Sample Distribution Function Research Articles

Geostatistical Simulation of Daily Rainfall Fields—Performance Assessment for Extremes in West Africa

Abstract The spatial description of high-resolution extreme daily rainfall fields is challenging because of the high spatial and temporal variability of rainfall, particularly in tropical regions due to the stochastic nature of convective rainfall. Geostatistical simulations offer a solution to this problem. In this study, a stochastic geostatistical simulation technique based on the spectral turning bands method is presented for modeling daily rainfall extremes in the data-scarce tropical Ouémé River basin (Benin). This technique uses meta-Gaussian frameworks built on Gaussian random fields, which are transformed into realistic rainfall fields using statistical transfer functions. The simulation framework can be conditioned on point observations and is computationally efficient in generating multiple ensembles of extreme rainfall fields. The results of tests and evaluations for multiple extremes demonstrate the effectiveness of the simulation framework in modeling more realistic rainfall fields and capturing their variability. It successfully reproduces the empirical cumulative distribution function of the observation samples and outperforms classical interpolation techniques like ordinary kriging in terms of spatial continuity and rainfall variability. The study also addresses the challenge of dealing with uncertainty in data-poor areas and proposes a novel approach for determining the spatial correlation structure even with low station density, resulting in a performance boost of 9.5% compared to traditional techniques. Additionally, we present a low-skill reference simulation method to facilitate a comprehensive comparison of the geostatistical simulation approaches. The simulations generated have the potential to provide valuable inputs for hydrological modeling.

Unification of particle size analysis results, part 1 − comparison of particle size distribution functions obtained by various measurement methods

This article concerns comparing the grain size distribution functions of mineral powder samples and analyzes errors obtained by various measurement methods. The research used three standard and currently most frequently used methods: sieve analysis, laser diffraction analysis and vision analysis. The most important research, from the point of view of unification of results, consisted in performing precise analyses of the grain size of mineral powders (fly ash, gneiss, quartz sand and Cu ore) in various grain classes. The measurement techniques used in the research and issues related to measurement analytics were characterized. The distribution functions of the grain size distributions of the tested material samples were obtained by different measurement methods and the measurement errors were compared. Using the coefficient of variation CV calculated for characteristic particle diameters, the accuracy of measurements made using various methods was analyzed. It has been shown that different particle size measurement techniques give significantly different particle size distributions for the same material, with the grain size distribution of the measured samples having a greater impact on the results than the material itself. The lowest values of the coefficients of variation were obtained for wet sieve analysis and the highest for laser diffraction. Reliable data informing about grain size distributions were generated for further model calculations necessary to standardize the results between measurement methods.

Study on the Population Balance Dynamics Simulation of Grinding under Impact Crushing

During the grinding process, the crushing of minerals mainly depends on the impact action of the grinding medium. Based on the JK drop weight test data of quartz and pyrrhotite and the research results of their impact crushing characteristic parameters, this paper calculates the specific crushing energy (Ecs) of mineral samples subjected to impact in a ball mill using the grinding medium motion theory and then calculates the cumulative particle size distribution under screening under any mesh size using the JK drop weight test method. On this basis, the breakage distribution function of mineral samples is calculated, and a selection function is obtained based on grinding experiments. Finally, using Matlab programming and function-fitting mathematical methods, as well as a particle size population balance dynamics simulation of grinding, the particle size distribution characteristics of the grinding products of the two mineral samples in the mill that are only subjected to impact action are calculated. The results show that the selection function of quartz and pyrrhotite decreases overall with the prolongation of the grinding time, and the selection function of the coarse particle size changes more significantly than that of the fine particle size. At the same time, the selection function decreases with the decrease in feed particle size, and the smaller the feed particle size, the lower the probability of impact crushing. The Ecs values of quartz and pyrrhotite at each particle level in the mill are different, and the degree of mineral crushing is closely related to the impact energy, feed particle size, and mineral properties.

Considerations on measurement of bidirectional transmittance distribution function of thick samples over a wide range of viewing zenith angles

Abstract We delve into theoretical and experimental considerations for determining the spectral bidirectional transmittance distribution function (BTDF) of thick samples across a broad viewing zenith angle range. Nominally, BTDF is defined as the ratio of transmitted radiance to incident irradiance measured from the same plane. However, when employing thick samples for BTDF measurements, the viewing plane of the transmitted beam may shift from the front to the rear surface of the sample, altering the measurement geometry compared to using the sample front surface as the reference plane. Consequently, the viewing zenith angle from the sample rear surface increases relative to the sample front surface, and the sample-to-detector-aperture distance decreases by an amount corresponding to the sample thickness. We introduce a method for determining the BTDF of thick samples, considering the transformation of practical measurement results to a scenario where the measurements are conducted at a very large distance from the sample. To validate the method, we utilize a BTDF facility equipped with two instruments that significantly differ in their sample-to-detector-aperture distances. We evaluate the impact of a 2 mm sample thickness on the BTDF by assessing the ratio of transmitted and incident radiant fluxes as a function of viewing zenith angle relative to the sample rear surface. The evaluation is conducted in the wavelength range from 550 nm to 1450 nm in 300 nm steps, and in the viewing zenith angle range from −70° to 70° in 5° steps. Measurements are performed in-plane at an incident zenith angle of 0°. It is concluded that consistent determination of BTDF of a thick sample is possible by converting the experimental parameters of the real measurements at relatively short distances from the sample to correspond to those that would be obtained from measurements at very large distances from the sample.

A multi-objective optimal collaborative gas flow regulation method for non-stationary ventilation network based on improved NSGA-Ⅲ algorithm

After the shockwave of a coal and gas outburst disappears, the influx of a high concentration of gas causes ventilation network disorder. This will further lead to the occurrence of secondary disasters, resulting in serious human and economic losses. This study focuses on solving the cooperative regulation problem of non-stationary ventilation networks (NSVNs) after a disaster. The NSVN solution model is dynamically combined with the ventilation network regulation method to simulate the results of post-disaster cooperative regulation. The Pareto optimal solution for decision variables is obtained with the goals of reducing the affected area, preventing the reversal of branch airflow, and rapidly discharging the high concentration of gas. In this regard, an NSGA-III algorithm based on segmented hybrid coding with conditional distribution sampling is designed to solve the problem of the population crossover operation under the dynamic change of the decision variables. In addition, according to the applicability of the decision variables in the regulation of NSVNs, the sampling distribution function that meets the practical application requirements is selected. Moreover, conditional distribution sampling is carried out for chromosome generation via real number coding, the aim of which is to improve the search efficiency and optimization effect. Via the hierarchical logical relationship between the decision variables, conversion is carried out to generate population individuals of different dimensions to realize the dynamic inputs of the NSVN solution model and calculate the corresponding target values. Finally, the feasibility of the proposed model and solution method is verified by studying and analyzing the case of an airflow disaster in a coal mine in Jiulishan, China. This study provides theoretical support for the cooperative regulation of NSVNs, as well as guidance for the post-disaster emergency rescue work in possible coal and gas herniation accidents.

An Adaptive Sampling Strategy for Real-Time Anomaly Detection with Unmanned Sensing Vehicles

Unmanned sensing vehicles (USVs) have been widely used for real-time anomaly detection in various applications, including environmental monitoring, precision agriculture, and military surveillance. The USVs collecting data can only provide partial information about the space being monitored. Thus, it is critical to decide where to deploy the USVs at each point in time to maximize the change detection capability, while minimizing deployment costs. This article proposes an adaptive sampling strategy for real-time anomaly detection with USVs. First, a novel spatio-temporal sequential tensor decomposition algorithm is developed to decompose the high-dimensional data collected by the USVs into three components, a spatial component, a temporal component, and a sparse component, that captures the locations suspicious of change. The spatial and temporal components are used for one-step prediction to guide the adaptive sampling strategy. The strategy is designed to maximize the detection power and control the deployment costs. The main idea is to balance exploration and exploitation by designing a sampling distribution function to decide where to collect data at each acquisition time. The movement of the USVs is controlled by using Voronoi tessellations on the sampling distribution function. The performance of the proposed framework is demonstrated through simulations and case studies.

Randomized empirical processes and confidence bands via virtual resampling

A data set of N labeled units, or labeled units of a finite population, may on occasions be viewed as if they were random samples {X1,…,XN}, N≥1, the first N of the labeled units from an infinite sequence X,X1,X2,… of independent real valued random variables with a common distribution function F. In case of such a view of a finite population, or when an accordingly viewed data set in hand is too big to be entirely processed, then the sample distribution function FN and the population distribution function F are both to be estimated. This, in this paper, is achieved via sampling the indices {1,…,N} of {X1,…,XN} with replacement mN≔∑i=1Nwi(N) times so that for each 1≤i≤N, wi(N) is the count of the number of times the index i of Xi is chosen in this virtual resampling process. The classical theory of weak convergence of empirical processes is extended along these lines to that of the thus created randomly weighted empirical processes, via conditioning on the weights, when N,mN→∞ so that mN=o(N2).

The investigation of multiple factors on elastic anisotropy of artificial shale based on the orthogonal experiment

Elastic anisotropy of shales is critical to accurate constraints for rock physical models, quantitative interpretation and hydraulic fracturing. However, the causes of elastic anisotropy of shales are very complicated, and the understanding of how multiple influence factors affect the elastic anisotropy of shales is still not clear. Hence, the orthogonal experiment, as an effective multiple factors experimental method, is adopted in this study to analyze the effect of multiple factors for shale elastic anisotropy. Three factors, clay content, organic matter (OM) content and compaction stress are selected as independent variables, the orthogonal test table L16(43) with four levels for each factor is adopted. According to the designed orthogonal table, sixteen artificial shales are constructed based on the cold-pressing method, and all the dry artificial shales are measured by the ultrasonic measurements. The influence of each factor on the elastic anisotropy and the sensitivity orders of three factors are obtained using the range analysis. The orders of sensitivity for selected factors follow the sequence clay content > compaction stress > OM content for velocity anisotropy parameters. The compaction mechanism of artificial shales is also discussed by the compaction factor, which are positively correlated with the velocity anisotropy parameters. The clay platelets orientation distribution function (ODF) of samples is evaluated by a theoretical model, the ODF coefficients are significantly affected by the clay content and compaction stress, and W200 are much more sensitive to these factors than W400. The results can provide a critical rock physics basis for quantitative interpretation and reservoir prediction of the low-maturity or maturity shale reservoir.

Sample distribution of observations of the falling number of corn flour

The sample distribution of observations is studied in order to study the variational feature, while the measured value is considered as random. For practical purposes, the empirical distribution of a random variable is estimated by proximity to the theoretical law. The statistical hypothesis of the sample data belonging to the general population is tested using the consent criteria. The object of this study was the observation of the falling number of corn flour, which is a prescription component of bakery products. In world practice, the falling number method for raw materials from corn is used as a reference for establishing reference interval values, detecting a variation of the studied trait. The purpose of this work was to study the sample distribution of observations of the falling number of corn flour to determine the representativeness of the sample of experimental data. Relying on Glivenko's theorem on the expediency of grouping sample data into a variation series in order to replace the distribution function of the general population with a sample distribution function, at the beginning of the research, the sample data were converted into a statistical series. The research material was an industrial sample of fine-ground corn flour that meets the requirements of GOST 14176-69 "Corn flour. Technical conditions". The falling number was studied when implementing the standard method on the PPP-99 device according to GOST ISO 2093-2016 "Grain and its processed products. Determination of the number of falls by the Hagberg-Perten method". The interval variation series was studied according to a wide list of characteristics: distribution center indicators (sample mean, mode, median, quartiles, deciles), variation indicators (span, average linear deviation, variance, unbiased variance estimate, mean square deviation, coefficient of variation, linear coefficient of variation, oscillation coefficient), distribution form indicators (relative quartile variation index, asymmetry coefficient, Pearson structural asymmetry coefficient, kurtosis index), indicators of interval estimation of the center of the general population (confidence intervals for the general average, interval estimation of the general share, i.e. the probability of an event). For the studied random variable of the falling number of corn flour, the hypothesis of a normal distribution was proved using the indicators of asymmetry and kurtosis, as well as using the 3σ sigma rule. As a result of the calculations, the representativeness of the sample data with respect to the variation of the studied trait in the general population was established

A Novel Approach to Estimate Electrothermal Aging of Epoxy–Alumina Nanocomposites Using Dielectric Relaxation Current Analysis

In this article, an advanced technique is applied to estimate the aging state of epoxy–alumina nanocomposite insulation. For this purpose, several epoxy–alumina nanocomposite samples are prepared in the laboratory. Samples are undergone into artificial electrothermal aging conditioning up to duration of 600 h. After each 100-h instant, the relaxation current is measured under 1-kV/mm dc stress through the developed experimental setup in the laboratory. From the experimentally measured current data, relaxation frequency distribution (RFD) function of the test samples is computed. Based on the relaxation distribution function, two aging sensitive parameters are evaluated. In order to correlate these two aging sensitive parameters with the aging state of insulation, two empirical relationships are proposed based on the experimental investigation. The effectiveness of these two empirical relationships is validated with the laboratory prepared epoxy nanocomposites (EPNCs) insulation having a definite aging state. The experimental investigation shows that the proposed method can effectively be applied for estimating the aging state of nanocomposites insulation used in real-life high-voltage equipment.

Elastic wave propagation in anisotropic polycrystals: inferring physical properties of glacier ice

An optimization problem is proposed for inferring physical properties of polycrystals given ultrasonic (elastic) wave velocity measurements, made across multiple sample orientations. The feasibility of the method is demonstrated by inferring both the effective grain elastic parameters and the grain c -axis orientation distribution function (ODF) of ice-core samples from Priestley glacier, Antarctica. The method relies on expanding the ODF in terms of a spherical harmonic series, which allows for a non-parametric estimation of the sample ODF. Moreover, any linear combination of the Voigt (strain) and Reuss (stress) homogenization scheme is allowed, although for glacier ice, the exact choice is found to matter little for bulk elastic behaviour, and thus for inferred physical properties, too. Finally, the accuracy of the inferred grain elastic parameters is discussed, including the well-posedness and shortcomings of the inverse problem, relevant for future adoptions in glaciology, geology and elsewhere.

A Simulation Study: Population Distribution Function Estimation Using Dual Auxiliary Information under Stratified Sampling Scheme

In survey sampling, information on auxiliary variables related to the main variable is often available in many practical problems. Since the mid-twentieth century, researchers have taken a keen interest in the use of auxiliary information, due to its usefulness in estimation methods. In this article, our main objective is to discover the problem associated with estimation of the finite population distribution function, using the known auxiliary variable, which occurs as the sample distribution function and the rank of the auxiliary variable. A new family of the finite population distribution function estimators is proposed in the stratified sampling scheme. The mathematical equations for the bias and mean square error have been obtained for each proposed estimator, along with the efficiency conditions. Besides theoretical efficiency comparison, an empirical study has also been conducted to analyze the performance of estimators. A simulation study is also performed to observe the efficiency of the proposed estimators. The implementation of the proposed sampling scheme is illustrated by a practical example.

Post-Strata Based on Sample Quantiles

AbstractThe standard method of creating post-strata is to define the boundaries of the strata on the basis of population characteristics of auxiliary variables. Estimation treats the post-strata as strata for standard stratified-sample estimation. Samples often contain empty post-strata requiring adjustment to the estimation procedure. To avoid empty post-strata, we propose using the sample distribution function of an auxiliary variable to define the post-strata. We show that the large-sample efficiency of the sample-based post-stratification procedure is the same as that of the equivalently defined population-based procedure. In the simulation, the sample-based procedure was slightly more efficient than the classical procedure. The Monte Carlo coverage of a nominal 95% interval was approximately 95% for the sample-based procedure and approximately 94% for the classical procedure.

Copula Correlation Modeling of Wind Farms Generation and Its Application in Power Dispatching

With the large-scale integration of wind power into the grid, a model that can accurately describe the randomness of wind farm output and the correlation between them is of great significance to be constructed. A joint distribution function of multiple wind plants output model based on Copula theory is constructed. By introducing correlation and fitting coefficient, the attribute recognition theory is put forward to select the optimal model based on entropy weight method. Finally, the validity of Copula modeling is verified by using the synchronized historical data of California coastal wind farms as a sample. The results show that t-copula can not only describe the correlation between the original variables well, but also fit the empirical distribution function of the original samples accurately.

SELECTION OF OPTIMAL AL–SI COMBINATIONS IN CAST IRON FOR CASTINGS FOR ENGINEERING PURPOSES

In this work, the optimal combinations of Al – Si in cast iron for cast parts for machine-building purposes were determined with the aim of subsequent selection of rational modes of modification and alloying, and the possibility of their implementation under industrial smelting conditions was checked.
 The graphical dependence Si=f (Al) is obtained, which is a set of optimal combinations of the content of Al and Si in cast iron, providing the maximum ultimate tensile strength UTS≈245 ... 334 MPa.
 The technological audit of the results of serial industrial smelting included the analysis of actual indicators, the calculation of sample distribution functions (mathematical expectation and dispersion) of the Al and Si content in the alloy, as well as the UTS value. The correspondence of the indicators of the content of Al and Si and the value of σ to the optimal values was assessed by testing the statistical hypotheses: H: M(Al)=Alopt, M(Si)=Siopt, M(σв)=σвopt.On the basis of the obtained results of the assessment of statistical characteristics and verification of hypotheses, it was established that at the chosen significance level α=0.05, the technological process of smelting satisfies the requirements of optimality in terms of the Si content, but in terms of the Al content, the technological process does not meet the requirements of optimality.
 The proposed procedure for choosing the optimal combinations of Al and Si makes it possible to choose the amount of correcting additives depending on the actual indicators of the chemical composition during the smelting process. To do this, it is necessary to assess the closeness of the actual composition to the optimal curve Si=f(Al) and choose the one that most satisfies the criteria of rationality. The latter can be the cost of ferroalloys, through which Al and Si are introduced

Updates to the Oxford Space Environment Goniometer to measure visible wavelength bidirectional reflectance distribution functions in ambient conditions.

Understanding how the surfaces of airless planetary bodies-such as the Moon-scatter visible light enables constraints to be placed on their surface properties and top boundary layer inputs to be set within thermal models. Remote sensing instruments-such as Diviner onboard the Lunar Reconnaissance Orbiter-measure thermal emission and visible light scattering functions across visible (∼0.38-0.7 µm) to thermal infrared (TIR) wavelengths (∼0.7-350 μm). To provide ground support measurements for such instruments, the Oxford Space Environment Goniometer (OSEG) was built. Initially, the OSEG focused on measuring TIR directional emissivity functions for regolith and regolith simulant samples in a simulated space environment, but it has recently been modified to measure visible wavelength Bidirectional Reflectance Distribution Functions (BRDFs) of samples in ambient conditions. Laboratory-measured BRDFs can be used (1) to test and to help interpret models-such as the Hapke photometric model-and (2) as visible scattering function inputs for thermal models. This paper describes the modifications to and initial calibration measurements taken by the Visible Oxford Space Environment Goniometer with a 532nm laser, and details how this setup can be used to measure BRDFs of regolith and regolith simulant samples of airless planetary bodies.

Effect of annealing close to Tg on the short-range order of lithium disilicate glass

Annealing of glasses at temperatures close to Tg is a usual procedure to reduce internal stresses induced by the conventional melting/quenching process. In this work, the effect of the annealing temperature and time on short-range order of lithium disilicate glass was investigated. The total structure factor and radial distribution function of annealed samples at distinct temperatures and times were derived from synchrotron XRD measurements. The results suggest that short and medium range-orders were affected by the annealing conditions, even for temperatures well below the glass transition temperature, Tg. After annealing at temperatures close to Tg, local arrangements were identified with those corresponding to crystalline phases of lithium disilicate and lithium metasilicate. For temperatures below Tg, the diffusion of lithium atoms was already taking place, while the rearrangements of the SiO4 tetrahedra from the network former started to happen for temperatures close to or higher than Tg.

Estimation of finite population distribution function with dual use of auxiliary information under non-response.

In this paper, we propose two new families of estimators for estimating the finite population distribution function in the presence of non-response under simple random sampling. The proposed estimators require information on the sample distribution functions of the study and auxiliary variables, and additional information on either sample mean or ranks of the auxiliary variable. We considered two situations of non-response (i) non-response on both study and auxiliary variables, (ii) non-response occurs only on the study variable. The performance of the proposed estimators are compared with the existing estimators available in the literature, both theoretically and numerically. It is also observed that proposed estimators are more precise than the adapted distribution function estimators in terms of the percentage relative efficiency.

An evolutionary multi-objective approach to learn from positive and unlabeled data

Positive and unlabeled (PU) learning has attracted increasing interests in recent years. Despite that a number of PU learning algorithms have been proposed, most of them are subject to some assumptions about unlabeled sample distribution and objective functions, which makes them difficult to be adopted for real applications. To this end, in this paper, an evolutionary multi-objective approach, namely MOEA-PUL, is suggested for PU learning, whose aim is to build a PU classifier without any prior assumption for data distribution and objective functions. To be specific, the PU learning is formulated as a bi-objective optimization problem, where the true positive rate (TPR) and a new metric, termed unlabeled accuracy rate (UAR) are used as the two objectives. A multi-objective evolutionary algorithm is proposed to solve this bi-objective optimization problem, under the framework of NSGA-II, where a PU similarity based initialization strategy and an elite label based learning strategy are developed. Empirical studies on 12 datasets demonstrate the superiority of MOEA-PUL over the existing PU learning algorithms.

On multiple imputation for unbalanced ranked set samples with applications in quantile estimation

We consider multiple imputation (MI) for unbalanced ranked set samples (URSS) by considering them as data sets with missing values. We replace each missing value with a set of plausible values drawn from a predictive distribution that represents the uncertainty about the appropriate value to impute. Using the structure of the MI dataset, we develop algorithms that imitate the structure of URSS to carry out the desired statistical inference. We provide results for the convergence of the empirical distribution functions of imputed samples to the population distribution function, under both URSS and simple random sampling (SRS). We obtain the variances of the imputed URSS, and the expected values of the variance estimators. We also study the problem of quantile estimation using an imputed URSS and propose a hybrid method based on the bootstrap and imputation of URSS data. We apply our results to estimate the mean and quantiles of the mercury in contaminated fish under perfect and imperfect URSS.