• Structural Engineering and Mechanics
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• v.64 no.4
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• pp.413-426
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• 2017

Probabilistic methods are used in engineering where a computational model contains random variables. The proposed method under development: Direct Optimized Probabilistic Calculation (DOProC) is highly efficient in terms of computation time and solution accuracy and is mostly faster than in case of other standard probabilistic methods. The novelty of the DOProC lies in an optimized numerical integration that easily handles both correlated and statistically independent random variables and does not require any simulation or approximation technique. DOProC is demonstrated by a collection of deliberately selected simple examples (i) to illustrate the efficiency of individual optimization levels and (ii) to verify it against other highly regarded probabilistic methods (e.g., Monte Carlo). Efficiency and other benefits of the proposed method are grounded on a comparative case study carried out using both the DOProC and MC techniques. The algorithm has been implemented in mentioned software applications, and has been used effectively several times in solving probabilistic tasks and in probabilistic reliability assessment of structures. The article summarizes the principles of this method and demonstrates its basic possibilities on simple examples. The paper presents unpublished details of probabilistic computations based on this method, including a reliability assessment, which provides the user with the probability of failure affected by statistically dependent input random variables. The study also mentions the potential of the optimization procedures under development, including an analysis of their effectiveness on the example of the reliability assessment of a slender column.