Computational & Technology Resources
an online resource for computational,
engineering & technology publications 

CivilComp Proceedings
ISSN 17593433 CCP: 86
PROCEEDINGS OF THE ELEVENTH INTERNATIONAL CONFERENCE ON CIVIL, STRUCTURAL AND ENVIRONMENTAL ENGINEERING COMPUTING Edited by: B.H.V. Topping
Paper 240
NonParametric Approach to Probabilistic Analysis of Structural Failures of Cast Iron Pipes A. Dehghan^{1}^{2}, K.J. McManus^{1} and E.F. Gad^{3}
^{1}Faculty of Engineering and Industrial Sciences, Swinburne University of Technology, Melbourne, Australia
A. Dehghan, K.J. McManus, E.F. Gad, "NonParametric Approach to Probabilistic Analysis of Structural Failures of Cast Iron Pipes", in B.H.V. Topping, (Editor), "Proceedings of the Eleventh International Conference on Civil, Structural and Environmental Engineering Computing", CivilComp Press, Stirlingshire, UK, Paper 240, 2007. doi:10.4203/ccp.86.240
Keywords: water mains, failure prediction, nonparametric, maximum likelihood estimation, probabilistic.
Summary
In addition to the physical characteristics, there are a range of environmental and operational factors influencing the mechanism of failure of pipes in water distribution systems [1]. Some of these, are nonstationary random variables. Resulting nonstationarity of pattern of failures over time can not be accurately modelled with specific probability distributions, with timeinvariant parameters. This study presents a nonparametric failure prediction technique which is considering the nonstationary nature of failure process. This technique is applied to the failure history of cast iron pipes in the Western suburbs of Melbourne to estimate the expected number of failures for each group of pipes, within a number of time intervals in future. Furthermore, an 80% confidence interval is determined for the estimations. The presented method implicitly considers the gradual variations of the factors influencing the deterioration process. In other words, the outputs of the prediction method are automatically updated with time.
At the first step, failure history is divided into some intervals considering the frequency of failures. The ensemble of probabilities of occurrence of k failures during each time interval are called the Likelihood of Number of Failures (LNF). For a homogeneous group of pipes, histogram technique is used to calculate the LNF values in each period (a number of time intervals). The binary proposition "k failures occur during the nth time interval" is denoted by NOF_{k}(n) where NOF stands for the "Number of Failures" and n is the interval number. The times elapsed between consecutive NOF_{k} events are the corresponding interfailuretimes. For each k, set of interfailuretimes are empirically calculated using the failure history. In this technique, the problem of prediction of LNF values is turned into prediction of interfailuretimes. To predict the interfailuretimes, Finite Impulse Response (FIR) filters are applied. Predicted interfailuretimes are used to estimate the LNF values in the next time interval. The probabilistic values for a given time in future are estimated based on convolution theorem. From these, expected number of failures in a time in future, are estimated, along with a confidence interval for the estimation. The method presented implicitly considers the gradual variations of the factors influencing the deterioration process. In other words, the outputs of the prediction method are automatically updated with time. This is because every time interval corresponds with a NOF value and adds a new time interval µ_{k} to the record. An inverse relationship between the accuracy of predictions made for interfailuretimes and the corresponding LNF values is realized and demonstrated. This shows the high tolerance of the method to the possible inaccuracies in selected interfailuretime predictions that is a point of strength for the technique. It is also illustrated that, the accuracy of prediction decreases as the range of prediction widens. A step by step algorithm for applying this technique on a pipe failure history is presented. An illustrative and quantitative comparison of the accuracy of estimations performed by proposed technique and simple averaging method exhibits the satisfactory performance of developed technique. References
purchase the fulltext of this paper (price £20)
go to the previous paper 
