Intelligent State Estimation for Continuous Fermenters Using Variational Bayesian Learning

Despite rapid sensor technology developments, monitoring a biological process using regular sensor measurements is challenging, making the process very difficult to characterize. Designing an optimal estimator is an attractive alternative to soft sensing for such complicated hybrid systems. In this paper, the variational Bayesian learning algorithms are proposed to estimate the continuous fermenters' actual states. Special attention is given to the random transition probability matrix (TPM), which is a prerequisite to improving estimation performance. Under the assumption of a time-invariant but random TPM, the Dirichlet distribution is utilized to specify the property of TPM. We then estimate it together with the system state and modal state to approximate the conditional posterior joint distribution. Testing the proposed algorithms using the fermenter model shows that the variational Bayesian learning algorithm can satisfactorily estimate conditions and track TPM in high accuracy.