Determination of bubble sizes in bubble column reactors with machine learning regression methods

Prediction of Bubble Sizes in Bubble Columns with Machine Learning Methods

“…At low bubble diameters, in contrast, performance quality differs clearly: while predicted mean values tend to underestimate bubble diameter in the LASSO model of this work and the conventional approach (Eq. 3) up to a bubble diameter of 4.1 mm, the previous LASSO model 8 – which includes only eight features, while the influence of regularization ( λ = 50) is high – tends to overestimate bubble diameters in the respective range. But, more importantly, the deviations of this works LASSO model are very high, especially in the range of small bubbles < 3 mm, so that negative bubble sizes are predicted even in the case of the highest positive deviations.…”

“…As it is mandatory for linear regression models, the data set was scaled with the scikit-learn (sklearn) Stand-ardScaler function. Although regularization parameter l was set to values significantly higher than 1 in a previous study [8], it was found in preliminary investigations that -using the present method for feature extraction -optimum results in terms of prediction quality and model stability were obtained with l < 1. Thus, l-range is set to 0-1, literally containing the case of a common multiple linear regression without any regularization at all.…”

“…The experimental data for the study presented here are taken from [3]; details of the experimental setup are provided in [8]. In [3] single bubbles were injected manually with syringes into a hemisphere which was placed within the bubble column (Fig.…”

“…Regarding the investigation and prediction of multiphase flow characteristics, ML algorithms have recently shown their capability and efficiency, i.e., in the identification of flow regimes in bubble column reactors [13] and horizontal pipes [14]. In this study, further developed and optimized ML algorithms based on the work of Theßeling et al [8] are presented, showing clear advantages in terms of prediction accuracy regarding bubble size determination based on multiphase flow measurement with WMS data compared to previous approaches. Model development and optimization is shown beginning from data preprocessing steps such as raw data conversion, data preparation and feature extraction.…”

“…While a strong relationship between estimated and injected bubble volume -using local void fraction as a regression parameter -for bubble sizes larger than the WMS spatial resolution was found in case of single bubble investigations [3], prediction accuracy was low for smaller bubbles. Thus, Theßeling et al [8] recently employed machine learning (ML) algorithms to derive regression models allowing for an increased prediction accuracy especially in case of small bubbles, which has been achieved with an ML classification technique. Nonetheless, prediction quality was not increased with linear regression models which are generally easier to handle, and a classificationbased model was unstable at higher bubble diameters.…”