# System Identification of Conveyor Belt Microwave Drying Process of Polymer Foams Using Electrical Capacitance Tomography

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## Abstract

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## 1. Introduction

## 2. Microwave Drying Process

## 3. Materials and Methods

#### 3.1. Electrical Capacitance Tomography

#### 3.2. Input–Output Data Collection

#### 3.3. System Inputs

#### 3.4. System Outputs

#### 3.5. Analyzing the Collected Data and Identifying the Process Model

- The data collected from any sensor are usually accompanied by unwanted measurement noise, which can be resolved by filtering the data. The measurement noise was trivial with the ECT sensor because of the efficient design and the reconstruction algorithm. However, since we used foam sheets instead of a very long continuous foam, the measurements had high peaks corresponding to the edge of foams. As observed during the experiments, drops of water were usually accumulated on the edges, resulting in increased moisture recognition. A stopband filter was applied to the collected dataset to remove high-frequency measurements. Figure 6 shows the collected and filtered output data.
- The objective of this research was to find a linear model of the process. Linear models cannot catch arbitrary differences between the input and output signal levels. Therefore, the mean values were removed from the input–output data. Removing the mean values (constant term) allows the analysis of the other signal contents, resulting in a more accurate model.
- Since the ECT sensor was located after the process, it was not straightforward to find the relation of the input power at each time to the measured output. Any point of the foam traveling through the ECT sensor was exposed to several power levels while traveling inside the oven. Therefore, in this study, the system was divided into two subsystems, SYS1 and SYS2, by introducing a virtual input, as shown in Figure 7. The new input signal, E, is the overall applied energy to each location of the foam that was calculated by integrating the power level signal in the travel time corresponding to that location as$$E\left(t\right)={\int}_{t-{t}_{f}-{t}_{c}}^{t-{t}_{f}}P\left(t\right)dt,$$

## 4. Results and Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

- Rattanadecho, P.; Makul, N. Microwave-assisted drying: A review of the state-of-the-art. Dry. Technol.
**2016**, 34, 1–38. [Google Scholar] [CrossRef] - Zhu, H.; Gulati, T.; Datta, A.K.; Huang, K. Microwave drying of spheres: Coupled electromagnetics-multiphase transport modeling with experimentation. Part I: Model development and experimental methodology. Food Bioprod. Process.
**2015**, 96, 314–325. [Google Scholar] [CrossRef] - Cuccurullo, G.; Giordano, L.; Albanese, D.; Cinquanta, L.; Di Matteo, M. Infrared thermography assisted control for apples microwave drying. J. Food Eng.
**2012**, 112, 319–325. [Google Scholar] [CrossRef] - Li, Z.; Raghavan, G.; Orsat, V. Optimal power control strategies in microwave drying. J. Food Eng.
**2010**, 99, 263–268. [Google Scholar] [CrossRef] - Adu, B.; Otten, L. Diffusion characteristics of white beans during microwave drying. J. Agric. Eng. Res.
**1996**, 64, 61–69. [Google Scholar] [CrossRef] - Kumar, C.; Joardder, M.U.H.; Farrell, T.W.; Karim, M. Investigation of intermittent microwave convective drying (IMCD) of food materials by a coupled 3D electromagnetics and multiphase model. Dry. Technol.
**2018**, 36, 736–750. [Google Scholar] [CrossRef] - Luikov, A.V. Systems of differential equations of heat and mass transfer in capillary-porous bodies. Int. J. Heat Mass Transf.
**1975**, 18, 1–14. [Google Scholar] [CrossRef] - Kocaefe, D.; Younsi, R.; Chaudry, B.; Kocaefe, Y. Modeling of heat and mass transfer during high temperature treatment of aspen. Wood Sci. Technol.
**2006**, 40, 371–391. [Google Scholar] [CrossRef] - Silva, F.R.; Gonçalves, G.; Lenzi, M.K.; Lenzi, E.K. An extension of the linear Luikov system equations of heat and mass transfer. Int. J. Heat Mass Transf.
**2013**, 63, 233–238. [Google Scholar] [CrossRef] - Hosseini, M.; Kaasinen, A.; Link, G.; Lähivaara, T.; Vauhkonen, M. LQR control of moisture distribution in microwave drying process based on a finite element model of parabolic PDEs. IFAC-PapersOnLine
**2020**, 53, 11470–11476. [Google Scholar] [CrossRef] - Kadem, S.; Younsi, R.; Lachemet, A. Computational analysis of heat and mass transfer during microwave drying of timber. Therm. Sci.
**2016**, 20, 1447–1455. [Google Scholar] [CrossRef][Green Version] - Favoreel, W.; De Moor, B.; Van Overschee, P. Subspace state space system identification for industrial processes. J. Process. Control.
**2000**, 10, 149–155. [Google Scholar] [CrossRef] - Kristinsson, K.; Dumont, G.A. System identification and control using genetic algorithms. IEEE Trans. Syst. Man, Cybern.
**1992**, 22, 1033–1046. [Google Scholar] [CrossRef] - Fu, L.; Li, P. The research survey of system identification method. In Proceedings of the 5th International Conference on Intelligent Human-Machine Systems and Cybernetics, Hangzhou, China, 26–27 August 2013; IEEE: Piscataway, NJ, USA, 2013; Volume 2, pp. 397–401. [Google Scholar]
- Krishna Murthy, T.P.; Manohar, B. Microwave drying of mango ginger (Curcuma amada Roxb): Prediction of drying kinetics by mathematical modelling and artificial neural network. Int. J. Food Sci. Technol.
**2012**, 47, 1229–1236. [Google Scholar] [CrossRef] - Li, J.; Xiong, Q.; Wang, K.; Shi, X.; Liang, S. A recurrent self-evolving fuzzy neural network predictive control for microwave drying process. Dry. Technol.
**2016**, 34, 1434–1444. [Google Scholar] [CrossRef] - Momenzadeh, L.; Zomorodian, A.; Mowla, D. Experimental and theoretical investigation of shelled corn drying in a microwave-assisted fluidized bed dryer using Artificial Neural Network. Food Bioprod. Process.
**2011**, 89, 15–21. [Google Scholar] [CrossRef] - Yuan, Y.; Liang, S.; Zhong, J.; Xiong, Q.; Gao, M. Black box system identification dedicated to a microwave heating process. In Proceedings of the 27th Chinese Control and Decision Conference (2015 CCDC), Qingdao, China, 23–25 May 2015; IEEE: Piscataway, NJ, USA, 2015; pp. 4116–4120. [Google Scholar]
- Sun, Y. Adaptive and Intelligent Temperature Control of Microwave Heating Systems with Multiple Sources; KIT Scientific Publishing: Karlsruhe, Germany, 2016; Volume 8. [Google Scholar]
- Lutfy, O.F.; Selamat, H.; Mohd Noor, S. Intelligent modeling and control of a conveyor belt grain dryer using a simplified type 2 neuro-fuzzy controller. Dry. Technol.
**2015**, 33, 1210–1222. [Google Scholar] [CrossRef][Green Version] - Lähivaara, T.; Yadav, R.; Link, G.; Vauhkonen, M. Estimation of moisture content distribution in porous foam using microwave tomography with neural networks. IEEE Trans. Comput. Imaging
**2020**, 6, 1351–1361. [Google Scholar] [CrossRef] - Hosseini, M.; Kaasinen, A.; Link, G.; Lähivaara, T.; Vauhkonen, M. Electrical capacitance tomography to measure moisture distribution of polymer foam in a microwave drying process. IEEE Sensors J.
**2021**, 21, 18101–18114. [Google Scholar] [CrossRef] - Arko, A. Development of electrical capacitance tomography for solids mass flow measurement and control of pneumatic conveying systems. In Proceedings of the 1st World Congress on Industrial Process Tomography, Buxton, UK, 14–17 April 1999. [Google Scholar]
- Voss, A.; Hosseini, P.; Pour-Ghaz, M.; Vauhkonen, M.; Seppänen, A. Three-dimensional electrical capacitance tomography–A tool for characterizing moisture transport properties of cement-based materials. Mater. Des.
**2019**, 181, 107967. [Google Scholar] [CrossRef] - Wang, W.; Zhao, K.; Zhang, P.; Bao, J.; Xue, S. Application of three self-developed ECT sensors for monitoring the moisture content in sand and mortar. Constr. Build. Mater.
**2020**, 267, 121008. [Google Scholar] [CrossRef] - Voss, A. Imaging Moisture Flows in Cement-Based Materials Using Electrical Capacitance Tomography. Ph.D. Thesis, University of Eastern Finland, Department of Applied Physics, Kuopio, Finland, 2020. [Google Scholar]
- Rimpiläinen, V.; Heikkinen, L.M.; Vauhkonen, M. Moisture distribution and hydrodynamics of wet granules during fluidized-bed drying characterized with volumetric electrical capacitance tomography. Chem. Eng. Sci.
**2012**, 75, 220–234. [Google Scholar] [CrossRef] - Somersalo, E.; Cheney, M.; Isaacson, D. Existence and uniqueness for electrode models for electric current computed tomography. SIAM J. Appl. Math.
**1992**, 52, 1023–1040. [Google Scholar] [CrossRef] - Watzenig, D.; Fox, C. A review of statistical modelling and inference for electrical capacitance tomography. Meas. Sci. Technol.
**2009**, 20, 052002. [Google Scholar] [CrossRef] - Soleimani, M.; Lionheart, W.R. Nonlinear image reconstruction for electrical capacitance tomography using experimental data. Meas. Sci. Technol.
**2005**, 16, 1987. [Google Scholar] [CrossRef] - Yang, W.; Peng, L. Image reconstruction algorithms for electrical capacitance tomography. Meas. Sci. Technol.
**2002**, 14, R1. [Google Scholar] [CrossRef] - Lei, J.; Liu, S.; Li, Z.; Sun, M.; Wang, X. A multi-scale image reconstruction algorithm for electrical capacitance tomography. Appl. Math. Model.
**2011**, 35, 2585–2606. [Google Scholar] [CrossRef] - Kaipio, J.; Somersalo, E. Statistical and Computational Inverse Problems; Springer: New York, NY, USA, 2006; Volume 160. [Google Scholar]
- Mehra, R. Optimal inputs for linear system identification. IEEE Trans. Autom. Control.
**1974**, 19, 192–200. [Google Scholar] [CrossRef] - Nelles, O. Nonlinear System Identification; IOP Publishing: Bristol, UK, 2002. [Google Scholar]
- Ljung, L. System Identification: Theory for the User, 2nd ed.; Prentice Hall PTR: Upper Saddle River, NJ, USA, 1999. [Google Scholar]

**Figure 1.**The microwave drying oven: (

**a**) The HEPHAISTOS microwave system operating at KIT, Germany. (

**b**) A schematic of one of the cavity modules with six microwave sources.

**Figure 2.**The ECT sensor design: six measuring electrodes and six grounded guard electrodes on the top surface and the same number of electrodes on the bottom surface.

**Figure 3.**The ECT sensor installed at the exit of the microwave oven. After the drying process, the foam enters and passes through the ECT sensor while the ECT estimates its moisture distribution.

**Figure 4.**The schematic of the continuous drying process of polymer foams. The gray rectangles indicate the polymer foams with a length of 150 cm and thickness of 3 cm while passing first through the oven and then the ECT sensor with a speed of 40 cm/min. It took 1129 s for every foam to travel from the entrance point and reach the ECT sensor.

**Figure 5.**Input signals for the system identification: (

**a**) PRBS signal. (

**b**) APRBS signal. (

**c**) Step signal as staircase.

**Figure 8.**The input–output dataset with the PRBS input signal used for estimating the process model: (

**a**) The applied input power percentage to the microwave sources. (

**b**) The input foam moisture variations. (

**c**) Comparison between the actual measurements and the model output.

**Figure 9.**The input–output dataset with the APRBS input signal used for validation of the process model: (

**a**) The applied input power percentage to the microwave sources. (

**b**) The input foam moisture variations. (

**c**) Comparison between the actual measurements and the model output.

**Figure 10.**The input–output dataset with the staircase input signal used for validation of the process model: (

**a**) The applied input power percentage to the microwave sources. (

**b**) The input foam moisture variations. (

**c**) Comparison between the actual measurements and the model output.

Parameter | b | ${\mathit{a}}_{1}$ | ${\mathit{a}}_{2}$ | ${\mathit{T}}_{\mathit{d}1}$ |
---|---|---|---|---|

Value | 5.109 | −1.992 | 0.992 | 261 |

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**MDPI and ACS Style**

Hosseini, M.; Kaasinen, A.; Aliyari Shoorehdeli, M.; Link, G.; Lähivaara, T.; Vauhkonen, M. System Identification of Conveyor Belt Microwave Drying Process of Polymer Foams Using Electrical Capacitance Tomography. *Sensors* **2021**, *21*, 7170.
https://doi.org/10.3390/s21217170

**AMA Style**

Hosseini M, Kaasinen A, Aliyari Shoorehdeli M, Link G, Lähivaara T, Vauhkonen M. System Identification of Conveyor Belt Microwave Drying Process of Polymer Foams Using Electrical Capacitance Tomography. *Sensors*. 2021; 21(21):7170.
https://doi.org/10.3390/s21217170

**Chicago/Turabian Style**

Hosseini, Marzieh, Anna Kaasinen, Mahdi Aliyari Shoorehdeli, Guido Link, Timo Lähivaara, and Marko Vauhkonen. 2021. "System Identification of Conveyor Belt Microwave Drying Process of Polymer Foams Using Electrical Capacitance Tomography" *Sensors* 21, no. 21: 7170.
https://doi.org/10.3390/s21217170