Category:Uncertainty Modelling

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The first step of the stochastic structural analysis is the rational quantification of the uncertainties involved in the structures. Realistic modeling of these uncertainties efficiently and accurately is extremely important. The basic definitions and general concepts of the probability theory are needed for a better understanding of the contents in this chapter (See e.g. [1] [2] for theory).


According to the probability theory, the uncertainties in the structures can be modelled using random variables or random processes. If the randomness in the considered component of the structure is assumed to be fully correlated, then a single random variable would suffice in order to represent this property. However, random processes are required if the fluctuations in the random input parameter are to be captured. These fluctuations can be with respect to time or with respect to location. In order take the spatial fluctuations into the account, random fields can be used for the representation.


Once the uncertainties in the structural input parameters are modelled, they can be propagated by means of stochastic structural analysis in order to assess the response statistics (Please refer to the uncertainty analysis page for further details). It should be noted that the adequate modelling of the uncertain parameters is very crucial for the sake of the validity of the analysis, since this issue directly affects the accuracy and the computational cost. 


References

  1. G. S. Fishman. Monte Carlo: concepts, algorithm, and applications. Springer Verlag, New York,Inc., 1996. ISBN-13: 978-0387945279
  2. M. Grigoriu. Stochastic mechanics. International Journal of Solids and Structures, 37(1-2):197–214, 2000. [1]

See Also