Statistical Moments Research Articles

Random field of homogeneous and multi-material structures by the smoothed finite element method and Karhunen–Loève expansion

A random field of homogeneous and multi-material structures with uncertain scenarios is addressed by constructed the generalized stochastic cell-based smoothed finite element model. Smoothed finite element method (S-FEM) is “Jacobian-free”, which is not only overcomes the limitations of “overly-stiff” and low accuracy of the standard FEM, but also demonstrates strong resistance to mesh distortion. This paper proposes an efficient non-intrusive stochastic smoothed finite element method (SS-FEM) based on cell-based smoothing domains (SD) for the stochastic analysis of elastic problems, which describe much more realistically real physical systems under uncertain scenarios. This SS-FEM starts from the Gaussian random field based on representation related to the spatial variability in material parameters based on the Karhunen-Loève (KL) expansion, and then establishes the basic formulation that considers the effects of uncertainties. A generalized solving framework based on numerical integration is further developed. The non-intrusive dimension reduction method is also adopted to obtain the statistical moments and probability density function. The proposed SS-FEM can capture the structural stochastic responses under uncertainty condition by combining gradient smoothing technology and uncertainty quantification. A number of engineering examples are compared with the solution of Monte Carlo simulation to demonstrate both the accuracy and the efficiency of the proposed method.

Order Statistics and Actuarial Measures from Powered Inverse Rayleigh Distribution

Nashaat [25] introduced the powered inverse Rayleigh (PIR) distribution. It provides a better fit other than (inverse Rayleigh, Rayleigh, and Weibull) distributions. The moments of order statistics and recurrence relations for the single and double moments have been established. The computation of the means and variances are enumerated. These computations can be trulyinteresting and applied in numerous domains of study. Moreover, cumulative entropy (C.E.) and actuarial measures (A.M.) are also calculated to address the uncertainty in portfolio optimization. The usages of C. E. and A.M. are widespread in many real-word applications specifically in physical sciences and insurance science.

Hubungan Indeks Massa Tubuh Terhadap Kelincahan Pemain Futsal Academy Al-Hadid Surabaya Usia 20 Tahun

The dominant characteristics of movement in futsal are fast and agile in changing direction of movement, which is explained as agility. To maximize the physical components of agility, an ideal body composition will certainly be needed, which can be seen through the body mass index. Body mass index is a measuring tool to determine a person's ideal body composition through the calculation of weight and height. This study investigates the relationship between body mass index and agility of futsal players at the AL-Hadid Academy Surabaya aged 20 years in 2024. This study uses a quantitative descriptive approach that focuses on correlation. The data collection method is carried out using 2 instruments, including measuring height and weight to calculate body mass index with the formula and conducting an agility test using the illinois agility test which is only measured once on each instrument. Body mass index is the independent variable in this study, and agility is the dependent variable. using descriptive statistical data analysis methods, linearity tests, and product moment correlation analysis. The results of data analysis show that body mass index has a linear relationship in the linearity test with a significant deviation form linearity value of 0.165> 0.05. Then in the product moment correlation test, a significance value of 0.000 and a correlation coefficient value of 0.709 were obtained, which can be said to be correlated, the direction of the relationship is positive, and indicates a very strong degree of relationship. Based on the statistical results, it can be concluded that body mass index has a very strong relationship to the agility of futsal players.

A point mapping strategy-based sparse grid integration method for statistical moments estimation and structural reliability analysis

The high-order moment-based method is an attractive non-intrusive approach for structural reliability analysis, while it remains a challenge to strike a balance between accuracy, efficiency, and versatility in estimating statistical moments of performance functions. In this paper, a point mapping strategy-based sparse grid integration (SGI) method is proposed for statistical moment estimation and structural reliability analysis, with improved efficiency while ensuring the accuracy. Firstly, a point mapping strategy (PMS) is developed based on the adaptive high dimensional model representation (HDMR), by which the traditional SGI is reconstructed as a sum of multiple integrations over the sparse grid point sets with different effective dimensions. With this new form of SGI, the estimation of statistical moments only requires the evaluation of the performance function at a small number of necessary reference points, once the effects of some interaction terms are negligible. The validity and feasibility of the proposed PMS-based SGI method for statistical moments estimation are verified by several numerical examples. Then, the proposed method is applied to structural reliability analysis with the aid of an improved maximum entropy method. Two engineering examples are investigated, including the strength failure problem of tubular tower K-shape connection joints and the fatigue failure problem of a marine riser resulting from the vortex-induced vibration (VIV). The results indicate that the proposed method provides a better trade-off between accuracy and efficiency in evaluating the first four order statistical moments and structural failure probability compared to conventional methods.

Bridge damage identification based on synchronous statistical moment theory of vehicle–bridge interaction

AbstractConsidering the weak noise resistance and low identification efficiency of traditional bridge damage identification methods, a data‐driven approach based on synchronous statistical moment theory and vehicle–bridge interaction vibration theory is proposed. This method involves two main steps. First, a two‐axle test vehicle is used to collect acceleration response signals synchronously from adjacent designated measurement points while stationary. This operation is repeated to calculate the second‐order statistical moment curvature (SOSMC) difference of entire bridge points corresponding signals in different states. By comparing with the reference value, the preliminary damage location of the bridge can be obtained. Second, the first‐order modal shape curve is constructed using the second‐order statistical moment (SOSM). The refined identification of bridge damage is then based on an improved direct stiffness back calculation of the bridge's stiffness. This article proposes the synchronization theory for the first time and combines it with the statistical moment clustering method, forming an innovative approach to obtaining structural vibration modes. The effectiveness of this method has been well validated through numerical simulations with different parameters and on‐site bridge tests. The research results indicate that SOSMC indicators have better noise resistance and higher recognition efficiency in identifying damage locations, compared to modal curvature and flexibility curvature indicators. Additionally, compared to transfer rate and random subspace methods, the SOSM method results in smaller error and higher identification efficiency.

Properties and applications of the Tan Weibull loss distribution

Probability models play crucial role in modeling loss in the finance and actuarial sciences. In this article, a new family of loss distributions known as the Tan F-Loss family of distributions is proposed with the Tan Weibull Loss distribution as a special case. The density exhibits decreasing, right skewed, symmetric, and approximately symmetric shapes. The hazard rate function shows decreasing and modified bathtub shapes. The statistical properties of the Tan Weibull Loss distribution including the quantile function, moments, expansion of the general rate, moment generating function, incomplete moment, and order statistics are studied. The maximum likelihood estimators of the distribution are also studied. Simulations are carried out to examine the behavior of the estimators. The results show that the estimators are consistent. The usefulness of the proposed distribution is demonstrated with two insurance loss datasets. The results show that the proposed distribution gives a better parametric to the two datasets compared with the competing distributions.

Melting curves of MgSiO3 and CaSiO3 perovskites with cubic structure at extreme conditions

In this work, we derive the analytical expression of Helmholtz free energy, mean nearest neighbor distance between two atoms, lattice constant, and molar volume using statistical moment method (SMM). Then, we present how to determine the melting temperature of cubic perovskite at high pressures by combining SMM and work-heat equivalence principle. The results of the melting theory of cubic perovskite are applied to two perovskites MgSiO3 and CaSiO3 under extreme conditions of the Earth’s lower mantle. Our obtained melting curves of MgSiO3 up to 1400 GPa and CaSiO3 up to 136 GPa were compared with available experiment and other calculations and were in good agreement. The present study provides an effective theoretical tool for finding the melting curves of strongly anharmonic materials under extreme conditions. Our theoretical calculations would be helpful to clarify geological formation process at the Earth’s lower mantle.

A novel skewed generalized normal distribution: properties, statistical inference, and its applications

In this paper, a novel skewed generalized normal distribution (NSGN), which encompasses several well-known distributions, is a two-component mixture model based on the generalized normal distribution. The NSGN distribution offers flexibility in modeling skewed data characterized by high kurtosis and strong skewness, making it highly applicable in finance, medicine, and engineering. The primary characteristics and properties of this new distribution are introduced, and the explicit expressions for the moments of order statistics are provided using recursive relations. The maximum likelihood estimation based on a profile likelihood approach, L-moments estimation, and a two-step estimation method combining Bayesian posterior maximum estimation with moment estimates are presented to estimate the four parameters of NSGN distribution. A simulation study compares the performance of these methods across different sample sizes and different parameters. The appropriateness of the proposed distribution has been tested by comparing it with several skewed distributions. Additionally, applications to real datasets showcase the beneficial properties of the NSGN for applied statistical research.

Bridging the Generational Gap between the Teachers and Students in the Utilization of Modern Technology in the Teaching Methods in Public Secondary Schools in Delta State

Purpose: The study focused on bridging the generational gap between the teachers and students in the utilization of modern technology in the teaching methods in secondary schools in Delta State. Two research questions were raised and two null hypotheses were formulated in the study. Methodology: The descriptive survey design was used. The population for this study comprised all public secondary school principals and teachers in Delta State. The sample for this study was 1533 and it is made up of 100 principals and 1433 teachers in Delta State public secondary schools selected from 12 Local Government Areas. Principals represented 50% while teachers represent 10% of the population. A self developed questionnaire was design titled “Bridging the Generational gap between the Teachers and Students in the Utilization of Modern Technology Questionnaire (BGTSUMTQ)”, validated and its reliability equally determined via a pilot study using test re-test reliability technique with a coefficient index of 0.96 was used. The research questions raised were answered using percentage for the study. The researcher employed descriptive statistic of mean scores and standard deviation to provide answers to the research questions while Pearson Product Moment Statistics was used to test the hypotheses at 0.05 level of significance. Findings: The findings revealed that there are factors that are associated with the utilization of modern technology in teaching methods in public secondary schools in Delta State. The use of technology in education is influenced by the following factors such as teacher factor, organizational factor, technological factor and student factor. It also showed that there are strategies to be adopted to improve teachers and students in the utilization of modern technology in teaching methods in public secondary schools in Delta State. Unique contribution to theory, practice and policy: Based on the findings, it therefore concluded that as a catalyst for massive change, technology has improved our existing understanding by assisting educators and students in making the most use of cutting-edge teaching techniques in Delta State public secondary schools.

A direct and analytical method for inverse problems under uncertainty in energy system design: combining inverse simulation and Polynomial Chaos theory

This article introduces and formalizes a novel stochastic method that combines inverse simulation with the theory of generalized Polynomial Chaos (gPC) to solve and study inverse problems under uncertainty in energy system design applications. The method is particularly relevant to design tasks where only a deterministic forward model of a physical system is available, in which a target design quantity is an input to the model that cannot be obtained directly, but can be quantified reversely via the outputs of the model. In this scenario, the proposed method offers an analytical and direct approach to invert such system models. The method puts emphasis on user-friendliness, as it enables its users to conduct the inverse simulation under uncertainty directly in the gPC domain by redefining basic algebra operations for computations. Moreover, the method incorporates an optimization-based approach to integrate supplementary constraints on stochastic quantities. This feature enables the solution of inverse problems bounding the statistical moments of stochastic system variables. The authors exemplify the application of the proposed method with proof-of-concept tests in energy system design, specifically performing uncertainty quantification and sensitivity analysis for a Multi-Energy System (MES). The findings demonstrate the high accuracy of the method as well as clear advantages over conventional sampling-based methods when dealing with a small number of stochastic variables in a system or model. However, the case studies also highlight the current limitations of the proposed method such as slow execution speed due to the optimization-based approach and the challenges associated with, for example, the curse of dimensionality in gPC.

Machine Learning Prediction of Small Molecule Accumulation in Escherichia Coli Enhanced with Descriptor Statistics.

Antibiotic resistance, particularly among Gram-negative bacteria, poses a significant healthcare challenge due to their ability to evade antibiotic action through various mechanisms. In this study, we explore the prediction of small molecule accumulation in Gram-negative bacteria by using machine learning techniques enhanced with statistical descriptors derived from molecular dynamics simulations. We begin by identifying a minimal set of molecular descriptors that maximize the model's predictive power while preserving human interpretability. We optimize model accuracy, precision, and the area under the receiver operating characteristic curve through an iterative process. We demonstrate that the inclusion of statistical descriptors significantly improves model performance across various prediction metrics. Particularly, the addition of statistical descriptors related to dipole moment and minimum projection radius enhances the model's predictive capabilities, shedding light on the physicochemical properties crucial for small molecule accumulation. Our findings highlight the importance of considering statistical moments beyond mean values in predictive modeling and suggest avenues for future research. Overall, our study provides insights into the complex dynamics of antibiotic accumulation in Escherichia coli bacterial cells, generalizable to other Gram-negative species, offering a promising approach for the discovery of effective antibacterial agents, identifying new hits, and improving them to define effective lead agents.

Lyapunov stability of suspension bridges in turbulent flow

In the era of sleek, super slender suspension bridges, facing the issue of stability against dynamic wind actions represents an increasingly complex challenge. Despite the significant progress over the last decades, the impact of atmospheric turbulence on bridge stability remains partially not understood, evoking the need for innovative research approaches. This study aims to address a gap in current research by investigating the random flutter stability associated with variations in the angle of attack due to turbulence, which has not formally been addressed yet. The present investigation employs the 2D rational function approximation model to express self-excited forces in a turbulent flow. The application of this type of models to bridge dynamics yields a viscoelastic coupled dynamic system characterized by memory effects and driven by broad-band long-time-scale noise, described here by a linear homogeneous time-variant differential equation, which shows apparent nonlinear features, and which has rarely been matter of research. Utilizing a Monte Carlo methodology, this work innovates in applying the largest Lyapunov exponent (LE) and the moment Lyapunov exponents (MLE) to study bridge random flutter stability. The calculation of LE and MLE under diverse turbulent wind conditions uncovers lower flutter stability than without turbulence effects. In most cases, sample and low-order p-th moment stability thresholds closely align with the bridge dynamic response pattern; therefore, the flutter critical wind speed is unequivocal. However, under certain turbulence scenarios, it is necessary to resort to MLE for a complete description of stability, evoking some additional consideration of which statistical moments should be considered for the engineering assessment of the flutter limit. Finally, this work provides a qualitative insight into the instability mechanisms by approximating the random parametric excitation with a sinusoidal gust and evaluating the time-periodic system stability via Floquet theory.

Nearest neighbour analysis as a new probe for fuzzy dark matter

ABSTRACT Fuzzy dark matter (FDM) is a promising candidate for dark matter (DM), characterized by its ultra-light mass, which gives rise to wave effects at astrophysical scales. These effects offer potential solutions to the small-scale issues encountered within the standard cold dark matter (CDM) paradigm. In this paper, we investigate the large-scale structure of the cosmic web using FDM simulations, comparing them to CDM-only simulations and a simulation incorporating baryonic effects. Our study employs the nearest neighbour (NN) analysis as a new statistical tool for examining the structure and statistics of the cosmic web in an FDM universe. This analysis could capture the information absent in the two-point correlation functions. In particular, we analyse data related to the spherical contact, nearest neighbour distances (NND), and the angle between the first and second nearest neighbours of haloes (NNA). Specifically, we utilize probability distribution functions, statistical moments, and fitting parameters, as well as G(x), F(x), and J(x) functions to analyse the above data. Remarkably, the results from the FDM simulations differ significantly from the others across these analyses, while no noticeable distinction is observed between the baryonic and CDM-only simulations. Moreover, the lower FDM mass leads to more significant deviations from the CDM simulations. These compelling results highlight the efficiency of the NN analysis – mainly through the use of the J(x) function, $s_3$, $l_{3}$, and $a_4$ parameters – as a prominent new tool for investigating FDM on large scales and making observational predictions.

Perceptual point cloud qality assessment for immersive metaverse experience

Perceptual quality assessment for point cloud is critical for immersive metaverse experience and is a challenging task. Firstly, because point cloud is formed by unstructured 3D points that makes the topology more complex. Second, the quality impairment generally involves both geometric attributes and color properties, where the measurement of the geometric distortion becomes more complex. We proposed a perceptual point cloud quality assessment model that follows the perceptual features of Human Visual System (HVS) and the intrinsic characteristics of the point cloud. The point cloud is first pre-processed to extract the geometric skeleton keypoints with graph filtering-based re-sampling, and local neighboring regions around the geometric skeleton keypoints are constructed by K-Nearest Neighbors (KNN) clustering. For geometric distortion, the Point Feature Histogram (PFH) is extracted as the feature descriptor, and the Earth Mover's Distance (EMD) between the PFHs of the corresponding local neighboring regions in the reference and the distorted point clouds is calculated as the geometric quality measurement. For color distortion, the statistical moments between the corresponding local neighboring regions are computed as the color quality measurement. Finally, the global perceptual quality assessment model is obtained as the linear weighting aggregation of the geometric and color quality measurement. The experimental results on extensive datasets show that the proposed method achieves the leading performance as compared to the state-of-the-art methods with less computing time. Meanwhile, the experimental results also demonstrate the robustness of the proposed method across various distortion types. The source codes are available at https://github.com/llsurreal919/PointCloudQualityAssessment.

Reduced‐Order Modeling for Linearized Representations of Microphysical Process Rates

AbstractRepresenting cloud microphysical processes in large scale atmospheric models is challenging because many processes depend on the details of the droplet size distribution (DSD, the spectrum of droplets with different sizes in a cloud). While full or partial statistical moments of droplet size distributions are the typical variables used in bulk models, prognostic moments are limited in their ability to represent microphysical processes across the range of conditions experienced in the atmosphere. Microphysical parameterizations employing prognostic moments are known to suffer from structural uncertainty in their representations of inherently higher dimensional cloud processes, which limit model fidelity and lead to forecasting errors. Here we investigate how data‐driven reduced‐order modeling can be used to learn predictors for microphysical process rates in bulk microphysics schemes in an unsupervised manner from higher dimensional bin distributions. Using simulations characteristic of marine stratiform clouds, we simultaneously learn lower dimensional representations of droplet size distributions and predict the evolution of the microphysical state of the system. Droplet collision‐coalescence, the main process for generating warm rain, is estimated to have an intrinsic dimension of three. This intrinsic dimension provides a lower limit on the number of degrees of freedom needed to accurately represent collision‐coalescence in models. We demonstrate how deep learning based reduced‐order modeling can be used to discover intrinsic coordinates describing the microphysical state of the system, where process rates such as collision‐coalescence are globally linearized. These implicitly learned representations of the DSD retain more information about the DSD than typical moment‐based representations.

STUDY ON SELF-DIFFUSION IN ALLOY AuCuSi WITH FCC STRUCTURE: DEPENDENCE ON TEMPERATURE, PRESSURE, CONCENTRATION OF SUBSTITUTIONAL ATOMS, CONCENTRATION OF INTERSTITIAL ATOMS AND STRAIN

This article presents a self-diffusion theory, including analytical expressions for activation energy, pre-exponential factor, and self-diffusion coefficient, dependent on temperature, pressure, the concentration of substitutional atoms, the concentration of interstitial atoms, and strain for substitutional and interstitial ternary alloys with the FCC structure, based on the statistical moment method (SMM). The theoretical results are applied to numerical calculations for the AuCuSi alloy. The SMM numerical results for AuCuSi are compared with those for AuSi, AuCu, and Au. The variation of self-diffusion quantities with temperature and strain in AuCuSi follows the same patterns as in AuCu, AuSi, and Au. The variation with the interstitial atom concentration in AuCuSi follows the same pattern as in AuSi, while the variation with the substitutional atom concentration follows the same pattern as in AuCu. The SMM numerical results for Au's self-diffusion quantities agree well with experimental data and other calculation results. Other SMM numerical results for self-diffusion quantities are novel and predict future experimental outcomes.

Scintillation Level of Scattered Radio Waves in the Equatorial Ionosphere

Scintillation effects of propagating and scattered radio waves (RWs) are considered analytically and numerically in the equatorial terrestrial ionosphere applying the statistical characteristics. Analytical calculations of the second-order statistical moments of the phase fluctuations of the ordinary and extraordinary RWs in the conductive collision ionospheric magnetoplasma (COCOIMA) are carried out for the first time using the Wentzel-Kramers-Brilluen method and the modified smooth perturbation method in consideration of the diffraction effects. Polarization coefficients of these waves in the equatorial ionosphere have been derived for the first time. The scintillation level includes the variance and the correlation functions of scattered RWs. Statistical moments contain complex refractive index, anisotropy coefficient characterizing irregular plasmonic structures, tilt angle of prolate irregularities concerning to the external magnetic field, permittivity components of the equatorial ionosphere, Hall's, Pedersen and longitudinal conductivities. A new feature of the "Fountain Effect" has been discovered in the equatorial ionosphere at weak and moderate scintillations caused due to anisotropy parameters of electron density fluctuations. Anisotropy parameters of electron density inhomogeneities influence the scintillation index of both the ordinary and extraordinary radio waves shifting maximums of the curves in the opposite directions at weak and moderate scintillations. Numerical calculations are carried out using the hybrid anisotropic correlation function of electron density fluctuations containing both exponential and power-law spectral functions having arbitrary spectral index, applying the experimental data.

DSWIN: Automated hunger detection model based on hand-crafted decomposed shifted windows architecture using EEG signals

Hunger is a physiological state that arises from complex interactions of multiple factors, including higher brain center control. We purposed to develop an accurate and efficient machine-learning model for the automated detection of hunger using EEG signals. We prospectively acquired 14-channel EEG (sampling frequency 128 Hz) from 43 and 48 fasted and post-prandial healthy subjects (hungry vs. control groups, respectively) using the EMOTIV EPOC+ mobile brain cap system. To augment the hunger response, fasted subjects were also shown video images of food during EEG recording. The EEG signals were divided into 15-second segments. 877 and 852 participants/subjects were in the hungry and control groups. We created a novel handcrafted architecture—decomposed shifted window (DSWIN)—that combined swin patch division with tunable Q-factor wavelet transform-based signal decomposition for multilevel feature extraction of EEG signals. Textural and statistical features were extracted from the multiple patches and decomposed signals using a novel penta pattern-based extractor and statistical moments, respectively, and then merged. Iterative neighborhood component analysis (INCA) and iterative ReliefF (IRF) were applied. Twenty-eight selected feature vectors were generated, which were then fed to a shallow k-nearest neighbors (kNN) classifier to calculate channel-wise prediction vectors. From the 28 channel-wise prediction vectors, another 26 modes of function-based voted results were calculated using iterative hard majority voting, and the best overall model result was selected using a greedy algorithm. Our model attained 99.54% and 82.71% binary classification accuracies of hungry status vs. control using 10-fold and leave-one-subject-out cross-validations, respectively.

Dynamic characteristics of vertically irregular structures with random fields of different probability distributions based on stochastic homotopy method

Considering the uncertainty of elastic modulus in different materials as well as the strong nonlinearity between the structural frequency and elastic modulus, it is a great challenge for computing the dynamic characteristics of vertically irregular structures. In this research, a new stochastic homotopy approach is presented to compute the basic dynamic characteristics of the vertically irregular structures, where the elastic modulus of different materials are assumed as the random fields with different probability distributions. To obtain the dynamic characteristics of the vertically irregular structures, a stochastic eigenvalue equation is established firstly. Then the stochastic eigenvalue and eigenvector are represented by the homotopy series, and the stochastic residual error in relation to the stochastic eigenvalue equation is minimized to obtain the coefficients of the homotopy series. Afterwards, the basic dynamic characteristics, including stochastic natural frequencies and modal shapes, of the vertically irregular structures are obtained. In comparison to the sampling-based stochastic surrogate model methods like the Kriging and non-intrusive arbitrary polynomial chaos methods, the presented approach can efficiently yield more stable statistical moments of the natural frequencies. Meanwhile the proposed method can generate the statistical moments of the modal shapes, which is difficult to achieve with the stochastic surrogate model methods. Finally, the effectiveness of the suggested method is testified through two examples of a reinforced concrete-steel column and a realistic reinforced concrete-steel frame structure.

Analytical robust design optimization for hybrid design variables: An active-learning methodology based on polynomial chaos Kriging

In robust design optimization, statistical moments of performance are widely adopted in formulating robustness metrics. To address the high computational costs stemming from the many-query nature of such optimizations with respect to robustness metrics, analytical formulas of the statistical moments have been developed based on surrogate models. However, existing methods consider random variables as the sole model input, which excludes, from the application scope, problems that also involve deterministic design variables. To remedy this issue, this paper proposes a new Polynomial Chaos Kriging-based methodology for efficient and accurate analytical robust design optimization. The analytical solutions for the statistical moments of performance are developed considering that the Polynomial Chaos Kriging model is established in the augmented space of the deterministic design and random variables. This is achieved by systematically decoupling associations with deterministic input from random input, providing effective solutions even when the orthonormality of the basis function is not applicable in the augmented space. This work also presents an active-learning framework enabling seamless implementation of various numerical optimization methods. Several numerical examples and a practical application illustrate the performance and superiority of the proposed method.