Empirical Models for the Evaluation of Global Solar Radiation for the Site of Abeche in the Province of Ouaddaï, in Chad

The global sustainability plan for future development relies on solar radiation which is the main source of renewable energy. Thus, this work studies the performance of six models to estimate global solar radiation on a horizontal surface for the Abeche site in Chad. The data used in this work were collected at the General Directorate of National Meteorology of Chad. The reliability and accuracy of different models for estimating global solar radiation were validated by statistical indicators to identify the most accurate model. The results show that among all the models, the Sabbagh model has the best performance in estimating the global solar radiation. The average is 6.354 kWh/m2 with an average of -3.704%. This model is validated against NASA data which is widely used.

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.

Application of New Empirical Models Based on Mathematical Statistics in the Through-Flow Analysis

The through-flow analysis is an important part in the compressor design process.In this part,lots of empirical models are used to predict the compressor aerodynamic performances.These models are all based on the early experimental results of low-load and low-speed compressors;so,they may not be suitable for modern compressor performance estimations.In this study,several empirical models were reviewed,and two new models to estimate the minimum blade profile loss and minimum-loss deviation angle were established using mathematical statistics.Then,the original models with poor accuracy were replaced by these two models in through-flow program.Next,three compressors(Rotor 67,Stage 35,and a 4-stage repeating stage)were simulated using both the original and new models.The final results show that the new models have better accuracy in estimating the performance parameters than the original models.This indicates that it is feasible to use mathematical statistical methods to establish the empirical models,and this method provides an idea for the improvement of other empirical models in through-flow program.

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.

Simulation and Analysis of the Effects of Pressure and Temperature on the Output Voltage of Proton Exchange Membrane Fuel Cells

Proton exchange membrane fuel cell has advantages of high energy conversion efficiency, high reliability, no pollution, low operating temperature and rapid start-up. It has become an ideal method of hydrogen energy utilization and is also ideally suited to be used as the main source of energy for automobiles. Currently, it constitutes a research hot spot in the field of new energy vehicles. Based on the working mechanism of proton exchange membrane fuel cells and empirical models, a terminal voltage dynamic model, an open circuit voltage model and three voltage loss models are established. Matlab/Simulink software is utilized to simulate the model and perform analyses in response to the impact of operating temperature and pressure on its performance. To enhance the efficiency of the proton exchange membrane fuel cell, the operating temperature should be increased in the medium and low current density zones and the operating pressure should be increased in the high current density zone.

A review of stand basal area growth models

Growth and yield modeling has a long history in forestry. The methods of measuring the growth of stand basal area have evolved from those developed in the U.S.A. and Germany during the last century. Stand basal area modeling has progressed rapidly since the first widely used model was published by the U.S. Forest Service. Over the years, a variety of models have been developed for predicting the growth and yield of uneven/even-aged stands using stand-level approaches. The modeling methodology has not only moved from an empirical approach to a more ecological process-based approach but also accommodated a variety of techniques such as： 1） simultaneous equation methods, 2） difference models, 3） artificial neural network techniques, 4） linear/nonlinear regression models, and 5） matrix models. Empirical models using statistical methods were developed to reproduce accurately and precisely field observations. In contrast, process models have a shorter history, developed originally as research and education tools with the aim of increasing the understanding of cause and effect relationships. Empirical and process models can be married into hybrid models in which the shortcomings of both component approaches can, to some extent, be overcome. Algebraic difference forms of stand basal area models which consist of stand age, stand density and site quality can fully describe stand growth dynamics. This paper reviews the current literature regarding stand basal area models, discusses the basic types of models and their merits and outlines recent progress in modeling growth and dynamics of stand basal area. Future trends involving algebraic difference forms, good fitting variables and model types into stand basal area modeling strategies are discussed.

Evolution and Development of the Information Concept in Biological Systems: From Empirical Description to Informational Modeling of the Living Structures

With the purpose to smooth the way of a correct understanding of information concepts and their evolution,in this paper,is discussed the evolution and development of the concept of information in biological systems,showing that this concept was intuitively perceived even since ancient times by our predecessors,and described according to their language level of that times,but the crystallization of the real meaning of information is an achievement of our nowadays,by successive contribution of various scientific branches and personalities of the scientific community of the world,leading to a modern description/modeling of reality,in which information plays a fundamental role.It is shown that our reality can be understood as a contribution of matter/energy/information and represented/discussed as the model of the Universal Triangle of Reality(UTR),where various previous models can be suggestively inserted,as a function of their basic concern.The modern concepts on information starting from a theoretic experiment which would infringe the thermodynamics laws and reaching the theory of information and modern philosophic concepts on the world structuration allow us to show that information is a fundamental component of the material world and of the biological structures,in correlation with the structuration/destructuration processes of matter,involving absorption/release of information.Based on these concepts,is discussed the functionality of the biologic structures and is presented the informational model of the human body and living structures,as a general model of info-organization on the entire biological scale,showing that a rudimentary proto-consciousness should be operative even at the low-scale biological systems,because they work on the same principles,like the most developed bio-systems.The operability of biologic structures as informational devices is also pointed out.

An accurate empirical correlation for predicting natural gas viscosity

Natural gas viscosity is an important parameter in many gas and petroleum engineering calculations.This study presents a new empirical model for quickly calculating the natural gas viscosity.The model was derived from 4089 experimental viscosity data with varieties ranging from 0.01 to 21,and 1 to 3 of pseudo reduced pressure and temperature,respectively.The accuracy of this new empirical correlation has been compared with commonly used empirical models,including Lee et al.,Heidaryan et al.,Carr et al.,and Adel Elsharkawy correlations.The comparison indicates that this new empirical model can predict viscosity of natural gas with average absolute relative deviation percentage AARD （%） of 2.173.

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.

An accurate empirical correlation for predicting natural gas compressibility factors

The compressibility factor of natural gas is an important parameter in many gas and petroleum engineering calculations. This study presents a new empirical model for quick calculation of natural gas compressibility factors. The model was derived from 5844 experimental data of compressibility factors for a range of pseudo reduced pressures from 0.01 to 15 and pseudo reduced temperatures from 1 to 3. The accuracy of the new empirical correlation has been compared with commonly used existing methods. The comparison indicates the superiority of the new empirical model over the other methods used to calculate compressibility factor of natural gas with average absolute relative deviation percent （AARD%） of 0.6535.

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.

Improvement of the prediction accuracy of polar motion using empirical mode decomposition

Previous studies revealed that the error of pole coordinate prediction will significantly increase for a prediction period longer than 100 days, and this is mainly caused by short period oscillations. Empirical mode decomposition （EMD）, which is increasingly popular and has advantages over classical wavelet decomposition, can be used to remove short period variations from observed time series of pole co- ordinates. A hybrid model combing EMD and extreme learning machine （ELM）, where high frequency signals are removed and processed time series is then modeled and predicted, is summarized in this paper. The prediction performance of the hybrid model is compared with that of the ELM-only method created from original time series. The results show that the proposed hybrid model outperforms the pure ELM method for both short-term and long-term prediction of pole coordinates. The improvement of prediction accuracy up to 360 days in the future is found to be 24.91% and 26.79% on average in terms of mean absolute error （MAE） for the xp and yp components of pole coordinates, respectively.

Prediction of salinity intrusion in the sheltered estuary of Terengganu River in Malaysia using 1-D empirical intrusion model

Generally one dimensional （l-D） empirical salinity intrusion model is limited to natural alluvial estuary. However, this study attempts to investigate its ability to model a sheltered alluvial estuary of the Terengganu River in Malaysia. The constructed breakwater at the mouth of the river shelters the estuary from direct influence of the open sea. The salinity density along the estuary was collected during the wet and dry seasons for scenarios before and after the constructed breakwater. Moreover, the freshwater discharges, tidal elevations and bathymetry data were also measured as model inputs. A good fit was demonstrated between simulated and observed variables, namely salinity distribution and intrusion length for both scenarios. Thus, the results show that 1-D empirical salinity model can be utilized for sheltered estuarine condition at the Terengganu Estuary, but with an appropriate determination of an initial point. Furthermore, it was observed that the salinity intrusion in the study area is largely dependent on the freshwater discharge rather than tidal elevation fluctuations. The scale of the salinity intrusion length in the study area is proportional to the river discharge of the -1/2 power. It was appeared that the two lines of the 1-D empirical salinity model and discharge power based equation fitted well to each other, with the average predicted minimum freshwater discharge of 150 m^3/s is going to be required to maintain acceptable salinity levels during high water slack （HWS） near the water intake station, which is located at 10.63 km from river mouth.

Statistical prediction of waterflooding performance by K-means clustering and empirical modeling

Statistical prediction is often required in reservoir simulation to quantify production uncertainty or assess potential risks.Most existing uncertainty quantification procedures aim to decompose the input random field to independent random variables,and may suffer from the curse of dimensionality if the correlation scale is small compared to the domain size.In this work,we develop and test a new approach,K-means clustering assisted empirical modeling,for efficiently estimating waterflooding performance for multiple geological realizations.This method performs single-phase flow simulations in a large number of realizations,and uses K-means clustering to select only a few representatives,on which the two-phase flow simulations are implemented.The empirical models are then adopted to describe the relation between the single-phase solutions and the two-phase solutions using these representatives.Finally,the two-phase solutions in all realizations can be predicted using the empirical models readily.The method is applied to both 2D and 3D synthetic models and is shown to perform well in the P10,P50 and P90 of production rates,as well as the probability distributions as illustrated by cumulative density functions.It is able to capture the ensemble statistics of the Monte Carlo simulation results with a large number of realizations,and the computational cost is significantly reduced.

An Empirical Model for Estimating Stratospheric Ozone Vertical Distributions over China

Based on the Stratospheric Aerosol and Gas Experiment （SAGE） Ⅱ and the Halogen Occultation Experiment （HALOE） ozone profiles and the Total Ozone Mapping Spectrometer （TOMS） total ozone data sets, an empirical model for estimating the vertical distribution of stratospheric ozone over China is proposed. By using this model, the vertical distribution of stratospheric （16-50 km） ozone can be estimated according to latitude, month and total ozone. Comparisons are made between the modeled ozone profiles and the SAGEII/HALOE monthly mean ozone measurements, and the results show that the model calculated ozone concentrations conform well with the SAGEII/HALOE measured values, with the differences being less than 15% between 16 km and 18 km, less than 5% between 19 km and 40 km, and less than 10% between 41 km and 50 kin. Comparisons of the model results with balloon-borne ozonesonde measurements performed in Beijing also show good agreement, within 5%, at altitudes between 19 km and 30 km.

“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.

Pyrolysis Empirical Modeling of Polyester Glass Fiber Reinforced Plastics Using Sestak-Berggren Model Method

Polyester Glass Fiber Reinforced Plastic(Polyester GFRP),a thermosetting plastic comprised of glass fiber and polyester polymer compounds,is extensively utilized in high-speed trains.Unraveling its pyrolysis mechanism is crucial as it significantly influences the combustion characteristics and fire safety aspects.Currently,kinetic research on polyester GFRP primarily focuses on employing the Coats-Redfern method to derive a theoretical kinetic model.However,the pyrolysis process of polyester GFRP is complex and the aforementioned theoretical model fails to accurately describe the pyrolysis mechanism.Therefore,this study seeks to utilize the Sestak and Berggren(SB) model as a methodological approach to reveal the complex reaction mechanism during the pyrolysis process.Based on thermogravimetric analysis,the entire pyrolysis process of polyester GFRP is divided into two primary stages.Furthermore,model-free methods are employed to ascertain the activation energy and pre-exponential factor.The results show that the fitted empirical models of the two main pyrolysis stages are f(α)=(1-α)^(1.47)[-ln(1-α)]^(1.50) and f(α)=(1-α)^(1.77)[-ln(1-α)]^(1.72),respectively.The predicted results are in good agreement with experimental data under different heating rates,which indicates that the empirical model can sufficiently describe the pyrolysis process of polyester GFRP.

Unloading-induced permeability recovery in rock fractures

Underground space creation and energy extraction, which induce unloading on rock fractures, commonly occur in various rock engineering projects, and rock engineering projects are subjected to high temperatures with increasing depth. Fluid flow behavior of rock fractures is a critical issue in many subsurface rock engineering projects. Previous studies have extensively considered permeability evolution in rock fractures under loading phase, whereas changes in fracture permeability under unloading phase have not been fully understood. To examine the unloading-induced changes in fracture permeability under different temperatures, we performed water flow-through tests on fractured rock samples subjected to decreasing confining pressures and different temperatures. The experimental results show that the permeability of fracture increases with unloading of confining pressure but decreases with loading-unloading cycles. Temperature may affect fracture permeability when it is higher than a certain threshold. An empirical model of fracture hydraulic aperture including two material parameters of initial normal stiffness and maximum normal closure can well describe the permeability changes in rough rock fracture subjected to loading-unloading cycles and heating. A coupled thermo-mechanical model considering asperity damage is finally used to understand the influences of stress paths and temperatures on fracture permeability.

An empirical model for high energy density lithium-(ion)batteries with ultra-thick electrodes

Increasing the electrode thickness is a significant method to decrease the weight and volume ratio of the inactive components for high energy density of the devices.In this contribution,we extracted a repeating unit in the configurations and establish the empirical energy density model based on some assumptions.In this model,the effects of the electrode thickness on the energy density for lithium-ion batteries(LIBs),lithium metal batteries(LMBs),and anode-free lithium batteries(ALBs)are evaluated quantitively with the current parameters of the batteries.The results demonstrate that the structure evolutions from LIBs,LMBs to ALBs with the reduction of the anode weight contribution,the energy density can be well improved exactly.While the increase of the thickness of the electrode provide another route to furthe r enhance the energydensity by decreasing the weight contribution of inactive materials;meanwhile the effects for ALBs are higher than LMBs and LIBs due to the higher weight ratio of inactive materials.This empirical energy density model is also applied into the practical system and provide intuitional results to guide the battery design for higher energy density.

Dew measurement and estimation of rain-fed jujube (Zizyphus jujube Mill) in a semi-arid loess hilly region of China

Dew is an important water source for plants in arid and semi-arid regions. However, information on dew is scarce in such regions. In this study, we explored dew formation, amount, and duration of rain-fed jujube（Zizyphus jujube Mill） trees in a semi-arid loess hilly region of China（i.e., Mizhi County）. The data included dew intensity and duration, relative humidity, temperature, and wind speed measured from 26 July to 23 October, 2012 and from 24 June to 17 October, 2013 using a micro-climate system（including dielectric leaf wetness sensors, VP-3 Relative Humidity/Temperature Sensor, High Resolution Rain Gauge, and Davis Cup Anemometer）. The results show that atmospheric conditions of relative humidity of 〉78% and dew point temperature of 1°C–3°C are significantly favorable to dew formation. Compared with the rainfall, dew was characterized by high frequency, strong stability, and long duration. Furthermore, heavy dew accounted for a large proportion of the total amount. The empirical models（i.e., relative humidity model（RH model） and dew point depression model（DPD model）） for daily dew duration estimation performed well at 15-min intervals, with low errors ranging between 1.29 and 1.60 h, respectively. But it should be noted that the models should be calibrated firstly by determining the optimal thresholds of relatively humidity for RH model and dew point depression for DPD model. For rain-fed jujube trees in the semi-arid loess hilly regions of China, the optimal threshold of relative humidity was 78%, and the optimal upper and lower thresholds of dew point depression were 1°C and 5°C, respectively. The study further demonstrates that dew is an important water resource that cannot be ignored for rain-fed jujube trees and may affect water balance at regional scales.