Inverse probabilistic modelling of the sources of uncertainty: a non-parametric simulated-likelihood method with application to an industrial turbine vibration assessment

Abstract

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.