M. Ahammed

Probabilistic estimation of remaining life of a pipeline in the presence of active corrosion defects

A methodology is presented for the assessment of remaining life of a pressurised pipeline containing active corrosion defects. A probabilistic approach is adopted to this methodology and the associated variables are represented by normal or non-normal probabilistic distributions. A failure pressure model based on fracture mechanics is adopted for the assessment of pipeline failure pressure and linear idealisation of the long-term corrosion growth rate is carried out. Because of the presence of nonlinearity in the limit state function and also of the presence of non-normal variables, the Level II advanced first order second moment iterative method is employed for carrying out reliability analyses. The methodology is applied to an example pipeline and the remaining useful life of this pipeline is assessed. Relative contribution of the random variables and the sensitivity of the reliability index to the change in variance of the random variables is also investigated.

Probabilistic analysis of underground pipelines subject to combined stresses and corrosion

This paper presents a nonlinear limit state model for the analysis of underground pipelines, stressed both in the circumferential and the longitudinal directions. The effects of internal fluid pressure, external soil and traffic loads, temperature and longitudinal pipe bending etc., are considered. A nonlinear corrosion model is used to represent the loss of pipe wall thickness with time. To allow for the uncertainties of the design variables, a reliability analysis technique has been adopted; this also allows calculation of the relative contribution of the random variables and the sensitivity of the reliability index or failure probability. Results obtained for typical pipelines are presented.

Reliability estimation of pressurised pipelines subject to localised corrosion defects

This paper describes a probabilistic method for the assessment of the suitability of corroded pipelines under pressure loading. The method takes into account the uncertainties of the variables that influence suitability. The paper starts with a review of the various available techniques for the assessment of failure pressure of corroded pipelines and then develops a probabilistic limit state model from the available deterministic failure equations. The advanced first-order second moment method is then employed to estimate reliability. This approach is then applied to some typical examples. The results are presented in graphical form.

Probabilistic analysis of pipelines subjected to pitting corrosion leaks

Abstract A methodology is described for the assessment of the service life of liquid carrying metallic pipelines subjected to pitting corrosion. The estimate of pipeline life is based on the loss of liquid through pit holes during transportation. The growth of corrosion pits is modelled by a two-parameter exponential function having time dependency and a decreasing rate of pit growth. Parameters which are related to corrosion, pipeline dimension and liquid flow are treated as probabilistic variables. The first-order reliability method is used to estimate the probability of failure and the relative contribution of the various uncertain parameters to it. Failure is defined in terms of a maximum allowable degree of loss or ingress of fluid. Numerical results are given for a typical example pipeline. A sensitivity study was also carried out for the example pipeline to reveal the effect of the level of variability of some of the random variables on the failure probability. The results show that the probability of failure increases nonlinearly with time and that the contribution of pit hole size and pitting corrosion parameters are very significant for long service lives.

Gradient and parameter sensitivity estimation for systems evaluated using Monte Carlo analysis

The performance evaluation of many practical systems can be handled only through computationally intensive Monte Carlo simulation. Although a number of specialist techniques have been proposed, in general, estimation of the sensitivity of the outcome to changes in parameters involves duplicate simulations and finite differences for each parameter of interest. An approximate technique for gradient sensitivity estimation was outlined previously. It is appropriate when the performance function is uni-modal and relatively smooth in the region of interest. It generates all gradients simultaneously by converting Monte Carlo simulation run outcomes to an approximate analytic problem defined by a simplified response surface. The gradients then follow immediately. No extra simulation runs are required. Herein that approach is extended to non-Normal random variables and to the estimation of parameter sensitivities for random variable means and standard deviations. Some illustrative examples are given with comparisons to sensitivities computed by conventional Monte Carlo. The influence of constraint function(s) defining the admissible solution region is also considered.

Prediction of remaining strength of corroded pressurised pipelines

In this paper a deterministic model is developed which can be used to evaluate the remaining strength of corroded steel pipeline over time. This model also can be used to evaluate the maximum allowable failure pressure of corroded pipelines. The motivation for the development of the model is that during in-service conditions the strength of pressurised pipelines may be impaired, for example, from the failure of the protective coatings, paint surfaces or cathodic protection or as a result of externally applied mechanical damage or as a result of ageing (e.g. fatigue). Any of these may lead to the initiation of corrosion at the damaged area if it is not repaired. Once initiated, corrosion increases gradually both in extent and depth with increased exposure period. This results in the reduction of the remaining strength and hence a reduction in the carrying capacity of a pipeline. It also creates uncertainty about the future capacity. The proposed model is related to accepted methods for estimating the remaining strength of pipelines, but uses a simple corrosion model to estimate future remaining life. A sensitivity analysis can be used to investigate the effect of corrosion parameters on the pipeline carrying capacity. A simple example is given to illustrate the approach.

FORM for discontinuous and truncated probability density functions

The common iterative FORM algorithm deals with random variables having continuous and smooth probability density functions. In some cases when the algorithm is applied to problems with discontinuous probability density functions difficulties may occur with convergence. For truncated density functions the routine may breakdown completely. Some examples illustrating these potential problems are given and the reasons described. Modifications to the standard iterative FORM algorithm are proposed.

Estimation of failure probabilities for intersections of non-linear limit states

This paper is concerned with estimating the failure probability associated with the intersection of two or more non-linear limit state functions. Previous work has relied on the use of general non-linear minimization routines to establish the intersection point of the limit states and then to use tangents to bound the region for estimating the failure probability. The present paper outlines two approaches based on successive approximation both to find the intersection point and to estimate the intersection probability. It is shown that the results for selected examples converge to the probabilities estimated using Monte Carlo analysis. Comments about extending the results to using second order or asymptotic probability estimates close the paper.

Gradient estimation for applied Monte Carlo analyses

Abstract For many practical applications of system analysis by Monte Carlo simulation, an important piece of information is the sensitivity of the outcome to input information. One matter of interest is the sensitivity of the outcome of the variables controlling it, that is the gradients with respect to the (usually implicit) performance function. Typically, analytical first (and higher) derivatives are not available and the usual numerical approach requires major computational effort. The present paper proposes estimation of gradients using a simplified (linear) response surface, which is a function of the random variables, and which is constructed after the Monte Carlo simulation has been performed. It uses all, or a subset of, the simulation run outcomes. No extra simulation runs are required. There are few restrictions on the form of the performance function and the gradients are estimated at small computational cost. The present paper is restricted to normal random variables.

Statistical Characterization of Corroded Steel Plate Surfaces

Perforation of steel plate is of considerable interest for the longer-term safety and integrity of ships hulls and tanks and for nuclear containment systems. This paper reports on the preliminary random field characterization of the surface of two sample corroded steel plates as a trial towards generating numerically the surface topology of larger areas of steel plate. Of particular interest is the maximum depth of penetration and its dependence structure across the plate area. The potential applications and the background to the modelling of corrosion loss and pitting are reviewed briefly to set the scene for appropriate surface characterization. Contrary to the assumptions often made for the statistical characterization of maximum pit penetrations, they are highly dependent. This makes representation using extreme value probability distributions questionable. An alternative probability-based form of representation is proposed.