Fatigue damage estimation in non-linear systems using a combination of Monte Carlo simulation and the First Order Reliability Method

2015 ◽  
Vol 44 ◽  
pp. 203-210 ◽  
Author(s):  
Jørgen Juncher Jensen
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Linear Systems ◽  
Fatigue Damage ◽  
Damage Estimation ◽  
First Order Reliability Method ◽  
First Order ◽  
Reliability Method ◽  
Non Linear ◽  
Non Linear Systems

Reliability Estimation of Buried Pipeline Using FORM, SORM and Monte Carlo Simulation

2006 ◽  
Vol 326-328 ◽  
pp. 597-600 ◽  
Author(s):  
Ouk Sub Lee ◽  
Dong Hyeok Kim
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Exposure Time ◽  
Failure Probability ◽  
Reliability Estimation ◽  
Buried Pipeline ◽  
First Order Reliability Method ◽  
First Order ◽  
Reliability Method ◽  
The Difference

In this paper, the failure probability is estimated by using the FORM (first order reliability method), the SORM (second order reliability method) and the Monte Carlo simulation to evaluate the reliability of the corroded pipeline. It is found that the FORM technique is more effective in estimating the failure probability than the SORM technique for B31G and MB31G models with three different corrosion models. Furthermore, it is noted that the difference between the results of the FORM, the SORM and the Monte Carlo simulation decreases with the increase of the exposure time.

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.

Numerical Simulations of the Rolling of a Ship in a Stochastic Sea: Evaluations by Use of MCS and FORM

2009 ◽  
Author(s):  
Ulrik D. Nielsen ◽  
Jo̸rgen J. Jensen
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Numerical Simulations ◽  
Simplified Model ◽  
Probabilistic Assessment ◽  
Parametric Roll ◽  
First Order Reliability Method ◽  
Efficient Approach ◽  
First Order ◽  
Reliability Method

The paper elaborates on the probabilistic assessment of a simplified model for the rolling of a ship in a stochastic seaway. The model can be easily integrated with a probabilistic tool which enables evaluations of numerical simulations by the first order reliability method (FORM) and by Monte Carlo simulation (MCS). Results are presented for synchronous roll as well as parametric roll, where e.g. mean outcrossing rates have been calculated. FORM offers an efficient approach for the computations, although the approach should be applied with care in cases of parametric roll. The paper also touches on issues such as ergodicity and transient versus stationary stages in the roll realisations.

scholarly journals Manifold Calculus in System Theory and Control—Fundamentals and First-Order Systems

Symmetry ◽  
2021 ◽  
Vol 13 (11) ◽  
pp. 2092
Author(s):  
Simone Fiori
Keyword(s):  
Control Systems ◽  
Linear Systems ◽  
Linear Control Systems ◽  
First Order ◽  
Curved Manifolds ◽  
Non Linear ◽  
Covariant Derivation ◽  
Non Linear Systems ◽  
And Control

The aim of the present tutorial paper is to recall notions from manifold calculus and to illustrate how these tools prove useful in describing system-theoretic properties. Special emphasis is put on embedded manifold calculus (which is coordinate-free and relies on the embedding of a manifold into a larger ambient space). In addition, we also consider the control of non-linear systems whose states belong to curved manifolds. As a case study, synchronization of non-linear systems by feedback control on smooth manifolds (including Lie groups) is surveyed. Special emphasis is also put on numerical methods to simulate non-linear control systems on curved manifolds. The present tutorial is meant to cover a portion of the mentioned topics, such as first-order systems, but it does not cover topics such as covariant derivation and second-order dynamical systems, which will be covered in a subsequent tutorial paper.

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