Stochastic Analysis and Modeling of Velocity Observations in Turbulent Flows

Highly turbulent water flows,often encountered near human constructions like bridge piers,spillways,and weirs,display intricate dynamics characterized by the formation of eddies and vortices.These formations,varying in sizes and lifespans,significantly influence the distribution of fluid velocities within the flow.Subsequently,the rapid velocity fluctuations in highly turbulent flows lead to elevated shear and normal stress levels.For this reason,to meticulously study these dynamics,more often than not,physical modeling is employed for studying the impact of turbulent flows on the stability and longevity of nearby structures.Despite the effectiveness of physical modeling,various monitoring challenges arise,including flow disruption,the necessity for concurrent gauging at multiple locations,and the duration of measurements.Addressing these challenges,image velocimetry emerges as an ideal method in fluid mechanics,particularly for studying turbulent flows.To account for measurement duration,a probabilistic approach utilizing a probability density function(PDF)is suggested to mitigate uncertainty in estimated average and maximum values.However,it becomes evident that deriving the PDF is not straightforward for all turbulence-induced stresses.In response,this study proposes a novel approach by combining image velocimetry with a stochastic model to provide a generic yet accurate description of flow dynamics in such applications.This integration enables an approach based on the probability of failure,facilitating a more comprehensive analysis of turbulent flows.Such an approach is essential for estimating both short-and long-term stresses on hydraulic constructions under assessment.

Stochastic Analysis of Low-Cost Single-Frequency GPS Receivers

Typically, dual-frequency geodetic grade GNSS receivers are utilized for positioning applications that require high accuracy. Single-frequency high grade receivers can be used to minimize the expenses of such dual-frequency receivers. However, user has to consider the resultant positioning accuracy. Since the evolution of low-cost single-frequency (LCSF) receivers is typically cheaper than single-frequency high grade receivers, it is possible to obtain comparable positioning accuracy if the corresponding observables are accurately modelled. In this paper, two LCSF GPS receivers are used to form short baseline. Raw GPS measurements are recorded for several consecutive days. The collected data are used to develop the stochastic model of GPS observables from such receivers. Different functions are tested to determine the best fitting model which is found to be 3 parameters exponential decay function. The new developed model is used to process different data sets and the results are compared against the traditional model. Both results from the newly developed and the traditional models are compared with the reference solution obtained from dual-frequency receiver. It is shown that the newly developed model improves the root-mean-square of the estimated horizontal coordinates by about 10% and improves the root-mean-square of the up component by about 39%.

Stochastic Analysis of Short-Term Structural Responses and Fatigue Damages of A Submerged Tension Leg Platform Wind Turbine in Wind and Waves

In connection with the design of floating wind turbines,stochastic dynamic analysis is a critical task considering nonlinear wind and wave forces.To study the random structural responses of a newly designed submerged tension leg platform(STLP)wind turbine,a set of dynamic simulations and comparison analysis with the MIT/NREL TLP wind turbine are carried out.The signal filter method is used to evaluate the mean and standard deviations of the structural response.Furthermore,the extreme responses are estimated by using the mean upcrossing rate method.The fatigue damages for blade root,tower,and mooring line are also studied according to the simulated time-series.The results and comparison analysis show that the STLP gives small surge and pitch motions and mooring line tensions in operational sea states due to the small water-plane area.Additionally,in severe sea states,the STLP gives lower extreme values of platform pitch,slightly larger surge and heave motions and better towerbase and mooring line fatigue performances than those of the MIT/NREL TLP.It is found that the STLP wind turbine has good performances in structural responses and could be a potential type for exploiting the wind resources located in deep waters.

Efficient stochastic analysis of unsaturated slopes subjected to various rainfall intensities and patterns

Rainfall infiltration poses a disastrous threat to the slope stability in many regions around the world.This paper proposes an extreme gradient boosting(XGBoost)-based stochastic analysis framework to estimate the rainfall-induced slope failure probability.An unsaturated slope under rainfall infiltration in spatially varying soils is selected in this study to investigate the influences of the spatial variability of soil properties(including effective cohesion c',effective friction angleφ'and saturated hydraulic conductivity k_(s)),as well as rainfall intensity and rainfall pattern on the slope failure probability.Results show that the proposed framework in this study is capable of computing the failure probability with accuracy and high efficiency.The spatial variability of k_(s)cannot be overlooked in the reliability analysis.Otherwise,the rainfall-induced slope failure probability will be underestimated.It is found that the rain-fall intensity and rainfall pattern have significant effect on the probability of failure.Moreover,the failure probabilities under various rainfall intensities and patterns can be easily obtained with the aid of the proposed framework,which can provide timely guidance for the landslide emergency management departments.

Data envelopment analysis for scale elasticity measurement in the stochastic case:with an application to Indian banking

In the nonparametric data envelopment analysis literature,scale elasticity is evaluated in two alternative ways:using either the technical efficiency model or the cost efficiency model.This evaluation becomes problematic in several situations,for example(a)when input proportions change in the long run,(b)when inputs are heterogeneous,and(c)when firms face ex-ante price uncertainty in making their production decisions.To address these situations,a scale elasticity evaluation was performed using a value-based cost efficiency model.However,this alternative value-based scale elasticity evaluation is sensitive to the uncertainty and variability underlying input and output data.Therefore,in this study,we introduce a stochastic cost-efficiency model based on chance-constrained programming to develop a value-based measure of the scale elasticity of firms facing data uncertainty.An illustrative empirical application to the Indian banking industry comprising 71 banks for eight years(1998–2005)was made to compare inferences about their efficiency and scale properties.The key findings are as follows:First,both the deterministic model and our proposed stochastic model yield distinctly different results concerning the efficiency and scale elasticity scores at various tolerance levels of chance constraints.However,both models yield the same results at a tolerance level of 0.5,implying that the deterministic model is a special case of the stochastic model in that it reveals the same efficiency and returns to scale characterizations of banks.Second,the stochastic model generates higher efficiency scores for inefficient banks than its deterministic counterpart.Third,public banks exhibit higher efficiency than private and foreign banks.Finally,public and old private banks mostly exhibit either decreasing or constant returns to scale,whereas foreign and new private banks experience either increasing or decreasing returns to scale.Although the application of our proposed stochastic model is illustrative,it can be potentially applied to all firms in the information and distribution-intensive industry with high fixed costs,which have ample potential for reaping scale and scope benefits.

Stochastic Failure Analysis of Reinforced Thermoplastic Pipes Under Axial Loading and Internal Pressure

This study explores how parametric uncertainties in the production affect failure tensile loads of reinforced thermoplastic pipes(RTPs)under combined loading conditions.The stress distributions in RTPs are examined with three-dimensional(3D)elasticity theory,and the analytical micromechanics of composites are evaluated.To evaluate the failure mechanisms for RTPs,3D Hashin–Yeh failure criteria are combined with the damage evolution model to establish a progressive failure model.The theoretical model has been validated through numerical simulations and axial tensile tests data.To analyze how randomness of relevant parameters affects the first-ply failure(FPF)tensile load and final failure(FF)tensile load in RTPs,many samples are produced with the Monte–Carlo approach.The stochastic analysis results are statistically evaluated through the Weibull probability density distribution function.For the randomness of production parameters,the failure tensile load of RTPs fluctuates near the mean value.As the ply number at the reinforced layer increases,the dispersion of failure tensile load increases,with a high probability that the FPF tensile load of RTPs is lower than the mean value.

STOCHASTIC ANALYSIS OF UNSATURATED FLOW WITH THE NORMAL DISTRIBUTION OF SOIL HYDRAULIC CONDUCTIVITY

Stochastic approaches are useful to quantitatively describe transportbehavior over large temporal and spatial scales while accounting for the influence of small-scalevariabilities. Numerous solutions have been developed for unsatu-rated soil water flow based on thelognormal distribution of soil hydraulic conductivity. To our knowledge, no available stochasticsolutions for unsaturated flow have been derived on the basis of the normal distribution ofhydraulic conductivity. In this paper, stochastic solutions were developed for unsaturated flow byassuming the normal distribution of saturated hydraulic conductivity (K_s). Under the assumptionthat soil hydraulic properties are second-order stationary, analytical expressions for capillarytension head variance (σ_h^2 ) and effective hydraulic conductivity (K_ii~*) in stratified soilswere derived using the perturbation method. The dependence of σ_h^2 and K_ii~* on soil variabilityand mean flow variables (the mean capillary tension head and its temporal and spatial gradients) andmean flow conditions (wetting and drying) were systematically analyzed. The calculated variance ofcapillary tension head with the analytical solution derived in this paper was compared with fieldexperimental data. The good agreement indicates that the analytical solution is applicable toevaluate the variance of capillary tension head of field soils with moderate variability.

Assessment of buckling-restrained braced frame reliability using an experimental limit-state model and stochastic dynamic analysis

Buckling-restrained braces （BRBs） have recently become popular in the United States for use as primary members of seismic lateral-force-resisting systems. A BRB is a steel brace that does not buckle in compression but instead yields in both tension and compression. Although design guidelines for BRB applications have been developed, systematic procedures for assessing performance and quantifying reliability are still needed. This paper presents an analytical framework for assessing buckling-restrained braced frame （BRBF） reliability when subjected to seismic loads. This framework efficiently quantifies the risk of BRB failure due to low-cycle fatigue fracture of the BRB core. The procedure includes a series of components that： （1） quantify BRB demand in terms of BRB core deformation histories generated through stochastic dynamic analyses; （2） quantify the limit-state of a BRB in terms of its remaining cumulative plastic ductility capacity based on an experimental database; and （3） evaluate the probability of BRB failure, given the quantified demand and capacity, through structural reliability analyses. Parametric studies were conducted to investigate the effects of the seismic load, and characteristics of the BRB and BRBF on the probability of brace failure. In addition, fragility curves （i.e., conditional probabilities of brace failure given ground shaking intensity parameters） were created by the proposed framework. While the framework presented in this paper is applied to the assessment of BRBFs, the modular nature of the framework components allows for application to other structural components and systems.

Stochastic Geometric Analysis of the Uplink Throughput in Cognitive Radio Cellular Networks

This paper investigates the uplink throughput of Cognitive Radio Cellular Networks(CRCNs).As oppose to traditional performance evaluation schemes which mainly adopt complex system level simulations,we use the theoretical framework of stochastic geometry to provide a tractable and accurate analysis of the uplink throughput in the CRCN.By modelling the positions of User Equipments(UEs)and Base Stations(BSs)as Poisson Point Processes(PPPs),we analyse and derive expressions for the link rate and the cell throughput in the Primary(PR)and Secondary(SR)networks.The expressions show that the throughput of the CRCN is mainly affected by the density ratios between the UEs and the BSs in both the PR and SR networks.Besides,a comparative analysis of the link rate between random and regular BS deployments is concluded,and the results confirm the accuracy of our analysis.Furthermore,we define the cognitive throughput gain and derive an expression which is dominated by the traffic load in the PR network.

Stochastic back analysis of permeability coefficient using generalized Bayesian method

Owing to the fact that the conventional deterministic back analysis of the permeability coefficient cannot reflect the uncertainties of parameters, including the hydraulic head at the boundary, the permeability coefficient and measured hydraulic head, a stochastic back analysis taking consideration of uncertainties of parameters was performed using the generalized Bayesian method. Based on the stochastic finite element method （SFEM） for a seepage field, the variable metric algorithm and the generalized Bayesian method, formulas for stochastic back analysis of the permeability coefficient were derived. A case study of seepage analysis of a sluice foundation was performed to illustrate the proposed method. The results indicate that, with the generalized Bayesian method that considers the uncertainties of measured hydraulic head, the permeability coefficient and the hydraulic head at the boundary, both the mean and standard deviation of the permeability coefficient can be obtained and the standard deviation is less than that obtained by the conventional Bayesian method. Therefore, the present method is valid and applicable.

The Stochastic Regression Analysis as a Tool in Ecotoxicological QSAR Studies

Correspondence factor analysis(CFA)was used in conjunction with linear regression analysis to examine the structure-activity relationships of 50 benzene derivatives tested on Pimephales promelas.From nine molecular descriptors(numbers of C,H,O,N,Br,Cl,NO_2,OH,and NH_2 included in the molecules),CFA made it possible to define five new independent variables which were introduced in a stepwise regression analysis procedure to describe the acute toxicity(96-h LC_(50))of the aromatic compounds.The model log 1/C=-0.727F_1+1.248F_3+4.052(r=0.918; s=0.270)is more relevant to describe the ecotoxicological behavior of the studied compounds on the fathead minnow than that obtained with principal components(log 1/C=0.151 PC_1 -0.271 PC_2+4.124;r=0.737;s=0.460).The heuristic potency of this particular statistical analysis,which is called stochastic regression analysis,is discussed in detail.1989 Academic Press,Inc.

An Interpolation Method for Karhunen-Loève Expansion of Random Field Discretization

In the context of global mean square error concerning the number of random variables in the representation,the Karhunen–Loève(KL)expansion is the optimal series expansion method for random field discretization.The computational efficiency and accuracy of the KL expansion are contingent upon the accurate resolution of the Fredholm integral eigenvalue problem(IEVP).The paper proposes an interpolation method based on different interpolation basis functions such as moving least squares(MLS),least squares(LS),and finite element method(FEM)to solve the IEVP.Compared with the Galerkin method based on finite element or Legendre polynomials,the main advantage of the interpolation method is that,in the calculation of eigenvalues and eigenfunctions in one-dimensional random fields,the integral matrix containing covariance function only requires a single integral,which is less than a two-folded integral by the Galerkin method.The effectiveness and computational efficiency of the proposed interpolation method are verified through various one-dimensional examples.Furthermore,based on theKL expansion and polynomial chaos expansion,the stochastic analysis of two-dimensional regular and irregular domains is conducted,and the basis function of the extended finite element method(XFEM)is introduced as the interpolation basis function in two-dimensional irregular domains to solve the IEVP.

STOCHASTIC CRACKING AND HEALING BEHAVIORS OF THIN FILMS DURING REACTION-DIFFUSION GROWTH

The stochastic cracking and healing behaviors of reaction-diffusion growth of thin filmswere studied by means of Markov processes analysis. We chose the thermal growth ofoxide scales on metals as an example of reaction-diffusion growth. The thermal growthof oxide films follows power law when no cracking occurs. Our results showed that thegrowth kinetics under stochastic cracking and healing conditions was different fromthat without cracking. It might be altered to either pseudo-linear or pseudo-power lawsdependent upon the intensity and frequency of the cracking of the films. When thehoping items dominated, the growth followed pseudo-linear law; when the diffusionalitems dominated, it followed pseudo-power law with the exponentials lower than theintrinsical values. The numerical results were in good agreement with the meassuredkinetics of isothermal and cyclic oxidation of NiAl-0.1 Y (at. %) alloys in air at 1273K.

The performance of stochastic designs in wellbore drilling operations

Wellbore drilling operations frequently entail the combination of a wide range of variables. This is underpinned by the numerous factors that must be considered in order to ensure safety and productivity. The heterogeneity and sometimes unpredictable behaviour of underground systems increases the sensitivity of drilling activities. Quite often the operating parameters are set to certify effective and efficient working processes. However, failings in the management of drilling and operating conditions sometimes result in catastrophes such as well collapse or fluid loss. This study investigates the hypothesis that optimising drilling parameters, for instance mud pressure, is crucial if the margin of safe operating conditions is to be properly defined. This was conducted via two main stages： first a deterministic analysis--where the operating conditions are predicted by conventional modelling procedures--and then a probabilistic analysis via stochastic simulations--where a window of optimised operation conditions can be obtained. The outcome of additional stochastic analyses can be used to improve results derived from deterministic models. The incorporation of stochastic techniques in the evaluation of wellbore instability indicates that margins of the safe mud weight window are adjustable and can be extended considerably beyond the limits of deterministic predictions. The safe mud window is influenced and hence can also be amended based on the degree of uncertainty and the permissible level of confidence. The refinement of results from deterministic analyses by additional stochastic simulations is vital if a more accurate and reliable representation of safe in situ and operating conditions is to be obtained during wellbore operations.

Technical efficiency of cocoa farms at varying elevation levels in Davao City, Philippines: implications to sustainable upland farming systems

Elevation is one of many components that influence agriculture, and this in turn affects the level of both inputs and outputs of farmers. This article focuses on the productivity and technical efficiency of 100 cocoa farms using cross-sectional data from areas ranging from 190 to 1021 m above sea level which were classified as low, medium, and high elevation in Davao City, considered as the chocolate capital of the Philippines. Using stochastic frontier analysis, the results showed that the cost of inputs per ha and the number of cocoa trees per ha significantly increase yield. Farms at high elevations were less technically efficient, as this entails lower temperatures and increased rainfall, and cocoa farming in those areas and conditions can be more challenging, especially with changes in farming practices, terrain, and distance to markets. Other significant variables were age of cocoa farms, married farmers, and age of the farmers. Older farms may be more developed, farmers who are married benefit from their spouses being able to readily contribute as farm labor, and lastly, older farmers' inefficiency may likely stem from nonadaptation of newer farming practices. With an average technical efficiency of 0.61, 0.63, and 0.26 in low, medium, and high elevation areas, respectively, farmers therefore have an incentive to improve farm practices and consider topographical variations found in high elevation areas. Recommendations for the improvement of technical efficiency of cocoa farms are better connectivity to markets, enhancing farm practices, and continuation and improvement of government programs on cocoa with an added emphasis on research. For farmers in high elevation areas, mitigating solutions such as sustainable agriculture practices and ecolabelling are key to improving efficiency and minimizing the potential negative impact on upland farming systems. Moreover, such adaptation measures may also contribute to sustainability of cocoa farming in high elevation areas.

A novel refined dynamic model of high-speed maglev train-bridge coupled system for random vibration and running safety assessment

Running safety assessment and tracking irregularity parametric sensitivity analysis of high-speed maglev train-bridge system are of great concern,especially need perfect refinement models in which all properties can be well characterized based on various stochastic excitations.A three-dimensional refined spatial random vibration analysis model of high-speed maglev train-bridge coupled system is established in this paper,in which multi-source uncertainty excitation can be considered simultaneously,and the probability density evolution method(PDEM)is adopted to reveal the system-specific uncertainty dynamic characteristic.The motion equation of the maglev vehicle model is composed of multi-rigid bodies with a total 210-degrees of freedom for each vehicle,and a refined electromagnetic force-air gap model is used to account for the interaction and coupling effect between the moving train and track beam bridges,which are directly established by using finite element method.The model is proven to be applicable by comparing with Monte Carlo simulation.By applying the proposed stochastic framework to the high maglev line,the random dynamic responses of maglev vehicles running on the bridges are studied for running safety and stability assessment.Moreover,the effects of track irregularity wavelength range under different amplitude and running speeds on the coupled system are investigated.The results show that the augmentation of train speed will move backward the sensitive wavelength interval,and track irregularity amplitude influences the response remarkably in the sensitive interval.

Relay selection region and system performance analysis for interfered cooperative ad-hoc networks

The performance of interfered cooperative ad-hoc networks is analyzed by stochastic geometry analysis and a selection region of relay is presented. First, assuming that the distribution of nodes in the random network follows the Poisson point process （PPP）, a closed-form expression of the outage probability is derived for the best relay selection （BRS） scheme. Secondly, the capacity of the network is presented for this scheme. Finally, a performance factor is defined to evaluate the performance gain obtained from the BRS. By using this factor, a relay selection region is found to guarantee the performance gain from the BRS. The analysis and simulation results show that the performance of the BRS not only depends on the densities of source nodes and relay nodes but also on the factors of networks such as the path loss factor and the decoding threshold. And the BRS has a greater advantage than direct transmission （DT） in hush environments such as the long transmission distances, much interference and the high decoding thresholds.

Probabilistic model and analysis of coupled train-ballasted track-subgrade system with uncertain structural parameters

Random dynamic responses caused by the uncertainty of structural parameters of the coupled train-ballasted track-subgrade system under train loading can pose safety concerns to the train operation.This paper introduced a computational model for analyzing probabilistic dynamic responses of three-dimensional(3D)coupled train-ballasted track-subgrade system(TBTSS),where the coupling effects of uncertain rail irregularities,stiffness and damping properties of ballast and subgrade layers were simultaneously considered.The number theoretical method(NTM)was employed to design discrete points for the multi-dimensional stochastic parameters.The time-histories of stochastic dynamic vibrations of the TBSS with systematically uncertain structural parameters were calculated accurately and efficiently by employing the probability density evolution method(PDEM).The model-predicted results were consistent with those by the Monte Carlo simulation method.A sensitivity study was performed to assess the relative importance of those uncertain structural parameters,based on which a case study was presented to explore the stochastic probability evolution mechanism of such train-ballasted track-subgrade system.

Orthogonal expansion of ground motion and PDEM-based seismic response analysis of nonlinear structures

This paper introduces an orthogonal expansion method for general stochastic processes. In the method, a normalized orthogonal function of time variable t is first introduced to carry out the decomposition of a stochastic process and then a correlated matrix decomposition technique, which transforms a correlated random vector into a vector of standard uncorrelated random variables, is used to complete a double orthogonal decomposition of the stochastic processes. Considering the relationship between the Hartley transform and Fourier transform of a real-valued function, it is suggested that the first orthogonal expansion in the above process is carried out using the Hartley basis function instead of the trigonometric basis function in practical applications. The seismic ground motion is investigated using the above method. In order to capture the main probabilistic characteristics of the seismic ground motion, it is proposed to directly carry out the orthogonal expansion of the seismic displacements. The case study shows that the proposed method is feasible to represent the seismic ground motion with only a few random variables. In the second part of the paper, the probability density evolution method （PDEM） is employed to study the stochastic response of nonlinear structures subjected to earthquake excitations. In the PDEM, a completely uncoupled one-dimensional partial differential equation, the generalized density evolution equation, plays a central role in governing the stochastic seismic responses of the nonlinear structure. The solution to this equation will yield the instantaneous probability density function of the responses. Computational algorithms to solve the probability density evolution equation are described. An example, which deals with a nonlinear frame structure subjected to stochastic ground motions, is illustrated to validate the above approach.

Primary Educational Productivity ： A Study Based on Stochastic Frontier Educational Production Function Model

This paper builds a stochastic frontier educational production function model, estimating the primary educational productivity with annual data of 31 provinces from 2007 to 2011. The conclusions are as follows： （1） in educational production function, output elasticity of public educational expenditure exceeds private educational expenditure＇s. The degrees of contribution of public and private educational expenditure reflect that China should increase public educational expenditure. （2） regional educational technical efficiency is affected by both structure of educational expenditure and levels of regional economic growth. Primary educational technical efficiency of east, middle and west regions all tended to fall down during 2007 to 2011.