The Effect of Corrosion Growth Model Assumptions on the Reliability Estimates of Corroded Pipelines

Author(s):  
Markus R. Dann ◽  
Luc Huyse

Corrosion growth models are used to estimate future metal loss and the safe remaining lifetime of corrosion features in pipelines. Probabilistic models have become increasingly important in practice for reliability and risk-based pipeline assessments. The unknown model variables are usually determined from in-line inspection (ILI) results. Corrosion growth models exhibit various levels of complexity to account for temporal and spatial uncertainties of the actual corrosion growth process, and measurement uncertainties associated with ILIs. Model diversity leads to significant differences in how the models approach the uncertainty of future corrosion growth. This paper builds upon previous work and provides some theoretical background to an application described in [1]. It compares four common probabilistic corrosion growth models with respect to reliability estimates of leak failure. The four models are two uncertain corrosion rate models and two stochastic process models where the features are considered to be either independent or exchangeable. The unknown random variables of each model are updated in a Bayesian manner using the same ILI results. The key findings of this paper are: • Proper truncation at zero of the probability distributions for the unknown random variables is necessary if the measured corrosion growth is near zero or negative. • A stochastic process leads to lower uncertainties when determining future metal loss and, consequently, an increased reliability against leak failure than corrosion rate models. • The assumption of exchangeable features causes a reduction in the probability of leak failure due to the effect of borrowing information compared to independent features. The four corrosion growth models provide similar results with respect to the probability of failure if the measured corrosion growth is large. As the measured corrosion growth decreases in size, the differences between the reliability estimates increase.

2011 ◽  
Vol 2011 ◽  
pp. 1-13 ◽  
Author(s):  
Linda Smail

Bayesian Networks are graphic probabilistic models through which we can acquire, capitalize on, and exploit knowledge. they are becoming an important tool for research and applications in artificial intelligence and many other fields in the last decade. This paper presents Bayesian networks and discusses the inference problem in such models. It proposes a statement of the problem and the proposed method to compute probability distributions. It also uses D-separation for simplifying the computation of probabilities in Bayesian networks. Given a Bayesian network over a family of random variables, this paper presents a result on the computation of the probability distribution of a subset of using separately a computation algorithm and D-separation properties. It also shows the uniqueness of the obtained result.


Entropy ◽  
2021 ◽  
Vol 23 (2) ◽  
pp. 241
Author(s):  
Arthur Matsuo Yamashita Rios de Sousa ◽  
Hideki Takayasu ◽  
Didier Sornette ◽  
Misako Takayasu

The Sigma-Pi structure investigated in this work consists of the sum of products of an increasing number of identically distributed random variables. It appears in stochastic processes with random coefficients and also in models of growth of entities such as business firms and cities. We study the Sigma-Pi structure with Bernoulli random variables and find that its probability distribution is always bounded from below by a power-law function regardless of whether the random variables are mutually independent or duplicated. In particular, we investigate the case in which the asymptotic probability distribution has always upper and lower power-law bounds with the same tail-index, which depends on the parameters of the distribution of the random variables. We illustrate the Sigma-Pi structure in the context of a simple growth model with successively born entities growing according to a stochastic proportional growth law, taking both Bernoulli, confirming the theoretical results, and half-normal random variables, for which the numerical results can be rationalized using insights from the Bernoulli case. We analyze the interdependence among entities represented by the product terms within the Sigma-Pi structure, the possible presence of memory in growth factors, and the contribution of each product term to the whole Sigma-Pi structure. We highlight the influence of the degree of interdependence among entities in the number of terms that effectively contribute to the total sum of sizes, reaching the limiting case of a single term dominating extreme values of the Sigma-Pi structure when all entities grow independently.


Author(s):  
RONALD R. YAGER

We look at the issue of obtaining a variance like measure associated with probability distributions over ordinal sets. We call these dissonance measures. We specify some general properties desired in these dissonance measures. The centrality of the cumulative distribution function in formulating the concept of dissonance is pointed out. We introduce some specific examples of measures of dissonance.


1995 ◽  
Vol 34 (1) ◽  
pp. 1-16 ◽  
Author(s):  
Anatoli I. Yashin ◽  
Kenneth G. Manton ◽  
Max A. Woodbury ◽  
Eric Stallard

1958 ◽  
Vol 10 ◽  
pp. 222-229 ◽  
Author(s):  
J. R. Blum ◽  
H. Chernoff ◽  
M. Rosenblatt ◽  
H. Teicher

Let {Xn} (n = 1, 2 , …) be a stochastic process. The random variables comprising it or the process itself will be said to be interchangeable if, for any choice of distinct positive integers i 1, i 2, H 3 … , ik, the joint distribution of depends merely on k and is independent of the integers i 1, i 2, … , i k. It was shown by De Finetti (3) that the probability measure for any interchangeable process is a mixture of probability measures of processes each consisting of independent and identically distributed random variables.


2018 ◽  
Vol 34 (3) ◽  
pp. 1247-1266 ◽  
Author(s):  
Hua Kang ◽  
Henry V. Burton ◽  
Haoxiang Miao

Post-earthquake recovery models can be used as decision support tools for pre-event planning. However, due to a lack of available data, there have been very few opportunities to validate and/or calibrate these models. This paper describes the use of building damage, permitting, and repair data from the 2014 South Napa Earthquake to evaluate a stochastic process post-earthquake recovery model. Damage data were obtained for 1,470 buildings, and permitting and repair time data were obtained for a subset (456) of those buildings. A “blind” prediction is shown to adequately capture the shape of the recovery trajectory despite overpredicting the overall pace of the recovery. Using the mean time to permit and repair time from the acquired data set significantly improves the accuracy of the recovery prediction. A generalized model is formulated by establishing statistical relationships between key time parameters and endogenous and exogenous factors that have been shown to influence the pace of recovery.


2012 ◽  
Vol 2012 ◽  
pp. 1-13 ◽  
Author(s):  
C. F. Lo

We have presented a new unified approach to model the dynamics of both the sum and difference of two correlated lognormal stochastic variables. By the Lie-Trotter operator splitting method, both the sum and difference are shown to follow a shifted lognormal stochastic process, and approximate probability distributions are determined in closed form. Illustrative numerical examples are presented to demonstrate the validity and accuracy of these approximate distributions. In terms of the approximate probability distributions, we have also obtained an analytical series expansion of the exact solutions, which can allow us to improve the approximation in a systematic manner. Moreover, we believe that this new approach can be extended to study both (1) the algebraic sum ofNlognormals, and (2) the sum and difference of other correlated stochastic processes, for example, two correlated CEV processes, two correlated CIR processes, and two correlated lognormal processes with mean-reversion.


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