Keywords: complex systems, human factors, model errors, cluster analysis, uncertainties, meta-modelling.

It is well-known that the analyses of complex structures are affected by a great amount of uncertainties and approximations [1,2]. Some uncertainties are related to the real mechanical characteristics of the structure, which are often known with little accuracy [3]. Nevertheless, the simplified numerical model of the structure [4] introduces other numerical approximations in the analyses. At last, but not less important, human factors can cause some evaluation errors due at the lack of experience or a bad planning of the tasks [5].

This paper classfies these approximations in three groups:

• numerical;
• modelling;
• human.

The author analyzes these approximation groups showing their influence on the results of the analyses. A conclusion of this part, is that important tools to understand the importance of the uncertainties on the analyses are introduced. In particular, the application of the model exploration (or sensitivity analyses) to a long suspension bridge model [6, 7] shows the importance of the uncertainties related to the main cable in relation to the others possible uncertainties. The paper shows that the effectiveness of the model exploration coupled with a cluster analyses to improve the understanding of the numerical results.

To handle so many uncertainties in complex structures analyses, the paper describes the importance of considering different models with various structural codes and different people, working in parallel and in an independent way. The structural analyses have to be accurately organized in a model of the tasks: a model to handle the modeling approximations, a model to handle the numerical approximations, and a model to handle the human factors. The collection of these different models comprises the meta-model of the structural analysis.

The paper shows an application of the meta-modeling approach on the structural analysis of a long suspension bridge in order to increase the reliability of the results. Horizontal and vertical displacements were investigated using different models and different structural codes. The results show as the hypotheses can provide an accurate evaluation for one variable (vertical displacement) but not an accurate response for others variables (transversal displacement).

Therefore, different types of numerical models and different people are required for a complex structure analysis. A meta-model approach is still appropriate to improve the results and to understand the importance of the approximations introduced in the numerical models.

1

W.X. Ren, G.E. Blandford and I.E. Harik "Roebling Suspension Bridge. I: Finite-Element Model and Free Vibration Response", Journal of Bridge Engineering, Vol. 9(2), March 2004. doi:10.1061/(ASCE)1084-0702(2004)9:2(110)

2

J. Berkoe "The Role of Modeling and Simulation in Extreme Engineering Projects", National Academy of Engineering Website, http://www.nae.edu

3

F. Bontempi, L. Catallo and L. Sgambi "Structural analysis and design of long span suspension bridges with regards to nonlinearities, uncertainties, interactions and sustainability", Proceedings of the IABMAS'04 Conference, Kyoto, Japan, 2004.

4

G. Bateson, "Mind and Nature, A Necessary Unity", Hardbound Edition, 1979.

5

L. Sgambi (In Italian) "I metodi dell'intelligenza artifi-ciale nell'analisi e nella progettazione di ponti sospesi", Ph.D. Thesis on Civil Engineering, University of Rome "La Sapienza", Advisor Prof. F. Bontempi. Available on-line http://padis.uniroma1.it/getfile.py?recid=267.

6

"Stretto di Messina S.p.A." Company, Preliminary Project, 1992, available on http://www.strettodimessina.it

7

L. Cavallo, L. Sgambi and M. Silvestri. "General aspects of the structural behavior in the Messina Strait Bridge design", Proceedings of the Second International Conference on Structural and Construction Engineering (ISEC-02), 23-26 September 2003, Rome, Italy.

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