# 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

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**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