Calibration and Uncertainty Quantification of Gas Turbine Performance Models

Abstract

Calibration and uncertainty quantification for gas turbine (GT) performance models is a key activity for GT manufacturers. The adjustment between the numerical model and measured GT data is obtained with a calibration technique. Since both, the calibration parameters and the measurement data are uncertain the calibration process is intrinsically stochastic. Traditional approaches for calibration of a numerical GT model are deterministic. Therefore, quantification of the remaining uncertainty of the calibrated GT model is not clearly derived. However, there is the business need to provide the probability of the GT performance predictions at tested or untested conditions. Furthermore, a GT performance prediction might be required for a new GT model when no test data for this model are available yet. In this case, quantification of the uncertainty of the baseline GT, upon which the new development is based on, and propagation of the design uncertainty for the new GT is required for risk assessment and decision making reasons. By using as a benchmark a GT model, the calibration problem is discussed and several possible model calibration methodologies are presented. Uncertainty quantification based on both a conventional least squares method and a Bayesian approach will be presented and discussed. For the general nonlinear model a fully Bayesian approach is conducted, and the posterior of the calibration problem is computed based on a Markov Chain Monte Carlo simulation using a Metropolis-Hastings sampling scheme. When considering the calibration parameters dependent on operating conditions, a novel formulation of the GT calibration problem is presented in terms of a Gaussian process regression problem.