Multi-electrode impedance void fraction method by Hilbert-Schmidt independence criterion (HSIC) lasso and plural long short-term memory (pLSTM)

Abstract

Hilbert-Schmidt independence criterion least absolute shrinkage and selection operator (HSIC Lasso) and plural long short-term memory (pLSTM) has been implemented in a multi-electrode impedance meter (MIM) to estimate void fraction α^ accurately in vertical gas-liquid flows. The MIM measures voltage vector V reflecting the spatial distribution of bubbles in the gas-liquid flows with multiple pairs of electrodes on the inner wall of the pipe. HSIC Lasso selects the electrode pairs which are strongly dependent on the void fraction and flow regime based on the nonlinear assumption to select the voltage vector V~ without any hyperparameters. pLSTM estimates α^ after identifying the time-dependent flow regime. In the experiments, V was measured by MIM under the conditions of 25 points of liquid and gas flow rate in gas-liquid upward flows for training, on the other hand, five points for testing, respectively. As the result, HSIC Lasso successfully selects highly dependent electrode pairs with regression coefficient β over 0.03. pLSTM achieves a 100% accuracy of flow regime identification and time mean relative error η with less than 0.0157 of void fraction estimation in bubble flow and slug flow, which decreases total mean relative error <η> by 69% compared with the existing method.

Keywords

• gas-liquid flow
• void fraction estimation
• flow regime identification
• feature selection
• long short term memory
• sparse model
• electrical sensor