scholarly journals A Multilevel Simulation Method for Time-Variant Reliability Analysis

2021 ◽  
Vol 13 (7) ◽  
pp. 3646
Author(s):  
Jian Wang ◽  
Xiang Gao ◽  
Zhili Sun
Keyword(s):  
Monte Carlo ◽  
Reliability Analysis ◽  
High Reliability ◽  
Computational Cost ◽  
Simulation Method ◽  
Probability Of Failure ◽  
Cumulative Probability ◽  
Time Interval ◽  
Random Samples ◽  
Geometric Sequence

Crude Monte Carlo simulation (MCS) is the most robust and easily implemented method for performing time-variant reliability analysis (TRA). However, it is inefficient, especially for high reliability problems. This paper aims to present a random simulation method called the multilevel Monte Carlo (MLMC) method for TRA to enhance the computational efficiency of crude MCS while maintaining its accuracy and robustness. The proposed method first discretizes the time interval of interest using a geometric sequence of different timesteps. The cumulative probability of failure associated with the finest level can then be estimated by computing corrections using all levels. To assess the cumulative probability of failure in a way that minimizes the overall computational complexity, the number of random samples at each level is optimized. Moreover, the correction associated with each level is independently computed using crude MCS. Thereby, the proposed method can achieve the accuracy associated with the finest level at a much lower computational cost than that of crude MCS, and retains the robustness of crude MCS with respect to nonlinearity and dimensions. The effectiveness of the proposed method is validated by numerical examples.

scholarly journals ANÁLISE DE CONFIABILIDADE ESTRUTURAL DE PROBLEMAS BASEADOS NA MECÂNICA DOS SÓLIDOS

2016 ◽  
Vol 12 (2) ◽  
Author(s):  
Vinícius Favaretto Defiltro ◽  
Wellison José Santana Gomes
Keyword(s):  
Monte Carlo ◽  
Reliability Analysis ◽  
Structural Reliability ◽  
Solid Mechanics ◽  
Structural Model ◽  
Simulation Method ◽  
Probability Of Failure ◽  
Structural Safety ◽  
Structural Element ◽  
Structural Problems

RESUMO: A Mecânica dos Sólidos, a partir de hipóteses simplificadoras, fornece modelos de cálculo que podem ser aplicados a vários problemas estruturais e estabelece as bases e o entendimento para o desenvolvimento de teorias e a construção de modelos mais complexos. Entretanto, dentro deste contexto, é comum desprezar as incertezas inerentes às propriedades dos materiais envolvidos, às condições de contorno e à geometria do problema. Neste artigo, ferramentas da Teoria da Confiabilidade Estrutural são aplicadas a problemas estruturais baseados na Mecânica dos Sólidos no intuito de analisá-los considerando algumas das incertezas envolvidas. Para isso, o método de Simulação de Monte Carlo é empregado na análise de confiabilidade de duas vigas. No estudo da primeira estrutura, busca-se investigar a influência da correlação entre variáveis aleatórias na probabilidade de falha do elemento estrutural. Na segunda estrutura, analisa-se o efeito da utilização de materiais com diferentes comportamentos (frágeis ou dúcteis) e, consequentemente, diferentes critérios de ruptura, sobre a probabilidade de falha estimada. Verifica-se que as análises de confiabilidade estrutural podem fornecer muitas informações que estão fora do escopo das soluções determinísticas. Tais informações permitem uma avaliação mais precisa da segurança estrutural e podem também levar a um melhor entendimento do modelo estrutural em questão. ABSTRACT: The Solid Mechanics, from simplifying assumptions, provides calculation models that can be applied to various structural problems and establishes the foundation and the understanding for the development of theories and the construction of more complex models. However, within this context, it is common to despise the uncertainties inherent to the properties of the materials involved, the boundary conditions and the geometry of the problem. In this article, Structural Reliability Theory tools are applied to structural problems based on Solid Mechanics in order to analyze them considering some of the uncertainties involved. For this, the Monte Carlo simulation method is used in the reliability analysis of two beams. In the first structure, study seeks to investigate the influence of correlation between random variables on the probability of failure of the structural element. In the second one, the effect of using materials with different behavior (ductile or brittle) and, consequently, different rupture criteria on the estimated probability of failure is analyzed. Structural reliability analysis can provide information which usually is outside the scope of deterministic solutions. Such information enables a more accurate assessment of structural safety and may lead to a better understanding of the structural model in question.

Hamiltonian Monte Carlo algorithms for target- and interval-oriented amplitude versus angle inversions

Geophysics ◽  
2020 ◽  
Vol 85 (3) ◽  
pp. R177-R194 ◽  
Author(s):  
Mattia Aleardi ◽  
Alessandro Salusti
Keyword(s):  
Monte Carlo ◽  
A Priori ◽  
Computational Cost ◽  
Model Space ◽  
Time Interval ◽  
Long Distance ◽  
Hamiltonian Monte Carlo ◽  
Zoeppritz Equations ◽  
Monte Carlo Algorithms ◽  
Amplitude Versus

A reliable assessment of the posterior uncertainties is a crucial aspect of any amplitude versus angle (AVA) inversion due to the severe ill-conditioning of this inverse problem. To accomplish this task, numerical Markov chain Monte Carlo algorithms are usually used when the forward operator is nonlinear. The downside of these algorithms is the considerable number of samples needed to attain stable posterior estimations especially in high-dimensional spaces. To overcome this issue, we assessed the suitability of Hamiltonian Monte Carlo (HMC) algorithm for nonlinear target- and interval-oriented AVA inversions for the estimation of elastic properties and associated uncertainties from prestack seismic data. The target-oriented approach inverts the AVA responses of the target reflection by adopting the nonlinear Zoeppritz equations, whereas the interval-oriented method inverts the seismic amplitudes along a time interval using a 1D convolutional forward model still based on the Zoeppritz equations. HMC uses an artificial Hamiltonian system in which a model is viewed as a particle moving along a trajectory in an extended space. In this context, the inclusion of the derivative information of the misfit function makes possible long-distance moves with a high probability of acceptance from the current position toward a new independent model. In our application, we adopt a simple Gaussian a priori distribution that allows for an analytical inclusion of geostatistical constraints into the inversion framework, and we also develop a strategy that replaces the numerical computation of the Jacobian with a matrix operator analytically derived from a linearization of the Zoeppritz equations. Synthetic and field data inversions demonstrate that the HMC is a very promising approach for Bayesian AVA inversion that guarantees an efficient sampling of the model space and retrieves reliable estimations and accurate uncertainty quantifications with an affordable 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.

Time-Dependent System Reliability Analysis Using Random Field Discretization

2015 ◽  
Vol 137 (10) ◽  
Author(s):  
Zhen Hu ◽  
Sankaran Mahadevan
Keyword(s):  
Random Field ◽  
Reliability Analysis ◽  
System Reliability ◽  
Probability Of Failure ◽  
Two Dimensions ◽  
Time Dependent ◽  
Time Interval ◽  
System Reliability Analysis ◽  
Reliability Method ◽  
Time Dependent System

This paper proposes a novel and efficient methodology for time-dependent system reliability analysis of systems with multiple limit-state functions of random variables, stochastic processes, and time. Since there are correlations and variations between components and over time, the overall system is formulated as a random field with two dimensions: component index and time. To overcome the difficulties in modeling the two-dimensional random field, an equivalent Gaussian random field is constructed based on the probability equivalency between the two random fields. The first-order reliability method (FORM) is employed to obtain important features of the equivalent random field. By generating samples from the equivalent random field, the time-dependent system reliability is estimated from Boolean functions defined according to the system topology. Using one system reliability analysis, the proposed method can get not only the entire time-dependent system probability of failure curve up to a time interval of interest but also two other important outputs, namely, the time-dependent probability of failure of individual components and dominant failure sequences. Three examples featuring series, parallel, and combined systems are used to demonstrate the effectiveness of the proposed method.

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.

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