Model updating using uncertain experimental modal data

The propagation of parameter uncertainty in structural dynamics has become a feasible method to determine the probabilistic description of the vibration response of industrial scale �nite element models. Though methods for uncertainty propagation have been developed extensively, the quanti�cation of parameter uncertainty has been neglected in the past. But a correct assumption for the parameter variability is essential for the estimation of the uncertain vibration response. This paper shows how to identify model parameter means and covariance matrix from uncertain experimental modal test data. The common gradient based approach from deterministic computational model updating was extended by an equation that accounts for the stochastic part. In detail an inverse approach for the identi�cation of statistical parametric properties will be presented which will be applied on a numerical model of a replica of the GARTEUR SM-AG19 benchmark structure. The uncertain eigenfrequencies and mode shapes have been determined in an extensive experimental modal test campaign where the aircraft structure was tested repeatedly while it was 130 times dis- and reassembled in between each experimental modal analysis

Evaluating Opportunities When People are Uncertainty Averse

We consider the problem of ranking sets of alternatives. Standard approaches to this problem regard the addition of an alternative to a set containing one element as enhancing choice. We argue that this monotonicity axiom may not be desirable when an agent is uncertain as to the value of this additional alternative. We replace monotonicity with an uncertainty aversion axiom, and also introduce an axiom that produces lexicographic behaviour. These axioms, in conjunction with an independence axiom, enable us to prove a characterisation theorem. This theorem says that sets are ranked in terms of the number of uncertain elements that they contain, the fewer the better. This is the only ranking rule that satisfies our axioms.

Research on Bridge Structural Health Assessment Based on Finite Element Analysis

In view of the content of bridge condition assessment and health monitoring, this paper is based on the finite element simulation analysis. The uncertain finite element model updating method based on sequential optimization strategy is studied, and the uncertain modal parameter data obtained by health monitoring system are applied to upgrade the uncertain finite element model of cable-stayed bridges, which provides a more accurate finite element model for subsequent reliability analysis. Firstly, the finite element dynamic analysis of the main span structure of the bridge is carried out, and the natural frequencies and modes are obtained. Then the measured natural frequencies of the structure are obtained by estimating the power spectrum of the dynamic monitoring data, and the theoretical values are compared with the measured ones. The dynamic characteristics of the modified two-stayed bridge finite element model are verified by the load test results. The results show that the modified finite element model can simulate the dynamic characteristics of the actual structure well. Most of the measured and calculated displacement increments were within the margin of error. The error is within 5%, which can accurately reflect the true stress state of the structure. The uncertainty model based on the sequential optimization strategy is simple and can be applied to the uncertainty of the finite element model of the actual bridge structure

Rubidium abundances in the globular clusters NGC 6752, NGC 1904 and NGC 104 (47 Tuc)

Large star-to-star variations of the abundances of proton-capture elements, such as Na and O, in globular clusters (GCs) are interpreted as the effect of internal pollution resulting from the presence of multiple stellar populations. To better constrain this scenario we investigate the abundance distribution of the heavy element rubidium (Rb) in NGC 6752, NGC 1904, and NGC 104 (47 Tuc). Combining the results from our sample with those in the literature, we found that Rb exhibits no star-to-star variations, regardless the cluster metallicity, with the possible intriguing, though very uncertain, exception of the metal-rich bulge cluster NGC 6388. If no star-to-star variations will be confirmed for all GCs, it implies that the stellar source of the proton-capture element variations must not have produced significant amounts of Rb. This element is observed to be enhanced at extremely high levels in intermediate-mass AGB (IM-AGB) stars in the Magellanic Clouds (i.e., at a metallicity similar to 47 Tuc and NGC 6388). This may present a challenge to this popular candidate polluter, unless the mass range of the observed IM-AGB stars does not participate in the formation of the second-generation stars in GCs. A number of possible solutions are available to resolve this conundrum, also given that the Magellanic Clouds observations are very uncertain and may need to be revised. The fast rotating massive stars scenario would not face this potential problem as the slow mechanical winds of these stars during their main-sequence phase do not carry any Rb enhancements; however, these candidates face even bigger issues such as the production of Li and the close over-imposition with core-collapse supernova timescales. Observations of Sr, Rb, and Zr in metal-rich clusters such as NGC 6388 and NGC 6441 are sorely needed to clarify the situation.Comment: Accepted for publication in The Astrophysical Journa