Efficient Calibration of a Turbine Disc Heat Transfer Model Under Uncertainty

Abstract

This paper presents a novel surrogate modeling approach that enables the application of Bayesian calibration to a gas turbine disc finite element (FE) heat transfer model. The surrogate modeling process begins with two transformations of the FE model predictions: first, principal components analysis “rotates” the multivariate FE model outputs into an uncorrelated and dimension-reduced subspace; second, active subspace (AS) reveals a linear combination of model parameters that form a simple mapping to individual principal components (PCs). These transformed input–output (i.e., active parameter to PC) relationships are found to enable standard polynomial regression fits to form the PC–AS surrogate model. The measured temperatures are also transformed into the model’s PC-space during calibration. The Bayesian calibration approach helps to address the inherent model-form uncertainties (e.g., approximations of complex boundary airflows), measurement uncertainties, and the ill-posed nature of inverse problems. The estimated uncertainties are instructive for use of the model predictions in postcalibration activities, for example, in determining model quality for use in turbine disc lifing analysis.