Probabilistic approach, structure effect

Nguyen, Q.B., Mdbarki, A., Mercier, E, Ami Saada, R. M. Reimeringer M. 2006. The Domino Effect and Integrated Probabilistic Approaches for Risk Analysis. Proc. Eight International Conference on Computational Structures. 

However, a global approach to structural health monitoring that consistently takes into account the various sources of uncertainty has been applied only in a few cases. From these studies, it has been concluded that the Bayesian approach is really efficient in characterizing the structural damage and its effects in probabilistic terms for example, to calculate the probability of damage in various structural elements. The main reason is that this approach gives as final result the probability density functions of the identified parameters, which in turn can be used in any structural reliability assessment. 

Uncertainties in computation of responses could be reduced by selecting appropriate configuration of parameters of the deterministic computation model. This way is lengthy and results are not guaranteed. Application of a stochastic model is limited due to pretentious computations. Another approach to account for uncertainties in response consists in modification of the given response spectrum. The modification of the response spectrum reduces e.g. the effects of random coincidences of computed frequencies with extremes of the spectrum course. Controlled broadening and lowering of the spectrum is recommended in (Cada et al. 2011, Holomek et al. 2012). The proposed response spectrum modification reduces effectively the uncertainties in response due to uncertainties in frequencies caused by variances of computation model parameters. The modification is based on the probabilistic description of natural frequencies of the analyzed structure, obtained by modal analysis of a stochastic model of the structure. 

A separated reliability analysis of structural and technical systems into dynamic by Eq. (12) and static by Eq. (14) or (15) parts helps designers to simplify probabilistic calculations. The presented unsophisticated probability-based approaches, design models and calculation equations may be convenient for many practitioners and can stimulate designers to use the full probabilistic methods in their practice more actively and effectively. 

This reference entry describes the use of Bayesian model class selection to determine, among a set of possible model classes, the prediction error model class most suited for Bayesian model updating, according to the available experimental data. It is demonstrated that, provided sufficient information is available, the Bayesian MCS approach is an effective tool to this end, ensuring a more realistic joint structural-probabilistic model and corresponding Bayesian model updating results. 

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