Analysis of the Bromate−Sulfite−Ferrocyanide pH Oscillator Using the Particle Filter: Toward the Automated Modeling of Complex Chemical Systems

This study was aimed at identifying a quantitatively accurate reaction model of the bromate−sulfilte−ferrocyanide (BSF) pH oscillator by using the simulation-based model estimation algorithm known as the particle filter. The Rábai−Kaminaga−Hanazaki (RKH) model proposed for the BSF system was extended by adding the protonation equilibrium of SO<sub>4</sub><sup>2−</sup>, for which the particle filter analysis was carried out to optimize the rate constants involved with reference to the measured pH oscillation data. The extended RKH model with the optimized rate constants almost completely reproduced the measured pH oscillations and the state diagram, showing the validity of the present analysis. Chemical oscillators such as the BSF system show drastic switching of the dominant reaction path, which strongly disturbs the convergence of the rate constants if the objective function is defined in a conventional manner to reflect only a single time step datum. In this study, the objective function was defined as the residual sum of squares with respect to pH taken over an interval longer than one oscillatory period, so that all of the relevant reaction steps can contribute to the objective function. This is the first report which exemplifies the effectiveness of the particle filter in the analysis of real complex chemical systems.