Fitting nonlinear models to continuous oxygen data with oscillatory signal variations via a loss based on Dynamic Time Warping

High throughput experimental systems play an important role in bioprocess development, as they provide an efficient way of analysing different experimental conditions and perform strain discrimination in previous phases to the industrial scale production. In the millilitre scale, these systems are combinations of parallel mini-bioreactors, liquid handling robots and automated workflows for data handling and model based operation. For successfully monitoring cultivation conditions and improving the overall process quality by model-based approaches, a proper model identification is crucial. However, the quality and amount of measurements makes this task challenging considering the complexity of the bio-processes. The Dissolved Oxygen Tension is often the only measurement which is available online, and therefore, a good understanding of the errors in this signal is important for performing a robust estimation. Some of the expected errors will provoke uncertainties in the time-domain of the measurement, and in those cases, the common Weighted Least Squares estimation procedure can fail providing good results. Moreover, these errors will have even a larger effect in the fed-batch phase where bolus feeding is applied, as this generates fast dynamic responses in the signal. In the present work, an insilico study of the performance of Weighted Least Squares estimator is analysed when the expected time-uncertainties are present in the oxygen signal. As an alternative, a loss based on the Dynamic Time Warping measure is proposed. The results show how this latter procedure outperforms the former reconstructing the oxygen signal, and in addition, returns less biased parameter estimates.