Density Distribution Function Research Articles

Testing symmetry of model errors for non linear multiplicative distortion measurement error models

To study the symmetry and asymmetry of the model error under multiplicative distortion measurement errors setting, we propose a correlation coefficient-based measure between the distribution function and the root of density function. The unknown distribution function and density function are estimated from four kinds of residuals: the conditional mean calibration-based residuals, the conditional absolute mean calibration-based residuals, the conditional variance calibration-based residuals, and the conditional absolute logarithmic calibration-based residuals. We study the asymptotic results of the estimators of correlation coefficient-based measure under four calibrations. Next, we consider statistical inference of the correlation coefficient-based measure by using the empirical likelihood method. The empirical likelihood statistics are shown to be an asymptotically standard chi-squared distribution. Simulation studies demonstrate the performance of the proposed estimators and test statistics. A real example is analyzed to illustrate its practical usage.

A diagnosis method for imbalanced bearing data based on improved SMOTE model combined with CNN-AM

Abstract A boundary enhancement and Gaussian mixture model (G) optimized synthetic minority oversampling technique (SMOTE) algorithm (BE-G-SMOTE) is proposed to improve diagnostic accuracy under imbalanced bearing fault data conditions. It is designed to solve the problem that the diversity of samples generated by the original SMOTE model is limited, as well as the deep learning model is limited by the size of training samples and processing speed. Firstly, a few bearing fault data are clustered by G to achieve cluster division. Secondly, according to the cluster density distribution function designed in this paper, the weights of different clusters and sample weights to achieve intra-class balance are determined and data quality is improved. Then, to take full advantage of the limited fault data, based on the sensitivity of the support vector machine (SVM) to imbalanced data, the enhanced boundary is established between generated data and the SVM classifier under different penalty factor (PF) values. According to the accuracy, the optimal PF is determined, and fault datasets satisfying diversity are obtained. To improve the classification accuracy, a convolutional neural network with an attention mechanism is built. Finally, analysis using two practical cases shows the effectiveness of the proposed method.

Renormalizing one-point probability distribution function for cosmological counts in cells

We study the one-point probability distribution function (PDF) for matter density averaged over spherical cells. The leading part to the PDF is defined by spherical collapse dynamics, whereas the next-to-leading part comes from the integration over fluctuations around the saddle-point solution. The latter calculation receives sizable contributions from short modes and must be renormalized. We propose a new approach to renormalization by modeling the effective stress-energy tensor for short perturbations. The model contains three free parameters. Two of them are related to the counterterms in the one-loop matter power spectrum and bispectrum, one more parameterizes their redshift dependence. This relation can be used to impose priors in fitting the model to the PDF data. We confront the model with the results of high-resolution N-body simulations and find excellent agreement for cell radii r * ≥ 10 Mpc/h at all redshifts down to z = 0. Discrepancies at a few per cent level are detected at low redshifts for r * ≤ 10 Mpc/h and are associated with two-loop corrections to the model.

Network alteration of cyclically loaded elastomers mediated by dynamic bonds

Elastomers and hydrogels with dynamic network structures have received considerable research interest due to their high strength and toughness, and self-healing ability. While the general mechanical responses of dynamic polymer networks have been investigated, the study on their fatigue behaviors is still in its infancy. In this work, we employ experimental and theoretical approaches to gain a comprehensive understanding of the mechanical response of an elastomer with physical crosslinkers under fatigue tests up to 10,000 cycles. The constitutive model characterizes the network configuration using the density distribution function of the polymer chains, which is represented by a state variable denoting the stress-free configuration of each individual chain. The model takes into account the reversible dissociation/association of dynamic bonding facilitated by the physical crosslinkers. As a result, polymer chains can repeatedly release the involved strain energy and transform between different stress-free configurations. A multi-dispersed reaction process is further employed to describe the state transition of polymer chains, enabling the model to elucidate the progressive damage in long-term relaxation and fatigue tests by recording and updating the density distribution function of chain state. In addition, the reversible transition of the polymer chain between different state configurations enables the model to capture the rate-dependent stress response and relaxation behaviors of physically crosslinked elastomers and gels. Remarkably, our microscopic model, which requires only five parameters, offers an efficient approach to describe the mechanical responses of elastomers and gels with dynamic bonds.

Unravelling the structural and dynamical properties of concentrated aqueous ammonium nitrate solutions: MD simulation studies

ABSTRACT In this work, we present, the concentration-dependent solvation structure and dynamics of an ammonium nitrate (AN) ion pair in aqueous media by means of classical molecular dynamics simulations. Structural properties were investigated by computing the potentials of mean force (PMFs), radial distribution functions (RDFs), cluster size distribution functions, and hydrogen bond dynamics. The change in the depth of the contact ion pair (CIP) and solvent-separated ion pair minima (SSIP) is marginal, whereas for the solvent-assisted ion pair (SAIP) is more stable at lower salt concentrations. The marginal difference in the depth of the CIP minimum of the PMF is explained based on cluster size distribution and hydrogen bonding. The solvation structure of the ions is not affected by the salt concentration. Ab-initio and classical molecular dynamics simulations (both constrained and unconstrained) give similar results for the solvation structure around the cation and the anion. The spatial density distribution functions of the anions around the cations show that the anions occupy the space around the ammonium hydrogen atoms. Profound differences in dynamical properties are found in the case of concentrated solutions as compared to dilute solutions.

A Target Damage Effectiveness Assessment Mathematical Calculation Method with Uncertain Information Based on an Adaptive Fuzzy Neural Network

Aiming to address the issue of assessing the effectiveness of target damage in air defense interception under projectile and target intersection, this paper proposes a novel target damage effectiveness assessment mathematical calculation method using an adaptive fuzzy neural network. The design and calculation methods introduce the target cabin’s damage weight factor, the dispersion error and coverage density and fire density of warhead fragment, and the ratio of the number of warhead fragments to the cross-sectional area of the target as the primary damage factors, and we establish a new model for calculating the target damage efficiency using Takagi-Sugeno adaptive fuzzy neural network with the multiple damage factors. In the designed model, we take the characteristic parameters of warhead fragments formed by the projectile explosion as the sample data and learn the mapping relationship between damage factors and damage effect expressed by the system of fuzzy rule. Combined with the vulnerability weight and damage factors of the target, the fuzzy rule system is applied to predict and calculate the damage probability and damage effectiveness. In addition, we use shot-line technology to set up the intersection criterion between warhead fragments and target, analyze the coordinate relationship of the projectile explosion relative to the target based on the ground coordinate system, and derive the distribution density function of warhead fragment and research a calculation model for target damage probability with multiple vulnerable cabins. Finally, we use the established model to train, test, and calculate the data from the actual projectile and target intersection damage test and present the comparison results to other damage calculation methods. By calculation and comparative analysis, the results show the smaller the distance between projectile and target, as well as the smaller the average intersection angle, and the larger the weight coefficient of the warhead fragment covering the target cabin, the total target damage probability increases obviously. In the two experimental calculations, the target cabin with the largest weight coefficient was considered, and compared with the existing literature, the damage probability of the proposed calculation method was increased by 9.13% and 10.93%, respectively, and it is clear that the proposed target damage assessment method can effectively reflect the real target damage effectiveness in the state of projectile and target intersection.

The Inverse Burr-Generalized Family of Distributions: Theory and Applications

This paper presents a new class of generalized distributions based on the inverse Burr (Burr III) distribution. Statistical properties of the proposed family of distributions such as the density and cumulative distribution functions, survival and hazard rate functions, quantile, moments, moment generating function, probability weighted moments, Renyi entropy and distribution of order statistics are derived. The maximum likelihood estimation method is employed to obtain the parameter estimates of the family of distributions. A Monte Carlo simulation study is conducted in order to investigate the asymptotic behaviour of the parameter estimates of a sub-model from the proposed family of distributions. Finally, the utility of proposed family of distributions in lifetime data fittings is illustrated using two real data sets and the results obtained were compared to some existing non-nested models. Based on some model selection criteria and goodness of fit test statistics, it was evident that the sub-model from the proposed family of distributions performed reasonably better than the competitor distributions in fitting the two data sets.

Families of Extended Exponentiated Generalized Distributions and Applications of Medical Data Using Burr III Extended Exponentiated Weibull Distribution

In this article, four new families named as Weibull extended exponentiated-X (WEE-X), Lomax extended exponentiated-X (LEE-X), Logistic extended exponentiated-X (LGCEE-X), and Burr III extended exponentiated-X (BIIIEE-X) with their quantile functions are proposed. The expressions for distribution function and density function of BIIIEE-X family are written in terms of linear combinations of the exponentiated densities based to parent model. New models, i.e., Weibul extended exponentiated Weibull (WEEW), Lomax extended exponentiated Weibull (LEEW), Logistic extended exponentiated Weibull (LGCEEW), and Burr III extended exponentiated-Weibull (BIIIEEW) distributions are derived, were plotted for functions of probability density and hazard rate at different levels of parameters. Some mathematical properties of the BIIIEEW model are disclosed. The maximum likelihood method for the BIIIEEW model are described. Numerical applications of the BIIIEEW model to disease of cancer datasets are provided.

Improved three-dimensional multiple-relaxation-time color-gradient lattice Boltzmann finite-difference model for thermocapillary flows

This study is devoted to developing a color-gradient lattice Boltzmann model capable of simulating thermocapillary flows with variable properties. To achieve the purpose, some modified work is conducted. The equilibrium distribution function for density is modified in the developed model. The scheme of multiple-relaxation-time is applied to deal with the single-phase and perturbation collision operators to enhance the algorithm stability, and a simple correction term is incorporated into the single-phase operator. In addition, the finite-difference method is adopted to solve the temperature field. The developed model is first used to simulate the layered two-phase flow in a horizontal channel to test the density ratio that can be achieved without temperature effect. Then two classical thermocapillary flow problems of thermocapillary-driven flow in a heated microchannel and thermocapillary migration of a deformable droplet or bubble are simulated, and the model is proven to successfully simulate the thermocapillary flows with density ratios up to 10.

Transmission system model in the track-vehicle relationship based on Long Term Evolution technology

Because of degradations of the wired infrastructure connecting the element of railroad control systems, and related primarily to their destruction, the use of the radio transmission medium for independent management of rail-road traffic control devices is increasingly being considered. An undoubted problem in implying such solutions is the security of transmission in such systems. It should be noted that security at a certain level of transmission is currently already offered by the radio transmission systems themselves, which has also been used in the GSM-R standard. The creation of a separate dedicated system for railroads involves huge expenditures for the design, testing, certification and, finally, construction and implementation of such technology. Therefore, in the opinion of the author of this dissertation, it is possible to use public open radio networks for the needs of railroads, which significantly reduces costs, since such a system is based on existing infrastructure. It is necessary to develop a way of transmitting information that meets the requirements of secure transmission in the sense of railroad traffic control systems. The task is to develop a general model for open radio transmission in traffic control systems based on the latest public radio standard, which is LTE, 5G or Future Railway Mobile Communications System (FRMCS). The article will present the concept of data transmission in the track vehicle relationship with the use of LTE (Long Term Evolution) technology. It will show the concept of transmission based on the PN-EN50159:2011 standard and the results of the tests conducted during control trips on the railway route. The main element that will be subject to the research will include the transmission safety and its delay. The impact of a type of transmission encryption on its delay will be estimated with the assumed blocks of data sent during the transmission. A probability distribution and density functions of the transmission delay probability distribution with the message sizes in the range from 16B to 10 kB with four ways of the signal encoding according to the PN-EN50159:2011 standard will be also analysed.

The distribution function of mass density — A tool for the analysis of sphere particle systems

A method for characterizing sphere particle systems based on the calculation of the distri- bution of the average mass density in concentric spherical layers surrounding an arbitrary center has been developed. The effectiveness of the method has been tested on several variants of polydisperse system models obtained in two different ways and one system obtained by full-scale modeling. The distribution of the mass density for both methods of generating model systems allows you to choose the better option. For a system obtained by the field simulation method, a difference in properties is shown depending on the position of the observation center. This paper introduces the MaDiS program which implements the developed method.

Effects of porous structure on the deformation failure mechanism of cement sheaths for wellbores

The influence and mechanism of porous structure on the deformation failure of cement sheaths under hydraulic pressure is still unclear. To solve this problem, a net slurry cement sheath and a liquid silicon cement sheath were prepared by using a cement material and a liquid silicon suspension. The distributions of the pore radius and spatial location were analyzed using computed tomography scanning and statistics to obtain their probability density distribution functions. Based on the distribution functions, the single-layer and double-layer porous reconstruction models of the net slurry cement sheath and liquid silicon cement sheath were constructed using a FLAC 3D program. A series of numerical simulations were conducted to study the deformation failure of the cement sheaths under in situ stress and hydraulic pressure. The effects of the porous and double-layer structures on the breakdown pressure, plastic failure zone, radial deformation, and stress distribution of the cement sheaths were analyzed. As a result, the mechanisms for the influence of the porous and double-layer structures on the failure mode, failure path, and interaction between the cement sheath and metal casing were revealed. The results of this research provide a theoretical basis for an in-depth understanding of the failure mechanisms of porous cement sheaths.

A New Extension of the Inverse Paralogistic Distribution using Gamma Generator with Application

This study proposed a three-parameter model called the gamma inverse paralogistic (GiPL) distribution model. The probability density and cumulative distribution functions were presented together with the quantile function. Properties such as measures of reliability, the kth raw moment and moment-generating function, partial moments, order statistics, log-likelihood functions for maximum likelihood estimations, Renyi entropy and the ordering of random variables were provided. To test the performance of the parameters, a simulation study was conducted. The simulation result was assessed using the mean, bias and root mean square errors. Finally, the data set on the number of COVID-19-infected individuals per age was used to apply the model and compared with various recently developed distribution models. Results showed the superiority of the GiPL distribution model over these models.

Copula-based JPDF of wind speed, wind direction, wind angle, and temperature with SHM data

Structural health monitoring (SHM) systems installed on long-span bridges can obtain environmental data around them. To deeply mine the correlation between types of data, this paper proposes a multivariant joint probability density distribution function (JPDF) based on copula theory. Specifically, the univariate probability density function (PDF) is characterized by the finite mixture (FM) method, that is, the 1D model. In addition, the parameters in the FM distribution are estimated by the genetic algorithm (GA). Then, the bivariate JPDF based on copula theory is established, i.e., the 2D model; next, the trivariate JPDF is derived, i.e., the 3D model. Furthermore, the quaternary JPDF of wind speed, wind direction, wind angle, and temperature is derived, i.e., the 4D model. The feasibility of the proposed model is verified by a case study of a specific bridge in China, on which the SHM system is installed to collect SHM data including wind speed, wind direction, wind angle, and temperature. The trivariate JPDF of wind speed, wind direction, and wind angle, and the trivariate JPDF of wind speed, wind direction, and temperature based on FM are established.

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

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

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

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

Mathematical and Statistical Model for Assessing the Impact of COVID-19 Waves on the Regional System (on the Example of the Kirov Region)

Since the f rst outbreak in China and the spread of COVID-19 in dif erent countries of the world, the study of mathematical models of the spread of the epidemic has begun and is intensively continuing. Such models are dynamic and of en based on dif erential or dif erence equations. As a rule, these models require an identif cation procedure to determine unknown parameters. But for a number of reasons, unambiguous identif cation of such parameters cannot be performed. For example, the preparation of statistical data for the identif cation procedure may be performed in various ways. T erefore, the preferred method of data preprocessing is to approximate them with the most appropriate functional dependence.T e study shows that epidemic curves may be represented by a superposition of several local waves — an outbreak of an epidemic in a particular region consists of many local waves and some of them may merge into one common wave. In this article, it is proposed to use analogs of the normal distribution density function to predict waves of new COVID-19 cases. T e purpose of the article was to develop a model of the dynamics of the total number of cases and new cases of COVID-19, taking into account the waves of the epidemic and the impact on the regional socioeconomic system.T e study was conducted on the basis of data on the incidence of COVID-19 in the Kirov region4 in 2020—2022. It is shown that the chosen model describes statistical data well and allows making realistic forecasts for the total number of diseases and new cases of diseases. T e results of the study may be used to develop preventive measures to prevent the spread of the disease and allow assessing the impact of the epidemiological situation on the socio-economic system of the region.

The Effect of Ethanol on Lipid Nanoparticle Stabilization from a Molecular Dynamics Simulation Perspective.

Lipid nanoparticles (LNPs) have emerged as a promising delivery system, particularly for genetic therapies and vaccines. LNP formation requires a specific mixture of nucleic acid in a buffered solution and lipid components in ethanol. Ethanol acts as a lipid solvent, aiding the formation of the nanoparticle's core, but its presence can also affect LNP stability. In this study, we used molecular dynamics (MD) simulations to investigate the physicochemical effect of ethanol on LNPs and gain a dynamic understanding of its impact on the overall structure and stability of LNPs. Our results demonstrate that ethanol destabilizes LNP structure over time, indicated by increased root mean square deviation (RMSD) values. Changes in the solvent-accessible surface area (SASA), electron density, and radial distribution function (RDF) also suggest that ethanol affects LNP stability. Furthermore, our H-bond profile analysis shows that ethanol penetrates the LNP earlier than water. These findings emphasize the importance of immediate ethanol removal in lipid-based systems during LNP production to ensure stability.

Effect of SARA fractions on the physical, structural and dynamic properties of bitumen using molecular dynamics simulation

The utilization of molecular dynamics simulation on bituminous materials usually adopts three classical bitumen models (AAA-1, AAK-1, AAM-1). However, the chemical compositions of bitumen, namely SARA fractions, vary significantly in reality, depending on the source of bitumen. In this regard, this study investigated the influence of SARA fractions on the simulated properties of bitumen. To this end, 21 bitumen models with different SARA fractions collected from the literature were established. The radial distribution function (RDF), density, and self-diffusion coefficient (SDC) were derived to characterize the structural, physical, and dynamic properties, respectively. Results indicated that the SARA fractions would not significantly influence the density and radial distribution function of bitumen models. However, the influence of heavy components on the equilibrium of dynamic sampling was pronounced. In the MSD analysis, the temperature variation contributed little to the self-diffusion capability of bitumen when the asphaltene index was close to one. The correlation between SDC and asphaltene index varied depending on the value of the asphaltene index. Specifically, the correlation was positive when the asphaltene index was larger than one, and negative when it was smaller than one.

Effects of root systems on crack formation: experiments, modeling, and analyses

Plant roots can increase soil shearing resistance directly by mechanical reinforcing. The 2D crack pattern of the surface soil near the plant were observed experimentally, and it was found that the soil cracking near the plant roots was inhibited, which may be due to the influence of the plant roots. This paper focuses on the mechanical reinforcement of soil by plant roots and investigates the development rule and formation mechanism of desiccation cracking under the influence of plant roots. A numerical model describing the process of desiccation cracking of soils in the presence of root systems, which is based on a lattice of Hooke springs model, was combined with a non-stationary random field characterized by a trend term and a random fluctuation term. The root density distribution function was introduced to describe the root distribution, and an exponential function of critical strain and root density was constructed to obtain the trend of critical strain distribution of the root systems (the root systems of a single plant). The random fluctuation term was generated by the conditional simulation technique. Minkowski densities (i.e., area density, length density and Euler number density) were adopted to quantify the crack patterns. Parameters of the model were calibrated and verified by the field experimental results, and its precision was evaluated. The effect of most input parameters (include the new parameters maximum critical strain value hc and the lateral distribution radius of RDDF rm) on the model output was analyzed. The results show that in the validation process the coefficients of determination R2 for the Minkowski densities is between 0.749 and 0.948. Root mean square error is between 0.000 2–0.120 9. BIAS is between 0.049 5–0.139 0, and the consistency index is between 0.908 and 0.987. The model is effective in predicting the formation and development of cracks in farmland soils under the influence of the root systems. The model produces the dynamic development of the desiccation cracking network of farmland soils under the influence of the root systems. The simulation results provide ample indication of the reinforcing effect of the root systems on the soil and the limiting effect of the root systems on desiccation cracking.