Managing the Computational Cost in a Monte Carlo Simulation by Considering the Value of Information

2012 ◽  
Author(s):  
Efstratios Nikolaidis ◽  
Vijitashwa Pandey ◽  
Zissimos Mourelatos
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Value Of Information ◽  
Computational Cost

scholarly journals Non-deterministic Approach for Reliability Evaluation of Steel Portal Frame

2019 ◽  
Vol 5 (8) ◽  
pp. 1684-1697
Author(s):  
Hawraa Qasim Jebur ◽  
Salah Rohaima Al-Zaidee
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Structural Reliability ◽  
Limit State ◽  
Computational Cost ◽  
Probability Of Failure ◽  
Ultimate Limit State ◽  
Axial Forces ◽  
Portal Frame ◽  
Ultimate Limit

In recent years, more researches on structural reliability theory and methods have been carried out. In this study, a portal steel frame is considered. The reliability analysis for the frame is represented by the probability of failure, P_f, and the reliability index, β, that can be predicted based on the failure of the girders and columns. The probability of failure can be estimated dependent on the probability density function of two random variables, namely Capacity R, and Demand Q. The Monte Carlo simulation approach has been employed to consider the uncertainty the parameters of R, and Q. Matlab functions have been adopted to generate pseudo-random number for considered parameters. Although the Monte Carlo method is active and is widely used in reliability research, it has a disadvantage which represented by the requirement of large sample sizes to estimate the small probabilities of failure. This is leading to computational cost and time. Therefore, an Approximated Monte Carlo simulation method has been adopted for this issue. In this study, four performances have been considered include the serviceability deflection limit state, ultimate limit state for girder, ultimate limit state for the columns, and elastic stability. As the portal frame is a statically indeterminate structure, therefore bending moments, and axial forces cannot be determined based on static alone. A finite element parametric model has been prepared using Abaqus to deal with this aspect. The statistical analysis for the results samples show that all response data have lognormal distribution except of elastic critical buckling load which has a normal distribution.

The Soft Ion Model in Monte Carlo Simulation of Molten Salts

1988 ◽  
Vol 43 (2) ◽  
pp. 129-132
Author(s):  
C. Margheritis ◽  
C. Sinistri
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Molten Salt ◽  
Molten Salts ◽  
Computational Cost ◽  
Coulomb Energy ◽  
Numerical Application ◽  
Polarization Energy ◽  
Simple Evaluation ◽  
Salt Systems

Abstract This paper describes a method for a simple evaluation of the polarization energy in molten salt systems, by which it is possible to go, without heavy computational cost, from the rigid to the soft ion model. The method is based on the observation that, within the movements of single ions in the Monte Carlo chain, the deviation of the polarization energy is a linear function of the deviation of the Coulomb energy.An extended numerical application has been carried out for molten Lil at 800, 1200 and 1453 (b. p.) K. The parameters that are mostly affected by the used model are put into evidence.

Local Monte Carlo Simulation for the Reliability Sensitivity Analysis

2011 ◽  
Vol 291-294 ◽  
pp. 2183-2188 ◽  
Author(s):  
Da Wei Li ◽  
Zhen Zhou Lu ◽  
Zhang Chun Tang
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Numerical Technique ◽  
Limit State ◽  
Computational Cost ◽  
Simulation Method ◽  
State Function ◽  
Local Domain ◽  
Monte Carlo Simulation Method ◽  
Reliability Sensitivity

An efficient numerical technique, namely the Local Monte Carlo Simulation method, is presented to assess the reliability sensitivity in this paper. Firstly some samples are obtained by the random sampling, then the local domain with a constant probability content corresponding to each sample point can be defined, finally the conditional reliability and reliability sensitivity corresponding to every local region can be calculated by using linear approximation of the limit state function. The reliability and reliability sensitivity can be estimated by the expectation of all the conditional reliability and reliability sensitivity. Three examples testify the applicability, validity and accuracy of the proposed method. The results computed by the Local Monte Carlo Simulation method and the Monte Carlo method are compared, which demonstrates that, without losing precision, the computational cost by the former method is much less than the later.

A Novel Reliability Analysis Method for Turbine Discs with the Mixture of Fuzzy and Probability-Box Variables

2018 ◽  
Vol 0 (0) ◽  
Author(s):  
Xiaoqiang Zhang ◽  
Huiying Gao ◽  
Yan-Feng Li ◽  
Hong-Zhong Huang
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Critical Point ◽  
Computational Cost ◽  
Saddlepoint Approximation ◽  
Aerospace Engineering ◽  
Equivalent Transformation ◽  
Analysis Method ◽  
Fuzzy Variables ◽  
Novel Method

Abstract Fuzzy and probability-box (p-box) variables exit widely in aerospace engineering. To evaluate the reliability of turbine discs under the mixture of these two types of variables and guarantee safety, the critical point lies in how to deal with the fuzzy variables. In this paper, a novel method based on equivalent transformation of entropy and saddlepoint approximation (SPA) is proposed to estimate the reliability of turbine discs with the mixture of fuzzy and p-box variables. The advantage of the proposed method is that it can transform fuzzy variables whose memberships are non-normal into normal random variables through entropy invariability; meanwhile, using the SPA, the required sample size and corresponding computational cost decreases greatly. An example is used to illustrate the proposed method and a comparison is also made with the interval Monte Carlo simulation (IMCS). The results indicate that the proposed method is promising and has higher efficiency with almost the same accuracy.

Design Under Uncertainty Using Monte Carlo Simulation and Probabilistic Sufficiency Factor

2003 ◽  
Author(s):  
Xueyong Qu ◽  
Raphael T. Haftka
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Failure Modes ◽  
Computational Cost ◽  
Probability Of Failure ◽  
Design Under Uncertainty ◽  
Random Errors ◽  
Safety Index ◽  
Design Variables ◽  
Variable Fidelity

Monte Carlo simulation is commonly employed to evaluate system probability of failure for problems with multiple failure modes in design under uncertainty. The probability calculated from Monte Carlo simulation has random errors due to limited sample size, which create numerical noise in the dependence of the probability on design variables. This in turn may lead the design to spurious optimum. A probabilistic sufficiency factor (PSF) approach is proposed that combines safety factor and probability of failure. The PSF represents a factor of safety relative to a target probability of failure, and it can be calculated from the results of Monte Carlo simulation (MCS) with little extra computation. The paper presents the use of PSF with a design response surface (DRS), which fits it as function of design variables, filtering out the noise in the results of MCS. It is shown that the DRS for the PSF is more accurate than DRS for probability of failure or for safety index. The PSF also provides more information than probability of failure or safety index for the optimization procedure in regions of low probability of failure. Therefore, the convergence of reliability-based optimization is accelerated. The PSF gives a measure of safety that can be used more readily than probability of failure or safety index by designers to estimate the required weight increase to reach a target safety level. To reduce the computational cost of reliability-based design optimization, a variable-fidelity technique and deterministic optimization were combined with probabilistic sufficiency factor approach. Example problems were studied here to demonstrate the methodology.

Efficient Reliability Analysis of Structural Systems With a High Number of Limit States

2010 ◽  
Author(s):  
Arvid Naess ◽  
Bernt J. Leira ◽  
Olexandr Batsevych
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Limit State ◽  
Computational Cost ◽  
Estimation Method ◽  
Structural Systems ◽  
Approximation Procedure ◽  
Tail Probabilities ◽  
Critical Limit ◽  
Failure Probabilities

In principle, the reliability of complicated structural systems can be accurately predicted by standard Monte Carlo simulation methods, but the computational burden may be prohibitive. A new Monte Carlo based method for estimating system reliability that aims at reducing the computational cost is therefore proposed. It exploits the regularity of tail probabilities to set up an approximation procedure for the prediction of the far tail failure probabilities based on the estimates of the failure probabilities obtained by Monte Carlo simulation at more moderate levels. In the paper the usefulness and accuracy of the estimation method is illustrated by application to some particular examples of structures with several thousand potentially critical limit state functions. The effect of varying the correlation of the load components is also investigated.

Structural reliability of corroded pipeline using the so-called Separable Monte Carlo method

2018 ◽  
Vol 53 (8) ◽  
pp. 730-737 ◽  
Author(s):  
Mohamed el Amine Ben Seghier ◽  
Mourad Bettayeb ◽  
José Correia ◽  
Abílio De Jesus ◽  
Rui Calçada
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Structural Reliability ◽  
Computational Cost ◽  
Simulation Method ◽  
Computational Method ◽  
Time Dependent ◽  
Monte Carlo Simulation Method ◽  
Corrosion Defects ◽  
Separable Monte Carlo

The evaluation of the failure probability of corroded pipelines is an important calculation to quantify the risk assessment and integrity of pipelines. Traditional Monte Carlo simulation method has been widely used to solve this type of problems, where it generates a very large number of simulations and takes longer time in computing. In this study, enhanced computational method called Separable Monte Carlo is employed to evaluate the time-dependent reliability of pipeline segments containing active corrosion defects, where a practical example was used. The results show that the Separable Monte Carlo simulation method not only minimizes the computational cost strongly but also improves the calculation precision.

Electron Scattering in Solids

1990 ◽  
Vol 48 (2) ◽  
pp. 4-5
Author(s):  
Ryuichi Shimizu ◽  
Ze-Jun Ding
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Angular Distribution ◽  
Elastic Scattering ◽  
Electron Scattering ◽  
Cross Sections ◽  
Expansion Method ◽  
Electron Excitation ◽  
Partial Wave Expansion ◽  
Backscattered Electrons

Monte Carlo simulation has been becoming most powerful tool to describe the electron scattering in solids, leading to more comprehensive understanding of the complicated mechanism of generation of various types of signals for microbeam analysis.The present paper proposes a practical model for the Monte Carlo simulation of scattering processes of a penetrating electron and the generation of the slow secondaries in solids. The model is based on the combined use of Gryzinski’s inner-shell electron excitation function and the dielectric function for taking into account the valence electron contribution in inelastic scattering processes, while the cross-sections derived by partial wave expansion method are used for describing elastic scattering processes. An improvement of the use of this elastic scattering cross-section can be seen in the success to describe the anisotropy of angular distribution of elastically backscattered electrons from Au in low energy region, shown in Fig.l. Fig.l(a) shows the elastic cross-sections of 600 eV electron for single Au-atom, clearly indicating that the angular distribution is no more smooth as expected from Rutherford scattering formula, but has the socalled lobes appearing at the large scattering angle.

Determination of Stoichiometry of GaAs Component in (Gaas)Ge Epitaxially Grown Thin Films by Electron Microprobe X-Ray Analysis

1990 ◽  
Vol 48 (2) ◽  
pp. 264-265
Author(s):  
D. R. Liu ◽  
S. S. Shinozaki ◽  
R. J. Baird
Keyword(s):  
Thin Film ◽  
Thin Films ◽  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Compound Semiconductors ◽  
Energy Dispersive Analysis ◽  
X Ray ◽  
Metastable Alloys ◽  
Lower Voltage

The epitaxially grown (GaAs)Ge thin film has been arousing much interest because it is one of metastable alloys of III-V compound semiconductors with germanium and a possible candidate in optoelectronic applications. It is important to be able to accurately determine the composition of the film, particularly whether or not the GaAs component is in stoichiometry, but x-ray energy dispersive analysis (EDS) cannot meet this need. The thickness of the film is usually about 0.5-1.5 μm. If Kα peaks are used for quantification, the accelerating voltage must be more than 10 kV in order for these peaks to be excited. Under this voltage, the generation depth of x-ray photons approaches 1 μm, as evidenced by a Monte Carlo simulation and actual x-ray intensity measurement as discussed below. If a lower voltage is used to reduce the generation depth, their L peaks have to be used. But these L peaks actually are merged as one big hump simply because the atomic numbers of these three elements are relatively small and close together, and the EDS energy resolution is limited.

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