Conventional Monte Carlo Simulation Research Articles

Probabilistic solution of floodplain inundation equation

Uncertainty in bed roughness is a dominant factor in providing a sufficiently accurate simulation of floodplain flows. This study describes a method to compute the transition probability density distribution of time-varying water elevations where the evolutionary process is based on a conventional one-dimensional storage cell model with governing stochastic differential equation. By including the random inputs (or noise terms) of bed roughness and initial water depth, time-dependent and spatially varying probability density function of the water surface leads to a Fokker–Planck equation. The model’s performance is evaluated by applying it to shallow water flow with a horizontal bed. Sensitivity of model predictions to variations in the bed friction parameters is shown. By comparing the result of the proposed method with that of conventional Monte Carlo simulation, the advantage of the former as a method for density function prediction is confirmed.

OS1318-354 材料特性と形状に不確かさを有する超細密プレートフィン構造体のクリープ特性に対するSLSモンテカルロシミュレーション

In this study, the creep properties of ultrafine plate-fin structures which possess uncertainty factors in material properties of a base metal and shapes are investigated using the Monte Carlo simulation. For this, a time-dependent homogenization theory is applied to the analysis of creep properties of ultrafine plate-fm structures. Moreover, Stepwise Limited Sampling (SLS) is introduced into the Monte Carlo simulation to reduce computational costs. Then, using the present analysis method, the effects of uncertainty factors on the creep properties of ultrafine plate-fin structures subjected to a macroscopic constant stress at high temperature are investigated. This enables us to obtain tail probability values of creep strain by one tenth of computational costs compared to the conventional Monte Carlo simulation.

810 材料特性と形状に不確かさを有する超細密プレートフィン構造体のクリープ挙動に対するモンテカルロシミュレーション(OS8-(3),OS8 オーガナイズドセッション≪複合材料の変形と破壊およびマルチスケール計算技術≫)

In this study, the creep behavior of ultrafine plate-fin structures which possess uncertainty factors in material properties of a base metal and shapes is investigated using the Monte Carlo simulation. For this, a time-dependent homogenization theory is applied to the analysis of creep behavior of ultrafine plate-fin structures. Moreover, Stepwise Limited Sampling (SLS) is introduced into the Monte Carlo simulation to reduce computational costs. Then, using the present analysis method, the effects of uncertainty factors on the creep behavior of ultrafine plate-fin structures subjected to a macroscopic constant stress at high temperature are investigated. This enables us to obtain tail probability values of creep strain by one tenth of computational costs compared to the conventional Monte Carlo simulation

Reliability Analysis using Genetic Algorithm under Seismic Load

The aim of present study is to propose a procedure for reliability analysis using Genetic Algorithm (GA) under seismic loading using Monte Carlo Simulation (MCS). GA is used as a tool for increasing computer efficiency. The procedure is specially referred as Genetic Algorithm Aided Reliability Analysis (GAAR Analysis) to solve problems of structural reliability. Chimney subjected to seismic loading is taken as examples for calculating structural reliability using the GAAR Analysis and comparison is made with conventional MCS method of reliability analysis. The results obtained for realistic structural problem indicates the applicability of the proposed procedure. A computer program is developed in MATLAB for GAAR Analysis.

Spectral representation-based neural network assisted stochastic structural mechanics

This paper explores the applicability of artificial neural networks (ANN) for predicting the spread of structural response under the presence of uncertain parameters described as random fields. The use of ANN is carried out in combination with Monte Carlo simulation (MCS) for calculating response statistics in stochastic analysis of structural systems using finite elements. To this extent, the ANNs are trained with a few samples, following a conventional MCS procedure and used henceforth to predict the stochastic response for the rest of samples. The basic idea is to achieve a dimensionality reduction of the input ANN training space by using as input vector the random phase angles of the spectral representation method instead of the random variables describing the uncertain input parameters. A further improvement of the efficiency of the proposed approach is achieved by exploiting the uniform distribution of the random phase angles, in order to span efficiently the training space using a latin hypercube sampling (LHS) technique. The advantage of this approach over conventional computation of stochastic response via a standard stochastic finite element-based MCS is the fast and reliable prediction of the required response sample space which can be accomplished at a fraction of computing time and is independent of the size of the finite element model. Numerical results are presented, demonstrating the efficiency and the applicability of the proposed methodology as well as its distinct advantages over existing ANN-based stochastic finite element methodologies (SFEM).

Progress toward Monte Carlo–thermal hydraulic coupling using low-order nonlinear diffusion acceleration methods

A new approach for coupled Monte Carlo (MC) and thermal hydraulics (TH) simulations is proposed using low-order nonlinear diffusion acceleration methods. This approach uses new features such as coarse mesh finite difference diffusion (CMFD), multipole representation for fuel temperature feedback on microscopic cross sections, and support vector machine learning algorithms (SVM) for iterations between CMFD and TH equations. The multipole representation method showed small differences of about 0.3% root mean square (RMS) error in converged assembly source distribution compared to a conventional MC simulation with ACE data at the same temperature. This is within two standard deviations of the real uncertainty. Eigenvalue differences were on the order of 10pcm. Support vector machine regression was performed on-the-fly during MC simulations. Regression results of macroscopic cross sections parametrized by coolant density and fuel temperature were successful and eliminated the need of partial derivative tables generated from lattice codes. All of these new tools were integrated together to perform MC–CMFD–TH–SVM iterations. Results showed that inner iterations between CMFD–TH–SVM are needed to obtain a stable solution.

Rapid calculation of diffuse reflectance from a multilayered model by combination of the white Monte Carlo and adding-doubling methods.

To rapidly derive a result for diffuse reflectance from a multilayered model that is equivalent to that of a Monte-Carlo simulation (MCS), we propose a combination of a layered white MCS and the adding-doubling method. For slabs with various scattering coefficients assuming a certain anisotropy factor and without absorption, we calculate the transition matrices for light flow with respect to the incident and exit angles. From this series of precalculated transition matrices, we can calculate the transition matrices for the multilayered model with the specific anisotropy factor. The relative errors of the results of this method compared to a conventional MCS were less than 1%. We successfully used this method to estimate the chromophore concentration from the reflectance spectrum of a numerical model of skin and in vivo human skin tissue.

Energy-Driven Kinetic Monte Carlo Method and Its Application in Fullerene Coalescence.

Mimicking the conventional barrier-based kinetic Monte Carlo simulation, an energy-driven kinetic Monte Carlo (EDKMC) method was developed to study the structural transformation of carbon nanomaterials. The new method is many orders magnitude faster than standard molecular dynamics or Monte Marlo (MC) simulations and thus allows us to explore rare events within a reasonable computational time. As an example, the temperature dependence of fullerene coalescence was studied. The simulation, for the first time, revealed that short capped single-walled carbon nanotubes (SWNTs) appear as low-energy metastable structures during the structural evolution.

超細密プレートフィン構造体の弾-粘塑性特性に対するモンテカルロシミュレーション

In this study, the elastic-viscoplastic properties of ultrafine plate-fin structures which possess uncertainty factors in material properties of a base material are investigated using the Monte Carlo simulation. For this, a time-dependent homogenization theory is applied to the analysis of the elastic-viscoplastic properties of ultrafine plate-fin structures. Moreover, the Monte Carlo simulation with the Stepwise Limited Sampling (SLS) is used to take into account uncertainty factors in material properties. Then, using the present analysis method, the effects of uncertainty factors of material properties on the elastic-viscoplastic behavior of ultrafine plate-fin structures under uniaxial tension at high temperature are investigated. From this analysis, we can obtain the macroscopic and microscopic tail probability values by one tenth of computational time compared to the conventional Monte Carlo simulation.

Semianalytic BER Estimation of SC-QPSK under Nakagami-m Frequency Selective Fading Channel with Diversity Reception

Semianalytic estimation of bit-error-rate (BER) is one of the efficient procedures for evaluating BER for modulation formats having circular constellation with noise component of the decision variable is circularly symmetric with Gaussian distribution. To ensure very rapid simulation run time analytical and simulation techniques are used together unlike conventional Monte Carlo simulation. This technique is demonstrated to estimate BER of SC-QPSK system under Nakagami-m frequency selective fading channel. Finally error rate estimation is extended to system having multiple channel reception using spatial diversity combiners. Our result shows that system performance degrades with increasing value of system parameter.

An Arbitrary Polynomial Chaos-Based Approach to Analyzing the Impacts of Design Parameters on Evacuation Time under Uncertainty

In performance-based design of buildings, much attention is paid to design parameters by fire engineers or experts. However, due to the time-consuming evacuation models, it is computationally prohibitive to adopt the conventional Monte Carlo simulation (MCS) to examine the effects of design parameters on evacuation time under uncertainty. To determine suitable design parameters under uncertainty with the reduced significantly computational cost, an arbitrary polynomial chaos-based method is presented in this paper. Arbitrary polynomial chaos expansion is used to construct surrogate models of evacuation time based on complex evacuation models. Afterwards, simple analytical method can be adapted to calculate the mean, standard deviation of evacuation time and Sobol sensitivity indices based on the arbitrary polynomial chaos coefficients. Moreover, the distribution of evacuation time can be generated by combining Latin hypercube sampling (LHS) with the obtained surrogate model. To demonstrate the proposed method, a hypothetical single-storey fire compartment with two exits is presented as a case in accordance with the Chinese code GB50016-2012, evaluating the impact of exit width on evacuation time under uncertain occupant density and child-occupant load ratio. And results show that the proposed method can achieve the distribution of evacuation time close to that from the MCS while dramatically reducing the number of evacuation simulations. When exit width per 100 persons is designed between 0.1 m and 0.5 m, the uncertainty of evacuation time is severely affected by exit width, which is more significant in smaller exit width. However, exit width has a small effect on Sobol sensitivity indices, the reliability level of a certain safety factor, and safety factor at a certain reliability level.

Frequency domain Monte Carlo simulation method for cross power spectral density driven by periodically pulsed spallation neutron source using complex-valued weight Monte Carlo

In an accelerator driven system (ADS), pulsed spallation neutrons are injected at a constant frequency. The cross power spectral density (CPSD), which can be used for monitoring the subcriticality of the ADS, is composed of the correlated and uncorrelated components. The uncorrelated component is described by a series of the Dirac delta functions that occur at the integer multiples of the pulse repetition frequency. In the present paper, a Monte Carlo method to solve the Fourier transformed neutron transport equation with a periodically pulsed neutron source term has been developed to obtain the CPSD in ADSs. Since the Fourier transformed flux is a complex-valued quantity, the Monte Carlo method introduces complex-valued weights to solve the Fourier transformed equation. The Monte Carlo algorithm used in this paper is similar to the one that was developed by the author of this paper to calculate the neutron noise caused by cross section perturbations. The newly-developed Monte Carlo algorithm is benchmarked to the conventional time domain Monte Carlo simulation technique. The CPSDs are obtained both with the newly-developed frequency domain Monte Carlo method and the conventional time domain Monte Carlo method for a one-dimensional infinite slab. The CPSDs obtained with the frequency domain Monte Carlo method agree well with those with the time domain method. The higher order mode effects on the CPSD in an ADS with a periodically pulsed neutron source are discussed.

Perturbation Monte Carlo methods for tissue structure alterations

This paper describes an extension of the perturbation Monte Carlo method to model light transport when the phase function is arbitrarily perturbed. Current perturbation Monte Carlo methods allow perturbation of both the scattering and absorption coefficients, however, the phase function can not be varied. The more complex method we develop and test here is not limited in this way. We derive a rigorous perturbation Monte Carlo extension that can be applied to a large family of important biomedical light transport problems and demonstrate its greater computational efficiency compared with using conventional Monte Carlo simulations to produce forward transport problem solutions. The gains of the perturbation method occur because only a single baseline Monte Carlo simulation is needed to obtain forward solutions to other closely related problems whose input is described by perturbing one or more parameters from the input of the baseline problem. The new perturbation Monte Carlo methods are tested using tissue light scattering parameters relevant to epithelia where many tumors originate. The tissue model has parameters for the number density and average size of three classes of scatterers; whole nuclei, organelles such as lysosomes and mitochondria, and small particles such as ribosomes or large protein complexes. When these parameters or the wavelength is varied the scattering coefficient and the phase function vary. Perturbation calculations give accurate results over variations of ∼15-25% of the scattering parameters.

PARALLEL MULTI-PROPOSAL AND MULTI-CHAIN MCMC FOR CALCULATING P-VALUE OF GENOME-WIDE ASSOCIATION STUDY

In this paper, by the novel idea of integrating multiple-proposal algorithm and multiple-chain algorithm by parallel computing, we develop a highly efficient sampler for approximating statistical distributions: parallel Multi-proposal and Multi-chain Markov Chain Monte Carlo (pMPMC3), and we illustrate the high performance of this sampler by calculating P-value (odds ratio significance) for Genome Wide Association Study (GWAS). Computational results show that, by setting the convergence condition as the standard deviation of P-value is less than 10−3, pMPMC3 with 4 proposals and 4 chains obtains a convergent P-value within 106 iterations, while the conventional method Monte Carlo simulation does not obtain convergent P-values even in 107 iterations. We also test pMPMC3 by changing the number of chains, the number of proposals and the size of the dataset on a cluster with maximum 600 processes, the algorithm scales well.

Analyzing the performance of a time-dependent probabilistic approach for bulk network reliability assessment

The conventional sequential Monte Carlo Simulation (MCS) considers states in which a component is both in and out of service. Sequential MCS has been applied in different analyses whilst considering both symmetrical and asymmetrical probability distributions. The Beta distribution is however not one of the commonly recommended distributions for use in sequential MCS due to the complexity in deriving its inverse transform. A new sequential MCS technique that applies the Beta distribution is proposed in this paper. The technique is a time-dependent probabilistic approach (TDPA) that uses probability density functions (PDFs) to characterize stochastic network parameters in terms of their season- and time-dependency and simulates the component down (failure) states. The effect of this simulation approach on reliability calculations is analyzed using a published test network. The impact of dispersion and skewness in PDF based input models on a reliability analysis is also investigated. The results show that the TDPA can replicate the conventional sequential MCS analysis. The TDPA computation is also significantly faster. The simulation results of the TDPA also show that dispersion and skewness of component failure rate PDFs significantly influence a reliability analysis.

A reverse Monte Carlo method for deriving optical constants of solids from reflection electron energy-loss spectroscopy spectra

A reverse Monte Carlo (RMC) method is developed to obtain the energy loss function (ELF) and optical constants from a measured reflection electron energy-loss spectroscopy (REELS) spectrum by an iterative Monte Carlo (MC) simulation procedure. The method combines the simulated annealing method, i.e., a Markov chain Monte Carlo (MCMC) sampling of oscillator parameters, surface and bulk excitation weighting factors, and band gap energy, with a conventional MC simulation of electron interaction with solids, which acts as a single step of MCMC sampling in this RMC method. To examine the reliability of this method, we have verified that the output data of the dielectric function are essentially independent of the initial values of the trial parameters, which is a basic property of a MCMC method. The optical constants derived for SiO2 in the energy loss range of 8-90 eV are in good agreement with other available data, and relevant bulk ELFs are checked by oscillator strength-sum and perfect-screening-sum rules. Our results show that the dielectric function can be obtained by the RMC method even with a wide range of initial trial parameters. The RMC method is thus a general and effective method for determining the optical properties of solids from REELS measurements.

Fault tree analysis considering sequence dependence and repairable input events

PurposeThis paper aims to present two methods for calculating the steady state probability of a repairable fault tree with priority AND gates and repeated basic events when the minimal cut sets are given.Design/methodology/approachThe authors consider a situation that the occurrence of an operational demand and its disappearance occur alternately. We assume that both the occurrence and the restoration of the basic event are statistically independent and exponentially distributed. Here, restoration means the disappearance of the occurring event as a result of a restoration action. First, we obtain the steady state probability of an output event of a single‐priority AND gate by Markov analysis. Then, we propose two methods of obtaining the top event probability based on an Inclusion‐Exclusion method and by considering the sum of disjoint probabilities.FindingsThe closed form expression of steady state probability of a priority AND gate is derived. The proposed methods for obtaining the top event probability are compared numerically with conventional Markov analysis and Monte Carlo simulation to verify the effectiveness. The result shows the effectiveness of the authors’ methods.Originality/valueThe methodology presented shows a new solution for calculating the top event probability of repairable dynamic fault trees.

Application of a stochastic differential equation to the prediction of shoreline evolution

Shoreline evolution due to longshore sediment transport is one of the most important problems in coastal engineering and management. This paper describes a method to predict the probability distributions of long-term shoreline positions in which the evolution process is based on the standard one-line model recast into a stochastic differential equation. The time-dependent and spatially varying probability density function of the shoreline position leads to a Fokker–Planck equation model. The behaviour of the model is evaluated by applying it to two simple shoreline configurations: a single long jetty perpendicular to a straight shoreline and a rectangular beach nourishment case. The sensitivity of the model predictions to variations in the wave climate parameters is shown. The results indicate that the proposed model is robust and computationally efficient compared with the conventional Monte Carlo simulations.

A New Sensitivity-Based Reliability Calculation Algorithm in the Optimal Design of Electromagnetic Devices

A new reliability calculation method is proposed based on design sensitivity analysis by the finite element method for nonlinear performance constraints in the optimal design of electromagnetic devices. In the proposed method, the reliability of a given design is calculated by using the Monte Carlo simulation (MCS) method after approximating a constraint function to a linear one in the confidence interval with the help of its sensitivity information. The validity and numerical efficiency of the proposed sensitivity-assisted MCS method are investigated by comparing its numerical results with those obtained by using the conventional MCS method and the first-order reliability method for analytic functions and the TEAM Workshop Problem 22.

Treatment of evacuation time uncertainty using polynomial chaos expansion

In order to deal with uncertainties in evacuation time associated with the uncertainty in input parameters at a reasonable computational cost, a probabilistic method based on polynomial chaos expansion is proposed that combines evacuation models with Latin hypercube sampling. Evacuation models enable the prediction of evacuation time; polynomial chaos expansion is used to construct a surrogate model of evacuation time; Latin hypercube sampling is adopted as post-processing of the surrogate model to predict numerically the distribution of evacuation times. Additionally, an Uncertainty Factor is defined to quantify the total effect of the uncertainty of input parameters on evacuation time. To illustrate the proposed probabilistic method, evacuation of a simplified fire compartment typical of large commercial buildings is analyzed while considering uncertain input parameters including occupant density, child-occupant load ratio and exit width. This case study indicates that when exit width is small, the Uncertainty Factor is almost constant with respect to exit width but increases with an increase in specified (acceptable) reliability level. Furthermore, if exit width exceeds a certain critical value, the Uncertainty Factor will decrease with an increase in exit width and its sensitivity to reliability level will become smaller. Finally, the case study shows that compared with the conventional Monte Carlo simulation, the proposed method can give similar estimations of evacuation time uncertainty at a significantly reduced computational cost. Language: en