Hybrid Approach to State Estimation for Bioprocess Control.

Rimvydas Simutis,Andreas Lübbert

doi:10.3390/bioengineering4010021

Abstract

An improved state estimation technique for bioprocess control applications is proposed where a hybrid version of the Unscented Kalman Filter (UKF) is employed. The underlying dynamic system model is formulated as a conventional system of ordinary differential equations based on the mass balances of the state variables biomass, substrate, and product, while the observation model, describing the less established relationship between the state variables and the measurement quantities, is formulated in a data driven way. The latter is formulated by means of a support vector regression (SVR) model. The UKF is applied to a recombinant therapeutic protein production process using Escherichia coli bacteria. Additionally, the state vector was extended by the specific biomass growth rate µ in order to allow for the estimation of this key variable which is crucial for the implementation of innovative control algorithms in recombinant therapeutic protein production processes. The state estimates depict a sufficiently low noise level which goes perfectly with different advanced bioprocess control applications.

Highlights

Producers of recombinant therapeutic proteins are increasingly forced to enhance the batch-to-batch reproducibility of their cultivation runs at a high level of productivity
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Process supervision is recommended with Unscented Kalman Filters where the dynamic equations are based on mass balances for the biomass, the substrate, and the product, and formulated by well-established ordinary differential equation systems

Summary

Introduction

Producers of recombinant therapeutic proteins are increasingly forced to enhance the batch-to-batch reproducibility of their cultivation runs at a high level of productivity. The state is considered a set of N random variables which, at a given time instant, are described by means of probability distribution density functions The propagation of these density functions with time step is computed using the dynamical process model. In processes with not too strong nonlinearities, the time increments can be kept so small that the model can be linearly approximated at each time step using a first-order Taylor series linearization of the nonlinear model in order to compute the new covariance matrix This approach is used in extended Kalman Filters (EKFs), where the density function can be propagated as in the original Kalman Filter. We will consider the Unscented Kalman Filter and propose a hybrid combination of a conventional system of ordinary differential equations to compute the propagation of the state from time step to time step and a data driven model in the form of a Support Vector Machine (SVM) for the mapping of the predicted state variable to the measurement quantities

Experimental Data

Process Modeling

State Propagation Model

Conclusions

Findings