Anisotropic time-dependent behaviors of shale under direct shearing and associated empirical creep models

Understanding the anisotropic creep behaviors of shale under direct shearing is a challenging issue.In this context,we conducted shear-creep and steady-creep tests on shale with five bedding orientations (i.e.0°,30°,45°,60°,and 90°),under multiple levels of direct shearing for the first time.The results show that the anisotropic creep of shale exhibits a significant stress-dependent behavior.Under a low shear stress,the creep compliance of shale increases linearly with the logarithm of time at all bedding orientations,and the increase depends on the bedding orientation and creep time.Under high shear stress conditions,the creep compliance of shale is minimal when the bedding orientation is 0°,and the steady-creep rate of shale increases significantly with increasing bedding orientations of 30°,45°,60°,and 90°.The stress-strain values corresponding to the inception of the accelerated creep stage show an increasing and then decreasing trend with the bedding orientation.A semilogarithmic model that could reflect the stress dependence of the steady-creep rate while considering the hardening and damage process is proposed.The model minimizes the deviation of the calculated steady-state creep rate from the observed value and reveals the behavior of the bedding orientation's influence on the steady-creep rate.The applicability of the five classical empirical creep models is quantitatively evaluated.It shows that the logarithmic model can well explain the experimental creep strain and creep rate,and it can accurately predict long-term shear creep deformation.Based on an improved logarithmic model,the variations in creep parameters with shear stress and bedding orientations are discussed.With abovementioned findings,a mathematical method for constructing an anisotropic shear creep model of shale is proposed,which can characterize the nonlinear dependence of the anisotropic shear creep behavior of shale on the bedding orientation.

Assessment of the three representative empirical models for zenith tropospheric delay(ZTD)using the CMONOC data

The precise correction of atmospheric zenith tropospheric delay(ZTD)is significant for the Global Navigation Satellite System(GNSS)performance regarding positioning accuracy and convergence time.In the past decades,many empirical ZTD models based on whether the gridded or scattered ZTD products have been proposed and widely used in the GNSS positioning applications.But there is no comprehensive evaluation of these models for the whole China region,which features complicated topography and climate.In this study,we completely assess the typical empirical models,the IGGtropSH model(gridded,non-meteorology),the SHAtropE model(scattered,non-meteorology),and the GPT3 model(gridded,meteorology)using the Crustal Movement Observation Network of China(CMONOC)network.In general,the results show that the three models share consistent performance with RMSE/bias of 37.45/1.63,37.13/2.20,and 38.27/1.34 mm for the GPT3,SHAtropE and IGGtropSH model,respectively.However,the models had a distinct performance regarding geographical distribution,elevation,seasonal variations,and daily variation.In the southeastern region of China,RMSE values are around 50 mm,which are much higher than that in the western region,approximately 20 mm.The SHAtropE model exhibits better performance for areas with large variations in elevation.The GPT3 model and the IGGtropSH model are more stable across different months,and the SHAtropE model based on the GNSS data exhibits superior performance across various UTC epochs.

Smoothed Empirical Likelihood Inference for Nonlinear Quantile Regression Models with Missing Response

In this paper, three smoothed empirical log-likelihood ratio functions for the parameters of nonlinear models with missing response are suggested. Under some regular conditions, the corresponding Wilks phenomena are obtained and the confidence regions for the parameter can be constructed easily.

A New Empirical Large Signal Model of 4H-SiC MESFETs for the Nonlinear Analysis

A new comprehensive empirical large signal model for 4H-SiC MESFETs is proposed. An enhanced drain current model,along with an improved charge conservation capacitance model,is presented by the improvement of the channel length modulation and the hyperbolic tangent function coefficient based on the Materka model. The Levenberg-Marquardt method is used to optimize the parameter extraction. A comparison of simulation resuits with experimental data is made,and good agreements of I-V curves, Pout （output power）, PAE （power added efficiency） ,and gain at the bias of Vos = 20V, Ips = 80mA as well as the operational frequency of 1.8GHz are obtained.

EMPIRICAL LIKELIHOOD-BASED INFERENCE IN LINEAR MODELS WITH INTERVAL CENSORED DATA

An empirical likelihood approach to estimate the coefficients in linear model with interval censored responses is developed in this paper. By constructing unbiased transformation of interval censored data,an empirical log-likelihood function with asymptotic X^2 is derived. The confidence regions for the coefficients are constructed. Some simulation results indicate that the method performs better than the normal approximation method in term of coverage accuracies.

EMPIRICAL BAYES TEST PROBLEMS OF VARIANCE COMPONENTS IN RANDOM EFFECTS MODEL

Bayes decision rule of variance components for one-way random effects model is derived and empirical Bayes (EB) decision rules are constructed by kernel estimation method. Under suitable conditions, it is shown that the proposed EB decision rules are asymptotically optimal with convergence rates near O(n-1/2). Finally, an example concerning the main result is given.

EMPIRICAL LIKELIHOOD FOR LINEAR MODELS UNDER m-DEPENDENT ERRORS

In this paper,the empirical likelihood confidence regions for the regression coefficient in a linear model are constructed under m-dependent errors.It is shown that the blockwise empirical likelihood is a good way to deal with dependent samples.

3-D numerical modelling of Domino failure of hard rock pillars in Fetr6 Chromite Mine, Iran, and comparison with empirical methods

Fetr6 is an underground mine using the stope-and-pillar mining method. As there was some evidence regarding pillar failure in this mine, improving works such as roof support and replacing existing pillars with concrete pillars (CP) were carried out. During the construction of the second CP, in the space between the remaining pillars, one of the pillars failed leading to the progressive failure of other pillars until 4 000 m 2 of mine had collapsed within a few minutes. In this work, this phenomenon is described by applying both numerical and empirical methods and the respective results are compared. The results of numerical modelling are found to be closer to the actual condition than those of the empirical method. Also, a width-to-height (W/H) ratio less than 1, an inadequate support system and the absence of a detailed program for pillar recovery are shown to be the most important causes of the Domino failure in this mine.

Direct Nitrous Oxide Emissions Related to Fertilizer-Nitrogen, Precipitation, and Soil Clay Fraction: Empirical Models

Direct nitrous oxide(N2O) emissions(DNEs) from croplands are required in national inventories of greenhouse gases. The Intergovernmental Panel on Climate Change(IPCC) guidelines provide an approach using direct emission factors(EFds) to estimate DNEs, which are constants for large regions. The goal of this paper is to establish empirical models to account for the temporal and spatial variations of EFds, which, apart from the nitrogen addition rate, also vary with a range of environmental factors, so as to enhance the accuracy of regional/national DNE estimates. Therefore, the seasonal/annual DNEs(n = 71) from upland croplands, which are the differences in N2 O emissions between fields with and without fertilizer-nitrogen addition, were used to statistically relate DNEs to regulating factors including the fertilizer-nitrogen addition rate(FN), and environmental(climate and soil) factors. The multivariate stepwise linear regression results showed positive combined effects of FN and clay fraction on DNEs(R2 = 0.61, p < 0.001). Furthermore, the nonlinear regression of FN, precipitation, and clay fraction was also adopted for prediction(R2 = 0.50, p < 0.001). Validation with an independent dataset(n = 31) suggested that both models were better predictors of DNEs than the IPCC model, which only depends on FN. These empirical models may provide simple but reliable approaches for compiling regional/national, and even global inventories of DNEs from croplands. However, both models were restricted to a limited sample size. Understandably, more field observations are still required to further validate the global applicability of these simple approaches.

THE SUPERIORITY OF EMPIRICAL BAYES ESTIMATION OF PARAMETERS IN PARTITIONED NORMAL LINEAR MODEL

In this article,the empirical Bayes（EB）estimators are constructed for the estimable functions of the parameters in partitioned normal linear model.The superiorities of the EB estimators over ordinary least-squares（LS）estimator are investigated under mean square error matrix（MSEM）criterion.

Empirical Likelihood Inference for AR（p） Model

In this article we study the empirical likelihood inference for AR（p） model. We propose the moment restrictions, by which we get the empirical likelihood estimator of the model parametric, and we also propose an empirical log-likelihood ratio base on this estimator. Our result shows that the EL estimator is asymptotically normal, and the empirical log-likelihood ratio is proved to be asymptotically standard chi-squared.

Empirical modeling of normal/cyclo-alkanes pyrolysis to produce light olefins

Due to the complexity of feedstock,it is challenging to build a general model for light olefins production.This work was intended to simulate the formation of ethylene,propene and 1,3-butadiene in alkanes pyrolysis by referring the effects of normal/cyclo-structures.First,the pyrolysis of n-pentane,n-hexane,n-heptane,n-octane,n-nonane,n-decane,cyclohexane,methylcyclohexane,n-hexane and cyclohexane mixtures,and n-heptane and methylcyclohexane mixtures were carried out at 650–800℃,and a particular attention was paid to the measurement of ethylene,propene and 1,3-butadiene.Then,pseudo-first order kinetics was taken to characterize the pyrolysis process,and the effects of feedstock composition were studied.It was found that chain length and cyclo-alkane content can be qualitatively and quantitively represented by carbon atom number and pseudo-cyclohexane content,which made a significant difference on light olefins formation.Furthermore,the inverse proportional/quadratic function,linear function and exponential function were proposed to simulate the effects of chain length,cycloalkane content and reaction temperature on light olefins formation,respectively.Although the obtained empirical model well reproduced feedstock conversion,ethylene yield and propene yield in normal/cycloalkanes pyrolysis,it exhibited limitations in simulating 1,3-butadiene formation.Finally,the accuracy and flexibility of the present model was validated by predicting light olefins formation in the pyrolysis of multiple hydrocarbon mixtures.The prediction data well agreed with the experiment data for feedstock conversion,ethylene yield and propene yield,and overall characterized the changing trend of 1,3-butadiene yield along with reaction temperature,indicating that the present model could basically reflect light olefins production in the pyrolysis process even for complex feedstock.

“Refractivity-from-clutter” based on local empirical refractivity model

Constructing sophisticated refractivity models is one of the key problems for the RFC(refractivity from clutter)technology. If prior knowledge of the local refractivity environment is available, more accurate parameterized model can be constructed from the statistical information, which in turn can be used to improve the quality of the local refractivity retrievals. The validity of this proposal was demonstrated by range-dependent refractivity profile inversions using the adjoint parabolic equation method to the Wallops’ 98 experimental data.

Empirical correction of kinetic model for polymer thermal reaction process based on first order reaction kinetics

Based on the theory of first-order reaction kinetics,a thermal reaction kinetic model in integral form has been derive.To make the model more applicable,the effects of time and the conversion degree on the reaction rate parameters were considered.Two types of undetermined functions were used to compensate for the intrinsic variation of the reaction rate,and two types of correction methods are provided.The model was explained and verified using published experimental data of different polymer thermal reaction systems,and its effectiveness and wide adaptability were confirmed.For the given kinetic model,only one parameter needs to be determined.The proposed empirical model is expected to be used in the numerical simulation of polymer thermal reaction process.

Evaluation and Improvement of a SVD-Based Empirical Atmospheric Model

An empirical atmospheric model(EAM) based on the singular value decomposition(SVD) method is evaluated using the composite El Ni(?)o/Southern Oscillation(ENSO) patterns of sea surface temperature (SST) and wind anomalies as the target scenario.Two versions of the SVD-based EAM were presented for comparisons.The first version estimates the wind anomalies in response to SST variations based on modes that were calculated from a pair of global wind and SST fields(i.e.,conventional EAM or CEAM).The second version utilizes the same model design but is based on modes that were calculated in a region-wise manner by separating the tropical domain from the remaining extratropical regions(i.e.,region-wise EAM or REAM). Our study shows that,while CEAM has shown successful model performance over some tropical areas, such as the equatorial eastern Pacific(EEP),the western North Pacific(WNP),and the tropical Indian Ocean(TIO),its performance over the North Pacific(NP) seems poor.When REAM is used to estimate the wind anomalies instead of CEAM,a marked improvement over NP readily emerges.Analyses of coupled modes indicate that such an improvement can be attributed to a much stronger coupled variability captured by the first region-wise SVD mode at higher latitudes compared with that captured by the conventional one. The newly proposed way of constructing the EAM(i.e.,REAM) can be very useful in the coupled studies because it gives the model a wider application beyond the commonly accepted tropical domain.

EMPIRICAL BAYES ESTIMATION FOR ESTIMABLE FUNCTION OF REGRESSION COEFFICIENT IN A MULTIPLE LINEAR REGRESSION MODEL

In this paper we consider the empirical Bayes (EB) estimation problem for estimable function of regression coefficient in a multiple linear regression model Y=Xβ+e. where e with given β has a multivariate standard normal distribution. We get the EB estimators by using kernel estimation of multivariate density function and its first order partial derivatives. It is shown that the convergence rates of the EB estimators are under the condition where an integer k > 1 . is an arbitrary small number and m is the dimension of the vector Y.

Empirical likelihood for first-order mixed integer-valued autoregressive model

In this paper, we not only construct the confidence region for parameters in a mixed integer-valued autoregressive process using the empirical likelihood method, but also establish the empirical log-likelihood ratio statistic and obtain its limiting distribution. And then, via simulation studies we give coverage probabilities for the parameters of interest. The results show that the empirical likelihood method performs very well.

Statistical Diagnostic for Varying-Coefficient Single-Index Models Based on Empirical Likelihood Method

Varying-coefficient single-index model( VCSIM) avoids the so-called "curse of dimensionality " and is flexible enough to include several important statistical models. This paper considers statistical diagnosis for VCSIM. First,the parametric estimation equation is established based on empirical likelihood. Then,some diagnosis statistics are defined. At last, an example is given to illustrate all the results.

Inference Based on Empirical Likelihood for Varying Coefficient Model with Random Effect

In this article, we develop a statistical inference technique for the unknown coefficient functions in the varying coeffi- cient model with random effect. A residual-adjusted block empirical likelihood (RABEL) method is suggested to inves- tigate the model by taking the within-subject correlation into account. Due to the residual adjustment, the proposed RABEL is asymptotically chi-squared distribution. We illustrate the large sample performance of the proposed method via Monte Carlo simulations and a real data application.

Vehicle-Bridge Interaction Simulation and Damage Identification of a Bridge Using Responses Measured in a Passing Vehicle by Empirical Mode Decomposition Method

To prevent early bridge failures, effective Structural Health Monitoring (SHM) is vital. Vibration-based damage assessment is a powerful tool in this regard, as it relies on changes in a structure’s dynamic characteristics as it degrades. By measuring the vibration response of a bridge due to passing vehicles, this approach can identify potential structural damage. This dissertation introduces a novel technique grounded in Vehicle-Bridge Interaction (VBI) to evaluate bridge health. It aims to detect damage by analyzing the response of passing vehicles, taking into account VBI. The theoretical foundation of this method begins with representing the bridge’s superstructure using a Finite Element Model and employing a half-car dynamic model to simulate the vehicle with suspension. Two sets of motion equations, one for the bridge and one for the vehicle are generated using the Finite Element Method, mode superposition, and D’Alembert’s principle. The combined dynamics are solved using the Newmark-beta method, accounting for road surface roughness. A new approach for damage identification based on the response of passing vehicles is proposed. The response is theoretically composed of vehicle frequency, bridge natural frequency, and a pseudo-frequency component related to vehicle speed. The Empirical Mode Decomposition (EMD) method is applied to decompose the signal into its constituent parts, and damage detection relies on the Intrinsic Mode Functions (IMFs) corresponding to the vehicle speed component. This technique effectively identifies various damage scenarios considered in the study.