SUMMARYThis paper deals with the transient response of a non-linear dynamical system with random uncertainties. The non-parametric probabilistic model of random uncertainties recently published and extended to nonlinear dynamical system analysis is used in order to model random uncertainties related to the linear part of the ÿnite element model. The non-linearities are due to restoring forces whose parameters are uncertain and are modeled by the parametric approach. Jayne's maximum entropy principle with the constraints deÿned by the available information allows the probabilistic model of such random variables to be constructed. Therefore, a non-parametric-parametric formulation is developed in order to model all the sources of uncertainties in such a non-linear dynamical system. Finally, a numerical application for earthquake engineering analysis is proposed concerning a reactor cooling system under seismic loads.
As probabilistic analyses spread in industrial practice, inverse probabilistic modelling of the sources of uncertainty enjoys a growing interest as it is often the only way to estimate the input probabilistic model of unobservable quantities. This article addresses the identification of intrinsic physical variability of the systems. After showing its theoretical differences with the more classical data assimilation or parameter identification algorithms, this article introduces a new non-parametric algorithm that does not require linear nor Gaussian assumptions. This technique is based on the simulation of the likelihood of the observed samples, coupled with a kernel method to limit the number of physical model runs and facilitate the subsequent maximization. It is implemented inside an industrial application in order to identify the key parameter that controls the vibration amplification of steam turbines. Hence, experimental resonance frequencies observations are used to adjust the probabilistic model of the unobservable manufacturing imperfections between theoretically identical units.
In the 2009 version of the ASME BPV Code, a set of new design fatigue curves were proposed to cover the various steels of the code. These changes occurred in the wake of publications [1] showing that the mean air curve used to build the former ASME fatigue curve did not always represent accurately laboratory results.
The starting point for the methodology to build the design curve is the mean air curve obtained through laboratory testing: coefficients are then applied to the mean air curve in order to bridge the gap between experimental testing and reactor conditions.
These coefficients on the number of cycles and on the strain amplitude are equal to 12 and 2 respectively in the 2009 ASME BPV code, using the mean air curve proposal from NUREG/CR-6909 [1]. Internationally, with the same mean air curve, other proposals have emerged and especially in France [2]-[3] where a consensus seems to be reached on the reduction of the coefficient on strain amplitude.
This paper provides statistical analyses of the experimental data obtained in France at high-cycle for austenitic stainless steels. It enables to bring arguments for the selection of a coefficient on strain amplitude in the French RCC-M code, where less scatter on the data is witnessed due to fewer material grades.
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