Noise Model for Realistic Simulations of Solid Substrate Fermentation Reactors

Measurements in large scale SSF bioreactors are contaminated with various kinds of disturbances, such as high, medium and low frequency noise, outliers and missing values. These make the operation of many control systems for SSF bioreactors unreliable and ineffective. In addition, it is difficult, time consuming and expensive to assess new control strategies in real time experiments. Alternatively, the design and assessment of control systems can be simplified by computer simulation. However, for this we need realistic models that not only include the complicated dynamic behavior of such reactors, but also a noise model that can reproduce those disturbances normally observed in SSF measurements. We processed historic raw data coming from several real time fermentations carried out in an aseptic pilot scale SSF reactor; these data contained all the disturbances mentioned above. First we developed a novel heuristic algorithm to deal with the many missing values that contaminated our data. Then we applied the Hampel filter to eliminate the outliers and finally we used the Savitsky-Golay algorithm to filter the high and medium frequency noise. Finally, we obtained the pure noise signal by extracting the filtered signals from the raw data. Applying this procedure to 11 measured signals of 9 fermentation runs, we were able to infer the statistics of the disturbance model for each measurement. For example, the outliers were classified in three groups, very high and medium values occurring infrequently, and low values appearing frequently. In addition, random noise was classified in clusters (could appear between 8 and 15 clusters, depending on the specific signal) with different amplitude and wideband frequency. Based on this analysis, we developed a noise model using the Matlab/Simulink® environment. The model provides a fixed amount of high and medium outliers, associated to each variable, and distributes them randomly along the fermentation run using a Gaussian distribution. On the other hand, the low level outliers are generated by an exponential distribution in time and a normal distribution in amplitude. Finally, each cluster of random noise was modeled and simulated by passing white noise through a low pass filter. The integrated model of the noise reproduces both the distribution of outliers and the random noise of the measurements of the pilot scale SSF reactor. The noise model developed here will be added to a deterministic phenomenological model to achieve realistic simulations that will allow us to develop and asses robust and effective control strategies.