Void fraction estimation in vertical gas-liquid flow by multi-layer long short-term memory implemented in current-voltage system (mlLSTM-SM-CV)

This study presents the void fraction αα estimation by multi-layer long short-term memory with sparse model implemented in multi-layer current-voltage system (mlLSTM-SM-CV) in a vertical gas-liquid flow. In mlLSTM-SM-CV, the voltage vector llVVnn is measured at measurement time number nn, in two layers ll which are upstream-layer uu and downstream-layer dd, for each measurement pair kk, under condition numbers cc. SM determines which kk is indispensable to αα estimation resulting in sparse voltage vector llVV-nn in ll. Here, the upstream-layer sparse voltage vector uuccVV-nn and downstream-layer sparse voltage vector ddccVV-nn are reflected by the spatial distribution of bubbles in gas-liquid flow. mlLSTM-SM-CV system consists of two LSTM layers which are 1st LSTM layer and 2nd LSTM layer. In the 1st LSTM layer, both llVVnn are arranged based on the time series of each ll. In the 2nd LSTM layer, arranged llVV-nn are used for αα estimation. For train dataset, both llVV-nn were experimentally measured under cc = 30 of the temporal-mean true void fraction ααttrruuee calculated by the drift flux model under all cc. For the test dataset, both llVV-nn were measured under cc = 18 of ααttrruuee. Model parameters are optimized resulting in the best parameters of SSiidd = 64, MM1 = 10, MM2 = 50 with RRMMSSEE = 0.0134 and MMAAPPEE = 5.3, respectively. © 2021 The Japan Society of Mechanical Engineers.