# 3D-Printed Multilayer Sensor Structure for Electrical Capacitance Tomography

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Theoretical Fundamentals of 3D ECT Sensor Modeling

## 3. 3D Modeling & Printing of ECT Capacitance Sensors

## 4. Experimental Setup

## 5. Results and Discussion

#### 5.1. Low-Contrast Objects Investigation

#### 5.2. High-Contrast Objects Investigation

## 6. Conclusions and Directions for Further Work

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

- Rybak, G.; Chaniecki, Z.; Grudzien, K.; Romanowski, A.; Sankowski, D. Non-invasive methods of industrial processes control. IAPGOS Inform. Control. Meas. Econ. Environ. Prot.
**2004**, 4, 41–45. [Google Scholar] [CrossRef] - Che, H.Q.; Ye, J.M.; Yang, W.Q.; Wang, H.G. Measurement of the gas-solid flow in a wurster tube using 3D electrical capacitance tomography sensor. Lect. Notes Electr. Eng.
**2019**, 506, 367–383. [Google Scholar] [CrossRef] - Grudzien, K.; Romanowski, A.; Sankowski, D.; Willams, R.A. Gravitational Granular Flow Dynamics Study Based on Tomographic Data Processing. Part. Sci. Technol.
**2007**, 26, 67–82. [Google Scholar] [CrossRef] - Wajman, R.; Banasiak, R.; Mazurkiewicz, L.; Dyakowski, T.; Sankowski, D. Spatial imaging with 3D capacitance measurements. Meas. Sci. Technol.
**2006**, 17, 2113–2118. [Google Scholar] [CrossRef] - Yang, W.Q.; Peng, L. Image reconstruction algorithms for electrical capacitance tomography. Meas. Sci. Technol.
**2003**, 14, R1–R13. [Google Scholar] [CrossRef] - Marashdeh, Q.; Wang, F.; Fan, L.S.; Warsito, W. Velocity measurement of multi-phase flows based on electrical capacitance volume tomography. Proc. IEEE Sens.
**2007**, 1017–1019. [Google Scholar] [CrossRef] - Plaskowski, A.; Beck, M.S.; Thorn, R.; Dyakowski, T. Imaging Industrial Flows—Applications of Electrical Process Tomography; CRC Press: Boca Raton, FL, USA, 1995. [Google Scholar]
- Rymarczyk, T. Using electrical impedance tomography to monitoring flood banks. Int. J. Appl. Electromagn. Mech.
**2014**, 45, 489–494. [Google Scholar] [CrossRef] - Zeeshan, Z.; Zuccarelli, C.E.; Acero, D.O.; Marashdeh, Q.M.; Teixeira, F.L. Enhancing Resolution of Electrical Capacitive Sensors for Multiphase Flows by Fine-Stepped Electronic Scanning of Synthetic Electrodes. IEEE Trans. Instrum. Meas.
**2019**, 68, 462–473. [Google Scholar] [CrossRef] - Banasiak, R.; Wajman, R.; Sankowski, D.; Soleimani, M. Three-dimensional nonlinear inversion of electrical capacitance tomography data using a complete sensor model. Insight Prog. Electromagn. Res. PIER
**2010**, 100, 219–234. [Google Scholar] [CrossRef] - Wang, Y.; Ren, S.; Dong, F. Focusing Sensor Design for Open Electrical Impedance Tomography Based on Shape Conformal Transformation. Sensors
**2019**, 19, 2060. [Google Scholar] [CrossRef] - Wajman, R.; Fiderek, P.; Fidos, H.; Jaworski, T.; Nowakowski, J.; Sankowski, D.; Banasiak, R. Metrological evaluation of a 3D electrical capacitance tomography measurement system for two-phase flow fraction determination. Meas. Sci. Technol.
**2013**, 24. [Google Scholar] [CrossRef] - Xie, W.Q.; Huang, S.M.; Lenn, C.P.; Stoll, A.L.; Beck, M.S. Experimental evaluation of capacitance tomographic flow imaging systems using physical models. IEE Proc. Circuits Devices Syst.
**1994**, 141, 357–368. [Google Scholar] [CrossRef] - Romanowski, A.; Grudzien, K.; Aykroyd, R.G.; Williams, R.A. Advanced Statistical Analysis as a Novel Tool to Pneumatic Conveying Monitoring and Control Strategy Development. Part. Part. Syst. Charact.
**2006**, 23, 289–296. [Google Scholar] [CrossRef] - Grudzien, K.; Romanowski, A.; Williams, R.A. Application of a Bayesian Approach to the Tomographic Analysis of Hopper Flow. Part. Part. Syst. Charact.
**2017**, 22, 246–253. [Google Scholar] [CrossRef] - Grudzien, K. Visualization System for Large-Scale Silo Flow Monitoring Based on ECT Technique. IEEE Sens. J.
**2017**, 17, 8242–8250. [Google Scholar] [CrossRef] - Romanowski, A. Big Data-Driven Contextual Processing Methods for Electrical Capacitance Tomography. IEEE Trans. Ind. Inform.
**2019**, 15, 1609–1618. [Google Scholar] [CrossRef] - Rymarczyk, T.; Sikora, J. Applying industrial tomography to control and optimization flow systems. Open Phys.
**2018**, 16, 332–345. [Google Scholar] [CrossRef] - Banasiak, R.; Wajman, R.; Soleimani, M. An efficient nodal Jacobian method for 3D electrical capacitance tomography image reconstruction. Insight Non-Destr. Test. Cond. Monit.
**2009**, 51, 36–38. [Google Scholar] [CrossRef] - Kryszyn, J.; Smolik, W.T.; Radzik, B.; Olszewski, T.; Szabatin, R. Switchless charge-discharge circuit for electrical capacitance tomography. Meas. Sci. Technol.
**2014**, 25. [Google Scholar] [CrossRef] - Mazurkiewicz, L.; Banasiak, R.; Wajman, R.; Dyakowski, T.; Sankowski, D. Towards 3D Capacitance Tomography. In Proceedings of the 4th World Congress Industrial Process Tomography, Aizu, Japan, 5–8 September 2005; pp. 546–551. [Google Scholar]
- Wajman, R.; Banasiak, R. Tunnel-based method of sensitivity matrix calculation for 3D-ECT imaging. Sens. Rev.
**2014**, 34, 273–283. [Google Scholar] [CrossRef] - Ye, J.; Wang, H.; Yang, W. Characterization of a multi-plane electrical capacitance tomography sensor with different numbers of electrodes. Meas. Sci. Technol.
**2016**, 27. [Google Scholar] [CrossRef] - Li, Y.; Holland, D.J. Optimizing the geometry of three-dimensional electrical capacitance tomography sensors. IEEE Sens. J.
**2015**, 15, 1567–1574. [Google Scholar] [CrossRef] - Huang, A.; Cao, Z.; Sun, S.; Lu, F.; Xu, L. An agile electrical capacitance tomography system with improved frame rates. IEEE Sens. J.
**2019**, 19, 1416–1425. [Google Scholar] [CrossRef] - Hu, X.; Yang, W. Planar capacitive sensors—Designs and applications. Sens. Rev.
**2010**, 30, 24–39. [Google Scholar] [CrossRef] - Wu, M.; Ye, J.; Wang, H.; Yang, W. Evaluation of Excitation Strategy for a Large-Scale ECT Sensor with Internal-External Electrodes. IEEE Sens. J.
**2017**, 17, 8091–8098. [Google Scholar] [CrossRef] - Xu, H.; Yang, H.; Wang, S. Effect of Axial Guard Electrodes on Sensing Field of Capacitance Tomographic Sensor. In Proceedings of the 1st World Congress on Industrial Process Tomography, Buxton, UK, 14–17 April 1999; pp. 348–352. [Google Scholar]
- Dichtl, C.; Sippel, P.; Krohns, S. Dielectric Properties of 3D Printed Polylactic Acid. Adv. Mater. Sci. Eng. Vol.
**2017**, 2017. [Google Scholar] [CrossRef] - Chen, C.; Woźniak, P.W.; Romanowski, A.; Obaid, M.; Jaworski, T.; Kucharski, J.; Grudzien, K.; Zhao, S.; Fjeld, M. Using Crowdsourcing for Scientific Analysis of Industrial Tomographic Images. Part. Part. Syst. Charact.
**2016**, 7, 52:1–52:25. [Google Scholar] [CrossRef] - Romanowski, A. Contextual processing of electrical capacitance tomography measurement data for temporal modeling of pneumatic conveying process. In Proceedings of the 2018 Federated Conference on Computer Science and Information Systems (FedCSIS), Annals of Computer Science and Information Systems, Poznan, Poland, 9–12 September 2018; IEEE: Piscataway, NJ, USA, 2018; Volume 15, pp. 283–286. [Google Scholar] [CrossRef]

**Figure 3.**Experimental setup hardware: left—32-channel ET3 measurement hardware, right—Agilent E4980A with 64-channel multiplexer device.

**Figure 6.**Arrangement of tested low-contrast objects according to Table 1—from the leftmost TestA, TestB, TestC.

**Figure 7.**A set of ten phantoms used during high-contrast media measurements tests. The mounting stand had 5 holes. Three 10 mm of diameter holes were positioned along the sensor profile diameter at given positions: “P1” at x = 70 mm, y = 70 mm; “P2” at x = 70 mm, y = 40 mm; “P3” at x = 70 mm, y = 10 mm. Two additional 40 mm of diameter holes were positioned symmetrically at x1 = 110 mm and x2 = 40 mm for y = 70 mm. All the rods were parallel to sensor walls.

**Figure 8.**The 1st electrode measurement cycle (S1: 1->32 and S2: 1->32)for Test${A}_{in}$ and S1—blue line, S2—red line. Cyan and magenta lines indicate calibration limits (0;1).

**Figure 9.**The 1st electrode measurement cycle (S1: 1->32 and S2: 1->32) for Test${A}_{out}$ and S1—blue line, S2—red line. Cyan and magenta lines indicate calibration limits (0;1).

**Figure 10.**The 1st electrode measurement cycle (S1: 1->32 and S2: 1->32) for Test${B}_{in}$ and S1—blue line, S2—red line. Cyan and magenta lines indicate calibration limits (0;1).

**Figure 11.**The 1st electrode measurement cycle (S1: 1->32 and S2: 1->32) for Test${B}_{out}$ and S1—blue line, S2—red line. Cyan and magenta lines indicate calibration limits (0;1).

**Figure 12.**The 1st electrode measurement cycle (S1: 1->32 and S2: 1->32) for Test${C}_{in}$ and S1—blue line, S2—red line. Cyan and magenta lines indicate calibration limits (0;1).

**Figure 13.**The 1st electrode measurement cycle (S1: 1->32 and S2: 1->32) for Test${C}_{out}$ and S1—blue line, S2—red line. Cyan and magenta lines indicate calibration limits (0;1).

**Figure 14.**The 1st electrode measurement cycle (S1: 1->32 and S2: 1->32) for Test$2x40$ and S1—blue line, S2—red line. Cyan line indicates lower calibration limit.

**Figure 15.**The 1st electrode measurement cycle (S1: 1->32 and S2: 1->32) for Test${20}_{P1}$ and S1—blue line, S2—red line. Cyan line indicates lower calibration limit.

**Figure 16.**The 1st electrode measurement cycle (S1: 1->32 and S2: 1->32) for Test${20}_{P2}$ and S1—blue line, S2—red line. Cyan line indicates lower calibration limit.

**Figure 17.**The 1st electrode measurement cycle (S1: 1->32 and S2: 1->32) for Test${20}_{P3}$ and S1—blue line, S2—red line. Cyan line indicates lower calibration limit.

**Figure 18.**The 1st electrode measurement cycle (S1: 1->32 and S2: 1->32) for Test${15}_{P1}$ and S1—blue line, S2—red line. Cyan line indicates lower calibration limit.

**Figure 19.**The 1st electrode measurement cycle (S1: 1->32 and S2: 1->32) for Test${15}_{P2}$ and S1—blue line, S2—red line. Cyan line indicates lower calibration limit.

**Figure 20.**The 1st electrode measurement cycle (S1: 1->32 and S2: 1->32) for Test${15}_{P3}$ and S1—blue line, S2—red line. Cyan line indicates lower calibration limit.

**Figure 21.**The 1st electrode measurement cycle (S1: 1->32 and S2: 1->32) for Test${10}_{P1}$ and S1—blue line, S2—red line. Cyan line indicates lower calibration limit.

**Figure 22.**The 1st electrode measurement cycle (S1: 1->32 and S2: 1->32) for Test${10}_{P2}$ and S1—blue line, S2—red line. Cyan line indicates lower calibration limit.

**Figure 23.**The 1st electrode measurement cycle (S1: 1->32 and S2: 1->32) for Test${10}_{P3}$ and S1—blue line, S2—red line. Cyan line indicates lower calibration limit.

Config | TestA | TestB | TestC |
---|---|---|---|

inside | Phantom Test${A}_{in}$ | Phantom Test${B}_{in}$ | Phantom Test${C}_{in}$ |

outside | Phantom Test${A}_{out}$ | Phantom Test${B}_{out}$ | Phantom Test${C}_{out}$ |

**Table 2.**Results of capacitance measurement (in pF) for selected electrode pairs and all testing phantoms.

$\mathit{RCD}$ | Test${\mathit{A}}_{\mathit{out}}$ | Test${\mathit{A}}_{\mathit{in}}$ | Test${\mathit{B}}_{\mathit{out}}$ | Test${\mathit{B}}_{\mathit{in}}$ | Test${\mathit{C}}_{\mathit{out}}$ | Test${\mathit{C}}_{\mathit{in}}$ |
---|---|---|---|---|---|---|

S1-1-2 | 7.446 | 7.291 | 7.460 | 7.278 | 7.408 | 7.336 |

S1-1-9 | 6.604 | 6.536 | 6.614 | 6.531 | 6.616 | 6.541 |

S1-1-17 | 3.926 | 3.914 | 3.928 | 3.911 | 3.918 | 3.930 |

S1-1-25 | 3.919 | 3.917 | 3.921 | 3.917 | 3.917 | 3.928 |

S2-1-2 | 4.909 | 4.626 | 4.922 | 4.617 | 4.827 | 4.673 |

S2-1-9 | 4.577 | 4.414 | 4.591 | 4.410 | 4.568 | 4.427 |

S2-1-17 | 3.920 | 3.912 | 3.921 | 3.911 | 3.913 | 3.916 |

S2-1-25 | 3.922 | 3.920 | 3.922 | 3.920 | 3.919 | 3.922 |

**Table 3.**The standard deviation indicators (std) calculated for the 1st electrode measurement cycle, where electrodes: 2->32 were grounded. Where 10, 15, 20, 40 stands for object diameter and P1, P2, P3 determine object positions along sensor radius, P1 = 70 mm, P2 = 35 mm, P3 = 10 mm respectively.

std | 2 × 40 | 20${}_{\mathit{P}1}$ | 20${}_{\mathit{P}2}$ | 20${}_{\mathit{P}3}$ | 15${}_{\mathit{P}1}$ | 15${}_{\mathit{P}2}$ | 15${}_{\mathit{P}3}$ | 10${}_{\mathit{P}1}$ | 10${}_{\mathit{P}2}$ | 10${}_{\mathit{P}3}$ |
---|---|---|---|---|---|---|---|---|---|---|

S1 | 0.0883 | 0.0132 | 0.0310 | 0.1403 | 0.0083 | 0.0201 | 0.0728 | 0.0038 | 0.0143 | 0.0349 |

S2 | 0.1296 | 0.0081 | 0.0223 | 0.1272 | 0.0057 | 0.0110 | 0.0717 | 0.0050 | 0.0097 | 0.0284 |

% | −32% | 63% | 39% | 10% | 46% | 83% | 1.5% | −24% | 47% | 23% |

**Table 4.**The mean value indicators (mean) calculated for the 1st electrode measurement cycle (with 2..32). Where 10, 15, 20, 40 stands for object diameter and P1, P2, P3 determine object positions along sensor radius, P1 = 70 mm, P2 = 35 mm, P3 = 10 mm respectively.

mean | 2 × 40 | 20${}_{\mathit{P}1}$ | 20${}_{\mathit{P}2}$ | 20${}_{\mathit{P}3}$ | 15${}_{\mathit{P}1}$ | 15${}_{\mathit{P}2}$ | 15${}_{\mathit{P}3}$ | 10${}_{\mathit{P}1}$ | 10${}_{\mathit{P}2}$ | 10${}_{\mathit{P}3}$ |
---|---|---|---|---|---|---|---|---|---|---|

S1 | 0.0330 | 0.0020 | 0.0099 | 0.0332 | 0.0011 | 0.0083 | 0.0299 | −0.0024 | 0.0031 | 0.0097 |

S2 | 0.0632 | 0.0028 | 0.0091 | 0.0683 | 0.0027 | 0.0046 | 0.0363 | 0.0011 | 0.0067 | 0.0143 |

% | 48% | 29% | −8% | 51% | 45% | −80% | −18% | >100% | >100% | 68% |

© 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Kowalska, A.; Banasiak, R.; Romanowski, A.; Sankowski, D.
3D-Printed Multilayer Sensor Structure for Electrical Capacitance Tomography. *Sensors* **2019**, *19*, 3416.
https://doi.org/10.3390/s19153416

**AMA Style**

Kowalska A, Banasiak R, Romanowski A, Sankowski D.
3D-Printed Multilayer Sensor Structure for Electrical Capacitance Tomography. *Sensors*. 2019; 19(15):3416.
https://doi.org/10.3390/s19153416

**Chicago/Turabian Style**

Kowalska, Aleksandra, Robert Banasiak, Andrzej Romanowski, and Dominik Sankowski.
2019. "3D-Printed Multilayer Sensor Structure for Electrical Capacitance Tomography" *Sensors* 19, no. 15: 3416.
https://doi.org/10.3390/s19153416