Keywords: direct determined fully probabilistic method, ProbCalc, reliability assessment, probability of failure, distribution function, histogram.

The direct determined fully probabilistic method (DDFPM) has been developed as an alternative to the Monte Carlo method in the assessment of structural reliability in probabilistic calculations. Input random quantities (such as the load, geometry, material properties or imperfections) are expressed as histograms in the calculations. In the DDFPM calculations, all input random variables are combined with each other. The number of possible combinations is equal to the product of classes (intervals) of all input variables. With rather many input random variables, the number of combinations is very high. Only a small portion of possible combinations results, typically, in failure. When the DDFPM is used, the calculation takes too much time, because combinations are taken into account that do not contribute to the failure. Efforts to reduce the number of calculation operations have resulted in the development of algorithms that provide the numerical solution of the integral that defines formally the failure probability with rather many random variables.

All techniques in question that are generally referred to as "optimizing techniques" have been applied in the ProbCalc software system [1,2] developed since 2004 for computation of some probabilistic applications. A lite version of ProbCalc can be downloaded [3]. It is rather easy to implement an analytical model of the specific probabilistic application into ProbCalc. The reliability function under consideration can be expressed in ProbCalc analytically as an arithmetic expression (using the so-called calculator) or using data from the dynamic library (DLL files). DDFPM can now be used to solve a number of probabilistic computations (e.g. the probabilistic solution of fatigue crack propagation in bridge structures [4]).

The method enables, for instance, properties of load-carrying structures to be analyzed and investigated for certain loads. It is desirable both for theoretical science and practice to develop the probabilistic methods for the assessment of structure reliability and other probability tasks, because a number of input variables are random and it is not always a good solution to regard them as deterministic quantities.

1

P. Janas, M. Krejsa, V. Krejsa, "Structural Reliability Assessment Using Direct Determined Fully Probabilistic Calculation (DDFPM)", Proceedings of International Asranet colloquium, Glasgow, UK, ISBN 978-0-9553550-0-4, pp. 8, 2006.

2

P. Janas, M. Krejsa, V. Krejsa, "Current Possibilities of Direct Determined Fully Probabilistic Method (DDPFM)", Proceedings of 4th International ASRANet Colloquium, Athens, Greece, ISBN 978-0-9553550-2-8, 2008.

3

P. Janas, M. Krejsa, V. Krejsa, "ProbCalc Software System", http://www.fast.vsb.cz/pdpv, 2008.

4

V. Tomica, M. Krejsa, "Optimal Safety Level of Acceptable Fatigue Crack", in L. Taerwe, D. Proske, (Editors), Proceedings of 5th International Probabilistic Workshop, Ghent, Belgium, ISBN 978-3-00-022030-2, 2007.

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