A Monte Carlo simulation for the assessment of Bayesian updating in dynamic systems

Targoutzidis, Antonis

doi:10.1016/j.ress.2011.12.020

Cited by 7 publications

(3 citation statements)

References 5 publications

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“…Considering the characteristics of the semi-enclosed spaces of the tunnels, the prior distributions could be dynamically determined by Bayesian updating [33][34][35][36][37][38][39]. The prior data of µ, σ, and λ are constantly added to the database with the tunnel excavation, as shown in Figure 7.…”

Section: Relative Error(%)mentioning

confidence: 99%

A New Perspective on Predicting Roughness of Discontinuity from Fractal Dimension D of Outcrops

et al. 2023

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In tunnel construction, predicting the roughness of discontinuity is significant for preventing the collapse of the excavation face. However, currently, we are unable to use a parameter with invariant properties to quantify and predict the roughness of discontinuity. Fractal dimension D is one such parameter that be used to characterize the roughness of discontinuity. The study proposes a new method to predict the roughness of discontinuity from the fractal dimension D of outcrops. The measurement method of the coordinates of outcrops is firstly summarized, and the most suitable method of calculating fractal dimension D is then provided. For characterizing the spatial variability of fractal dimension D, the random field of fractal dimension D is discretized, and the prediction model is then established based on Bayesian theory. The proposed method is applied to one tunnel for predicting the roughness of discontinuity, and the results indicate that the relative errors of prediction are less than 1.5%. The sensitivities of correlation function and discontinuity size are analyzed. It is found that the different correlation functions have no obvious effect on the prediction results, and the proposed method is well applied to relatively large sizes of discontinuity.

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Section: Relative Error(%)mentioning

confidence: 99%

A New Perspective on Predicting Roughness of Discontinuity from Fractal Dimension D of Outcrops

et al. 2023

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“…Diagram models provide efficient inference of modeling and lead to satisfied solutions using dynamic diagram modeling methods such as dynamic fault tree (DFT), 5 reliability block diagram, 6 binary decision diagram, 7 Markov chain, 8 and dynamic Bayesian network (DBN) 9–11 . Among others, the DBN is one of the most extensively used tools for the dynamic systems modeling by discrete‐time Bayesian network (DTBN), 12 continuous‐time Bayesian network (CTBN), 13 and Monte Carlo simulation (MCS) 14 …”

Section: Introductionmentioning

confidence: 99%

“…Meanwhile, Yeh 19 combined the Swarm Optimization and the MCS techniques to efficiently evaluate the reliability of complex networks. Targoutzidis 14 employed the MCS to assess the effectiveness of Bayesian updating on the dynamic system. Aslett 20 proposed a multilevel MCS method to solve the reliability evaluation problems for both repairable and nonrepairable components in large systems.…”

Section: Introductionmentioning

confidence: 99%

An algorithm of discrete‐time Bayesian network for reliability analysis of multilevel system with warm spare gate

et al. 2020

Quality & Reliability Eng

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Discrete‐time Bayesian network (DTBN) is a popular tool for the reliability analysis of dynamic systems, which, however, is insufficient in analyzing the reliability of multilevel system (MLS) with warm spare (WSP) gates. Additionally, conventional DTBNs are not able to consider the situation that dormant components and primary components may fail during the same time interval. To this end, this paper analyzes the dynamic reliability characteristics of dormant systems with WSP gates by utilizing DTBNs. Moreover, an algorithm of modeling the conditional probability table (CPT) for WSP gates together with a new schedule of constructing dynamic Bayesian networks is put forward. The validation of the proposed techniques is implemented by Monte Carlo simulation (MCS) and reliability analysis of an actual communication station system.

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Relevance of control theory to design and maintenance problems in time-variant reliability: The case of stochastic viability

Rougé¹,

Mathias²,

Deffuant³

2014

Reliability Engineering & System Safety

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The goal of this paper is twofold: 1) to show that time-variant reliability and a branch of control theory called stochastic viability address similar problems with different points of view, and 2) to demonstrate the relevance of concepts and methods from stochastic viability in reliability problems. On the one hand, reliability aims at evaluating the probability of failure of a system subjected to uncertainty and stochasticity. On the other hand, viability aims at maintaining a controlled dynamical system within a survival set. When the dynamical system is stochastic, this work shows that a viability problem belongs to a specific class of design and maintenance problems in time-variant reliability. Dynamic programming, which is used for solving Markovian stochastic viability problems, then yields the set of design states for which there exists a maintenance strategy which guarantees reliability with a confidence level β for a given period of time T . Besides, it leads to a straightforward computation of the date of the first outcrossing, informing on when the system is most likely to fail. We illustrate this approach with a simple example of population dynamics, including a case where load increases with time.

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A Monte Carlo simulation for the assessment of Bayesian updating in dynamic systems

Cited by 7 publications

References 5 publications

A New Perspective on Predicting Roughness of Discontinuity from Fractal Dimension D of Outcrops

A New Perspective on Predicting Roughness of Discontinuity from Fractal Dimension D of Outcrops

An algorithm of discrete‐time Bayesian network for reliability analysis of multilevel system with warm spare gate

Relevance of control theory to design and maintenance problems in time-variant reliability: The case of stochastic viability

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