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.

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.

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.

Circular Arc Gear Reliability Study Based on Modified FOSM Method

2013 ◽  
Vol 760-762 ◽  
pp. 2216-2219
Author(s):  
Zhong Li ◽  
Bo Yu Cheng
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Limit State ◽  
Point Method ◽  
Reliability Study ◽  
Circular Arc ◽  
Gear Case ◽  
Improve Reliability ◽  
State Functions

As different limit state functions are used to analyze reliability, there is a great distinctness among the calculated results. In this paper an improved LOSM method is proposed, namely, checking point method. The circular arc gear case is employed to demonstrate this method. In contrast to the results of Monte Carlo simulation, this method can greatly improve reliability calculations precision.

Determination of Failure Probabilities and Sensitivity Factors Based on First Order Reliability Method

1994 ◽  
Author(s):  
Nataraj Parameswaran ◽  
Lidvin Kjerengtroen
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Transfer Problem ◽  
First Order Reliability Method ◽  
First Order ◽  
Advantages And Disadvantages ◽  
Distributed Parameters ◽  
Reliability Method ◽  
Sensitivity Factors ◽  
Failure Probabilities

Abstract Traditionally, most engineering problems are modeled in such a manner that all the variables involved in the design equations are deterministic. By nature, however, seldom does such a phenomenon exist. Most of the variables involved are randomly distributed with a certain mean and standard deviation and follow a certain type of statistical distribution. This investigation compares two such statistical based design processes to evaluate failure probabilities of a one dimensional heat transfer problem with various statistically distributed parameters in its performance function. The methods developed are the Monte Carlo simulation and First Order Reliability Method (FORM). Comparison is made between the Monte Carlo simulation and FORM based upon the investigated problem and the relative advantages and disadvantages of both methods are noted at the end of the investigation. The investigation demonstrates that FORM can be used effectively to determine failure probabilities and sensitivity factors in a manner better than Monte Carlo simulation.

ON THE PROPERTIES AND MLEs OF GENERALIZED ODD GENERALIZED EXPONENTIAL- EXPONENTIAL DISTRIBUTION

2021 ◽  
Vol 4 (4) ◽  
pp. 155-165
Author(s):  
Aminu Suleiman Mohammed ◽  
Badamasi Abba ◽  
Abubakar G. Musa
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Maximum Likelihood ◽  
Exponential Distribution ◽  
Estimation Method ◽  
Likelihood Method ◽  
Parameter Estimates ◽  
Lifetime Data ◽  
Failure Rates ◽  
Simulation Experiments

For proper actualization of the phenomenon contained in some lifetime data sets, a generalization, extension or modification of classical distributions is required. In this paper, we introduce a new generalization of exponential distribution, called the generalized odd generalized exponential-exponential distribution. The proposed distribution can model lifetime data with different failure rates, including the increasing, decreasing, unimodal, bathtub, and decreasing-increasing-decreasing failure rates. Various properties of the model such as quantile function, moment, mean deviations, Renyi entropy, and order statistics.  We provide an approximation for the values of the mean, variance, skewness, kurtosis, and mean deviations using Monte Carlo simulation experiments. Estimating of the distribution parameters is performed using the maximum likelihood method, and Monte Carlo simulation experiments is used to assess the estimation method. The method of maximum likelihood is shown to provide a promising parameter estimates, and hence can be adopted in practice for estimating the parameters of the distribution. An application to real and simulated datasets indicated that the new model is superior to the fits than the other compared distributions

A polynomial chaos meta‐model for non‐linear stochastic magnet variations

2013 ◽  
Vol 32 (4) ◽  
pp. 1211-1218 ◽  
Author(s):  
Peter Offermann ◽  
Kay Hameyer
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Flux Density ◽  
Polynomial Chaos ◽  
Epistemic Uncertainty ◽  
Limit State ◽  
Element Model ◽  
State Function ◽  
Content Type ◽  
Meta Model

PurposeDue to the production process, arc segment magnets with radial magnetization for surface‐mounted permanent‐magnet synchronous machines (PMSM) can exhibit a deviation from the intended ideal, radial directed magnetization. In such cases, the resulting air gap field may show spatial variations in angle and absolute value of the flux‐density. For this purpose, this paper aims to create and evaluate a stochastic magnet model.Design/methodology/approachIn this paper, a polynomial chaos meta‐model approach, extracted from a finite element model, is compared to a direct sampling approach. Both approaches are evaluated using Monte‐Carlo simulation for the calculation of the flux‐density above one sole magnet surface.FindingsThe used approach allows representing the flux‐density's variations in terms of the magnet's stochastic input variations, which is not possible with pure Monte‐Carlo simulation. Furthermore, the resulting polynomial‐chaos meta‐model can be used to accelerate the calculation of error probabilities for a given limit state function by a factor of ten.Research limitations/implicationsDue to epistemic uncertainty magnet variations are assumed to be purely Gaussian distributed.Originality/valueThe comparison of both approaches verifies the assumption that the polynomial chaos meta‐model of the magnets will be applicable for a complete machine simulation.

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.

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