Lyapunov comparison of noise‐filtering methods for oscillating yeast cultures

Abstract

Under certain conditions, continuous cultures of the budding yeast Saccharomyces cerevisiae exhibit steady oscillations with time in some key concentrations such as those of the cell mass, carbon substrate (glucose), product (ethanol), storage carbohydrate, and dissolved oxygen. These oscillations have been reported in small, laboratory-scale reactors (Bellgardt, 1994;Beuse et al., 1998;Murray et al., 2001;Satroutdinov et al., 1992), which are largely unaffected by environmental disturbances. The nature of the oscillations, including the absence of oscillatory behavior itself, depends on the operating conditions, notably the dilution rate and the mass transfer rate of oxygen to the fermentation broth (Beuse et al., 1998;Jones and Kompala, 1999).Both metabolic processes and transport between the cells and the extracellular fluid contribute to the occurrence and control of oscillations, and their interactions are complex and not yet fully understood (Patnaik, 2003). This limitation makes it difficult to propose quantitative descriptions of oscillatory fermentations that are adequate without being too complicated. Most modeling efforts have thus focused either in detail on the cellular metabolism with little attention to extracellular transport or primarily on the macroscopic variables of interest through mass balances coupled to heavily lumped kinetics. Both kinds of models have been reviewed recently (Duboc et al., 1996;Patnaik, 2003) and are therefore not discussed here.These models were based on observations with small, laboratory-scale reactors, where nonideal features such as process noise and spatial gradients can usually be ignored. However, these effects become significant in the realistic conditions of production-scale bioreactors, thus making it difficult to translate laboratory-scale models directly to larger bioreactors (Gillard and Tragardh, 1999;Rohner and Meyer, 1995). To facilitate this scale-up and be able to replicate the high performances achievable in the laboratory, the control of disturbances is one important aspect of bioreactor optimization.Process noise complicates measurements and control, and can seriously affect bioreactor performance. Published industrial data (Glassey et al., 1994;Montague and Morris, 1994;Rohner and Meyer, 1995) illustrate the extent of fluctuations possible. Analyses of ethanol production by S. cerevisiae (Sweere et al., 1988) and Zymomonas mobilis (Patnaik, 1994) under nonoscillatory conditions show that noise carried by a feed stream can undermine productivity and also drive a fermentation to chaotic behavior. Because fed-batch and continuous fermentations are practiced in many applications, inflow noise is of serious concern on an industrial scale.Despite the recognized importance of noise in bioreactor operation, there is limited information on transitions from monotonic to chaotic behavior and on restoration of the original noise-free performance. Such information is even more scanty for oscillating fermentations. However, in view of the prevalence and importan...

Hybrid filtering of feed stream noise from oscillating yeast cultures by combined Kalman and neural network configurations

“…Of these, the concentration and flow rate of glucose are monitored while only the flow rate of air may be adjusted since its composition is fixed. It has been shown earlier [12,18] that the fermentation is less sensitive to fluctuations in DO concentration than in those of glucose. Therefore, consistent with a preceding study [13], the flow rate of air was passed through the EKF and the two variables characterizing glucose inflow through the neural filter.…”

“…Therefore, a common practice is to add noise to an experimentally validated laboratory-scale model and solve the model to generate data simulating a real noise-affected fermentation [17,23,24]. This practice was followed in previous studies of oscillating S. cerevisiae fermentations [12,15,16,18], and the data generated there were used in the present analyses also, thus maintaining consistency.…”

“…Algorithmic filters are also limited in their ability to adapt to a changing stochastic environment. Neural networks do not have these limitations [14] and are therefore more efficient than algorithmic filters for noise-affected oscillating fermentations [15,18].…”

“…1. Since the extended Kalman filter (EKF) is widely preferred and was the best algorithmic filter for S. cerevisiae oscillations [15,18], this was selected for the hybrid filter.…”

“…Recent publications [13,15,18] related to oscillatory fermentation by S. cerevisiae have shown that the Lyapunov exponent [27] provides a compact and reliable measure of the extent of restoration of noise-free performance. This exponent provides a measure of the long-term deviation of a disturbed trajectory from its original path.…”