CURRENT POSSIBILITIES OF DIRECT DETERMINED FULLY PROBABILISTIC METHOD (DDPFM)

Abstract eng:
A close form evaluation of failure likelihood in case of more than two random variables is a complicated task. A lot of powerful stochastic methods have been developed or are under development in order to manage this task. The DDPFM method allows computing the probability of failure for problems of more than two random variables using direct determined numerical calculation without the aid of simulation techniques. The DDPFM was developed as an alternative to Monte Carlo simulation procedure in case of probabilistic reliability assessment as was already presented by authors in the ASRANet 2006. Random input variables (eg. loading, geometry, material properties, or imperfections) are characterized by histograms. A number of possible combinations of all random input parameters is equal to a product of a number of intervals in histogram of each involved random variable. This number of combinations may be high in case of large number of input variables leading to extreme number of combinations that cause high computer demand in case of DDPFM. In the last conference, there were indicated ways how to reduce the computer demand because not all combinations that are possible in reliability assessment are involved in the calculation of probability of failure. In principle, there can be indicated region in the histogram that is always involved in probability of failure. It is called zone 1. Zone 2 may or may not participate in the calculation of the failure likelihood while zone 3 does not participate at all. The highest number of operation is in the zone 2 and even here one does not need to consider all the possible combinations. The so-called “trend optimization” was developed to address reduction of necessary calculations in the zone 2. Trend optimization allows eliminating some of the combinations that are not involved in the failure based on the knowledge about input variables and based on the previous computations. Presented algorithms significantly reduce the number of necessary combinations and lead, in principle, to numerical solution of the integral that formally defines the probability of failure in case of large numbers of random variables. Algorithms presented here in are implemented in the ProbCalc program. Data from measurement or observation serve as random input variables. These can be expressed by both non parametric histograms as well as continuous parametric distribution. There is a broad variety of continuous distributions with a best fit option available.

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