Parameters Of Distribution Function Research Articles

Efficient Probabilistic Approach to Analyze Tunnel Support with Uncertain Probability Distribution Function of Input Parameters

Efficient Probabilistic Approach to Analyze Tunnel Support with Uncertain Probability Distribution Function of Input Parameters

Probabilistic Approach for Assessing the Occupational Risk of Olfactometric Examiners: Methodology Description and Application to Real Exposure Scenario.

Human examiners, known as panelists, are exposed to an unknown occupational exposure risk while determining odor concentration (Cod) using dynamic olfactometry. In the literature, a few papers, based on a deterministic approach, have been proposed to establish this occupational risk. As a result, the purpose of this study is to develop and apply a probabilistic approach, based on the randomization of exposure parameters, for assessing and evaluating the occupational exposure risk among olfactometric examiners. In this methodology, the risk is assessed by computing the hazard index (HI) and inhalation risk (IR) to determine the non-carcinogenic and carcinogenic risks. To randomize the exposure parameters, a Monte Carlo simulation was described and then applied in real exposure scenario to establish the exposure risk in terms of probability. Therefore, a one-year survey of the working activity of olfactometric examiners of Laboratorio Olfattometrico of Politecnico di Milano university was conducted. Based on this data collection (exposure parameters and chemical data, divided according to sample categories), a randomized exposure scenario was constructed to estimate the probability and cumulative distribution function of risk parameters. Different distributions were obtained for different industrial samples categories and were compared with respect to acceptability criteria (the value of HI and IR at 95th percentile of distribution). The elaboration provided evidence that negligible non-carcinogenic and carcinogenic risks are associated with the panelists' activity, according to an entire annual dataset. The application of probabilistic risk assessment provides a more comprehensive and effective characterization of the general exposure scenario for olfactometric examiners, surpassing the limitations of a deterministic approach. This method can be extended to future exposure scenarios and enables the selection of the most effective risk management strategies to protect the health of olfactometric examiners.

Optimization of distribution function and model parameters for molecular communication via diffusion with OtoO approximation

The analysis is generally conducted in stationary receiver and transmitter models in a diffusion environment for the fundamental Molecular communication (MOC) models. However, a mobile MOC model is employed in this study, deviating from the existing literature. This mobile MOC model considers the mobility of all variables in the diffusion environment, including the transmitter, receiver, and molecules. Firstly, a novel MOC model is proposed, departing from the conventional normal distribution for the mobility of variables. Instead, alternative distribution functions such as the Pareto distribution, extreme value distribution, t-distribution, and generalized extreme value distribution are employed. Furthermore, the system's performance is enhanced by optimizing the distribution function and model parameters, such as the diffusion coefficient, using the optimization of optimization (OtoO) approach. In this approach, the Multi-Verse Optimization (MVO) algorithm serves as the primary algorithm, while the Grey Wolf Optimization (GWO) algorithm functions as the auxiliary algorithm. Essentially, the MVO algorithm optimizes the parameters of the MOC model, while simultaneously, the GWO algorithm optimizes the impact of the optimization processes of MVO on the parameters ``p'' and ``N'' as well as the constant parameter of the distribution function. By optimizing both the parameters of the MOC model and the distribution function, the number of received molecules is significantly increased. Therefore, this study not only improves the results of the MOC model structure based on different distribution functions but also optimizes all parameters of the proposed model using the MVO-GWO OtoO approach.

Variational time reversal for free-energy estimation in nonequilibrium steady states.

Studying the structure of systems in nonequilibrium steady states necessitates tools that quantify population shifts and associated deformations of equilibrium free-energy landscapes under persistent currents. Within the framework of stochastic thermodynamics, we establish a variant of the Kawasaki-Crooks equality that relates nonequilibrium free-energy corrections in overdamped Langevin systems to heat dissipation statistics along time-reversed relaxation trajectories computable with molecular simulation. Using stochastic control theory, we arrive at a general variational approach to evaluate the Kawasaki-Crooks equality and use it to estimate distribution functions of order parameters in specific models of driven and active matter, attaining substantial improvement in accuracy over simple perturbative methods.

Probabilistic short-term load forecasting models based on a parametric approach

The forecasting of electric load plays an essential role in the effective management of electric power systems. Specifically, short-term models, which predict hourly load over the 24 hours of the subsequent day, hold significant value for applications within the realm of electricity markets. In this context, research efforts have predominantly concentrated on the development of point load forecasting models. These models provide solely the estimated value of hourly load, omitting any information regarding its associated uncertainty. Probabilistic forecasting models aim to address this limitation by offering comprehensive information on forecasted values, including their associated uncertainty, thereby enabling their more effective utilization in risky decision-making environments. This paper presents a parametric probabilistic model designed for hourly load forecasting. The model is refined through a multi-objective genetic algorithm optimization process that identifies explanatory variables from a specified set. The selected variables are combined linearly to predict the parameters of a probability distribution function for the hourly load. The process also selects the type of distribution from among those characterized by two parameters. The model is applied to data from a real distribution substation, yielding superior forecasting evaluation indexes compared to those achieved by two benchmark probabilistic load forecasting models.

Dust particle surface potential in an argon-helium plasma using the (r,q)-distribution function

Abstract In this paper, the dust particle surface potential for argon-helium plasma is evaluated analytically and numerically in the context of negatively charged dust particles by employing a power-law r , q -distribution function. Recent studies have reported the argon-helium plasma and conducted a brief theoretical and experimental survey. To deepen our understanding further, this study aims to analyze the argon-helium plasma comprehensively using the same pattern but with the r , q -distribution function. For this purpose, the current balance equations are derived for electron, helium and argon ions, when these charge species attain the quasineutrality condition. We numerically examined the currents of plasma species for a broad range of effective distribution function parameters r and q . It is revealed that the surface potential of dust particles is significantly affected by the parameters r and q , helium ion-to-electron temperature ratio, argon ion-to-electron temperature ratio, and helium ion to argon ion number density ratio. By incorporating the multi-ion (argon-helium) species, the significance of low-temperature non-Maxwellian dusty (complex) plasma is briefly examined.

Configuration entropy and potential energy landscape in thermodynamics and dynamics of supercooled liquids

In thermodynamics of supercooled liquids, sub-molecular units, referred to as “beads,” are used. It has been reported that all thermodynamic functions as well as the parameters in the empirical distribution functions of the potential energy landscape approach appear to be explicit functions of the number of beads in molecules. This finding opens the possibility of measuring the number of beads from each of these functions and estimating the configuration and vibration components in their formation. An enthalpy factor has been introduced and found that within the temperature domain of the invariable enthalpy factor, the molecules partition to a constant number of beads. A correlation has been observed between temperature dependence of the potential barriers, restricting cooperative rearrangement of beads and heat capacity of liquids. Relations connecting the landscape approach with the number of beads in the molecules have been estimated. The molecular equation for configuration entropy obtained can provide guidance for the development of new materials with a desirable configuration entropy. A method for predicting thermodynamic and statistical quantities of supercooled liquids from kinetics is also suggested.

An Angle Effect Correction Method for High-Resolution Satellite Side-View Imaging Data to Improve Crop Monitoring Accuracy

In recent years, the advancement of CubeSat technology has led to the emergence of high-resolution, flexible imaging satellites as a pivotal source of information for the efficient and precise monitoring of crops. However, the dynamic geometry inherent in flexible side-view imaging poses challenges in acquiring the high-precision reflectance data necessary to accurately retrieve crop parameters. This study aimed to develop an angular correction method designed to generate nadir reflectance from high-resolution satellite side-swing imaging data. The method utilized the Anisotropic Flat Index (AFX) in conjunction with a fixed set of Bidirectional Reflectance Distribution Function (BRDF) parameters to compute the nadir reflectance for the Jilin-1 GP01/02 multispectral imager (PMS). Crop parameter retrieval was executed using regression models based on vegetation indices, the leaf area index (LAI), fractional vegetation cover (FVC), and chlorophyll (T850 nm/T720 nm) values estimated based on angle corrected reflectance compared with field measurements taken in the Inner Mongolia Autonomous Region. The findings demonstrate that the proposed angular correction method significantly enhances the retrieval accuracy of the LAI, FVC, and chlorophyll from Jilin-1 GP01/02 PMS data. Notably, the retrieval accuracy for the LAI and FVC improved by over 25%. We expect that this approach will exhibit considerable potential to improve crop monitoring accuracy from high-resolution satellite side-view imaging data.

Multiparametric cardiac magnetic resonance in patients with thalassemia intermedia: new insights from the E-MIOT network.

In a relatively large cohort of thalassemia intermedia (TI) patients, we systematically investigated myocardial iron overload (MIO), function, and replacement fibrosis using cardiac magnetic resonance (CMR), we assessed the clinical determinants of global heart T2* values, and we explored the association between multiparametric CMR findings and cardiac complications. We considered 254 beta-TI patients (43.14 ± 13.69years, 138 females) consecutively enrolled in the Extension-Myocardial Iron Overload in Thalassemia project. MIO was quantified by T2* technique and biventricular function and atrial areas by cine images. Macroscopic myocardial fibrosis was detected by late gadolinium enhancement technique. Compared to never/sporadically transfused patients, regularly transfused (RT)-TI patients exhibited significantly lower global heart T2* values, biventricular end-diastolic volume indexes, left ventricular mass index, and cardiac index. In RT-TI patients, age and serum ferritin levels were the strongest predictors of global heart T2* values. Independently from the transfusional state, cardiac T2* values were not associated with biventricular function. Of the 103 (40.6%) patients in whom the contrast medium was administrated, 27 (26.2%) had replacement myocardial fibrosis. Age, sex distribution, cardiac iron, and biventricular function parameters were comparable between patients without and without replacement myocardial fibrosis. Twenty-five (9.8%) patients had a history of cardiac complications (heart failure and arrhythmias). Increased age and replacement myocardial fibrosis emerged as significant risk markers for cardiac complications. In TI, regular transfusions are associated with less pronounced cardiac remodeling but increase the risk of MIO. Replacement myocardial fibrosis is a frequent finding associated with cardiac complications.

Parametric description of intermittent probability distribution functions in solar wind and magnetohydrodynamic turbulence

ABSTRACT In this work, we find empirical evidence that the scale-dependent statistical properties of solar wind and magnetohydrodynamic (MHD) turbulence can be described in terms of a family of parametric probability distribution functions (PDFs) known as Normal Inverse Gaussian (NIG). Understanding these PDFs is one of the most important goals in turbulence theory, as they are inherently connected to the intermittent properties of solar wind turbulence. We investigate the properties of PDFs of Elsasser increments based on a large statistical sample from solar wind observations and high-resolution numerical simulations of MHD turbulence. In order to measure the PDFs and their corresponding properties, three experiments are presented: fast and slow solar wind for experimental data and a simulation of reduced MHD (RMHD) turbulence. Conditional statistics on a 23-yr-long sample of WIND data near 1 au and high-resolution pseudo-spectral simulation of steadily driven RMHD turbulence on a $2048^3$ mesh are used to construct scale-dependent PDFs. The empirical PDFs are fitted to NIG distributions, which depend on four free parameters. Our analysis shows that NIG distributions accurately capture the evolution of the PDFs, with scale-dependent parameters, from large scales characterized by a Gaussian distribution, turning to exponential tails within the inertial range and stretched exponentials at dissipative scales. We also show that empirically-measured NIG parameters exhibit well-defined scaling properties that are similar across the three empirical data sets, which may be indicative of universal behaviour.

Estimation of Weibull Probability Distribution Parameters with Optimization Algorithms and Foça Wind Data Application

In this study, the scale and shape parameters of the Weibull probability distribution function (W.pdf) used in determining the profitability of wind energy projects are estimated using optimization algorithms and the moment method. These parameters are then used to estimate the wind energy potential (WEP) in Foça region of İzmir in Turkey. The values of Weibull parameters obtained using Particle Swarm Optimization (PSO), Sine Cosine Algorithm (SCA), Social Group Optimization (SGO), and Bat Algorithm (BA) were compared with the estimation results of the Moment Method (MM) as reference. Root mean square error (RMSE) and chi-square (χ^2) tests were used to compare the parameter estimation methods. The wind speed measurement values of the observation station in Foça were used. As a result of Foça speed data analysis, the annual average wind speed was determined as 6.15 m/s, and the dominant wind direction was found as northeast. Wind speed frequency distributions were compared with the measurement results and calculated with the estimated parameters. When RMSE and χ^2 criteria are evaluated together; it can be concluded that each used method behaves similarly for the given parameter estimation problem, with minor variations. As a result, it has been found that the optimization parameters produce very good results in wind speed distribution and potential calculations.

Energetic and Entropic Motifs in Vesicle Morphogenesis in Amphiphilic Diblock Copolymer Solutions

Coarse-grained molecular dynamic simulations are employed to investigate the spatiotemporal evolution of vesicles (polymersomes) via self-assembly of randomly distributed amphiphilic diblock copolymers PB-PEO (Poly(Butadiene)-b-Poly(Ethylene Oxide)) in water. The vesiculation pathway consists of several intermediate structures, such as spherical/rodlike aggregates, wormlike micelles, lamellae, and cavities. The lamella-to-vesicle transition occurs at a constant aggregation number and is accompanied by a reduction in the solvent-accessible surface area. Simulation predictions are in qualitative agreement with the mechanism of vesicle formation in which the unfavorable hydrophobic interactions between water molecules and polymer segments, along the edge of the lamella, are eliminated at the expense of gaining curvature energy. However, rod–lamella–vesicle transition is accompanied by an increase in copolymer packing density. Hence, the change in the surface area accompanying vesiculation predicted by the simulations is significantly lower than theoretical estimates. Changes in information entropy, quantified by the expectation of the logarithm of the probability distribution function of the segmental stretch parameter s, defined as the difference between the maximum and instantaneous segmental extension, are statistically insignificant along the vesiculation pathway. For rods, lamellae, and polymersomes, s follows a log normal distribution. This is explained based on the configurational dynamics of a single diblock chain in water.

Bayesian Spectral Decomposition for Efficient Modal Identification Using Ambient Vibration

Modal parameter identification via ambient vibration is popular but faces challenges from uncertainties due to unknown inputs and low signal‐to‐noise ratio. Bayesian methods are gaining increasing attention for operational modal identification due to their ability to quantify uncertainties. However, improvements in computational efficiency are needed, particularly when addressing numerous modes and degrees of freedom. To address this challenge, this study proposes an innovative approach, termed the “Bayesian spectral decomposition” method (BSD), employing the decompose‐and‐conquer strategy. This novel method, operating within the frequency domain, identifies each mode individually by exploiting their inherent separated modal characteristics. For each mode, the response spectrum matrix undergoes an eigenvalue decomposition, yielding crucial eigenvalues (incorporating frequency and damping information) and eigenvectors (containing mode shape information). Subsequently, statistical properties of the eigenvalues and eigenvectors are utilized to establish likelihood functions for Bayesian parameter identification. By combining prior information, the posterior probability distribution functions of modal parameters are derived. The optimal solution is then obtained by resolving the maximum posterior probability distribution function problem. To further quantify the uncertainty of modal parameters, Gaussian distributions are employed to approximate the posterior probability distribution functions. The adoption of the decomposition approach circumvents the joint identification of all modal parameters, substantially reducing the parameter dimensions for optimization. Consequently, this strategy leads to decreased computational complexity and significantly improved computational stability. The effectiveness of the BSD is confirmed through simulated data generated from an 8‐story shear building as well as measured data collected from both an experimental shear frame and the Canton Tower. The results demonstrate that the proposed method achieves high accuracy in identifying modal parameters, greatly improves computational efficiency, and effectively quantifies the uncertainties in modal parameters.

Quasi-two-dimensional dispersions of Brownian particles with competitive interactions: phase behavior and structural properties.

Competing short-range attractive (SA) and long range repulsive (LR) particle interactions can be used to describe three-dimensional charge-stabilized colloid or protein dispersions at low added salt concentrations, as well as membrane proteins with interaction contributions mediated by lipid molecules. Using Langevin dynamics (LD) simulations, we determine the generalized phase diagram, cluster shapes and size distributions of a generic quasi-two-dimensional (Q2D) dispersion of spherical SALR particles confined to in-plane motion inside a bulk fluid. The SA and LR interaction parts are modelled by a generalized Lennard-Jones potential and a screened Coulomb potential, respectively. The microstructures of the detected equilibrium and non-equilibrium Q2D phases are distinctly different from those observed in three-dimensional (3D) SALR systems, by exhibiting different levels of hexagonal ordering. We discuss a thermodynamic perturbation theory prediction for the metastable binodal line of a reference system of particles with SA interactions only, which in the explored Q2D-SALR phase diagram region separates cluster from non-clustered phases. The transition from the high-temperature (small SA) dispersed fluid (DF) phase to the lower-temperature equilibrium cluster (EC) fluid phase is characterised by a low-wavenumber peak height of the static structure factor (corresponding to a thermal correlation length of about twice the particle diameter) featuring a distinctly smaller value (≈1.4) than in 3D SALR systems. With decreasing temperature (increasing SA), the cluster morphology changes from disk-like shapes in the equilibrium cluster phase, to double-stranded anisotropic hexagonal cluster segments formed in a cluster-percolated (CP) gel-like phase. This transition can be quantified by a hexagonal order parameter distribution function. The mean cluster size and coordination number of particles in the CP phase are insensitive to changes in the attraction strength.

The Fatigue Response’s Fingerprint of Composite Materials Subjected to Constant and Variable Amplitude Loadings

This paper discusses the theoretical and experimental correlations between fatigue and static strength statistical distributions. We use a two-parameter residual strength model that obeys the qualitative strength-life equal rank assumption (SLERA) for guidance. The modeling approach consists of recovering the model’s parameters by best fitting the constant amplitude (CA) fatigue data at a given stress ratio, R, and the experimental Weibull parameters of the static strength distribution function. An extensive set of fatigue life and residual strength data for AS4 carbon/epoxy 3k/E7K8 Plain Weave Fabric with [45/−45/90/45/−45/45/−45/0/45/−45]S layups, obtained at different stress ratios, R, have been analyzed. The modeling approach consists of recovering the model’s parameters from pure tension or compression fatigue data at R = 0.1 and R = 5, respectively. Once the parameters are fixed, the model’s capabilities, potential, and limits are discussed by comparing its predictions with residual strength and fatigue life data obtained at stress ratios with mixed tension/compression loadings, namely R = −0,2 and R = −1. Moreover, from a preliminary analysis, the theoretical extension of the model’s capabilities to variable amplitude loadings is conceptualized. The application of Miner’s rule is also discussed and compared with a new damage rule to analyze the fatigue responses under variable amplitude loadings.

Bayesian calibration and fitting of nuclear thermal–hydraulic models by Markov chain Monte Carlo methods using the Gibbs sampler

This paper applies Bayesian methods to obtain the joint probability distribution function (PDF) of the unknown parameters of some of the correlation types used in thermal hydraulics, which are conditioned to a set of results of separate effect experiments. The problem is solved by Markov chain Monte Carlo methods using the Gibbs sampler. In this paper it is shown how to obtain the conditional PDFs for each one of the parameters, which define two typical correlations that appear in thermal–hydraulic problems, i) the heat transfer in the walls of a pipe and ii) the penetration length of steam discharged in a subcooled pool. The equations for the conditional probabilities of each one of the parameters are deduced and then used to build the Gibbs sampler which is then programmed in R. The PDFs are obtained for each one of the parameters and from these the maximum a posteriori of each one of the parameters is obtained. The new correlations obtained in this way are compared with the experimental data and show satisfactory performance for the case of the penetration of steam in a subcooled pool. Also, we study two cases one with a small number of experimental data and another one with a large number, it is observed that if the number of parameters is small the Markov chain converges fast to the region of high probability of the parameters for both cases with a small number of data and with large number of data, but if the number of parameters increases then the convergence for the case with small number of data becomes poor, however the convergence continuous being very fast for the case with large number of experimental data.

Multi-axial load spectrum extrapolation method for fatigue durability of special vehicles based on extreme value theory

A method for the multi-axial load spectrum extrapolation based on extreme value theory has been proposed herein, for the first time to the best of our knowledge. The relationship between the internal damage of the structure with the external multi-axial load spectrum is first established prior to extrapolation. The multi-axial load spectrum is then equivalently synthesized into a uni-axial load spectrum based on the interaction between the external forces and the internal stress state of the structure. The basic theory of the time-domain multi-axial load spectrum extrapolation method is developed, including (1) the multi-axial load spectrum extrapolation model establishment; (2) the optimal threshold determination based on grey relational analysis (GRA); (3) the fitting of the distribution function parameters based on the Bayesian parameter estimation method; and (4) the judgment of phase relationship between each channel of the multi-axial load spectrum. The rationality of the method proposed in this paper is verified through an application example. In the example, the multi-axial load spectrum measurement of a special vehicle is introduced, and the proposed multi-axial extrapolation method is applied. Finally, the validation of the multi-axial load spectrum extrapolation method – in terms of the characterized comparison and the durability simulation – is performed.

Monte Carlo modeling of temporal point spread functions and sensitivity functions for mesoscopic time-resolved fluorescence molecular tomography

The paper describes a TurbidMC code that implements a perturbative Monte Carlo method to model temporal point spread functions and sensitivity functions for time-resolved fluorescence molecular tomography (FMT). The code is aimed at working with a particular FMT method published earlier (Ref. [22]) which defines the specificity of sensitivity function calculation. The method solves the inverse problem first for a generalized fluorescence parameter distribution function and then calculates separate distributions for the fluorophore absorption coefficient and the fluorescence lifetime. The proper operation of the code was verified through a comparison between fluorescence temporal point spread functions from test calculations and data from experiments where a phantom with a fluorophore was scanned with a three-channel probe in the mesoscopic reflectance regime. An example is given on the reconstruction of fluorescence parameter distributions. It shows that the sensitivity functions are calculated correctly.

Simulating non-homogeneous non-Gaussian corrosion fields on pipelines based on inline inspection data

This study presents a methodology to simulate non-homogeneous non-Gaussian corrosion fields on the external surface of buried steel pipelines by using inline inspection (ILI) data. It is assumed that the non-homogeneous non-Gaussian corrosion field consists of multiple homogeneous non-Gaussian anomalies that can be characterized by the marginal distribution and spatial autocorrelation function of the corresponding corrosion depths. Based on corrosion data collected from in-service pipelines, empirical relationships are developed to estimate parameters of the marginal distribution and autocorrelation function from the ILI information. To generate a synthetic corrosion field, one first generates realizations of corrosion anomalies and then merge the generated anomalies into a single non-homogeneous field by applying a spatial modulating function to each anomaly. The proposed methodology will improve the accuracy of the fitness-for-service assessment of corroded pipelines in practice as the burst capacity of the corroded pipeline can be more accurately evaluated by using the synthetic corrosion field than using the idealized corrosion field obtained from the ILI data.

Diffusion and incidence of helium on tungsten surface

In this study, we investigated the diffusion and incidence of helium on tungsten surfaces using first principles and molecular dynamics methods. For three common tungsten surfaces (100, 111, 110), we found that the diffusion barrier of helium is positively/negatively correlated with the interatomic spacing/surface atomic density. The diffusion barriers of helium are relatively similar on the three surfaces, ranging from 5.82 to 6.50 eV. The diffusion barrier of helium on the tungsten surface represents the lower limit of the incidence barrier for helium implantation into tungsten. In our simulation, only helium with an incidence energy greater than 7 eV has the potential to be implanted into tungsten. Generally speaking, the implantation ratio of helium increases with increasing incidence energy and decreases with increasing substrate temperature (although the effect is minor). At a constant temperature, the implantation ratio of helium exhibits an exponential relationship with the incidence energy. The depth distribution of helium can be well described by Gamma distribution function, and the shape and scale parameters of the gamma distribution function can be determined based on the mean and variance of the helium depth distribution. The proposed fitting function allows for the quantitative description of the mean and variance of the helium depth distribution based on the incidence conditions (incident energy E and substrate temperature T), thereby determining the helium depth distribution. This has important implications for the in-depth study of helium-induced tungsten surface fuzz formation.