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This paper proposes an approach to the choice and evaluation of engineering models with the aid of a typical application in geotechnics. An important issue in the construction of shallow tunnels, especially in weak ground conditions, is the tunnel face stability. Various theoretical and numerical models for predicting the necessary support pressure have been put forth in the literature. In this paper, we combine laboratory experiments performed at the University of Innsbruck with current methods of uncertainty and sensitivity analysis for assessing adequacy, predictive power and robustness of the models. The major issues are the handling of the twofold uncertainty of test results and of model predictions as well as the decision about what are the influential input parameters.
Bead-on-plate butt joints of 2.5 mm hot rolled DP600/DP600 and 1.2 mm cold rolled TRIP700/TRIP700 steel sheets were performed using 6 kW CO2 laser beam welding. The welding speed ranged from 1.5 to 3.0 and from 2.1 to 3.9 m/min in DP/DP and TRIP/TRIP steel weldments respectively. A top surface helium gas was used as a shielding gas at a flow rate of 20 l/min. Metallographic examinations and transverse tensile testing (DIN EN 895: 1995) were carried out to characterize the weldments. The formability of base metals and weldments were investigated by standard Erichsen test (DIN EN ISO 20482). It was found that the uniaxial plastic behavior of both DP600 and TRIP700 base metals was in agreement with Swift and modified Mecking–Kocks models respectively. In a perpendicular tensile test to the weld line, all specimens were fractured at the base metal however the strengths were somewhat higher than those of base metal. There was a significant reduction in formability caused by welding of both DP/DP and TRIP/TRIP steel weldments and the formability has been improved with the increase of the welding speed.
Unitary Operator
(2009)
We investigate interaction networks that we derive from multivariate time series with methods frequently employed in diverse scientific fields such as biology, quantitative finance, physics, earth and climate sciences, and the neurosciences. Mimicking experimental situations, we generate time series with finite length and varying frequency content but from independent stochastic processes. Using the correlation coefficient and the maximum cross-correlation, we estimate interdependencies between these time series. With clustering coefficient and average shortest path length, we observe unweighted interaction networks, derived via thresholding the values of interdependence, to possess non-trivial topologies as compared to Erdös-Rényi networks, which would indicate small-world characteristics. These topologies reflect the mostly unavoidable finiteness of the data, which limits the reliability of typically used estimators of signal interdependence. We propose random networks that are tailored to the way interaction networks are derived from empirical data. Through an exemplary investigation of multichannel electroencephalographic recordings of epileptic seizures – known for their complex spatial and temporal dynamics – we show that such random networks help to distinguish network properties of interdependence structures related to seizure dynamics from those spuriously induced by the applied methods of analysis.