Inverse Capacitive Flow Metering in Industrial Pneumatic Conveying Processes
Model-based signal processing and probabilistic inverse methods for ECT-based industrial mass flow measurement.
Project Overview
This PhD project focused on non-invasive mass flow measurement in horizontal pneumatic conveying processes using electrical capacitance tomography (ECT). In these systems, particles are transported through pipes by air flow, resulting in spatially inhomogeneous, dynamic, and difficult-to-observe particle distributions.
The work investigated how indirect capacitive measurements can be transformed into quantitative flow information by combining sensor modeling, signal processing, inverse reconstruction, velocity estimation, uncertainty-aware interpretation, and experimental validation.
Context: Academic research · TU Graz · PhD Thesis
Role: Doctoral research, method development, signal processing, inverse problem formulation, Bayesian estimation, uncertainty analysis, experimental evaluation, and first-author publications.
Methods: Electrical Capacitance Tomography · Signal Processing · Inverse Problems · Bayesian Estimation · Industrial Flow Measurement · Mass Flow Estimation
Problem
Reliable mass flow measurement in pneumatic conveying is challenging because the material distribution inside the pipe is not directly observable and can vary strongly over time and across the pipe cross-section.
Electrical capacitance tomography provides indirect measurements that depend on the permittivity distribution inside the sensor. However, reconstructing material concentration from capacitance data is an ill-posed inverse problem: the number of measurements is limited, the sensor response is spatially distributed, and measurement signals are affected by noise, temperature effects, geometry, and material properties.
The central challenge was to develop methods that extract physically meaningful flow information from indirect, noisy, and application-specific sensor data.
Key challanges
- Indirect measurement of particle distributions inside the pipe
- Ill-posed reconstruction from limited capacitance measurements
- Spatially inhomogeneous and time-varying flow profiles
- Cross-sensitivities with respect to temperature and moisture
- Combination of concentration and velocity information for mass flow estimation
Approach
The project combined physical sensor modeling, statistical signal processing, inverse problem methods, and experimental evaluation to estimate flow-related quantities from ECT data.
1. Capacitive sensing and measurement data
ECT sensors measure capacitances between electrodes arranged around the pipe. These measurements are influenced by the spatial material distribution inside the sensor and provide indirect information about particle concentration.
2. Sensor modeling and inverse reconstruction
A model-based reconstruction framework was used to estimate spatial material distributions from measured capacitance data. The inverse problem was formulated with application-specific assumptions and prior information to obtain physically plausible concentration estimates.
3. Velocity estimation from dynamic measurements
Dynamic ECT measurements were used to estimate particle velocity by analyzing the temporal shift of flow structures between measurement positions or reconstructed signal patterns.
4. Mass flow evaluation
Mass flow estimation was obtained by combining concentration information from ECT reconstruction with particle velocity estimates and relevant pipe or material parameters.
5. Robustness and uncertainty
The work also addressed measurement uncertainty, model assumptions, and sensor cross-sensitivities, including temperature-related effects that are relevant for industrial measurement conditions.
Figures
Figure 1: Workflow for inverse capacitive flow metering in pneumatic conveying. A horizontal pneumatic conveying process is monitored using dual-plane electrical capacitance tomography. Capacitance measurements are interpreted using sensor, noise, and prior models to reconstruct the mass concentration distribution, estimate flow velocity from dynamic dual-plane data, and derive the mass flow rate from concentration and velocity information.
Figure 2: Example results of the inverse capacitive flow metering workflow. The upper panels show the reconstructed mass concentration distribution and the corresponding particle velocity profile used for mass flow estimation. The lower panels show the resulting time-resolved mass flow rate and the cumulative mass obtained by temporal integration.
The cumulative ECT-based estimate is compared with the balance signal as an independent reference measurement.
Figure 1: Workflow for inverse capacitive flow metering in pneumatic conveying. A horizontal pneumatic conveying process is monitored using dual-plane electrical capacitance tomography. Capacitance measurements are interpreted using sensor, noise, and prior models to reconstruct the mass concentration distribution, estimate flow velocity from dynamic dual-plane data, and derive the mass flow rate from concentration and velocity information.
Figure 2: Example results of the inverse capacitive flow metering workflow. The upper panels show the reconstructed mass concentration distribution and the corresponding particle velocity profile used for mass flow estimation. The lower panels show the resulting time-resolved mass flow rate and the cumulative mass obtained by temporal integration.
The cumulative ECT-based estimate is compared with the balance signal as an independent reference measurement.
Outcome
The project demonstrated how a complex industrial measurement problem can be addressed by combining physical sensor understanding, model-based signal processing, inverse problem methods, and uncertainty-aware estimation.
Rather than treating ECT as a purely image-reconstruction problem, the work focused on extracting flow-related quantities from indirect capacitance measurements. This included the estimation of spatial concentration distributions, particle velocity, and mass flow under realistic measurement conditions.
The project illustrates the methodological foundation behind TS-Analytics: combining signals, models, uncertainty, and domain knowledge to obtain interpretable and reproducible analytical results from complex measurement data.
- Model-based interpretation of indirect capacitive measurement data
- Inverse reconstruction of spatial material distributions
- Use of application tailored prior information and physical constraints for robust estimates
- Velocity estimation from dynamic ECT measurements
- Mass flow evaluation from concentration and velocity information
- Analysis of uncertainty and sensor cross-sensitivities under industrial conditions, including model-based compensation approaches
Related Services
Signal Processing →
Processing and interpretation of measurement, sensor, and time-series data, including feature extraction, dynamic signal analysis, and visualization.
Modeling & Inference →
Model-based estimation, inverse problems, probabilistic reconstruction, and uncertainty-aware interpretation of indirectly observed quantities.
Automated Workflows →
Development of reproducible computational workflows for processing, reconstruction, visualization, and repeated analysis of measurement datasets.
Related Thesis
PhD Thesis
Inverse Capacitive Flow Metering in Industrial Pneumatic Conveying Processes
Graz University of Technology
Institute of Electrical Measurement and Sensor Systems
This doctoral thesis received the Award of Excellence 2024 from the Austrian Federal Ministry of Education, Science and Research.
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