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ABSTRACT In most of fermentation processes, the substrate and biomass concentrations greatly influence the yield of the targeted product. In this paper, considering the nonlinear and non-Gaussian nature of the fermentation processes, the particle filter method is introduced to estimate the substrate and biomass states, and an algorithm integrating optimization strategy with resampling is proposed to deal with constraints on states. The proposed approach investigates the constraint directly on the estimated value rather than on particles. If the estimation violates constraints, the optimal estimation is firstly obtained by the optimization approach, and then, the resampling and optimization strategy are iteratively used to randomly draw a particle each time among the violated posterior particles and project it onto the feasible region. The resampling and optimization steps are iterated until the state estimation, derived from posterior particles, reaches better performance than that through previous optimization formulation or all the violated posterior particles have been projected onto the feasible region. Compared with the other previous optimization approaches, the proposed method results in a better balance between reducing the on-line computation load and obtaining more effective posterior particles. © 2012 Curtin University of Technology and John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Abstract: This paper investigates constrained Bayesian state estimation problems by using a Particle Filter (PF) approach. Constrained systems with nonlinear model and non-Gaussian uncertainty are commonly encountered in practice. However, most of the existing Bayesian methods are unable to take constraints into account and require some simplifications. In this paper, a novel constrained PF algorithm based on acceptance/rejection and optimization strategies is proposed. The proposed method retains the ability of PF in nonlinear and non-Gaussian state estimation, while take advantage of optimization techniques in constraints handling. The performance of the proposed method is compared with other accepted Bayesian estimators. Extensive simulation results from three examples show the efficacy of the proposed method in constraints handling and its robustness against poor prior information. [Copyright &y& Elsevier]