Analysis of Information Loss on Composition Measurement in Stiff Chemically Reacting Systems

Gas sampling methods have been crucial for the advancement of combustion science, enabling analysis of reaction kinetics and pollutant formation. However, the measured composition can deviate from the true one because of the potential residual reactions in the sampling probes. This study formulates the initial composition estimation in stiff chemically reacting systems as a Bayesian inference problem, solved using the No-U-Turn Sampler (NUTS). Information loss arises from the restriction of system dynamics by low dimensional attracting manifold, where constrained evolution causes initial perturbations to decay or vanish in fast eigen-directions in composition space. This study systematically investigates the initial value inference in combustion systems and successfully validates the methodological framework in the Robertson toy system and hydrogen autoignition. Furthermore, a gas sample collected from a one-dimensional hydrogen diffusion flame is analyzed to investigate the effect of frozen temperature on information loss. The research highlights the importance of species covariance information from observations in improving estimation accuracy and identifies how the rank reduction in the sensitivity matrix leads to inference failures. Critical failure times for species inference in the Robertson and hydrogen autoignition systems are analyzed, providing insights into the limits of inference reliability and its physical significance.