gaofen-3 satellite and Sentinel-1 satellite, the experiment verifies that the method can improve the detection performance in multiple scenarios.

A data-driven maximum entropy method for probability uncertainty analysis based on the B-spline theory

The probability density function (PDF) is quite important for structural reliability analysis; thus, accurate PDF modeling methods draw increasing attention. This paper proposes a novel metaheuristic data-driven paradigm of the maximum entropy method (MEM) based on the B-spline function theory. Firstly, a B-spline proxy of the MEM PDF is proposed for probability uncertainty analysis. We derive the parameter calculation formulation and calculate the undetermined parameters via the raw data of structural responses. Then, to determine the knots of the B-spline functions, we propose a novel data-driven approach with the aid of a powerful metaheuristic algorithm and the response data information. Different from the traditional MEM, the proposed method is a complete data-driven solution approach and does not involve the statistical moment calculation and the nonlinear equations composed of statistical moments. Combining the advantages of the B-spline theory and the MEM, the proposed method can reconstruct the response PDF with a complex shape, such as the PDF with multiple peaks or heavy tails. For verification, two numerical examples and one engineering example are analyzed, and compared with some classical PDF modeling methods. The results show that the proposed method is superior to the compared methods in terms of computational accuracy, when the same sample data is used.

Capacity Optimization for RSMA-Based Multi-User System over Underwater Turbulence Channel

The underwater environment used for communication is harsh and complex, necessitating heightened standards for spectral efficiency and reliability in underwater wireless optical communication (UWOC) systems. The focus of this work is on the performance of multi-user UWOC systems operating in oblique channels of ocean turbulence downlink, where users are randomly distributed at a certain depth. A joint optimization scheme is proposed, which joints rate-splitting multiple access (RSMA) and power allocation so that the system’s ergodic sum capacity is optimized to improve the transmission bandwidth. Furthermore, the probability density function (PDF) and cumulative distribution function (CDF) models for the received signal-to-noise ratio (SNR) of a multi-user multiple-input multiple-output (MIMO) system operating in the turbulent underwater oblique channels are established, accounting for the avalanche photodiode (APD) shot noise and solar radiation noise. Theoretical derivations are presented to quantify the ergodic capacity and outage probability of the multi-user system utilizing the RSMA technology. Subsequently, a numerical analysis is conducted to investigate the influence of the power allocation coefficient, RSMA, and the joint optimization algorithm on the performance of a two-user MIMO system leveraging RSMA. The simulation results show that our optimization scheme effectively reduces the outage probability, thereby achieving the maximum system sum rate and validating the practical feasibility and efficacy of the proposed scheme.

Correlation analysis and joint probability density function model of wind pressures: Focusing on multivariate wind loads field on low-rise building under typhoon climate

The characteristics of the multivariate wind loads field on the roof are crucial to the wind-resistant design of low-rise buildings, which contain the correlation characteristics in space and probability characteristics in the time domain. This paper proposes a framework for constructing a Joint Probability Density Function (Joint PDF) model for a multivariate wind loads field. It provides a detailed correlation analysis for the first time. This paper employs wind pressure data collected from the roof of a low-rise building during Typhoon Muifa. It was found that the correlation becomes more robust with increasing roof pitch and the wind pressures are strongly correlated with a correlation coefficient exceeding 0.50 when the roof pitch is above 15°. The mixture distribution model is applied to the probability density function fitting procedure of wind pressure time series under typhoon climate, and the fitting effect is significantly better than other classical probability density functions. The optimal copula function is determined according to the Akaike Information Criterion (AIC) and Bayesian Information Criterion (BIC) for estimating the Joint PDF. The results reveal that Gumbel-copula and Student-copula have the highest proportion in optimal copula functions, accounting for over 90% of the total copula functions. Then, a bivariate Joint PDF for wind pressures are established with the optimal copula function. Additionally, the comparison between measured bivariate Joint PDF and that constructed using copula functions verifies the accuracy of the proposed framework for constructing Joint PDFs. The Joint PDF of wind pressures can enhance the understanding of the stochastic characteristics of local wind load fields on roofs, and the correlation characteristics in space provide crucial references for improving the accuracy of wind load random field simulation and saving the cost of wind resistance design.

Probability density function models for adaptive optical systems operating in turbulence

Probability density function models for adaptive optical systems operating in turbulence

Long-term trends and probability distribution functions of air pollutant concentrations in the megacity of São Paulo

Air quality conditions in many urban areas have improved in the last decades as a consequence of air pollution control policies and regulations. Mitigation strategies have been successful in reducing the concentration of primary pollutants like inhalable particulate matter (PM10), but the control of secondary pollutants like tropospheric ozone (O3) is still challenging in megacities like the Metropolitan Area of São Paulo (MASP) in Brazil. To support the development of effective mitigation strategies, it is crucial to characterize the statistical behavior of air pollutant concentrations and its long-term evolution. Probability Density Functions (PDF) can be useful to model site-specific air quality conditions, providing estimates for the frequency of extreme pollution events and exceedance of air quality standards. The current study aims to characterize which PDF model better fits and characterizes the variability of PM10 and O3 concentrations in the MASP. For that, daily maximum moving average concentrations were analyzed between 2000 and 2023, characterizing the long-term trends and the frequency of exceedance of air quality standards. PM10 concentrations followed a lognormal PDF, with an expected value of 31 ± 15 µg.m-3. O3 followed a Gamma PDF, with an expected value of 68 ± 25 µg.m-3. A consistent long-term decrease was observed for PM10 (-1.04 ± 0.09 µg.m-3.yr-1), while O3 showed an increasing trend of 0.51 ± 0.04 µg.m-3.yr-1 in the summer. In recent years (2021-2023), the probability of exceedance of the World Health Organization guideline was 17.4 and 11.0%, respectively, for PM10 and O3. In 2020, a statistically significant increase in O3 expected values was observed, possibly associated with changes in the emission patterns of precursors due to the mobility restrictions imposed by the COVID-19 pandemic.

Experimental Study on the Crack Concrete Repaired via Enzyme-Induced Calcium Carbonate Precipitation (EICP).

A low-carbon and environmentally friendly EICP method for repairing concrete cracks is presented to prolong the service life of concrete. In this study, we took concrete as the research object and quartz sand as the filling medium and employed the EICP injection method to repair concrete cracks. The internal repair effect of EICP on concrete cracks was evaluated with a combination of ultrasonic and compressive strength tests. The concrete repair mechanism of EICP was identified with a combination of EDS, XRD, and SEM tests. The results indicate that with an increase in the fracture depth, the ultrasonic sound time of the crack specimen increased gradually, and the ultrasonic wave transit time value of the crack specimen decreased significantly after EICP repair. After repair, the compressive strength rose. The highest compressive-strength recovery rate of a 0.3 mm wide specimen is 98.41%. The calcium carbonate crystal formed using EICP is vaterite. The probability density function model of the Laplace distribution was constructed, which showed good applicability and consistency in the ultrasonic sound time and compressive strength measured via experiments. The formed calcium carbonate crystals can be tightly and evenly attached to the cracks with the EICP injection repair method, resulting in a better repair effect.

A new statistical fading model for loss factor induced by angle-of-arrival fluctuations in free space optical communication.

The impact of angle-of-arrival (AOA) fluctuations on the loss factor is investigated, and a new fading model is proposed to describe the associated attenuation. Distinct decay characteristics induced by AOA fluctuations are revealed, which depend on the ratio of detector size to beam width (M). The fading model can be divided into two sub-models based on the value of M0, where M0 is the value of M when the root-mean-square errors of the two sub-models are equal. In the case of M⩾M0, this fading model follows an inverse S-shaped pattern to describe the impact of AOA fluctuations. When M < M0, an exponential function to characterize the attenuation induced by AOA fluctuations. The numerical computation results indicate that the proposed fading model offers higher accuracy compared to traditional methods. Furthermore, the continuous analytical expressions for the probability density function (PDF) and cumulative density function (CDF) of the presented fading model caused by AOA are derived. Based on the proposed PDF and CDF models, the outage probability of inter-satellite laser link is analyzed.

Liouville models of particle-laden flow

Langevin (stochastic differential) equations are routinely used to describe particle-laden flows. They predict Gaussian probability density functions (PDFs) of a particle's trajectory and velocity, even though experimentally observed dynamics might be highly non-Gaussian. Our Liouville approach overcomes this dichotomy by replacing the Wiener process in the Langevin models with a (small) set of random variables, whose distributions are tuned to match the observed statistics. This strategy gives rise to an exact (deterministic, first-order, hyperbolic) Liouville equation that describes the evolution of a joint PDF in the augmented phase-space spanned by the random variables and the particle position and velocity. Analytical PDF solutions for canonical models of particle-laden flows serve to establish a relationship between the Langevin and Liouville approaches. Finally, our framework is used to derive a new analytical PDF model for fluidized homogeneous heating systems.

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.