Reservoir Stochastic Modeling Constrained by Quantitative Geological Conceptual Patterns

This paper discusses the principles of geologic constraints on reservoir stochastic modeling. By using the system science theory, two kinds of uncertainties, including random uncertainty and fuzzy uncertainty, are recognized. In order to improve the precision of stochastic modeling and reduce the uncertainty in realization, the fuzzy uncertainty should be stressed, and the ＂geological genesis-controlled modeling＂ is conducted under the guidance of a quantitative geological pattern. An example of the Pingqiao horizontal-well division of the Ansai Oilfield in the Ordos Basin is taken to expound the method of stochastic modeling.

3D Stochastic Modeling of Grain Structure for Aluminum Alloy Casting

A 3D stochastic modeling was carried out to simulate the dendritic grains during solidification of aluminum alloys, including time-dependent calculations for temperature field, solute redistribution in liquid, curvature of the dendritic tip, and growth anisotropy. The nucleation process was treated by continuous nucleation. A 3D simplified grain shape model was established to represent the equiaxed dendritic grain. Based on the Cellular Automaton method, a grain growth model was proposed to capture the neighbor cells of the nucleated cell. During growing, each grain continues to capture the nearest neighbor cells to form the final shape. When a neighbor cell was captured by other grains, the grain growth along this direction would be stopped. Three-dimensional calculations were performed to simulate the evolution of dendritic grain. In order to verify the modeling results, the predictions were compared with the observation on samples cast in the sand mold and the metal mold.

Stochastic modeling for starting-time of phase evolution of random seismic ground motions

In response to the challenge inherent in classical high-dimensional models of random ground motions, a family of simulation methods for nonstationary seismic ground motions was developed previously through employing a wave-group propagation formulation with phase spectrum model built up on the frequency components’ starting-time of phase evolution. The present paper aims at extending the formulation to the simulation of non-stationary random seismic ground motions. The ground motion records associated with N–S component of Northridge Earthquake at the type-II site are investigated. The frequency components’ starting-time of phase evolution of is identified from the ground motion records, and is proved to admit the Gamma distribution through data fitting. Numerical results indicate that the simulated random ground motion features zeromean, non-stationary, and non-Gaussian behaviors, and the phase spectrum model with only a few starting-times of phase evolution could come up with a sound contribution to the simulation.

Stochastic Modeling of Total Ground Irradiance of Horizontal Surface

This paper describes relatively simple stochastic model of the total ground irradiance of horizontal surface. For this purpose clearness index is modeled as a stochastic signal. The parameters of clearness index stochastic signal are chosen to fit values of daily mean insolation for each month for the location of Zagreb, Croatia. Complete model has been done in MATLAB. This model can be used for Monte Carlo simulations of technical solar systems such as photovoltaic systems or solar thermal energy systems.

Theoretical Study on Stochastic Modeling of Combined Gravity-Magnetic-Electric-Seismic Inversion and Its Application

As gravity field, magnetic field, electric field and seismic wave field are all physical fields, their object function, reverse function and compound function are certainly infinite continuously differentiable functions which can be expanded into Taylor (Fourier) series within domain of definition and be further reduced into solving stochastic distribution function of series and statistic inference of optimal approximation. This is the basis of combined gravity-magnetic-electric-seismic inversion of stochastic modeling. It is an uncertainty modeling technology of combining gravity-magnetic-electric-seismic inversion built on the basis of separation of field and source gravity-magnetic difference-value (D-value) trend surface, taking distribution-independent fault system as its unit, depths of seismic and electric interfaces of interests as its corresponding bivariate compound reverse function of gravity-magnetic anomalies and using high order polynomial (high order trigonometric function) approximating to its series distribution. The difference from current dominant inversion techniques is that, first, it does not respectively create gravity-seismic, magnetic-seismic deterministic inversion model from theoretical model, but combines gravity-magnetic-electric-seismic stochastic inversion model from stochastic model; second, after the concept of equivalent geological body being introduced, using feature of independent variable of gravity-magnetic field functions, taking density and susceptibility related to gravity-magnetic function as default parameters of model, the deterministic model is established owing to better solution to the contradiction of difficulty in identifying strata and less test analytical data for density and susceptibility in newly explored area; third, under assumption of independent parent distribution, a real modeling by strata, the problem of difficult plane closure arising in profile modeling is avoided. This technology has richer and more detailed fault and strata information than sparse pattern seismic data in newly explored area, successfully inverses and plots structural map of Indosinian discontinuity in Hefei basin with combined gravity-magnetic-electric-seismic inversion. With development of high precision gravity-magnetic and overall geophysical technology, it is certain for introducing new methods of stochastic modeling and computational intelligence and promoting the development of combined gravity-magnetic-electric-seismic inversion to open a new substantial path.

Stochastic Modeling for Coliform Count Assessment in Ground Water

Stochastic models are derived to estimate the level of coliform count in terms of MPN index, one of the most important water quality characteristic in ground water based on a set of water source location and soil characteristics. The study is based on about twenty location and soil characteristics, majority of them are observed through laboratory analysis of soil and water samples collected from nearly thee hundred locations of drinking water sources, wells and bore wells selected at random from the district of Kasaragod. The water contamination in wells are found to be relatively more as compared to bore wells. The study reveals that only 7 % of the wells and 40 o~ of the bore wells of the district are within the permissible limit of WHO standard of drinking water quality. The level of contamination is very high in the hospital premises and is very low in the forest area. Two separate multiple ordinal logistic regression models are developed to predict the level of coliform count, one for well and the other for bore well. The significant feature of this study is that in addition to scientifically proving the dependence of the water quality on the distances from waste disposal area and septic tanks etc., it highlights the dependence of two other very significant soil characteristics, the soil organic carbon and soil porosity. The models enable to predict the quality of water in a location based on the set of soil and location characteristics. One of the important uses of the model is in fixing safe locations for waste dump area, septic tank, digging well etc. in town planning, designing residential layouts, industrial layouts, hospital/hostel construction etc. This is the first ever study to describe the ground water quality in terms of the location and soil characteristics.

Stochastic modeling and analysis of hepatitis and tuberculosis co-infection dynamics

Several mathematical models have been developed to investigate the dynamics of tuberculosis(TB)and hepatitis B virus(HBV).Numerous current models for TB,HBV,and their co-dynamics fall short in capturing the important and practical aspect of unpredictability.It is crucial to take into account a stochastic co-infection HBV–TB epidemic model since different random elements have a substantial impact on the overall dynamics of these diseases.We provide a novel stochastic co-model for TB and HBV in this study,and we establish criteria on the uniqueness and existence of a nonnegative global solution.We also looked at the persistence of the infections as long its dynamics are governable by the proposed model.To verify the theoretical conclusions,numerical simulations are presented keeping in view the associated analytical results.The infections are found to finally die out and go extinct with certainty when L´evy intensities surpass the specified thresholds and the related stochastic thresholds fall below unity.The findings also demonstrate the impact of noise on the decline in the co-circulation of HBV and TB in a given population.Our results provide insights into effective intervention strategies,ultimately aiming to improve the management and control of TB and HBV co-infections.

A modified stochastic model for LS+AR hybrid method and its application in polar motion short-term prediction

Short-term(up to 30 days)predictions of Earth Rotation Parameters(ERPs)such as Polar Motion(PM:PMX and PMY)play an essential role in real-time applications related to high-precision reference frame conversion.Currently,least squares(LS)+auto-regressive(AR)hybrid method is one of the main techniques of PM prediction.Besides,the weighted LS+AR hybrid method performs well for PM short-term prediction.However,the corresponding covariance information of LS fitting residuals deserves further exploration in the AR model.In this study,we have derived a modified stochastic model for the LS+AR hybrid method,namely the weighted LS+weighted AR hybrid method.By using the PM data products of IERS EOP 14 C04,the numerical results indicate that for PM short-term forecasting,the proposed weighted LS+weighted AR hybrid method shows an advantage over both the LS+AR hybrid method and the weighted LS+AR hybrid method.Compared to the mean absolute errors(MAEs)of PMX/PMY sho rt-term prediction of the LS+AR hybrid method and the weighted LS+AR hybrid method,the weighted LS+weighted AR hybrid method shows average improvements of 6.61%/12.08%and 0.24%/11.65%,respectively.Besides,for the slopes of the linear regression lines fitted to the errors of each method,the growth of the prediction error of the proposed method is slower than that of the other two methods.

A Stochastic Model to Assess the Epidemiological Impact of Vaccine Booster Doses on COVID-19 and Viral Hepatitis B Co-Dynamics with Real Data

A patient co-infected with COVID-19 and viral hepatitis B can be atmore risk of severe complications than the one infected with a single infection.This study develops a comprehensive stochastic model to assess the epidemiological impact of vaccine booster doses on the co-dynamics of viral hepatitis B and COVID-19.The model is fitted to real COVID-19 data from Pakistan.The proposed model incorporates logistic growth and saturated incidence functions.Rigorous analyses using the tools of stochastic calculus,are performed to study appropriate conditions for the existence of unique global solutions,stationary distribution in the sense of ergodicity and disease extinction.The stochastic threshold estimated from the data fitting is given by:R_(0)^(S)=3.0651.Numerical assessments are implemented to illustrate the impact of double-dose vaccination and saturated incidence functions on the dynamics of both diseases.The effects of stochastic white noise intensities are also highlighted.

Analytical and NumericalMethods to Study the MFPT and SR of a Stochastic Tumor-Immune Model

The Mean First-Passage Time (MFPT) and Stochastic Resonance (SR) of a stochastic tumor-immune model withnoise perturbation are discussed in this paper. Firstly, considering environmental perturbation, Gaussian whitenoise and Gaussian colored noise are introduced into a tumor growth model under immune surveillance. Asfollows, the long-time evolution of the tumor characterized by the Stationary Probability Density (SPD) and MFPTis obtained in theory on the basis of the Approximated Fokker-Planck Equation (AFPE). Herein the recurrenceof the tumor from the extinction state to the tumor-present state is more concerned in this paper. A moreefficient algorithmof Back-Propagation Neural Network (BPNN) is utilized in order to testify the correction of thetheoretical SPDandMFPT.With the existence of aweak signal, the functional relationship between Signal-to-NoiseRatio (SNR), noise intensities and correlation time is also studied. Numerical results show that both multiplicativeGaussian colored noise and additive Gaussian white noise can promote the extinction of the tumors, and themultiplicative Gaussian colored noise can lead to the resonance-like peak on MFPT curves, while the increasingintensity of the additiveGaussian white noise results in theminimum of MFPT. In addition, the correlation timesare negatively correlated with MFPT. As for the SNR, we find the intensities of both the Gaussian white noise andthe Gaussian colored noise, as well as their correlation intensity can induce SR. Especially, SNR is monotonouslyincreased in the case ofGaussian white noisewith the change of the correlation time.At last, the optimal parametersin BPNN structure are analyzed for MFPT from three aspects: the penalty factors, the number of neural networklayers and the number of nodes in each layer.

Numerical Analysis of Bacterial Meningitis Stochastic Delayed Epidemic Model through Computational Methods

Based on theWorld Health Organization(WHO),Meningitis is a severe infection of the meninges,the membranes covering the brain and spinal cord.It is a devastating disease and remains a significant public health challenge.This study investigates a bacterial meningitis model through deterministic and stochastic versions.Four-compartment population dynamics explain the concept,particularly the susceptible population,carrier,infected,and recovered.The model predicts the nonnegative equilibrium points and reproduction number,i.e.,the Meningitis-Free Equilibrium(MFE),and Meningitis-Existing Equilibrium(MEE).For the stochastic version of the existing deterministicmodel,the twomethodologies studied are transition probabilities and non-parametric perturbations.Also,positivity,boundedness,extinction,and disease persistence are studiedrigorouslywiththe helpofwell-known theorems.Standard and nonstandard techniques such as EulerMaruyama,stochastic Euler,stochastic Runge Kutta,and stochastic nonstandard finite difference in the sense of delay have been presented for computational analysis of the stochastic model.Unfortunately,standard methods fail to restore the biological properties of the model,so the stochastic nonstandard finite difference approximation is offered as an efficient,low-cost,and independent of time step size.In addition,the convergence,local,and global stability around the equilibria of the nonstandard computational method is studied by assuming the perturbation effect is zero.The simulations and comparison of the methods are presented to support the theoretical results and for the best visualization of results.

Stochastic Simulation of Saline Intrusion in the Coastal Aquifer of Saloum, Senegal

In the Saloum region of central-western Senegal, water needs are essentially met by tapping an underground aquifer associated with the sandy-clay formations of the Continental Terminal, in contact with both the ocean to the west and the highly saline waters of the Saloum River to the north. In this estuarine and deltaic zone with its very low relief, the hydraulic loads in the water tables are generally close to zero or even negative, creating a reversal of the natural flow and encouraging saline intrusion into this system, which makes it very vulnerable. This study concerns the implementation of a numerical model of saline intrusion to provide a better understanding of the vulnerability of the water table by analyzing the variability of the freshwater/saltwater interface. The Modflow-2005 code is used to simulate saline intrusion using the SWI2 module, coupled with the GRASS (Geographic Resources Analysis Support System) software under the Linux operating system with the steep interface approach. The probable expansion of the wedge is studied in three scenarios, taking into account its position relative to the bedrock at 1 m, 5 m and 10 m. Simulations carried out under imposed potential and river conditions, based on variations in groundwater reserves using two effective porosity values, 10−1 and 10−2, show that the water table is highly vulnerable in the northwest sector. The probable expansion of the wedge increases as the storage coefficient decreases and is more marked with river conditions in the areas surrounding the Saloum River, reaching 6 km with a probability of 1. The probability of the wedge reaching a certain degree of expansion decreases from 1 to 0.5, and then cancels out as it moves inland. The probable position of the wedge is limited to 500 m or even 1 km depending on the corner around the coast to the southwest and in the southern zone. This modelling, carried out under natural conditions, will be developed further, taking into account climatic parameters and pumping from wells and boreholes.

Improvements of corner frequency and scaling factor for stochastic finite-fault modeling

In this paper, three existing source spectral models for stochastic finite-fault modeling of ground motion were reviewed. These three models were used to calculate the far-field received energy at a site from a vertical fault and the mean spectral ratio over 15 stations of the Northridge earthquake, and then compared. From the comparison, a necessary measure was observed to maintain the far-field received energy independent of subfault size and avoid overestimation of the long- period spectra/level. Two improvements were made to one of the three models （i.e., the model based on dynamic comer frequency） as follows： （i） a new method to compute the subfault comer frequency was proposed, where the subfault comer frequency is determined based on a basic value calculated from the total seismic moment of the entire fault and an increment depending on the seismic moment assigned to the subfault; and （ii） the difference of the radiation energy from each suhfault was considered into the scaling factor. The improved model was also compared with the unimproved model through the far-field received energy and the mean spectral ratio. The comparison proves that the improved model allows the received energy to be more independent of subfault size than the unimproved model, and decreases the overestimation degree of the long-period spectral amplitude.

Stochastic and upscaled analytical modeling of fines migration in porous media induced by low-salinity water injection

Fines migration induced by injection of low-salinity water(LSW) into porous media can lead to severe pore plugging and consequent permeability reduction. The deepbed filtration(DBF) theory is used to model the aforementioned phenomenon, which allows us to predict the effluent concentration history and the distribution profile of entrapped particles. However, the previous models fail to consider the movement of the waterflood front. In this study, we derive a stochastic model for fines migration during LSW flooding, in which the Rankine-Hugoniot condition is used to calculate the concentration of detached particles behind and ahead of the moving water front. A downscaling procedure is developed to determine the evolution of pore-size distribution from the exact solution of a large-scale equation system. To validate the proposed model,the obtained exact solutions are used to treat the laboratory data of LSW flooding in artificial soil-packed columns. The tuning results show that the proposed model yields a considerably higher value of the coefficient of determination, compared with the previous models, indicating that the new model can successfully capture the effect of the moving water front on fines migration and precisely match the effluent history of the detached particles.

Biomechanical risk factors of non-contact ACL injuries:A stochastic biomechanical modeling study

Significant efforts have been made to identify modifiable risk factors of non-contact anterior cruciate ligament(ACL)injuries in male and female athletes.However,current literature on the risk factors for ACL injury are purely descriptive.An understanding of biomechanical relationship between risk and risk factors of the non-contact ACL injury is necessary to develop effective prevention programs.Purpose:To compare lower extremity kinematics and kinetics between trials with and without non-contact ACL injuries and to determine if any difference exists between male and female trials with non-contact ACL injuries regarding the lower extremity motion patterns.Methods:In this computer simulation study,a stochastic biomechanical model was used to estimate the ACL loading at the time of peak posterior ground reaction force(GRF)during landing of the stop-jump task.Monte Carlo simulations were performed to simulate the ACL injuries with repeated random samples of independent variables.The distributions of independent variables were determined from in vivo laboratory data of 40 male and 40 female recreational athletes.Results:In the simulated injured trials,both male and female athletes had significantly smaller knee flexion angles,greater normalized peak posterior and vertical GRF,greater knee valgus moment,greater patella tendon force,greater quadriceps force,greater knee extension moment,and greater proximal tibia anterior shear force in comparison to the simulated uninjured trials.No significant difference was found between genders in any of the selected biomechanical variables in the trials with simulated non-contact ACL injuries.Conclusion:Small knee flexion angle,large posterior GRF,and large knee valgus moment are risk factors of non-contact ACL injury determined by a stochastic biomechanical model with a cause-and-effect relationship.Copyright(c)2012,Shanghai University of Sport.Production and hosting by Elsevier B.V.All rights reserved.

STOCHASTIC OBJECT-ORIENTED PETRI NETS (SOPNS) AND ITS APPLICATION IN MODELING OF MANUFACTURING SYSTEM RELIABILITY

Object-oriented Petri nets (OPNs) is extended into stochastic object-oriented Petri nets (SOPNs) by associating the OPN of an object with stochastic transitions and introducing stochastic places. The stochastic transition of the SOPNs of a production resources can be used to model its reliability, while the SOPN of a production resource can describe its performance with reliability considered. The SOPN model of a case production system is built to illustrate the relationship between the system's performances and the failures of individual production resources.

Stochastic Dynamic Modeling of Rain Attenuation: A Survey

Satellite communication systems(SCS) operating on frequency bands above 10 GHz are sensitive to atmosphere physical phenomena, especially rain attenuation. To evaluate impairments in satellite performance, stochastic dynamic modeling(SDM) is considered as an effective way to predict real-time satellite channel fading caused by rain. This article carries out a survey of SDM using stochastic differential equations(SDEs) currently in the literature. Special attention is given to the different input characteristics of each model to satisfy specific local conditions. Future research directions in SDM are also suggested in this paper.

Modeling the dynamic optimal advertising in stochastic condition

An effort to model the dynamic optimal advertising was made with the uncertainty of sales responses in consideration. The problem of dynamic advertising was depicted as a Markov decision process with two state variables. When a firm launches an advertising campaign, it may predict the probability that the campaign will obtain the sales réponse. This probability was chosen as one state variable. Cumulative sales volume was chosen as another state variable which varies randomly with advertising. The only decision variable was advertising expenditure. With these variables, a multi-stage Markov decision process model was formulat ed. On the basis of some propositions the model was analyzed. Some analytical results about the optimal strategy have been derived, and their practical implications have been explained.

Optimal Quota-Share and Excess-of-Loss Reinsurance and Investment with Heston’s Stochastic Volatility Model

An optimal quota-share and excess-of-loss reinsurance and investment problem is studied for an insurer who is allowed to invest in a risk-free asset and a risky asset.Especially the price process of the risky asset is governed by Heston's stochastic volatility(SV)model.With the objective of maximizing the expected index utility of the terminal wealth of the insurance company,by using the classical tools of stochastic optimal control,the explicit expressions for optimal strategies and optimal value functions are derived.An interesting conclusion is found that it is better to buy one reinsurance than two under the assumption of this paper.Moreover,some numerical simulations and sensitivity analysis are provided.

Stochastic Models to Mitigate Sparse Sensor Attacks in Continuous-Time Non-Linear Cyber-Physical Systems

Cyber-Physical Systems are very vulnerable to sparse sensor attacks.But current protection mechanisms employ linear and deterministic models which cannot detect attacks precisely.Therefore,in this paper,we propose a new non-linear generalized model to describe Cyber-Physical Systems.This model includes unknown multivariable discrete and continuous-time functions and different multiplicative noises to represent the evolution of physical processes and randomeffects in the physical and computationalworlds.Besides,the digitalization stage in hardware devices is represented too.Attackers and most critical sparse sensor attacks are described through a stochastic process.The reconstruction and protectionmechanisms are based on aweighted stochasticmodel.Error probability in data samples is estimated through different indicators commonly employed in non-linear dynamics(such as the Fourier transform,first-return maps,or the probability density function).A decision algorithm calculates the final reconstructed value considering the previous error probability.An experimental validation based on simulation tools and real deployments is also carried out.Both,the new technology performance and scalability are studied.Results prove that the proposed solution protects Cyber-Physical Systems against up to 92%of attacks and perturbations,with a computational delay below 2.5 s.The proposed model shows a linear complexity,as recursive or iterative structures are not employed,just algebraic and probabilistic functions.In conclusion,the new model and reconstructionmechanism can protect successfully Cyber-Physical Systems against sparse sensor attacks,even in dense or pervasive deployments and scenarios.