MONTE CARLO SIMULATION OF TRIBLOCK COPOLYMER/HOMOPOLYMER BLEND FILMS

The morphologies of triblock copolymer/homopolymer blend films, ABA/A and ABAIB, confined between two neutral hard walls were studied via Monte Carlo （MC） simulation on a simple .cubic lattice. The effects of φh （the volume fraction of homopolymer） and Md/Mb （the molecular weight of homopolymer in relation to that of the corresponding blocks in the copolymer） on the morphologies were investigated in detail.

GEANT4 simulation study of over-response phenomenon of fiber x-ray sensor

The purpose of this article is to explore the cause of the over-response phenomenon of fiber x-ray sensor.The sensor is based on a length of PMMA fiber,whose end is filled with the scintillation material Gd_(2)O_(2)S:Tb.The Monte Carlo simulation software GEANT4 uses the phase space file provided by the International Atomic Energy Agency(IAEA),by irradiating the fiber x-ray sensor in the water phantom,counting the fluorescence signal of the optical fiber x-ray sensor after propagation through the fiber.In addition,the number of Cerenkov photons propagating through the fiber is also counted.Comparing this article with previous research,we believe that one of the reasons for the over-response of the fiber x-ray sensor is the non-linear response of the deposition energy of the scintillator to the fluorescence.By establishing a region of interest and counting the x-rays in this region,the simulation results show that the counted number of x-rays that may affect the fiber x-ray sensor is the biggest in the area of interest at a water depth of 5 cm.This result is close to the maximum dose point of the experimental and simulated percentage depth dose(PDD) curve of fiber x-ray sensor.Therefore,the second reason of the over-response phenomenon is believed to be fact that the inorganic materials such as Gd_(2)O_(2)S:Tb have larger effective atomic numbers,so the fiber x-ray sensors will cause more collisions with x-ray in a low energy region of 0.1 MeV-1.5 MeV.

Eulerian-Lagranigan simulation of aerosol evolution in turbulent mixing layer

The formation and evolution of aerosol in turbulent flows are ubiquitous in both industrial processes and nature. The intricate interaction of turbulent mixing and aerosol evolution in a canonical turbulent mixing layer was investigated by a direct numerical simulation （DNS） in a recent study （Zhou, K., Attili, A., Alshaarawi, A., and Bisetti, F. Simulation of aerosol nucleation and growth in a turbulent mixing layer. Physics of Fluids, 26, 065106 （2014））. In this work, Monte Carlo （MC） simulation of aerosol evolution is carried out along Lagrangian trajectories obtained in the previous simulation, in order to quantify the error of the moment method used in the previous simulation. Moreover, the particle size distribution （PSD）, not available in the previous works, is also investigated. Along a fluid parcel moving through the turbulent flow, temperature and vapor concentration exhibit complex fluctuations, triggering complicate aerosol processes and rendering complex PSD. However, the mean PSD is found to be bi-modal in most of the mixing layer except that a tri-modal distribution is found in the turbulent transition region. The simulated PSDs agree with the experiment observations available in the literature. A different explanation on the formation of such PSDs is provided.

Research on Application of Monte Carlo Simulation in the Income Approach of Asset Valuation A listed Company in China as an Example

The income approach of asset valuation estimates the asset value according to the asset-discounted future earnings or the capitalizing process. As a result, a reasonable prediction of asset-expected future returns has become one of the core contents of the income approach. The forecast on expected future earnings is generally based on many uncertain factors, such as strict conditions of assumption and the complexity of environment. However, the current valuation practice in this aspect varies greatly and sometimes depends on personally experienced judgment of appraisers. Therefore, the obtained valuation results tend to be simplified and absolutized. This paper takes a listed company in China as an example to explore the way of inserting an uncertainty analysis into the prediction of the income approach, and then to obtain a series of valuation results within a certain probability fluctuation range. Finally, it puts forward some suggestions about the Monte Carlo simulation （MCS）.

Stochastic analysis of load-transfer mechanism of energy piles by random finite difference model

The surge in demand for renewable energy to combat the ever-escalating climate crisis promotes development of the energy-saving,carbon saving and reduction technologies.Shallow ground-source heat pump(GSHP)system is a promising carbon reduction technology that can stably and effectively exploit subsurface geothermal energy by taking advantage of load-bearing structural elements as heat transfer medium.However,the transformation of conventional geo-structures(e.g.piles)into heat exchangers between the ground and superstructures can potentially induce variable thermal axial stresses and displacements in piles.Traditional energy pile analysis methods often rely on deterministic and homogeneous soil parameter profiles for investigating thermo-mechanical soil-structure interaction,without consideration of soil spatial variability,model uncertainty or statistical uncertainty associated with interpolation of soil parameter profiles from limited site-specific measurements.In this study,a random finite difference model(FDM)is proposed to investigate the thermo-mechanical load-transfer mechanism of energy piles in granular soils.Spatially varying soil parameter profile is interpreted from limited site-specific measurements using Bayesian compressive sensing(BCS)with proper considering of soil spatial variability and other uncertainties in the framework of Monte Carlo simulation(MCS).Performance of the proposed method is demonstrated using an illustrative example.Results indicate that the proposed method enables an accurate evaluation of thermally induced axial stress/displacement and variation in null point(NP)location with quantified uncertainty.A series of sensitivity analyses are also carried out to assess effects of the pile-superstructure stiffness and measurement data number on the performance of the proposed method,leading to useful insights.

Effects of tissue absorption on calculation of mean photon path length using modified Beer-Lambert law

The mean path length(MPL)of photons is a critical parameter to calculate tissue absorption coefficient as well as blood oxygenation using modified Beer-Lambert law,where in the differential path factor(DPF)is often assumed as constant over range of tissue absorption.By utilizing the Monte Carlo(MC)simulation of photon migrations in the leg,this study used four approaches to estimate MPL,and compared them with that determined by the MPL definition.The simulation results indicate that the DPF is remarkably affected by tissue absorption,at approximate 10% variation.A linear model is suggested to calculate MPL for measurements of tissue absorption as well as blood oxygenation using modified Beer-Lambert law.

Probabilistic prediction of expected ground condition and construction time and costs in road tunnels

Ground condition and construction （excavation and support） time and costs are the key factors in decision-making during planning and design phases of a tunnel project. An innovative methodology for probabilistic estimation of ground condition and construction time and costs is proposed, which is an integration of the ground prediction approach based on Markov process, and the time and cost variance analysis based on Monte-Carlo （MC） simulation. The former provides the probabilistic description of ground classification along tunnel alignment according to the geological information revealed from geological profile and boreholes. The latter provides the probabilistic description of the expected construction time and costs for each operation according to the survey feedbacks from experts. Then an engineering application to Hamro tunnel is presented to demonstrate how the ground condition and the construction time and costs are estimated in a probabilistic way. In most items, in order to estimate the data needed for this methodology, a number of questionnaires are distributed among the tunneling experts and finally the mean values of the respondents are applied. These facilitate both the owners and the contractors to be aware of the risk that they should carry before construction, and are useful for both tendering and bidding.

LS-SVM and Monte Carlo methods based reliability analysis for settlement of soft clayey foundation

A method which adopts the combination of least squares support vector machine（LS-SVM） and Monte Carlo（MC） simulation is used to calculate the foundation settlement reliability.When using LS-SVM,choosing the training dataset and the values for LS-SVM parameters is the key.In a representative sense,the orthogonal experimental design with four factors and five levels is used to choose the inputs of the training dataset,and the outputs are calculated by using fast Lagrangian analysis continua（FLAC）.The decimal ant colony algorithm（DACA） is also used to determine the parameters.Calculation results show that the values of the two parameters,and δ2 have great effect on the performance of LS-SVM.After the training of LS-SVM,the inputs are sampled according to the probabilistic distribution,and the outputs are predicted with the trained LS-SVM,thus the reliability analysis can be performed by the MC method.A program compiled by Matlab is employed to calculate its reliability.Results show that the method of combining LS-SVM and MC simulation is applicable to the reliability analysis of soft foundation settlement.

Robust design and optimization for autonomous PV-wind hybrid power systems

This study presents a robust design method for autonomous photovoltaic (PV)-wind hybrid power systems to obtain an optimum system configuration insensitive to design variable variations. This issue has been formulated as a constraint multi-objective optimization problem, which is solved by a multi-objective genetic algorithm, NSGA-II. Monte Carlo Simulation (MCS) method, combined with Latin Hypercube Sampling (LHS), is applied to evaluate the stochastic system performance. The potential of the proposed method has been demonstrated by a conceptual system design. A comparative study between the proposed robust method and the deterministic method presented in literature has been conducted. The results indicate that the proposed method can find a large mount of Pareto optimal system configurations with better compromising performance than the deterministic method. The trade-off information may be derived by a systematical comparison of these configurations. The proposed robust design method should be useful for hybrid power systems that require both optimality and robustness.

Effects of fracture distribution and length scale on the equivalent continuum elastic compliance of fractured rock masses

Fracture systems have strong influence on the overall mechanical behavior of fractured rock masses dueto their relatively lower stiffness and shear strength than those of the rock matrix. Understanding theeffects of fracture geometrical distribution, such as length, spacing, persistence and orientation, isimportant for quantifying the mechanical behavior of fractured rock masses. The relation betweenfracture geometry and the mechanical characteristics of the fractured rock mass is complicated due tothe fact that the fracture geometry and mechanical behaviors of fractured rock mass are stronglydependent on the length scale. In this paper, a comprehensive study was conducted to determine theeffects of fracture distribution on the equivalent continuum elastic compliance of fractured rock massesover a wide range of fracture lengths. To account for the stochastic nature of fracture distributions, threedifferent simulation techniques involving Oda＇s elastic compliance tensor, Monte Carlo simulation （MCS）,and suitable probability density functions （PDFs） were employed to represent the elastic compliance offractured rock masses. To yield geologically realistic results, parameters for defining fracture distributionswere obtained from different geological fields. The influence of the key fracture parameters andtheir relations to the overall elastic behavior of the fractured rock mass were studied and discussed. Adetailed study was also carried out to investigate the validity of the use of a representative elementvolume （REV） in the equivalent continuum representation of fractured rock masses. A criterion was alsoproposed to determine the appropriate REV given the fracture distribution of the rock mass.

Bifurcation in most probable phase portraits for a bistable kinetic model with coupling Gaussian and non-Gaussian noises

The phenomenon of stochastic bifurcation driven by the correlated non-Gaussian colored noise and the Gaussian white noise is investigated by the qualitative changes of steady states with the most probable phase portraits.To arrive at the Markovian approximation of the original non-Markovian stochastic process and derive the general approximate Fokker-Planck equation(FPE),we deal with the non-Gaussian colored noise and then adopt the unified colored noise approximation(UCNA).Subsequently,the theoretical equation concerning the most probable steady states is obtained by the maximum of the stationary probability density function(SPDF).The parameter of the uncorrelated additive noise intensity does enter the governing equation as a non-Markovian effect,which is in contrast to that of the uncorrelated Gaussian white noise case,where the parameter is absent from the governing equation,i.e.,the most probable steady states are mainly controlled by the uncorrelated multiplicative noise.Additionally,in comparison with the deterministic counterpart,some peculiar bifurcation behaviors with regard to the most probable steady states induced by the correlation time of non-Gaussian colored noise,the noise intensity,and the non-Gaussian noise deviation parameter are discussed.Moreover,the symmetry of the stochastic bifurcation diagrams is destroyed when the correlation between noises is concerned.Furthermore,the feasibility and accuracy of the analytical predictions are verified compared with those of the Monte Carlo(MC)simulations of the original system.

Deformation and stability of the seawall,considering the strength uncertainty of cement mixing piles

The cement mixing (CM) pile is a common method of improving soft offshore ground. The strength growth of CM piles under complex conditions is affected by many factors, especially the cement and moisture contents, and shows significant uncertainty. To investigate the stochasticity of the early strength of CM piles and its impact on the displacement and stability of a seawall, a series of laboratory tests and numerical analyses were carried out in this study. Vane shear tests were conducted on the cement-solidified soil to determine the relationships between the undrained shear strength s_(u) of the cement soil curing in the seawater and the cement content a_(c), as well as the in situ soil moisture content w. It can be inferred that the 24 h undrained shear strength follows a normal distribution. A numerical model considering the random CM pile strength was established to investigate the deformation of the seawall. Due to the uncertainty of CM pile strength, the displacement of the seawall demonstrates a certain discreteness. The decrease of the mean undrained shear strength of CM piles causes a corresponding increase in the average displacement of the seawall. When the mean strength of CM piles is lower than a certain threshold, there is a risk of instability. Furthermore, the heterogeneity of the strength within an individual CM pile also has an impact on seawall displacement. Attention should be paid to the uncertainty of CM pile strength to control displacement and stability.

A sequential method for estimating the optical properties of two-layer agro-products from spatially-resolved diffuse reflectance: Simulation

A sequential method for estimating the optical properties of two-layer biological tissues with spatially-resolved diffuse reflectance was proposed and validated using Monte Carlo simulations.The relationship between the penetration depth of detected photons and source-detector separation was first studied.Photons detected at larger source-detector separations generally penetrated deeper into the medium than those detected at small source-detector separations.The effect of each parameter involved in the two-layer diffusion model(i.e.,the absorption and reduced scattering coefficients(μa andμs′)of each layer,and the thickness of top layer)on reflectance was investigated.It was found that the relationship between the optical properties and thickness of top layer was a critical factor in determining whether photons would have sufficient interactions with the top layer and also penetrate into the bottom layer.The constraints for the proposed sequential estimation method were quantitatively determined by the curve fitting procedure coupledwith error contourmap analyses.Results showed that the optical properties of top layer could be determinedwithin 10%error using the semi-infinite diffusion model for reflectance profiles with properly selected start and end points,when the thickness of top layer was larger than two times its mean free path(mfp′).And the optical properties of the bottom layer could be estimatedwithin 10%error by the two-layer diffusion model,when the thickness of top layerwas b16 times its mfp′.The proposed sequential estimation method is promising for improving the estimation of the optical properties of two-layer tissues from the same spatially-resolved reflectance.

An improved probabilistic load flow in distribution networks based on clustering and Point estimate methods

Clustering approaches are one of the probabilistic load flow(PLF)methods in distribution networks that can be used to obtain output random variables,with much less computation burden and time than the Monte Carlo simulation(MCS)method.However,a challenge of the clustering methods is that the statistical characteristics of the output random variables are obtained with low accuracy.This paper presents a hybrid approach based on clustering and Point estimate methods.In the proposed approach,first,the sample points are clustered based on the𝑙-means method and the optimal agent of each cluster is determined.Then,for each member of the population of agents,the deterministic load flow calculations are performed,and the output variables are calculated.Afterward,a Point estimate-based PLF is performed and the mean and the standard deviation of the output variables are obtained.Finally,the statistical data of each output random variable are modified using the Point estimate method.The use of the proposed method makes it possible to obtain the statistical properties of output random variables such as mean,standard deviation and probabilistic functions,with high accuracy and without significantly increasing the burden of calculations.In order to confirm the consistency and efficiency of the proposed method,the 10-,33-,69-,85-,and 118-bus standard distribution networks have been simulated using coding in Python®programming language.In simulation studies,the results of the proposed method have been compared with the results obtained from the clustering method as well as the MCS method,as a criterion.

VOC emission caps constrained by air quality targets based on response surface model:A case study in the Pearl River Delta Region,China

Because of the recent growth in ground-level ozone and increased emission of volatile organic compounds(VOCs),VOC emission control has become a major concern in China.In response,emission caps to control VOC have been stipulated in recent policies,but few of them were constrained by the co-control target of PM_(2.5)and ozone,and discussed the factor that influence the emission cap formulation.Herein,we proposed a framework for quantification of VOC emission caps constrained by targets for PM_(2.5)and ozone via a new response surface modeling(RSM)technique,achieving 50%computational cost savings of the quantification.In the Pearl River Delta(PRD)region,the VOC emission caps constrained by air quality targets varied greatly with the NOxemission reduction level.If control measures in the surrounding areas of the PRD region were not considered,there could be two feasible strategies for VOC emission caps to meet air quality targets(160μg/m^(3)for the maximum 8-hr-average 90th-percentile(MDA8-90%)ozone and 25μg/m^(3)for the annual average of PM_(2.5)):a moderate VOC emission cap with<20%NOxemission reductions or a notable VOC emission cap with>60%NOxemission reductions.If the ozone concentration target were reduced to 155μg/m^(3),deep NOxemission reductions is the only feasible ozone control measure in PRD.Optimization of seasonal VOC emission caps based on the Monte Carlo simulation could allow us to gain higher ozone benefits or greater VOC emission reductions.If VOC emissions were further reduced in autumn,MDA8-90%ozone could be lowered by 0.3-1.5μg/m^(3),equaling the ozone benefits of 10%VOC emission reduction measures.The method for VOC emission cap quantification and optimization proposed in this study could provide scientific guidance for coordinated control of regional PM_(2.5)and O_(3)pollution in China.

Security Constrained Unit Commitment with Extreme Wind Scenarios

The rapid development of economy and society stimulates the increase of power demand. Wind power has received great attention as a typical renewable energy, and the share of wind power is continually increasing in recent years.However, the high integration of wind power brings challenges to the secure and reliable operation of power grid due to the intermittent characteristic of wind power. In order to solve the operation risk caused by wind power uncertainty, this paper proposes to solve the problem of stochastic security-constrained unit commitment(SCUC) by considering the extreme scenarios of wind power output. Firstly, assuming that the probability density distribution of wind power approximately follows a normal distribution, a great number of scenarios are generated by Monte Carlo(MC) simulation method to capture the stochastic nature of wind power output. Then, the clustering by fast search and find of density peaks(CSFDP) is utilized to separate the generated scenarios into three types: extreme, normal and typical scenarios. The extreme scenarios are identified to determine the on/off statuses of generators, while the typical scenarios are used to solve the day-ahead security-constrained economic dispatch(SCED) problem. The advantage of the proposed method is to ensure the robustness of SCUC solution while reducing the conservativeness of the solution as much as possible.The effectiveness of the proposed method is verified by IEEE test systems.