Euro-SiBRAM’2002 Prague, June 24 to 26, 2002, Czech Republic

Session 1 – Comments

Editional comments on session 1

T. Vaňura

Following my Moderator’s Motions published in Volume 1 of this SiBRAM colloquium it must be considered that the designed structure is not an isolated object but a part of a clasped system: Structure – Load – Environment (S-L-E). There is no doubt that all elements of this chain are highly stochastic.

To do justice to such mutually tied system using accurate methods of mathematical analysis succeeded in few simple cases only. On the contrary simulation technique offers unlimited chance to study the behavior of the S-L-E system exploiting applied mathematics commonly used by engineers.

Certainly for this must be paid by a large amount of computational operations. However, this represents an unessential problem with regard to the powerful development of recent computational systems.

In spite of this the size of n (n stands for number of trials independently drawn from the population) remains the general problem of structural safety simulation. The increasing n effects favorably on precision of simulation results at all, e.g. the approximations of the mean, the standard deviation… It reduces spans of so-called Confidence Intervals etc. etc. On the other hand it is necessary to keep it within rational limits.

It follows that the settlement of optimal value of n is an important business connected with simulation technique.

No less attention should be paid to the connected problem of acceleration of the convergence of simulation process. With other words the matter is to make the best use of given number of trials n.

Passing away the crude (simple, classic) Monte Carlo method there were developed improved simulation concepts directed to the saving of computational time which profit by a certain kind of knowledge about the solution of the simulated problem. The method called Importance Sampling method gives better chance of being drawn to the region closed to the expected solution. The other called Stratified Sampling method works by dividing the sampling space into subspaces and choosing one point randomly into each of them. Again some knowledge about the solution enables to improve the convergence and thereby to diminish the number of trials n.

Here very often the Latin hyper cube technique is implemented for sampling from very high-dimensional space. This scheme can be used much more efficient than simple random sampling scheme. Simple random sampling is for high-dimensional space inefficient because it typically gives higher probability to the middle of a distribution than to its tails especially in above noticed high dimensions. Latin hyper cube efficient scheme would sample the tails quickly. This can be accomplished by stratifying the support of the distribution. Latin hyper cube gives a hope that all possible combinations were handled in a balanced way.

However, one should take into account that the classic Monte Carlo method preserves much more certainty against fault and is independent upon subjective strains. Thus, one must weigh up the decision considering the common usefulness of chosen method.