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.

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.

Reliability analysis of a cohesive slope in a spreadsheet using FOSM, FORM and Monte-Carlo Simulation

2021 ◽  
pp. 391-402
Author(s):  
Saurav Shekhar Kar ◽  
Avijit Burman ◽  
Lal Bahadur Roy
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Shear Strength ◽  
Reliability Index ◽  
Factor Of Safety ◽  
Undrained Shear Strength ◽  
Excel Spreadsheet ◽  
First Order ◽  
Reliability Method ◽  
Undrained Shear

In geotechnical engineering uncertainties arises from loads, soil characteristics and their properties, calculation models etc. To minimize these uncertainties in geotechnical problem, various reliability based and (or probabilistic based) approaches have been developed. This abstract presents a MS-Excel spreadsheet environment based practical framework for estimating the reliability index and failure probability of a cohesive finite slope using First-order second moment method, First-order reliability method and Monte Carlo Simulation. The height and the angle of slope is considered to be 5 m and 45º respectively. The inclination of the slope is 2H:1V and the hard stratum is assumed to be present at 15 m below the soil. The values of saturated unit weight and undrained shear strength are assumed to be 18 kN/m3 and 20 kPa respectively. The stability analysis is carried out using Swedish slice method under undrained condition. The excel spreadsheet developed in the study is mainly divided into two forms i.e. deterministic model worksheet for calculating the factor of safety and uncertainty model for generating the random variables of uncertain parameters. The undrained shear strength is considered as an uncertain parameter. The nominal factor of safety value is found out to be 1.248 and the critical slip circle has coordinate (2.6, 8.8), having radius of 16 m. The reliability index is found out using FOSM, FORM and MCS.

A Probabilistic Model-Based Prognostics Using Meshfree Modeling: A Case Study on Fatigue Life of a Cantilever Beam

2016 ◽  
Author(s):  
Haileyesus B. Endeshaw ◽  
Fisseha M. Alemayehu ◽  
Stephen Ekwaro-Osire ◽  
João Paulo Dias
Keyword(s):  
Monte Carlo ◽  
Fatigue Life ◽  
Monte Carlo Method ◽  
Cantilever Beam ◽  
Research Question ◽  
Computational Framework ◽  
First Order Reliability Method ◽  
First Order ◽  
Reliability Method

Accurate prediction of remaining useful life (RUL) will improve reliability and reduce maintenance cost. Therefore, prognostics is essential to predict the RUL of systems and components. However, a big issue of uncertainty prevails in prognostics due to the fact that prognostics pertains to prediction of future state, which is affected by uncertainty. While various researches have been done in areas of prognostics and health management, they lack to perform RUL predictions efficiently. There is a need for an efficient comprehensive framework for quantifying uncertainty in prognostics. The research question to this study is: can meshfree modeling be used in probabilistic prognostics to efficiently predict RUL? The specific aims developed to answer the research question are (1) develop a computational framework for probabilistic prognostics of a fatigue life of a component using meshfree modeling, and (2) perform case study analyses on fatigue life of a cantilever beam. A probabilistic framework was developed that efficiently predicts the RUL of a component using a combination of the meshfree method known as local radial point interpolation method and a fatigue degradation model. Loading uncertainty is quantified and employed in the framework. The computational framework is easily customizable and computationally efficient and, hence, aids in decision making and fault mitigation. As a case study, the RUL of a cantilever beam under plane stress subjected to fatigue loadings was analyzed. Uncertainties in the RUL were quantified in terms of probability density functions, cumulative distribution functions, and 98% bounds of confidence interval. Sensitivity analysis was studied and computational efficiency of the framework was also investigated using first order reliability method and Monte Carlo method. When compared to the Monte Carlo method, first order reliability method provides reasonably good results and is found to be computationally more efficient.

scholarly journals A simplified approach to reliability evaluation of deep rock tunnel deformation using First-Order Reliability Method and Monte Carlo simulations

2022 ◽  
Vol 15 (1) ◽  
Author(s):  
Caio Cesar Cardoso da Silva ◽  
Mauro de Vasconcellos Real ◽  
Samir Maghous
Keyword(s):  
Monte Carlo ◽  
Reliability Analysis ◽  
Numerical Models ◽  
Limit State ◽  
Random Variables ◽  
Support Pressure ◽  
First Order Reliability Method ◽  
First Order ◽  
Reliability Method ◽  
Shotcrete Lining

abstract: The Monte Carlo simulation (MCS) and First-Order Reliability Method (FORM) provide a reliability analysis in axisymmetric deep tunnels driven in elastoplastic rocks. The Convergence-Confinement method (CV-CF) and Mohr-Coulomb (M-C) criterion are used to model the mechanical interaction between the shotcrete lining and ground through deterministic parameters and random variables. Numerical models synchronize tunnel analytical models and reliability methods, whereas the limit state functions control the failure probability in both ground plastic zone and shotcrete lining. The results showed that a low dispersion of random variables affects the plastic zone's reliability analysis in unsupported tunnels. Moreover, the support pressure generates a significant reduction in the plastic zone's failure, whereas the increase of shotcrete thickness results in great reduction of the lining collapse probability.

Probabilistic Risk Evaluation for Overall Stability of Composite Caisson Breakwaters in Korea

2020 ◽  
Vol 8 (3) ◽  
pp. 148
Author(s):  
Nhu Son Doan ◽  
Jungwon Huh ◽  
Van Ha Mac ◽  
Dongwook Kim ◽  
Kiseok Kwak
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Bearing Capacity ◽  
Failure Modes ◽  
Skewed Distribution ◽  
Resistance Force ◽  
First Order ◽  
Reliability Method ◽  
Overall Stability ◽  
Rubble Mound

In the present study, the overall stability of typical Korean composite caisson breakwaters that were initially designed following the conventional deterministic approach is investigated using reliability approaches. Therefore, the sensitivity of critical uncertainties regarding breakwater safety is analyzed. Uncertainty sources related to the structure, ocean conditions, and properties of the subsoil and rubble mound are considered in the reliability analysis. Sliding and overturning failures are presented as explicit equations, and three reliability methods, i.e., the mean value first-order second-moment, first-order reliability method, and Monte Carlo simulation, are applied in the evaluation process. Furthermore, the bearing capacity of the rubble mound and subsoil are analyzed using the discrete slice method conjugated with the Monte Carlo simulation. The results of this study establish that the sliding failure generally is the most frequent failure occurring among the above-mentioned overall stability failures (around 15 times more common than failures observed in the foundation). Additionally, it is found that the horizontal wave force primarily contributes to the sliding of the caisson body, whereas the friction coefficient is the main factor producing the resistance force. Furthermore, a much small probability of overturning failure implies that the overturning of a caisson around its heels uncommonly occurs during their lifetime, unlike other overall failure modes. Moreover, the failure in foundations may commonly encounter in the breakwater that has a high rubble mound structure compared with sliding mode. Particularly, the performance function of the all foundation bearing capacities presents a nonlinear behavior and positively skewed distribution when using the Monte Carlo simulation method. This phenomenon proves that simulation methods might be an appropriate approach to evaluate the bearing capacity of a breakwater foundation that can overcome several drawbacks of the conventional design approach.

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