scholarly journals Calculation of Failure Probability of Constantly Loaded Cantilever Beam by Monte Carlo Method

2014 ◽  
Vol 17 (3) ◽  
pp. 80-82
Author(s):  
Dušan Páleš ◽  
Milada Balková ◽  
Ingrid Karandušovská
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Method ◽  
Cantilever Beam ◽  
Probability Distributions ◽  
Probabilistic Approach ◽  
Constant Load ◽  
Probability Of Failure ◽  
The Subject ◽  
Individual Variables ◽  
The Mathematical Model

Abstract In this paper, we demonstrate a probabilistic approach to the design of structures on a cantilever beam with constant load. Individual variables in the mathematical model are not represented deterministically by their specifc values but randomly by probability distributions. Normal distribution is used for all random variables. The resulting probability of failure is calculated using a simple Monte Carlo method, for which a brief overview is also provided in this article. Such a probabilistic proposal is the subject matter of newly emerging feld Reliability of Structures.

scholarly journals Technical-Economic Analysis of Grapple Saw

2020 ◽  
Vol 41 (2) ◽  
pp. 219-229 ◽  
Author(s):  
Ricardo Hideaki Miyajima ◽  
Paulo Torres Fenner ◽  
Gislaine Cristina Batistela ◽  
Danilo Simões
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Monte Carlo Method ◽  
Probability Distributions ◽  
Simulation Method ◽  
Forest Harvesting ◽  
Production Costs ◽  
Wood Harvesting ◽  
Food And Agriculture ◽  
The Monte Carlo Method

The processing of Eucalyptus logs is a stage that follows the full tree system in mechanized forest harvesting, commonly performed by grapple saw. Therefore, this activity presents some associated uncertainties, especially regarding technical and silvicultural factors that can affect productivity and production costs. To get around this problem, Monte Carlo simulation can be applied, or rather a technique that allows to measure the probabilities of values from factors that are under conditions of uncertainties, to which probability distributions are attributed. The objective of this study was to apply the Monte Carlo method for determining the probabilistic technical-economical coefficients of log processing using two different grapple saw models. Field data were obtained from an area of forest planted with Eucalyptus, located in the State of São Paulo, Brazil. For the technical analysis, the time study protocol was applied by the method of continuous reading of the operational cycle elements, which resulted in production. As for the estimated cost of programmed hour, the applied methods were recommended by the Food and Agriculture Organization of the United Nations. The incorporation of the uncertainties was carried out by applying the Monte Carlo simulation method, by which 100,000 random values were generated. The results showed that the crane empty movement is the operational element that most impacts the total time for processing the logs; the variables that most influence the productivity are specific to each grapple saw model; the difference of USD 0.04 m3 in production costs was observed between processors with gripping area of 0.58 m2 and 0.85 m2. The Monte Carlo method proved to be an applicable tool for mechanized wood harvesting for presenting a range of probability of occurrences for the operational elements and for the production cost.

scholarly journals Application of Monte Carlo Methods to Consider Probabilistic Effects in a Race Simulation for Circuit Motorsport

2020 ◽  
Vol 10 (12) ◽  
pp. 4229 ◽  
Author(s):  
Alexander Heilmeier ◽  
Michael Graf ◽  
Johannes Betz ◽  
Markus Lienkamp
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Monte Carlo Method ◽  
State Of The Art ◽  
Probability Distributions ◽  
Strategic Decisions ◽  
The Monte Carlo Method ◽  
Random Events ◽  
Example Variability

Applying an optimal race strategy is a decisive factor in achieving the best possible result in a motorsport race. This mainly implies timing the pit stops perfectly and choosing the optimal tire compounds. Strategy engineers use race simulations to assess the effects of different strategic decisions (e.g., early vs. late pit stop) on the race result before and during a race. However, in reality, races rarely run as planned and are often decided by random events, for example, accidents that cause safety car phases. Besides, the course of a race is affected by many smaller probabilistic influences, for example, variability in the lap times. Consequently, these events and influences should be modeled within the race simulation if real races are to be simulated, and a robust race strategy is to be determined. Therefore, this paper presents how state of the art and new approaches can be combined to modeling the most important probabilistic influences on motorsport races—accidents and failures, full course yellow and safety car phases, the drivers’ starting performance, and variability in lap times and pit stop durations. The modeling is done using customized probability distributions as well as a novel “ghost” car approach, which allows the realistic consideration of the effect of safety cars within the race simulation. The interaction of all influences is evaluated based on the Monte Carlo method. The results demonstrate the validity of the models and show how Monte Carlo simulation enables assessing the robustness of race strategies. Knowing the robustness improves the basis for a reasonable determination of race strategies by strategy engineers.

Simplified Strength Reliability and Integrity Analysis of TTRs

2014 ◽  
Author(s):  
Mir Emad Mousavi ◽  
Sanjeev Upadhye ◽  
Kevin Haverty
Keyword(s):  
Extreme Events ◽  
Structural Reliability ◽  
Probability Distributions ◽  
Probabilistic Approach ◽  
Reliability Assessment ◽  
Cost Effective ◽  
Probability Of Failure ◽  
Annual Probability ◽  
Reliability Methods ◽  
Integrity Analysis

The design of riser systems can be improved if structural reliability methods are used to assess their safety and integrity and confirm that such design meets a target annual probability of failure. TTRs are typically multi–bore assemblies involving several sub-assemblies. The failure of any of the components of a TTR under extreme or service environmental conditions can lead to an immediate failure of the entire assembly and impose a direct risk of damaging the wellheads, conductors, casing and tubing hangers, or other subsea equipment, because they are installed directly on top of the wellhead. However, the actual strength safety of the TTR cannot be examined unless after it is installed and examined under extreme events. Because of the numerous uncertainties associated with the design of TTRs, a probabilistic approach based on structural reliability methods can account for many of those uncertainties and serve as a basis for their reliable and cost-effective design. In turn, a comprehensive reliability assessment of a TTR requires extensive analysis that is considerably more complex and time consuming compared to a conventional deterministic-based analysis. This paper presents a probabilistic-based simplified methodology for the strength reliability assessment of TTR systems. In this method, marginal values on some uncertain model inputs are considered similar to the conventional analysis methods but, some key random variables related to environmental demands and component capacities are considered with their associated probability distributions. As a result, this method can be used to estimate the minimum level of safety of the TTR under extreme events. Additionally, results of the proposed method are discussed for integrity analysis and integrity-based optimal design of the TTR system, which compare the safety of the TTR components and estimate the component Optimality Factors for improving the design integrity and meeting a target minimum annual probability of failure.

scholarly journals Planning Tunnel Construction Using Markov Chain Monte Carlo (MCMC)

2015 ◽  
Vol 2015 ◽  
pp. 1-8 ◽  
Author(s):  
Juan P. Vargas ◽  
Jair C. Koppe ◽  
Sebastián Pérez ◽  
Juan P. Hurtado
Keyword(s):  
Monte Carlo ◽  
Markov Chain ◽  
Markov Chain Monte Carlo ◽  
Monte Carlo Method ◽  
Probability Distributions ◽  
Financial Risks ◽  
Underground Excavation ◽  
Construction Time ◽  
Tunnel Excavation ◽  
Unit Operations

Tunnels, drifts, drives, and other types of underground excavation are very common in mining as well as in the construction of roads, railways, dams, and other civil engineering projects. Planning is essential to the success of tunnel excavation, and construction time is one of the most important factors to be taken into account. This paper proposes a simulation algorithm based on a stochastic numerical method, the Markov chain Monte Carlo method, that can provide the best estimate of the opening excavation times for the classic method of drilling and blasting. Taking account of technical considerations that affect the tunnel excavation cycle, the simulation is developed through a computational algorithm. Using the Markov chain Monte Carlo method, the unit operations involved in the underground excavation cycle are identified and assigned probability distributions that, with random number input, make it possible to simulate the total excavation time. The results obtained with this method are compared with a real case of tunneling excavation. By incorporating variability in the planning, it is possible to determine with greater certainty the ranges over which the execution times of the unit operations fluctuate. In addition, the financial risks associated with planning errors can be reduced and the exploitation of resources maximized.

A probability model for fibrous composites with local load sharing

1980 ◽  
Vol 372 (1751) ◽  
pp. 539-553 ◽  
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Method ◽  
Extreme Value Theory ◽  
Probabilistic Analysis ◽  
Asymptotic Theory ◽  
Probability Model ◽  
Probability Of Failure ◽  
Value Theory ◽  
Fibrous Composites ◽  
The Monte Carlo Method

The chain-of-bundles model for fibrous composites is reviewed, and an approximation to the probability of failure is derived. This leads to formulae for predicting the strength of such a composite. These formulae are developed in the context of an asymptotic theory, and the Monte Carlo method is used to study a specific case in more detail. We also discuss the size effect. The probabilistic analysis relies heavily on extreme value theory, and a brief survey of the relevant parts of that theory is included.

Exit Condition for Probabilistic Assessment Using Monte Carlo Method

2010 ◽  
Vol 10 (1) ◽  
pp. 1-9
Author(s):  
Jakub Valihrach ◽  
Petr Konečný
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Monte Carlo Method ◽  
Optimization Design ◽  
Random Variable ◽  
Probability Of Failure ◽  
Probabilistic Assessment ◽  
Theoretical Derivation ◽  
The Monte Carlo Method ◽  
The Relationship

Exit Condition for Probabilistic Assessment Using Monte Carlo Method This paper introduces a condition used to exit a probabilistic assessment using the Monte Carlo simulation, and to evaluate it with regard to the relationship between the computed estimate of the probability of failure and the target design probability. The estimation of probability of failure is treated as a random variable, considering its variance that is dependent on the number of performed Monte Carlo simulation steps. After theoretical derivation of the decision condition, it is tested numerically with regard to its accuracy and computational efficiency. The condition is suitable for optimization design using the Monte Carlo method.

Estimation of Random Variable Distribution Parameters by the Monte Carlo Method

2013 ◽  
Vol 20 (2) ◽  
pp. 249-262 ◽  
Author(s):  
Sergiusz Sienkowski
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Method ◽  
Random Variable ◽  
Statistical Parameters ◽  
The Monte Carlo Method ◽  
Variable Distribution ◽  
Distribution Parameters ◽  
The Subject ◽  
The Mean ◽  
Typical Measurement

Abstract The paper is concerned with issues of the estimation of random variable distribution parameters by the Monte Carlo method. Such quantities can correspond to statistical parameters computed based on the data obtained in typical measurement situations. The subject of the research is the mean, the mean square and the variance of random variables with uniform, Gaussian, Student, Simpson, trapezoidal, exponential, gamma and arcsine distributions.

Balanced Incomplete Block Designs Used in the Method of Simulation

1969 ◽  
Vol 95 (2) ◽  
pp. 323-334
Author(s):  
A. W. Joseph
Keyword(s):  
Monte Carlo ◽  
Random Error ◽  
Probability Distributions ◽  
The Other ◽  
Block Designs ◽  
Incomplete Block ◽  
Balanced Incomplete Block Designs ◽  
The Monte Carlo Method ◽  
The Subject ◽  
Balanced Incomplete Block

The method of simulation, alternatively known as the Monte Carlo method, to which Sidney Benjamin drew our attention is a lazy way of solving problems that could be solved accurately but for the large number of different logical situations that have to be considered. The method traces out what actually happens if the conditions of a problem are observed and if certain unknown events are presumed to occur at random. The solution is taken to be the average of the results of all the experiments. Inevitably, however, this method gives rise to random error. Now certain actuarial problems depend on making assumptions on such things as the mortality to be expected to be experienced by a life or set of lives. It is of little consequence if random error is imposed on top of such assumptions. On the other hand the shape of the probability distributions that the random variables in the problem are to follow may be known exactly. For such a problem the introduction of random error is a blemish that should be made as small as possible. In this note one such problem will be considered. The argument will introduce the subject of balanced incomplete block designs, which, as far as the writer knows, have only once been touched on by an actuary and that over one hundred years ago. The problem is the chance that a Jackpot may be opened at the game of Poker, discussed by Redish and Ross.

scholarly journals A Markov chain Monte Carlo method family in incomplete data analysis

2003 ◽  
Vol 44 (159) ◽  
pp. 147-158
Author(s):  
Vladimir Vasic
Keyword(s):  
Monte Carlo ◽  
Markov Chain ◽  
Markov Chain Monte Carlo ◽  
Monte Carlo Method ◽  
Incomplete Data ◽  
Probability Distribution Function ◽  
Random Variable ◽  
Target Distribution ◽  
Direct Sampling ◽  
The Subject

A Markov chain Monte Carlo method family is a collection of techniques for pseudorandom draws out of probability distribution function. In recent years, these techniques have been the subject of intensive interest of many statisticians. Roughly speaking, the essence of a Markov chain Monte Carlo method family is generating one or more values of a random variable Z, which is usually multidimensional. Let P(Z) = f(Z) denote a density function of a random variable Z, which we will refer to as a target distribution. Instead of sampling directly from the distribution f, we will generate [Z(1), Z(2)..., Z(t),... ], in which each value is, in a way, dependant upon the previous value and where the stationary distribution will be a target distribution. For a sufficient value of t, Z(t) will be approximately random sampling of the distribution f. A Markov chain Monte Carlo method family is useful when direct sampling is difficult, but when sampling of each value is not.

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