A Machine Learning Approach for Electrical Capacitance Tomography Measurement of Gas-Solid Fluidized Beds

A Machine Learning
Approach for Electrical Capacitance Tomography Measurement of Gas-Solid Fluidized
Beds

Gas-solid
fluidized beds are commonly used in industry, such as coal conversion, power
generation, pharmaceutical granulation, and polymerization. Accurate
measurement of the hydrodynamic characteristics is of paramount importance to
the design, control, and optimization of fluidized beds in these processes. In
the past decades, both intrusive and non-intrusive measurement techniques have
been developed. Normally, intrusive methods provide only single point
measurements and tend to disrupt the hydrodynamics in the region of the
vicinity of the probe. Non-intrusive methods such as process tomography,
meanwhile, can be used to visualize the entire flow field without causing any
disturbance to the flow. Compared to other process tomographic methods,
electrical capacitance tomography (ECT) is the most mature and ideal for
measurement of gas-solid fluidized beds because of the advantages of no
radiation, high temporal resolution, robustness, withstanding high temperature
and high pressure, and low cost.

In ECT
measurement, a set of electrodes is mounted around the periphery of the
fluidized bed under investigation. Because the gas and fluidized particles have
different permittivity, once the distribution and/or concentration of the
fluidized particles vary, the inter-electrode capacitance will change
accordingly. These changes in capacitance are measured by the sensing
electronics and further used to reconstruct an image, in which each pixel is
assigned a gray level to represent the material distribution, i.e., the solid
concentration, by a specific image reconstruction algorithm. By post-processing
the obtained image, some key hydrodynamic parameters, such as the overall solid
concentration, number of bubbles, bubble position, and bubble size can then be
estimated. Therefore, the key hydrodynamic parameters are obtained in an
indirect manner.

However, there are
two main difficulties associated with ECT image reconstruction. First, it is
severely under-determined due to the number of independent capacitance
measurements is much less than the number of pixels in an image. Second, the
characteristics of soft-field sensing make the reconstructed images sensitive to
noise in raw capacitance measurements. Many image reconstruction algorithms
have been proposed so far, and the Landweber iteration algorithm is the most
popular for generating high quality images in most cases. However, the
iterative process is time-consuming and hence not suitable for on-line
measurement. In addition, it is laborious to carry out post-processing of the
reconstructed images to obtain key hydrodynamic parameters since additional
computing time is needed. Therefore, it is essential to develop an alternative
approach for on-line monitoring of key hydrodynamic parameters for flow regime
identification, fluidization quality characterization, feedback control, and
fault detection of gas-solid fluidized beds by use of ECT.

Note that although
the two-phase flow in gas-solid fluidized beds exhibits very complex chaotic
behavior, many researches indicated recurrence of similar flow patterns. In
this regard, most of the expensive calculations needed for the material
distribution reconstruction and post-processing are repetitive and can be
possibly avoided via a universal data-driven key parameter prediction recipe.

The aim of this
work is to apply machine learning to ECT without image reconstruction for
on-line measurement of key hydrodynamic parameters in real gas-solid fluidized
beds. To this end, a machine learning approach was proposed. Figure 1 shows the
flowchart of the proposed approach. At first, u_g
linear-increasing strategy was used to perform high-throughput experiments to
collect a large amount of training samples that traverse many possible flow
patterns in a short time period. Then at the second step, the key hydrodynamic parameters
in the training samples were calculated by post-processing the material
distribution reconstructed by the Landweber iteration algorithm off-line. Next,
supervised machine learning was used to train a map from the measured
capacitance to the calculated key hydrodynamic parameters. With the trained
model, the key hydrodynamic parameters can be monitored on-line. The proposed machine
learning approach can be used to predict any key hydrodynamic parameters in
gas-solid fluidized beds, such as the overall solid concentration, number of
bubbles, bubble position, and bubble size using the same procedure with little modification.

Figure 1. Flowchart
of the proposed machine learning
approach for the measurement of gas-solid fluidized beds using ECT.