Various Coefficients Of Variation Research Articles

Seismic responses of rectangular tunnels in liquefiable soil considering spatial variability of soil properties

The objective of this paper was to investigate the dynamic response of a tunnel-soil system in the soil with spatial variability of shear modulus with various coefficients of variation and scales of fluctuation. The soil shear modulus was highlighted and modeled as an isotropic random field using the spectral representation method, then mapped into the finite difference model. The dynamic stochastic responses of the excess pore water pressure ratio, the liquefied zone, the ground displacement, and the uplift displacement of the tunnel were discussed. It was observed that the effect of coefficient of variation was pronounced in which an increase of the coefficient of variation brought out a reduction in the corresponding dynamic stochastic responses. However, the scale of fluctuation was found to be insignificant in the tunnel soil system.

Variability response function approach for foundation reliability

This paper explores the applicability of variability response functions to nonlinear soil–structure interaction problems, focusing on the impacts of spatially variable soil properties on foundation reliability regarding the settlement response. An estimation scheme is proposed to obtain the response functions, which involves a periodic function to approximate the relationship between foundation response and phase angles representing the soil variability patterns. Using a single set of realizations, the response function approach enables the evaluation of foundation reliability under various spatial variability patterns, including different autocovariance distances in three dimensions and the rotated anisotropy features of soil variations. This leads to significant reductions in computational demands compared to previous attempts of random field modelling, which often involved individual Monte Carlo simulations for each combination of spatial variability parameters. The proposed approach is applied to both shallow foundation and piled foundation cases, illustrating its range of applicability. For linear-elastic systems, the approach is shown to be effective for various coefficients of variation in soil variability. For elastic–plastic pile group analyses, the approach leads to efficient evaluation of the statistics of average and differential settlements of the pile group, both of which compare favourably with conventional random field simulation techniques. Since it does not require multiple random field realizations, the approach is particularly efficient in identifying the worst-case scenario of autocovariance distances that corresponds to the largest uncertainty in foundation response. This can become a useful tool for conservative reliability assessments under a project setting, since site-specific estimates of random field parameters are often imprecise due to limited site data.

The influence of the coefficient of variation on the process reliability of brick production

The goal of research was studying the influence of the variation coefficient values during statistical tests of building structures on the destruction probability and reliability of brick building structures. The article focuses on comparing the theoretical values of the probability theory problems with their practical application in building structures behavior calculation. The scientific novelty lies in the comparison of the calculated data according to the normal distribution with the practical values of the experiment carried out on brick structures. As a result, a dependence graph dependence of the reliability coefficient k on the brick grade was, taking into account various coefficients of variation.

Role of metrology inaccuracy for variance of test results under reproducibility conditions

A source of inaccuracy in regression models is supposed to be the statistical nature of a model and metrology inaccuracy related to the measuring explanatory and response variables. A number of approaches to the assessing inaccuracy of regression models are available. However, their use in searching for a solution to engineering problems concerning the assessing multiple regression inaccuracy is restricted by insufficiently developed mathematical tools. When explanatory variables assigned appropriately the inaccuracy of a regression depends on the reproducibility of test results. The reported simulation study investigates the importance of a measurement error to the variance of a normally distributed random variable for small sample sizes between 2 and 30 and coefficients of variation 1, 2, 10, 20, 40, 60. The effect of inaccuracy is analyzed relying on a relative confidence interval of variances estimated as a difference between variance intervals for a variable measured inaccurately and accurately divided by a confidence interval of the variance for an accurately measured variable. The outcomes to emerge from the study are quantity-related estimates for the effect of metrology inaccuracy in the measuring random variables with various coefficients of variation for small sample sizes and different relative measurement errors. For the assessing we use 106 retests and a maximal variance for the same number of repeated tests. The results make possible to evaluate an effect of metrology inaccuracy for diverse coefficients of test results variation, as well as determine an appropriate extent of testing for assigned model inaccuracies and a known measurement error. In addition, practical application of obtained results is shown.

Determining the Reduction Factor in Predicting the Contribution of Concrete to Shear Strength by Using a Probabilistic Method

The reliability of a structure can be defined as the probability of the structure to fulfil its intended purpose throughout its design lifespan. In the codes, it is aimed to provide the target failure probability by means of safety factors in the form of load factors and strength reduction factors. This paper presents an investigation of the reduction factor for the contribution of concrete to the shear strength of reinforced concrete beams without stirrups designed according to the Turkish Code. In this code, the contribution of concrete to the shear strength is calculated by multiplying the diagonal cracking strength by a reduction factor of 0.8. In this study, based upon a second moment probabilistic analysis procedure, the change in the strength reduction factor was investigated for various coefficients of variation of concrete compressive strength and failure probabilities by using experimental data available in the literature. It is assumed that the considered random variables are statistically independent, and the correlation effects are not taken into account. The results show that the reduction factor decreases with the increase in the coefficient of variation of concrete compressive strength and the reduction factor given by the Turkish Code corresponds to a variation coefficient of 0.12 and a failure probability of 10−6.

Probabilistic simulation of advection-reaction-dispersion equation using random lattice Boltzmann method

Mass transfer is subject to numerous sources of uncertainties due to scarcity of observational data. In this research, a numerical procedure was developed for the probabilistic study of a two-dimensional advection-dispersion problem, while considering chemical reactions. Innovatively, the lattice Boltzmann method was coupled with the concept of random field theory for the probabilistic simulations. The effects of various coefficients of variations (COV) and a number of autocorrelation distances were considered for the stochastic parameters, including dispersion coefficient, pore velocity, and the reaction term. The results indicated that the introduced probabilistic framework can be employed to effectively describe the effects of uncertainties in parameters related to the advection-dispersion equation. Moreover, it was deduced that the mass travel time and the time-concentration curves were influenced significantly by the variations of COV and autocorrelation distance for pore velocity. Interestingly, the mass transfer in the transverse direction increased (through the dispersion phenomenon) with a rise in the values of COV for longitudinal pore velocity. However, different values of COV and autocorrelation distances for the dispersion coefficient and the reaction term caused small alterations in the mass travel time and time-concentration curve.

Historical floods in flood frequency analysis: Is this game worth the candle?

In flood frequency analysis (FFA) the profit from inclusion of historical information on the largest historical pre-instrumental floods depends primarily on reliability of the information, i.e. the accuracy of magnitude and return period of floods. This study is focused on possible theoretical maximum gain in accuracy of estimates of upper quantiles, that can be obtained by incorporating the largest historical floods of known return periods into the FFA. We assumed a simple case: N years of systematic records of annual maximum flows and either one largest (XM1) or two largest (XM1 and XM2) flood peak flows in a historical M-year long period. The problem is explored by Monte Carlo simulations with the maximum likelihood (ML) method. Both correct and false distributional assumptions are considered. In the first case the two-parameter extreme value models (Gumbel, log-Gumbel, Weibull) with various coefficients of variation serve as parent distributions. In the case of unknown parent distribution, the Weibull distribution was assumed as estimating model and the truncated Gumbel as parent distribution. The return periods of XM1 and XM2 are determined from the parent distribution. The results are then compared with the case, when return periods of XM1 and XM2 are defined by their plotting positions. The results are presented in terms of bias, root mean square error and the probability of overestimation of the quantile with 100-year return period. The results of the research indicate that the maximal profit of inclusion of pre-instrumental foods in the FFA may prove smaller than the cost of reconstruction of historical hydrological information.

Shock-induced stochastic dynamic analysis of cylinders made of saturated porous materials using MLPG method: considering uncertainty in mechanical properties

The stochastic meshless local Petrov–Galerkin method is employed for dynamic analysis of cylinders made of fully saturated porous materials with considering uncertainties in the constitutive mechanical properties. The porous cylinder is assumed to be under shock loading. To approximate the trial functions in the radial point interpolation method, the radial basis functions are utilized. The Monte Carlo simulation is used to generate the random fields for mechanical properties. The results are obtained for various random variables, which are simulated by uniform, normal and lognormal probability density functions with various coefficients of variation (COV), changing from 0 to 20%. The obtained results from the presented stochastic analysis are compared to those obtained from analysis with considering deterministic mechanical properties. The results show that the uncertainty in mechanical properties has a significant effect on the structural responses, especially for big values of COVs.

Stochastic analysis of elastic wave and second sound propagation in media with Gaussian uncertainty in mechanical properties using a stochastic hybrid mesh-free method

The main objective of this article is the exploitation of a stochastic hybrid mesh-free method based on stochastic generalized finite difference (SGFD), Newmark finite difference (NFD) methods and Monte Carlo simulation for thermoelastic wave propagation and coupled thermoelasticity analysis based on GN theory (without energy dissipation). A thick hollow cylinder with Gaussian uncertainty in mechanical properties is considered as an analyzed domain for the problem. The effects of uncertainty in mechanical properties with various coefficients of variations on thermo-elastic wave propagation are studied in details. Also, the time histories and distribution on thickness of cylinder of maximum, mean and variance values of temperature and radial displacement are studied for various coefficients of variations (COVs).

Safety Analysis of the Patch Load Resistance of Plate Girders: Influence of Model Error and Variability

This study aims to undertake a statistical study to evaluate the accuracy of nine models that have been previously proposed for estimating the ultimate resistance of plate girders subjected to patch loading. For each model, mean errors and standard errors, as well as the probability of underestimating or overestimating patch load resistance, are estimated and the resultant values are compared one to another. Prior to that, the models are initially calibrated in order to improve interaction formulae using an experimental data set collected from the literature. The models are then analyzed by computing design factors associated with a target risk level (probability of exceedance). These models are compared one to another considering uncertainties existed in material and geometrical properties. The Monte Carlo simulation method is used to generate random variables. The statistical parameters of the calibrated models are calculated for various coefficients of variations regardless of their correlation with the random resistance variables. These probabilistic results are very useful for evaluating the stochastic sensitivity of the calibrated models.

Experimental Evidence of Mixture Segregation by Particle Size Distribution

In this study, we discuss experimental segregation results obtained for two industrial cases, namely, ammonium perchlorate and a polymeric resin. These results show a segregation effect due to particle size distribution rather than particle size itself. We used a heap-pouring device as a tester, for which a visual knowledge of the segregation state was observed. The analysis of segregation is based on various coefficients of variations related to the size fractions or particle size distribution's global characteristics, indicating heterogeneities in the heaps formed. Both cases indicate that wide particle size distributions, as opposed to narrow ones, are limiting segregation risks. This collective, and maybe astonishing, effect is extremely marked for the cases studied, and demonstrates again the mesoscopic nature of granular media.

Transient analysis of thermo-elastic waves in thick hollow cylinders using a stochastic hybrid numerical method, considering Gaussian mechanical properties

This article attempts to study the stochastic coupled thermo-elasticity of thick hollow cylinders subjected to thermal shock loading considering uncertainty in mechanical properties. The thermo-elastic governing equations based on Green–Naghdi theory (without energy dissipation) are stochastically solved using a hybrid numerical method (combined Galerkin finite element and Newmark finite difference methods). The mechanical properties are considered as random variables with Gaussian distribution, which are generated using Monte Carlo simulation method with various coefficients of variations (COVs). The effects of uncertainty in mechanical properties with various coefficients of variations on thermo-elastic wave propagation are studied in detail. Also, the maximum, mean and variance of temperature, displacement and stresses are illustrated across thickness of cylinder in various times.

Stochastic meshless local Petrov-Galerkin (MLPG) method for thermo-elastic wave propagation analysis in functionally graded thick hollow cylinders

The thermo-elastic wave propagation based on Green-Naghdi (GN) coupled thermo-elasticity (without energy dissipation) is studied in a function- ally graded thick hollow cylinder considering uncertainty in constitutive mechan- ical properties under thermal shock loading. The meshless local Petrov-Galerkin method accompanied with Monte-Carlo simulation is developed to solve the stochas- tic boundary value problem. In the presented method, the mechanical properties of FGM are considered to be as random variables with Gaussian distribution and mean values equal to deterministic values reported in previous works, which are gener- ated using Monte-Carlo simulation with various coefficients of variations (COVs). The time evolution for transient problems is treated by using the Newmark finite difference method. The FG cylinder is assumed to be under axisymmetric and plane strain conditions. The mechanical properties of FGM are nonlinearly graded along the radial direction. A weak formulation for the set of coupled governing equations is transformed into local integral equations on local subdomains by using a Heav- iside test function. All nodal points are regularly distributed along the thickness of the FG cylinder in radial direction and each node is located in a uni-directional subdomain to which a local integral equation is applied. The distributions of the temperature and radial displacements as well as the time history of them are ob- tained for some grading patterns of FGM at several time instants and for some COVs. The propagation of thermal and elastic waves along the radial direction in the FG thick hollow cylinder as well as the statistical characteristics of the variance and maximum values of the temperature and displacement are discussed in details.

함수 근사 모멘트 방법에서 추정한 1∼4차 통계적 모멘트의 수치적 검증

This research aims to examine accuracy and efficiency of the first four moments corresponding to mean, standard deviation, skewness, and kurtosis, which are estimated by a function approximation moment method (FAMM). In FAMM, the moments are estimated from an approximating quadratic function of a system response function. The function approximation is performed on a specially selected experimental region for accuracy, and the number of function evaluations is taken equal to that of the unknown coefficients for efficiency. For this purpose, three error-minimizing conditions are utilized and corresponding canonical experimental regions constructed accordingly. An interpolation function is then obtained using a D-optimal design and then the first four moments of it are obtained as the estimates for the system response function. In order to verify accuracy and efficiency of FAMM, several non-linear examples are considered including a polynomial of order 4, an exponential function, and a rational function. The moments calculated from various coefficients of variation show very good accuracy and efficiency in comparison with those from analytic integration or the Monte Carlo simulation and the experimental design technique proposed by Taguchi and updated by D’Errico and Zaino.

An alternative method for the estimation of the terminal slope when a few data points are available

Phase plane plots are graphical expressions for differential equations ploting the state derivative dc/dt versus the state c. Using these plots, we developed a novel method for the estimation of the terminal slope from time–concentration data. The values of the derivatives used for the construction of the phase plane plots were calculated by two different methods of numerical differentiation. The first method (D1) is based on the classical calculation of slope of the line connecting two successive data points. The alternative method (D2) relies on an initial second‐order polynomial interpolation utilizing three successive data points followed by the calculation of the derivative at each one of the concentration values. A forced‐through‐zero linear regression of the phase plane plot data is used to derive an estimate for the slope. For comparative purposes, the standard approach based on the semilogarithmic plot was also applied. For a hypothetical drug absorbed by first‐order process into a one‐compartment model, simulated time–concentration data disturbed by a Gaussian zero mean random error with various coefficients of variation were generated. Various sampling schedules, with two, three, four, or five data points, were utilized for the estimation of the terminal slope. Performances of the proposed methods on simulated data were expressed by means of root‐mean‐squared error, bias, and standard deviation. In all cases, D2 was superior to D1. The D2 method outperforms the standard method in that it furnishes estimates closer to the real values in all cases when two data points and in most cases when three data points were used. All methods behave similarly when four or five data points were used.

Task routing and resequencing in a multiprocessor system

The effects of task routing and resequencing on system and program performance of a multiprocessor system are studied using simulation techniques. A closed queueing network model is considered. It consists of the CPU and the I/O channel. The CPU consists of four homogeneous and independent processors each serving its own queue. Resequencing of jobs after CPU service ensures that jobs leave the CPU on a first-in-first-out basis. We examine the performance of four task routing strategies in conjunction with the subsequent resequencing of jobs for various coefficients of variation of processor service times (exponential and Branching Erlang distributions) and for different degrees of multiprogramming.

Comparison of the whistle structure of six species of dolphin

Spectral and statistical analyses were used to compare the whistle structure of six species of dolphin; Stenella longirostris, Stenella frontalis, Stenella attenuata, Lagenorhynchus obscurus, Tursiops truncatus, and Sotalia fluviatilis. A consistent pattern existed in the various coefficients of variation calculated for the different species. In general, the frequency variables had the lowest coefficients of variation (cv). The values of cv for maximum frequency were usually the lowest. Compared to other species Tursiops had relatively large coefficients of variation of the frequency variables indicating that the frequencies of Tursiops whistles were more diverse. The other five species had similar frequency ranges which had higher upper frequencies than Tursiops. The results of discriminate analysis indicated that here were significant differences between the whistle structures of the different species, and that these differences were related to taxonomic relations, body size, and habitat. The magnitude ...

A transient stochastic failure model for unidirectional composites under impact loading

A dynamic failure model is unidirectionally reinforced composites under impact loading. It comprises two parts the first of which involves double-edge notched composites with a matrix split. The second part is a complete stochastic simulation of sequential failure processes for various coefficients of variation of fibre strength. The predicted final fracture surfaces for both CFRP and GRP are consistent with observations from previous experimental work on tensile impact of composites.

The Utilization of a Known Coefficient of Variation in the Estimation Procedure

Abstract An estimator, γ, of μ is developed which utilizes a priori information concerning the value of the population coefficient of variation. γ′ is shown to have a smaller mean squared error than the sample mean, γ. A table of relative efficiencies for various coefficients of variation and sample sizes is presented.