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.

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.

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.

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.

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.

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.

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.

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.

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.

Exit problem of stochastic SIR model with limited medical resource

Nonlinearity and randomness are both the essential attributes for the real world,and the case is the same for the models of infectious diseases,for which the deterministic models can not give a complete picture of the evolution.However,although there has been a lot of work on stochastic epidemic models,most of them focus mainly on qualitative properties,which makes us somewhat ignore the original meaning of the parameter value.In this paper we extend the classic susceptible-infectious-removed(SIR)epidemic model by adding a white noise excitation and then we utilize the large deviation theory to quantitatively study the long-term coexistence exit problem with epidemic.Finally,in order to extend the meaning of parameters in the corresponding deterministic system,we tentatively introduce two new thresholds which then prove rational.

The Stochastic Asymptotic Stability Analysis in Two Species Lotka-Volterra Model

The asymptotic stability of two species stochastic Lotka-Volterra model is explored in this paper. Firstly, the Lotka-Volterra model with random parameter is built and reduced into the equivalent deterministic system by orthogonal polynomial approximation. Then, the linear stability theory and Routh-Hurwitz criterion for nonlinear deterministic systems are applied to the equivalent one. At last, at the aid of Lyapunov second method, we obtain that as the random intensity or statistical parameter of random variable is changed, the stability about stochastic Lotka-Volterra model is different from the deterministic system.

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.

3D modeling of deepwater turbidite lobes:a review of the research status and progress

Deepwater turbidite lobe reservoirs have massive hydrocarbon potential and represent one of the most promising exploration targets for hydrocarbon industry.Key elements of turbidite lobes internal heterogeneity include the architectural hierarchy and complex amalgamations at each hierarchical level leading to the complex distribution of shale drapes.Due to limitation of data,to build models realistically honoring the reservoir architecture provides an effective way to reduce risk and improve hydrocarbon recovery.A variety of modeling techniques on turbidite lobes exist and can be broadly grouped into pixel-based,process-based,process-oriented,surface-based,object-based and a hybrid approach of two or more of these methods.The rationale and working process of methods is reviewed,along with their pros and cons.In terms of geological realism,object-based models can capture the most realistic architectures,including the multiple hierarchy and the amalgamations at different hierarchical levels.In terms of data conditioning,pixel-based and multiple-point statistics methods could honor the input data to the best degree.In practical,dif?ferent methods should be adopted depending on the goal of the project.Such a review could improve the understanding of existing modeling methods on turbidite lobes and could benefit the hydrocarbon exploration activities of such reservoirs in offshore China.

Algorithms and statistical analysis for linear structured weighted total least squares problem

Weighted total least squares(WTLS)have been regarded as the standard tool for the errors-in-variables(EIV)model in which all the elements in the observation vector and the coefficient matrix are contaminated with random errors.However,in many geodetic applications,some elements are error-free and some random observations appear repeatedly in different positions in the augmented coefficient matrix.It is called the linear structured EIV(LSEIV)model.Two kinds of methods are proposed for the LSEIV model from functional and stochastic modifications.On the one hand,the functional part of the LSEIV model is modified into the errors-in-observations(EIO)model.On the other hand,the stochastic model is modified by applying the Moore-Penrose inverse of the cofactor matrix.The algorithms are derived through the Lagrange multipliers method and linear approximation.The estimation principles and iterative formula of the parameters are proven to be consistent.The first-order approximate variance-covariance matrix(VCM)of the parameters is also derived.A numerical example is given to compare the performances of our proposed three algorithms with the STLS approach.Afterwards,the least squares(LS),total least squares(TLS)and linear structured weighted total least squares(LSWTLS)solutions are compared and the accuracy evaluation formula is proven to be feasible and effective.Finally,the LSWTLS is applied to the field of deformation analysis,which yields a better result than the traditional LS and TLS estimations.

Stochastic Epidemic Model of Covid-19 via the Reservoir-People Transmission Network

The novel Coronavirus COVID-19 emerged in Wuhan,China in December 2019.COVID-19 has rapidly spread among human populations and other mammals.The outbreak of COVID-19 has become a global challenge.Mathematical models of epidemiological systems enable studying and predicting the potential spread of disease.Modeling and predicting the evolution of COVID-19 epidemics in near real-time is a scientific challenge,this requires a deep understanding of the dynamics of pandemics and the possibility that the diffusion process can be completely random.In this paper,we develop and analyze a model to simulate the Coronavirus transmission dynamics based on Reservoir-People transmission network.When faced with a potential outbreak,decision-makers need to be able to trust mathematical models for their decision-making processes.One of the most considerable characteristics of COVID-19 is its different behaviors in various countries and regions,or even in different individuals,which can be a sign of uncertain and accidental behavior in the disease outbreak.This trait reflects the existence of the capacity of transmitting perturbations across its domains.We construct a stochastic environment because of parameters random essence and introduce a stochastic version of theReservoir-Peoplemodel.Then we prove the uniqueness and existence of the solution on the stochastic model.Moreover,the equilibria of the system are considered.Also,we establish the extinction of the disease under some suitable conditions.Finally,some numerical simulation and comparison are carried out to validate the theoretical results and the possibility of comparability of the stochastic model with the deterministic model.

Stochastic simulation of ground motions based on NGA-West2 strong motion records

Stochastic modeling of ground motion is a simple tool to predict ground shaking level for future earthquake and less time consuming than physics-based deterministic modeling.In this paper,a record-based stochastic method that considers the time-and frequency-evolution of ground motion is used to estimate ground motion for scenario earthquakes in tectonic active region.The stochastic method employs a time-domain modulation function to describe the temporal nonstationarity and a filter impulse response function that describe the evolution of frequency content.For characterizing the modulation function and the filter impulse function,six parameters(Ia,D5-95,tmid,ωmid,ω',ξf)are defined,and 2,571 pairs of ground motion recording in the NGA-west2 database are selected to identify the six parameters.Probabilistic density function is assigned to each of the parameter by fitting the frequency distribution histogram.The parameters are then transformed into standard normal space where regression analysis is performed by considering each parameter as function of moment magnitude,rupture distance,vS30(The time-averaged shear wave velocity of the top 30 m of soil).The prediction equations are used to generate ground motions for several scenario earthquakes and compared to NGA-West2 GMPEs.

A genetic algorithm based stochastic programming model for air quality management

This paper presents a model that can aid planners in defining the total allowable pollutant discharge in the planning region, accounting for the dynamic and stochastic character of meteorological conditions. This is accomplished by integrating Monte Carlo simulation and using genetic algorithm to solve the model. The model is demonstrated by using a realistic air urban scale SO 2 control problem in the Yuxi City of China. To evaluate effectiveness of the model, results of the approach are shown to compare with those of the linear deterministic procedures. This paper also provides a valuable insight into how air quality targets should be made when the air pollutant will not threat the residents' health. Finally, a discussion of the areas for further research are briefly delineated.