Keywords: direct optimized probabilistic calculation, DOProC, probability of failure, fatigue crack propagation, inspection of structure, random variable.

This paper deals with application of the newly developed direct optimized probabilistic calculation (DOProC) the theoretical background of which has been explained in detail elsewhere [1,2]. DOProC is used typically for probabilistic tasks where certain input quantities are of a random nature and can be described using stochastic empirical or parametric distributions. DOProC is used mainly in probabilistic reliability assessment of load carrying structures or in probabilistic designs of structural elements with the specified reliability.

In many cases, this calculation method is very efficient and provides accurate estimates of the probabilities. Only a numerical error and an error resulting from discretizing of input and output quantities are involved there. A disadvantage is that much machine time is needed for calculation of the task because the task comprises rather many random quantities which are discretized by rather many intervals or classes. This means, optimizing techniques should be used to reduce the machine time required for tcalculation and maintaining, at the same time, the correctness of the solution [1,2].

DOProC has been successfully applied, among others, in the probabilistic calculation of fatigue cracks in steel structures and bridges which are subject to cyclical loads where cracks were propagating from both the surface and edge. The software developed for that purpose, FCProbCalc [3], makes it possible to monitor efficiently and operatively the development of fatigue damage to the structure. The goal of the probabilistic calculation is to determine the time for the first inspection which should reveal damage to the structure. If no fatigue cracks are found, the analysis of inspection results gives the conditional probability during the occurrence and the time for future inspections. The methods and application can considerably improve the estimation of maintenance costs for the structures and bridges subject to cyclical loads.

1

P. Janas, M. Krejsa, V. Krejsa, "Structural Reliability Assessment using a Direct Determined Probabilistic Calculation", in B.H.V. Topping, L.F. Costa Neves, R.C. Barros, (Editors), "Proceedings of the Twelfth International Conference on Civil, Structural and Environmental Engineering Computing", Civil-Comp Press, Stirlingshire, UK, Paper 72, 2009. doi:10.4203/ccp.91.72

2

P. Janas, M. Krejsa, V. Krejsa, "Using the Direct Determined Fully Probabilistic Method (DDFPM) for determination of failure", in R. Bris, C.G. Soares, S. Martorell, (Editors), "Reliability, Risk and Safety: Theory and Applications", CRC Press-Taylor & Francis Group, London, Vols 1-3, 1467-1474, 2010. WOS 000281188500203

3

M. Krejsa, V. Krejsa, "Program FCProbCalc [EXE] - Program for Probability Calculation of Fatigue Crack Progression", authorized software, VSB-Technical University Ostrava, 2011. http://www.fast.vsb.cz/popv

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