scholarly journals The Effect of the Selection of Three-Dimensional Random Numerical Soil Models on Strip Foundation Settlements

2021 ◽  
Vol 11 (16) ◽  
pp. 7293
Author(s):  
Kamil Żyliński ◽  
Karol Winkelmann ◽  
Jarosław Górski
Keyword(s):  
Standard Deviation ◽  
Random Field ◽  
Three Dimensional ◽  
Gaussian Model ◽  
Random Variables ◽  
Fe Model ◽  
Strip Foundation ◽  
Mean Values ◽  
Standard Deviations ◽  
Selection Of

This paper delivers a probabilistic attempt to prove that the selection of a random three-dimensional finite element (FE) model of a subsoil affects the computed settlements. Parametric analysis of a random soil block is conducted, assuming a variable subsoil Young’s modulus in particular finite elements. The modulus is represented by a random field or different-sized sets of random variables; in both cases, the same truncated Gaussian model is assumed. Mean values and standard deviations of random soil settlement are estimated by a Monte Carlo simulation procedure. With regard to the adopted FE model, the estimated settlement mean values do not vary significantly, but standard deviations do strongly. Similarities also appear in the diagrams of random field correlation length versus settlement standard deviation and the diagrams displaying a total number of model random variables versus settlement standard deviation. Thus, relevant single random variable models represent the random field approach well with regard to settlement parameter estimation. This remark is verified upon a settlement analysis of a three-dimensional FE model of a hypothetical strip foundation. Following the preliminary model observations, various probabilistic geotechnical analyses may be supported, e.g., continuous footing design, slope stability analysis, and foundation reliability assessment.

Estimation of the integral of the square of derivatives of symmetric probability densities of one-dimensional random variables

Metrologiya ◽  
2020 ◽  
pp. 15-27
Author(s):  
Aleksandr V. Lapko ◽  
Vasiliy A. Lapko
Keyword(s):  
Standard Deviation ◽  
Probability Density ◽  
Random Variables ◽  
Random Variable ◽  
Density Estimates ◽  
One Dimensional ◽  
Probability Densities ◽  
The One ◽  
Derivatives Of ◽  
Selection Of

When substantiating the method of fast selection of the bandwidth of kernel probability density estimates, a constant was found that is a functional of the second density derivative. In this paper, the obtained result is generalized to derivatives of symmetric probability densities of different orders. The functional dependences of the constants under study on the coeffi cient of antikurtosis of a random variable are established. The regularities peculiar to them are investigated. Based on the results obtained, a method for estimating functionals from derived probability densities has been developed, which involves the following actions. In the original sample estimated standard deviation of the one-dimensional random variables and the coeffi cient of antikurtosis. Using the reconstructed functional dependences on the antikurtosis coeffi cient, the constants are estimated, which are functionals of the derivatives of the probability density. With known estimates of the standard deviation of the investigated random variable and the considered constant, the values of the functional from the derivative of the probability density of the selected order are calculated. The obtained results are confi rmed by the analysis of the data of computational experiments. It is established that with increasing order of the derivative, the values of the estimates of the studied functionals increase. This fact is explained by the complication of the integrand function in the considered functionals. The proposed method provides objective results for the fi rst three derivatives of the probability density of a random variable. The obtained conclusions are confi rmed by the results of the confi dence estimation of the investigated functionals.

scholarly journals Choice of positive distribution law for nuclear data

2018 ◽  
Vol 4 ◽  
pp. 38
Author(s):  
Sébastien Lahaye
Keyword(s):  
Standard Deviation ◽  
Nuclear Data ◽  
Mean Value ◽  
Distribution Law ◽  
Mean Values ◽  
Relative Standard ◽  
Distribution Laws ◽  
The Mean ◽  
Standard Deviations ◽  
Truncated Gaussian

Nuclear data evaluation files in the ENDF6 format provide mean values and associated uncertainties for physical quantities relevant in nuclear physics. Uncertainties are denoted as Δ in the format description, and are commonly understood as standard deviations. Uncertainties can be completed by covariance matrices. The evaluations do not provide any indication on the probability density function to be used when sampling. Three constraints must be observed: the mean value, the standard deviation and the positivity of the physical quantity. MENDEL code generally uses positively truncated Gaussian distribution laws for small relative standard deviations and a lognormal law for larger uncertainty levels (>50%). Indeed, the use of truncated Gaussian laws can modify the mean and standard deviation value. In this paper, we will make explicit the error in the mean value and the standard deviation when using different types of distribution laws. We also employ the principle of maximum entropy as a criterion to choose among the truncated Gaussian, the fitted Gaussian and the lognormal distribution. Remarkably, the difference in terms of entropy between the candidate distribution laws is a function of the relative standard deviation only. The obtained results provide therefore general guidance for the choice among these distributions.

Repeatability of Mae-Geri-Keage in Traditional Karate: A Three-Dimensional Analysis with Black-Belt Karateka

2002 ◽  
Vol 95 (2) ◽  
pp. 433-444 ◽  
Author(s):  
Chiarella Sforza ◽  
Michela Turci ◽  
Gian Piero Grassi ◽  
Yuri F. Shirai ◽  
Giuliano Pizzini ◽  
...  
Keyword(s):  
Standard Deviation ◽  
Dimensional Analysis ◽  
Horizontal Plane ◽  
Body Shape ◽  
Three Dimensional ◽  
Black Belt ◽  
Spatial Coordinates ◽  
Standard Deviations ◽  
Lower Variability

In karate, performance also depends on a correct body shape, and the repeatability of standardized movements conditions the effectiveness of techniques. The execution of mae-geri-keage (frontal snap kick) was studied in 13 karateka (1st–5th dan). The 3D trajectories of 13 body landmarks were analyzed by an optoelectronic instrument while each karateka performed 10 repetitions of the movement. For each karateka and repetition, the standard deviations of the spatial coordinates x, y, z for each landmark were computed. A total standard deviation of the single participant was also calculated. Two experienced karateka performed with the best repeatability (smaller standard deviation) while executing the studied kick. Generally, the best repeatability was observed in the horizontal plane. The lower variability was observed in hips and head. Ankle and knee of the dominant limb had the worse. The method could detect athletes particularly gifted for the discipline. Moreover, it could help in the identification of those parts of body that do not repeat the movement with the desired precision.

scholarly journals On determining the undrained bearing capacity coefficients of variation for foundations embedded on spatially variable soil

2020 ◽  
Vol 42 (2) ◽  
pp. 125-136
Author(s):  
Marcin Chwała
Keyword(s):  
Shear Strength ◽  
Random Field ◽  
Bearing Capacity ◽  
Covariance Matrix ◽  
Three Dimensional ◽  
Random Variables ◽  
Undrained Shear Strength ◽  
Spatial Averaging ◽  
The Matrix ◽  
Undrained Shear

AbstractThis paper presents an efficient method and its usage for the three-dimensional random bearing capacity evaluation for square and rectangular footings. One of the objectives of the study is to deliver graphs that can be used to easily estimate the approximated values of coefficients of variations of undrained bearing capacity. The numerical calculations were based on the proposed method that connects three-dimensional failure mechanism, simulated annealing optimization scheme and spatial averaging. The random field is used for describing the spatial variability of undrained shear strength. The proposed approach is in accordance with a constant covariance matrix concept, that results in a highly efficient tool for estimating the probabilistic characteristics of bearing capacity. As a result, numerous three-dimensional simulations were performed to create the graphs. The considered covariance matrix is a result of Vanmarcke’s spatial averaging discretization of a random field in the dissipation regions to the single random variables. The matrix describes mutual correlation between each dissipation region (or between those random variables). However, in the presented approach, the matrix was obtained for the expected value of undrained shear strength and keep constant during Monte Carlo simulations. The graphs were established in dimensionless coordinates that vary in the observable in practice ranges of parameters (i.e., values of fluctuation scales, foundation sizes and shapes). Examples of usage were given in the study to illustrate the application possibility of the graphs. Moreover, the comparison with the approach that uses individually determined covariance matrix is shown.

scholarly journals Meta-analysis of the variance ratio

2017 ◽  
Author(s):  
Nicolas Traut
Keyword(s):  
Standard Deviation ◽  
Meta Analysis ◽  
Mean Difference ◽  
Variance Ratio ◽  
Mean Values ◽  
Variance Ratios ◽  
The Mean ◽  
Standard Deviations ◽  
The Difference ◽  
Fisher’S Ratio

IntroductionThe most commonly used effect size when using meta-analysis to compare a measurement of interest in two different populations is the standardised mean difference. This is the mean difference of the measurement divided by the pooled standard deviation in the two groups. The standard deviation is usually supposed to be the same for both groups, although this assumption is often made without any particular evidence. It is possible, however, that the difference of the measurement in the two populations resides precisely in their standard deviations. This could be the case, for example, if a population of patients exhibited more “abnormal” values than a control population – both large and small – even if the mean values were the same. Fisher’s test of equality of variance is designed to compare standard deviations. A variance ratio is a Fisher’s ratio and Fisher distribution can be used to give confidence intervals to the estimate for one study. However, confidence interval for one study can be very wide if the study does not contain enough subjects. Here we present an approach to combine variance ratios of different studies in a meta-analytic way which produces more robust estimates under these circumstances.

Modified algorithm for fast bandwidth selection for kernel estimates of multidimensional probability densities

2020 ◽  
pp. 9-13
Author(s):  
A. V. Lapko ◽  
V. A. Lapko
Keyword(s):  
Probability Density ◽  
Optimal Parameter ◽  
Random Variables ◽  
Kernel Functions ◽  
Independent Random Variables ◽  
Functional Dependencies ◽  
Approximation Properties ◽  
Probability Density Estimation ◽  
Multidimensional Probability ◽  
Selection Of

An original technique has been justified for the fast bandwidths selection of kernel functions in a nonparametric estimate of the multidimensional probability density of the Rosenblatt–Parzen type. The proposed method makes it possible to significantly increase the computational efficiency of the optimization procedure for kernel probability density estimates in the conditions of large-volume statistical data in comparison with traditional approaches. The basis of the proposed approach is the analysis of the optimal parameter formula for the bandwidths of a multidimensional kernel probability density estimate. Dependencies between the nonlinear functional on the probability density and its derivatives up to the second order inclusive of the antikurtosis coefficients of random variables are found. The bandwidths for each random variable are represented as the product of an undefined parameter and their mean square deviation. The influence of the error in restoring the established functional dependencies on the approximation properties of the kernel probability density estimation is determined. The obtained results are implemented as a method of synthesis and analysis of a fast bandwidths selection of the kernel estimation of the two-dimensional probability density of independent random variables. This method uses data on the quantitative characteristics of a family of lognormal distribution laws.

On the sensibility of the Pairs Trading strategy: the case of the FTS stock market index

2020 ◽  
Vol 38 (3) ◽  
Author(s):  
Ainhoa Fernández-Pérez ◽  
María de las Nieves López-García ◽  
José Pedro Ramos Requena
Keyword(s):  
Standard Deviation ◽  
Stock Market ◽  
Trading Strategy ◽  
Stock Market Index ◽  
Pairs Trading ◽  
Empirical Application ◽  
Statistical Arbitrage ◽  
Market Index ◽  
Standard Deviations ◽  
Using Data

In this paper we present a non-conventional statistical arbitrage technique based in varying the number of standard deviations used to carry the trading strategy. We will show how values of 1 and 1,2 in the standard deviation provide better results that the classic strategy of Gatev et al (2006). An empirical application is performance using data of the FST100 index during the period 2010 to June 2019.

scholarly journals Crystal structure of K[Hg(SCN)3] – a redetermination

2014 ◽  
Vol 70 (9) ◽  
pp. i46-i46 ◽  
Author(s):  
Matthias Weil ◽  
Thomas Häusler
Keyword(s):  
Crystal Structure ◽  
Room Temperature ◽  
Three Dimensional ◽  
Lattice Parameters ◽  
Bond Lengths ◽  
Dimensional Network ◽  
Anisotropic Displacement Parameters ◽  
Precision And Accuracy ◽  
Standard Deviations ◽  
Atomic Coordinates

The crystal structure of the room-temperature modification of K[Hg(SCN)3], potassium trithiocyanatomercurate(II), was redetermined based on modern CCD data. In comparison with the previous report [Zhdanov & Sanadze (1952).Zh. Fiz. Khim.26, 469–478], reliability factors, standard deviations of lattice parameters and atomic coordinates, as well as anisotropic displacement parameters, were revealed for all atoms. The higher precision and accuracy of the model is, for example, reflected by the Hg—S bond lengths of 2.3954 (11), 2.4481 (8) and 2.7653 (6) Å in comparison with values of 2.24, 2.43 and 2.77 Å. All atoms in the crystal structure are located on mirror planes. The Hg2+cation is surrounded by four S atoms in a seesaw shape [S—Hg—S angles range from 94.65 (2) to 154.06 (3)°]. The HgS4polyhedra share a common S atom, building up chains extending parallel to [010]. All S atoms of the resulting1∞[HgS2/1S2/2] chains are also part of SCN−anions that link these chains with the K+cations into a three-dimensional network. The K—N bond lengths of the distorted KN7polyhedra lie between 2.926 (2) and 3.051 (3) Å.

scholarly journals Quantification of Measurement and Model Effects in Monopile Foundation Scour Protection Experiments

2021 ◽  
Vol 9 (6) ◽  
pp. 585
Author(s):  
Minghao Wu ◽  
Leen De Vos ◽  
Carlos Emilio Arboleda Chavez ◽  
Vasiliki Stratigaki ◽  
Maximilian Streicher ◽  
...  
Keyword(s):  
Standard Deviation ◽  
Flow Field ◽  
Three Dimensional ◽  
Small Scale ◽  
Maximum Wave Height ◽  
Chaotic Flow ◽  
The Mean ◽  
Scour Protection ◽  
Damage Number ◽  
Measurement Effects

The present work introduces an analysis of the measurement and model effects that exist in monopile scour protection experiments with repeated small scale tests. The damage erosion is calculated using the three dimensional global damage number S3D and subarea damage number S3D,i. Results show that the standard deviation of the global damage number σ(S3D)=0.257 and is approximately 20% of the mean S3D, and the standard deviation of the subarea damage number σ(S3D,i)=0.42 which can be up to 33% of the mean S3D. The irreproducible maximum wave height, chaotic flow field and non-repeatable armour layer construction are regarded as the main reasons for the occurrence of strong model effects. The measurement effects are limited to σ(S3D)=0.039 and σ(S3D,i)=0.083, which are minor compared to the model effects.

scholarly journals Forest Height Estimation Based on P-Band Pol-InSAR Modeling and Multi-Baseline Inversion

2020 ◽  
Vol 12 (8) ◽  
pp. 1319
Author(s):  
Xiaofan Sun ◽  
Bingnan Wang ◽  
Maosheng Xiang ◽  
Liangjiang Zhou ◽  
Shuai Jiang
Keyword(s):  
Standard Deviation ◽  
Vertical Structure ◽  
Incidence Angle ◽  
Three Dimensional ◽  
Solution Space ◽  
Model Complexity ◽  
Two Dimensional ◽  
Dimensional Parameter ◽  
Model Inversion ◽  
Forest Height

The Gaussian vertical backscatter (GVB) model has a pivotal role in describing the forest vertical structure more accurately, which is reflected by P-band polarimetric interferometric synthetic aperture radar (Pol-InSAR) with strong penetrability. The model uses a three-dimensional parameter space (forest height, Gaussian mean representing the strongest backscattered power elevation, and the corresponding standard deviation) to interpret the forest vertical structure. This paper establishes a two-dimensional GVB model by simplifying the three-dimensional one. Specifically, the two-dimensional GVB model includes the following three cases: the Gaussian mean is located at the bottom of the canopy, the Gaussian mean is located at the top of the canopy, as well as a constant volume profile. In the first two cases, only the forest height and the Gaussian standard deviation are variable. The above approximation operation generates a two-dimensional volume only coherence solution space on the complex plane. Based on the established two-dimensional GVB model, the three-baseline inversion is achieved without the null ground-to-volume ratio assumption. The proposed method improves the performance by 18.62% compared to the three-baseline Random Volume over Ground (RVoG) model inversion. In particular, in the area where the radar incidence angle is less than 0.6 rad, the proposed method improves the inversion accuracy by 34.71%. It suggests that the two-dimensional GVB model reduces the GVB model complexity while maintaining a strong description ability.

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