Application of the Lyapunov Exponent to Evaluate Noise Filtering Methods for a Fed-batch Bioreactor for PHB Production

Large-scale fed-batch fermentations are often subject to noise carried by the feed streams. This noise corrupts the process data and may destabilize the fermentation. So it is important to retrieve clear signals from noisy data. This is done by noise filters. The performances of some commonly used filters have been studied for poly-β-hydroxybutyrate production by Ralstonia eutropha. In simulated experiments, Gaussian noise was added to the flow rates of the carbon and nitrogen substrates. The filters were compared by means of the Lyapunov exponents of the outputs and their closeness to the noise-free performance. Negative exponents indicate a stable fermentation. An auto-associative neural filter performed the best, followed by a combination of a cusum filter and an extended Kalman filter. Butterworth filters were inferior and inadequate.