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.

Stochastic Inverse Problem with Noisy Simulator. Application to aeronautical model

“…The main dierence lies in the absence of assumptions, in the present paper, on the distribution of the error between observation data and reference data. Thus, it dierentiates the estimation procedures we propose from the ones developed in [3].…”

“…This topic is often treated in the eld of uncertainty management: the goal may for instance be to identify the intrinsic uncertainty of a system, see for instance the PhD works [1] and [5]. Another reference is the paper of E. de Rocquigny and S. Cambier [3], where the purpose is to identify a parameter of interest which controls the vibration amplication of stream turbines. Our framework is dierent.…”

A unified framework for multilevel uncertainty quantification in Bayesian inverse problems

“…(32) as in Eq. (16), one can base inference of θ X on an inherently marginal problem formulation [32,35]. Similar to Eqs.…”

“…Previously established approaches to this interesting type of problems with latent/hidden variable structure subsume various approximate solutions. A frequentist technique that is premised on the simulation of an explicitly marginalized likelihood is proposed in [32]. There are also attempts to compute approximate solutions based on variants of the expectation-maximization algorithm within a linearized Gaussian frame [33] or with the aid of Kriging surrogates [34].…”

A Bayesian Multilevel Approach to Optimally Estimate Material Properties

“…The objective of probabilistic inversion focuses on the estimation of the hyperparameters θ. Application examples can be found in (Rocquigny 2009;Barbillon 2011). A likelihood for this class of problems can be obtained by the marginalization L(y 1 , .…”