Mass flow rate measurement of pneumatically conveyed solids in a square-shaped pipe through multi-sensor fusion and data-driven modelling

Online continuous measurement of the mass flow rate of pneumatically conveyed solids in a square-shaped pipe is desirable for monitoring and optimizing industrial processes. However, existing techniques using a single type of sensor have limitations in measuring the mass flow rate of solids because of the complexity of the dynamics of solids flow due to the four sharp corners of a square-shaped pipe. This paper proposes a multi-sensor fusion and data-driven modelling-based method to tackle this challenge. A multi-sensor system based on acoustic, capacitive, and electrostatic sensing principles is designed and implemented to obtain the sound pressure level in the flow, volumetric concentration of solids, and solids velocity, respectively. Simultaneously, a range of statistical features is obtained by performing time-domain, frequency-domain, and time-frequency domain analyses on all sensor signals. The statistical features reflecting the variation of the mass flow rate of solids, as well as solids velocity and volume concentration of solids, are then fed into a data-driven model. A data-driven model based on a combined convolutional neural network and long short-term memory (CNN-LSTM) network is established, and its performance is compared with those of the back-propagation artificial neural network, support vector machine, CNN, and LSTM models. Experimental tests were conducted on a laboratory-scale rig on both horizontal and vertical pipelines to train and evaluate the CNN-LSTM model with solids velocity ranging from 11 to 23 m/s and the mass flow rate of solids from 8 to 26 kg/h. The CNN-LSTM model outperforms all other models with a relative error within ±1% under all test conditions.