Bayesian model calibration for vacuum-ultraviolet photoionisation mass spectrometry

Abstract

We investigate the calibration of an instrument model for a high-pressure chemical reactor and vacuum ultraviolet photoionisation mass spectrometry apparatus, using a collection of ‘static’ mass spectrometry data (i.e. from unreactive samples). A Bayesian calibration method is applied to characterise the uncertainty of the model parameters, the associated model error, and the predicted mass spectrum. A partitioning algorithm is introduced to decompose the mass spectrum into several independent calibration problems, making the analysis of complex mass spectrometry data sets tractable. The a priori mass spectrometer model poorly predicts some portions of the ion time-of-flight spectrum due to both, parametric (i.e. uncertain parameter values) and mechanistic (i.e. missing physics) inadequacies; however, by incorporating an additive model error the prediction model is vastly improved and closely replicates the measured spectrum. We found that the model calibration and additive model error reveals a set of experimental problems, including chemical contamination of the sample, the presence of high harmonics of the ionising radiation, and a systematic fluctuation in ion flight times due to instability of the ion optics power supplies. This approach results in a calibrated instrument model with well-defined parameter uncertainties, which is critical to the analysis of ‘dynamic’ data (i.e. from reacting gas samples).