Electrical Capacitance Tomography to Measure Moisture Distribution of Polymer Foam in a Microwave Drying Process

Moisture distribution information is a critical element in drying processes. The drying of products by employing high-power microwave (MW) technology is widely used in the industry. Although microwaves allow volumetric and selective heating resulting in a significant reduction of processing time and energy consumption, there is always a risk of non-uniform moisture distribution in the final product. This paper investigates the capability of a designed electrical capacitance tomography (ECT) sensor to estimate the moisture distribution of polymer foams in a microwave drying process. The moisture distribution is estimated based on the non-intrusive contactless measurements of the electrical capacitances between the electrodes mounted on a frame around the target polymer foam. The obtained moisture information can be employed as feedback to a controller to adjust the power level of each microwave source in the microwave system to reduce or eliminate the non-homogeneity of the moisture distribution inside the polymer foam. In a series of experiments, we first examine the capability of the ECT sensor in estimating the moisture distribution in a stationary foam. We extend the tests to estimating the moisture distribution in a case where the foam is moving on a conveyor belt. Several study variables are taken, including the sample size, the sample location, the moisture percentage, the conveyor belt speed, and the microwave power. These experiments show that the sensor has a satisfactory accuracy in estimating the moisture distribution of the foam, and the ECT measurements can be further used in a closed-loop control system.

drying is becoming an attractive candidate for drying high moisture materials [1]- [3]. Volumetric and selective heating in microwave drying results in the fast internal evaporation of moisture. In this process, the wet material is exposed to several microwave sources in an oven cavity until the water inside the material evaporates.
One of the main goals of microwave drying technology is to achieve as uniform moisture distribution inside the material as possible since it has a high impact on the final product quality. Typically, the aim is to reach a certain level of moisture in the dried material. Designing an advanced moisture controller for the microwave drying process can help to reach a homogenous moisture distribution. Such kind of controller has not been designed for drying processes since it needs in situ information about the moisture distribution of the material.
As one of the traditional methods, the temperature of the material is monitored to control the drying process [4]- [7]. In [4], [6], [7], the authors used the temperature measurement from one point on the sample to control the drying temperature by adjusting the microwave power. Authors in [5] employed This work is licensed under a Creative Commons Attribution 4.0 License. For more information, see https://creativecommons.org/licenses/by/4.0/ infrared thermography to identify the instant hot spots on the samples rather than monitoring the temperature of one fixed position. However, temperature control can only prevent overheating, and the temperature distribution does not necessarily correspond with the moisture distribution. Therefore, this method is insufficient for having a homogenous moisture distribution.
The moisture distribution can only be obtained using tomographic sensors. In general, the benefits of combining process tomography with a feedback controller have been widely recognized [8], [9], and the idea has been tested with simulations [10]. Recently, microwave tomography has been studied to estimate the moisture distribution in a simulated microwave drying process [11]. However, tomographic sensors have not been used yet in monitoring the moisture distribution in microwave drying processes. The most practiced method of measuring the moisture content in this process is by measuring the sample weight during or after the process [12]- [17]. In most cases, like in [12], the authors attached the sample to a digital balance by a hook and recorded the sample weight loss during the drying process. This method can only give the average moisture of the material. Moreover, it is impossible to use this method for larger samples or in continuous processes where the wet material moves through the oven cavity.
Electrical capacitance tomography (ECT) has shown to be an attractive tool for monitoring moisture distribution in several applications since it is non-intrusive, non-invasive, and inexpensive [18]- [23]. In [20], the author employed the ECT sensor in imaging three-dimensional (3D) unsaturated moisture flow in cement-based materials. The ECT sensor consisted of several electrode plates to make 3D imaging possible. In [23], the authors used the ECT sensor designed with eight electrodes on one plate rounded around woody biomass samples to estimate their moisture content. They compared the results with the near-infrared spectroscopy method to find the best way to estimate the moisture content of the samples.
One of the microwave drying process applications is the drying of polymer foams in the heat insulation industry. In this process, it is essential to dry the foam below a certain level (e.g., 15-20% on a wet basis), and the remaining moisture should have as homogenous distribution as possible. If some parts of the foam dry while other parts are still wet, the product can be damaged due to overheating or burning. The overheating of the foam can also destroy the whole microwave system and the production line. This paper aims to design an ECT sensor to estimate the moisture distribution of polymer foams in a continuous microwave drying process. The ECT sensor measures the contact-free capacitances between the electrodes mounted on a frame around the foam. The measurements are then employed in a reconstruction algorithm to estimate the foam permittivity distribution. Since the material permittivity strongly correlates with the material moisture, a calibration curve between the estimated permittivity and the actual moisture of the material is determined to estimate the moisture distribution. The moisture estimates can further be integrated into a closed-loop controller to counteract an inhomogeneous moisture distribution in the foam. Even though the basic principles of how an ECT sensor works are the same for any application, the designs can be completely different. Each application requires its specifications regarding the frame size, the number of the electrodes, the electrode size, and the electrode locations. Each of these factors can highly affect the reconstruction results. In this paper, an ECT sensor is developed based on the most efficient design according to the simulations and experiments to estimate the moisture distribution of moving polymer foams. The application has some unique requirements considered in the sensor design, such as the mobility of the material and its large size, which results in very low measured electrical capacitances between most of the electrodes. The ECT measurements are fast, and they can be used in in-line, real-time measurements. In this paper, the performance of the ECT in the case of stationary and moving foams is evaluated through a series of experiments.

II. MICROWAVE DRYING PROCESS
The microwave drying process has been an attractive technology during the past decades by demonstrating time and energy efficiency in many applications. Figure 1 illustrates a schematic picture of the microwave drying system considered in this study with three oven cavity modules, each equipped with six 2 kW, 2.45 GHz microwave sources distributed on the hexagonal sides of the oven. This system is a combination oven with convective heating, which allows the transport of the evaporated moisture out of the system.
The microwave drying technology is associated with the dielectric heating of poorly conductive products such as polymer foams, the test material in this study. In the heat insulation industry, the impregnation of polymer foams introduces new features to the foam by dipping it into a bath, squeezing it, and then drying it by passing it through an oven. The squeezing step is designed to ensure the most homogenous moisture distribution inside the foam at the beginning of the drying process. After the impregnation process, the wet foam enters the oven on a conveyor belt, passes through the oven cavity modules, and exits from the other side of the system. Figure 2 shows a schematic of a cross-section of one of the cavity modules.
The infrared cameras installed in each module can monitor the surface temperature distribution of the foam throughout the drying process. However, there is no available information on the moisture distribution of the foam during and after the process. So far, no sensor for monitoring the moisture distribution of the drying material has been designed for this process.
In this study, an ECT sensor is developed to estimate the moisture distribution of polymer foams right after the drying process. For safety reasons, the ECT sensor cannot be placed inside the microwave oven. The information obtained from the sensor will be an essential part of the moisture control unit [24].

III. ELECTRICAL CAPACITANCE TOMOGRAPHY
Electrical capacitance tomography is an imaging sensor employed to reconstruct the material permittivity, which strongly correlates with the moisture distribution inside the material.
The ECT device works based on inter-electrode capacitance measurements between the electrodes mounted on a frame around the target material. Figure 3 shows an illustration of the ECT sensor. The measurement procedure involves applying an electrical voltage to excite one of the measurement electrodes while the rest are grounded. The electrical capacitance between the exciting electrode and the other grounded ones is measured, and then the same operation is repeated to other measurement electrodes. It should be noted that there is a narrow electrically grounded electrode installed between every adjacent measurement electrodes to improve the sensitivity of the measurements. However, they are not involved in the measurement procedure, and the electrical capacitance is only measured between the measurement electrodes. By having N el measurement electrodes, m = N el (N el − 1) /2 measurements are gathered in each frame. Based on the obtained measurements, the permittivity distribution is reconstructed.
To solve the reconstruction problem, which is also referred to as the inverse problem, we need to solve the forward problem first. The forward problem formulates a model to connect the ECT measurements, the electric potential distribution, and the permittivity distribution. In our study, the forward model is adopted from the complete electrode model, which is placed in the imaging area. Measurement electrodes are mounted around the foam. There is an electrically grounded electrode between adjacent measurement electrodes to improve the sensitivity of their measurements. An electrically grounded metal screen is surrounding the electrode plates to reduce the background noise. Also, the electrode plates are separated from the metal screen and the imaging area by insulating layers.
has different boundary conditions than the conventional ECT model. The complete electrode model takes the electrode model into account more accurately. It has been developed first for the electrical impedance tomography [25] and then derived for the ECT [26].
Let x ∈ denote the spatial coordinate in the computational domain . The permittivity (x) can be defined as where 0 ≈ 8.8542 × 10 −12 Fm −1 is the vacuum permittivity, and r (x) ≥ 1 is the relative permittivity of the material. The complete electrode model for ECT can be written as with the boundary conditions where N el is the total number of measuring and grounded electrodes, ν is the outward unit normal vector of the electrode surface or the target boundary, u(x) is the electric potential distribution, ζ l is a small coefficient modeling an almost negligible potential drop on the electrodes, U l is the applied potential on the l-th electrode, q l is the unknown electric charge on the l-th electrode, and ∂ el = ∪ N el l=1 ∂ (l) el is the union of the electrode surfaces. Based on experimental tests [26], the parameter ζ l is taken as ζ l = ζ = 10 −9 , l = 1, . . . , N el .
The forward model is numerically solved using the finite element method [26], [27]. By augmenting the models corresponding to a set of m measurements in a vector and assuming additive measurement noise, the observation model for ECT can be formulated as where C = [C 1 , . . . , C m ] T denotes the vector of the measured electrical capacitances between the electrodes, = [ 1 , . . . , n ] T is the discretized permittivity distribution, n is the number of the discretization points, T is the map between the permittivity distribution, , and capacitances, C, resulting from the finite element (FE) approximation, and v = [v 1 , . . . , v m ] T is the additive measurement noise.
The forward model of ECT connects the measured electrical capacitances with the permittivity distribution and is mathematically a well-posed problem. However, the inverse problem is an ill-posed problem that aims to reconstruct the permittivity distribution based on the capacitance measurements. There are many techniques proposed to solve the inverse problem of ECT [28]- [31]. Some methods have the capability of finding the absolute value of the permittivity. However, they are usually computationally expensive and slow. In this study, the difference imaging method is employed to reconstruct the permittivity changes of the wet material compared to the permittivity of the dry material. The chosen technique is a linear method; therefore, it is computationally fast and suitable for real-time measurements. However, due to the approximation error of the linearization, there can be a relatively high estimation error for the permittivity change value when using the difference imaging method. This drawback can be overcome in our application by using a calibration curve between the estimated permittivity and the actual material moisture.
In the difference imaging method, the observation model (6) is approximated by the first-order Taylor polynomial as where J ( * ) = ∂H ( * ) /∂ is the Jacobian matrix [26], and * is the linearization point. Two sets of measurements are collected: C ref , which denotes the measurements before the change in the permittivity (the measurements of the dry material), and C M , the measurements after the permittivity change (the measurements of the wet material). With these measurements, the approximated model for the difference data C = C M − C ref can be computed as where = − ref is the change in the permittivity compared to the dry material permittivity, ref , and v is the change of the noise term.
The permittivity change can be estimated using the Bayesian framework leading to the optimization problem [32] = arg min is a smoothness promoting prior, calculated through the Cholesky factorization as calculated in [33]. Eventually, the difference imaging solution can be calculated as where K is the reconstruction matrix and is calculated as [32] Equation (10) calculates the permittivity change distribution of the material. The calibration curve between the estimated permittivity change and the actual moisture of the foam can be used afterward to calculate the estimates of the moisture distribution. The calibration curve is obtained in this paper using the experimental data.

IV. MATERIALS AND METHODS
The capability of the ECT sensor when estimating the moisture distribution of polymer foams is investigated in this study through several experiments. In the following sections, the devices, materials, and experimental procedures are described in detail.

A. Samples
Polymer foams have many applications in the heat insulation industry, such as sealing tapes of windows. In this study, we used raw polymer foams with a density of 23 ± 2 kg/m 3 . The foam width was 493 mm, and it had a thickness of 30 mm. The studied process is continuous; however, a limited length of the foam was used in our experiments. Figure 4 shows three samples of this polymer foam.

B. ECT Device
The measurement procedure and the theory behind the ECT were explained in Section III. Several factors in designing the ECT sensor can considerably affect the reconstruction accuracy and the sensor spatial resolution. In our application, the ECT sensor and consequently the 2D image of the cross-section were rectangular, while most common ECT setups are round. Moreover, the large width of the foam required a wide structure for the ECT which resulted in a considerable distance between the non-neighboring electrodes. Therefore, only a few measurements were large enough to affect the reconstructions. This issue made the permittivity distribution reconstructions challenging and required a sensor design to address the practical limitations and reduce their effects on the measurement signal. In designing the ECT sensor, it was essential to have the electrodes on both the top and bottom surface of the foam. The simulation results predicted that the moisture on the bottom parts of the foam could not be detected without the electrodes on the bottom surface. Therefore, modifying the metallic table on which the conveyor belt was moving was required since the table prevented transmitting any signal from the bottom electrodes. Furthermore, since the thickness of the foam was only 30 mm, no electrodes were needed on the sides of the ECT sensor. The design of the developed ECT sensor is similar to the illustration shown in Fig. 3.
The dimension of the sensor structure was 870 mm × 250 mm × 40 mm. The height of the sensor was adjustable as the foam thickness can be different in future studies. Six measurement electrodes were mounted on the top surface and another six measurement electrodes on the bottom surface of the ECT sensor. Each measurement electrode was 100 mm × 81 mm, and the electrically grounded electrodes between every adjacent measurement electrodes were of the size of 100 mm × 3 mm. A thin electrically grounded aluminum shield was covering the sensor structure to reduce the background noise. Furthermore, the electrode plane was separated from the metal shield and foam with insulating layers.
Since the foam was moving through the sensor, there was an air gap of 10 mm between the foam and the electrodes on the top surface of the sensor. The ECT sensor can conduct contact-free imaging; however, the air gap required for the foam movement increased the distances between the electrodes and the foam, which could degrade the ECT signal. In our design, we overcame this problem by considering a large width for the measurement electrodes, improving the measurement signal. Figure 5 shows the designed and built ECT sensor to be installed at the microwave exit.
The sensor was connected to a measurement device built by Rocsole Ltd., Kuopio, Finland. The measurement device applied AC voltage with the magnitude of 2.5 V and frequency of 625 kHz to the exciting electrodes and measured the inter-electrode capacitances. The frequency resulting in the best reconstruction was determined based on experimental results, and the voltage magnitude was chosen automatically by the measurement device. The measurements were transferred in real-time to a laptop connected to the device. Each frame of the measurements took less than a second. The measured electrical capacitances were used in the difference imaging algorithm to reconstruct the permittivity distribution of the foam.
The reconstruction algorithm computes the 2D permittivity distribution of the material. In 2D reconstruction, it is assumed that the permittivity in the y-direction, which is the foam moving direction, is constant, and the permittivity distribution is reconstructed in only a cross-section of the foam. The FE mesh representing the reconstructed permittivity in this study has a density of 824 nodes with 1430 elements, which provides enough spatial resolution considering our application.

C. Microwave Drying System
Our testbed system is called HEPHAISTOS, a large-scale microwave oven located at Karlsruhe Institute of Technology (KIT), Germany. The oven includes three cavity modules, each 100 cm in length, as explained in Section II. Since the system is an open oven, two microwave filters, each 150 cm in length, are installed at both sides of the oven to block the microwave power leakage from the entering and exit points. The whole length of the system is 729 cm.
A picture of this device is shown in Fig. 6. The system is operated by software named SIMPAC developed by the manufacturing company of the microwave system, Vötsch Industrietechnik GmbH, Germany. The microwave sources are the sources of heating energy, which result in the evaporation of the foam moisture. Moreover, there is hot air circulating in the device to remove the evaporated moisture. The power levels of the microwave sources, the hot air temperature, and the conveyor belt speed can be controlled using SIMPAC.

D. Experiments 1) Stationary Measurements:
In the first set of experiments, a stationary case was studied. In this test, a board of foam with a dimension of 493 mm × 250 mm × 30 mm was inserted inside the sensor. The purpose of this experiment was to identify the wet parts of the foam. Three pieces denoted as P1, P2, and P3, of the foam, were cut, moisturized up to  a certain amount, and returned to their original locations to validate the results. Figure 7 shows a picture of the foam, which includes the three wet pieces. All pieces were cut in the same size of 50 mm × 50 mm × 30 mm and arranged at an equal distance. The first and the third piece also had the same distance from the left and right sides of the foam. The moisture distribution of the foam was estimated in three different experiments. These experiments were conducted to evaluate the sensor sensitivity to the moisture level and its accuracy in identifying the moisture locations.
In the first experiment, P1 had more moisture than the other two pieces. In the second experiment, the moisture content of P2 was increased to almost the same level as P1, while P3 had the lowest moisture level. Finally, in the third experiment, all pieces were wet with the same amount of moisture. The weight of every piece was measured both while dry and after adding the water to compute the actual moisture percentage. The wet basis moisture percentage was calculated as where W d is the weight of the dry piece and W w is the weight of the same piece after adding the water. 2) Dynamic Measurements: After evaluating the sensor performance in the stationary measurements, the sensor was installed on the microwave system right after the microwave filter on the exit point. The following experiments aimed to measure the moisture distribution of a polymer foam while passing through the sensor on a conveyor belt. Figure 8 shows the ECT sensor while measuring the electrical capacitances as the foam was moving through the sensor. The sample foam for this experiment was of a dimension of 493 mm × 1000 mm × 30 mm. It contained 13 different pieces, which were cut, moisturized, and returned to their original locations in nine rows. Figure 9 shows this board of foam, while the nine rows are indicated in the picture. The size, location, and moisture content of the pieces in this sample foam were chosen such that several factors can be studied throughout the experiments.
Three different experiments were conducted with the moving foam to study the effects of the belt speed and the microwaves on the reconstructions. In the microwave drying of polymer foams, the conveyor belt speed can be chosen from 20 cm/min to 40 cm/min. In the first experiment, the microwave power sources were off, and the foam was wet with the known moisture amounts before passing through the sensor. The belt speed in this experiment was 40 cm/min. Since the ECT sensor should be able to work while the microwave sources are on, the second experiment was done with the same belt speed while the microwave sources were working. The third experiment was conducted with a 20 cm/min belt speed while the microwave sources were off.
3) Moisture Calibration: In the microwave drying process, the goal is to determine the moisture distribution of the drying material. However, the difference imaging method only estimates the change in the permittivity distribution, which is correlated to the moisture. A mapping between the estimated permittivity changes calculated from (10) and the actual moisture values was determined to calculate the moisture distribution of the foam.
In both stationary and dynamic experiments, the actual wet basis moisture percentage of the pieces was computed from (12). Let M i , i = 1, 2, 3 be the actual moisture percentage of the i -th piece in one of the stationary experiments. The estimated permittivity change distribution in this experiment was calculated using (10). This distribution can be employed to compute the dry basis permittivity change (in percentage), where ref is the best homogeneous estimate of the dry foam permittivity. It is assumed that the dry foam has a homogenous permittivity distribution, so only one value was estimated for the whole permittivity distribution. Since the wet basis was used to compute the moisture percentage in our application, the dry basis permittivity change was converted to the wet basis permittivity change, w (in percentage), before determining the mapping. The dry and wet basis permittivity change are related as As only the average moisture percentage of each piece was known, instead of using the whole permittivity distribution, the average value of w in the corresponding area to the i -th piece, referred to as w,i , was calculated. A mapping between the w,i and M i was found using the data obtained from different stationary experiments with various moisture percentages for every piece. The calculated mapping was used to transform the estimated permittivity distribution of the foam to the moisture distribution in the stationary experiments. The same procedure was followed for the dynamic experiments to map the estimated permittivity change and the actual moisture when the foam was moving. The foam movement and the long length of the sample foam in the dynamic experiments resulted in different reconstructed permittivity values than the stationary experiment. Therefore, the same calibration as in the stationary experiments could not be used in the dynamic experiments but required a different calibration.

V. RESULTS AND DISCUSSIONS A. Reconstruction Results of the Stationary Measurements
Three different experiments were conducted in the stationary measurements where a board of foam with three moisture locations was placed inside the ECT sensor. As noted in Section II, the difference imaging method requires the electrical capacitance measurements of both the dry and wet foams. Figure 10 displays the measured capacitances of the wet and the dry foams in Experiment 1 of the stationary experiments. Here, the electrical capacitance of the wet foam in some measurements is larger than in the dry foam measurements due to the increased moisture level near the corresponding electrode plates. Moreover, as mentioned in Section IV-B, because of the rectangular structure of the ECT sensor and its large width, only 26 out of 66 measurements are adequately large, which can be seen as the peaks in Fig. 10. The peaks in both measurement sets correspond to the neighboring or opposing electrodes, and the rest of the measurements are close to zero. Therefore, effectively the reconstructions were calculated based on the 26 highest measurements.
Based on the reconstruction results of these experiments, a calibration map between the actual moisture values and their corresponding estimated permittivity change percentage on the wet basis was found. A linear mapping proved to be sufficient considering the measurement data. This mapping was obtained as w = (0.745 ± 0.083)M − 1.538 ± 3.660.
(15) Figure 11 shows the measured data, the fitted curve, and the 95% confidence interval for the stationary experiments. The mapping (15) was used to find the estimated moisture distributions from the stationary experiments illustrated in Fig. 12. In this figure, the actual locations of the wet pieces are indicated in every subfigure with a red rectangle accompanied by a corresponding label (P1, P2, and P3). The actual moisture percentage, M, of every piece in these experiments and its estimated value, M e , are given in Table I. The relative moisture estimation error, e M , is also computed for every piece and indicated in Table I for a more straightforward evaluation of the results. The relative estimation error was determined as where M e is the estimated moisture percentage.   Figure 12a shows a case where P1 has more moisture than P2 and P3, while those two pieces have almost the same moisture. As shown in this figure, all the moisture locations are identified correctly, and the moisture estimations are higher in the P1 location than in the other two places. The higher average moisture estimate of P1 can also be seen from the values of M e in Table I. As seen from this table, the average moisture estimate of all three pieces follows their actual values. The estimation error in this experiment varies from 0.8% to 9.2%.
In the second experiment, the moisture content of P2 was increased to reach the same amount as P1. The estimated moisture distribution for P2 in Fig. 12b clearly shows the increase in moisture compared to the estimated moisture distribution in Experiment 1. Moreover, the information given in Table I shows that the average estimated moisture for P2 has increased in Experiment 2 compared to Experiment 1. In this experiment, P3 had the least average estimated moisture as it contained the lowest amount of water among all the pieces.
The third experiment studied a case where the moisture level of P3 was increased compared to the previous experiments. In this experiment, all the pieces had almost the same amount of moisture. Figure 12c displays the reconstruction result of this measurement. As shown in this figure and can be followed from Table I, the first and second moisture locations are identified correctly. However, there is a position error in identifying P3, probably due to water leakage from P3 to the neighboring area. As the third experiment was done right after the first two experiments, and it involved more moisture, the amount of water moving to the surroundings could be higher. It can be seen from the estimation errors shown in Table I that the estimation errors for P1 and P2 are 6.8% and 4.3%, respectively, while it is 27.3% for P3 for the possible reasons mentioned. The average estimation error for all the stationary experiments was 7.6%. Although the relatively high estimation error for P3 in the third experiment raised the average estimation error, the error is satisfactory and close to process control requirements.

B. Reconstruction Results of Dynamic Measurements
In this section, the reconstruction results of the dynamic experiments where the foam was continually moving on the conveyor belt are discussed. Each frame of measurements in ECT takes almost 720 ms. As the speed of the conveyor belt is relatively slow (20-40 cm/min), the measurement time and the reconstruction time are short enough and make it possible to use these measurements in a closed-loop moisture controller unit. In the following experiments, the sample time was taken as 1 s.
The sample foam tested in these experiments is shown in Fig. 9. While the foam passed through the electrode plane of the ECT sensor, 2D reconstructions were calculated at each time instant. As mentioned in Section IV-B, it was assumed that the permittivity in the foam moving direction is constant. With this assumption, mostly the cross-section of the target foam under the electrode plane was reconstructed. As the electrodes were larger than the wet pieces, there were some effects from the neighboring area to that cross-section. A mapping between the actual moisture of pieces in these experiments and the normalized estimated permittivity change, w , was obtained as The measured data, the fitted curve, and the 95% confidence interval for the mapping in the dynamic experiments are shown in Fig. 13.
In the first experiment, the sensor performance was evaluated while the foam moved on a conveyor belt with a speed of 40 cm/min. In this experiment, the actual microwave heating effect was not considered because the heating would have resulted in the evaporation of the moisture in the foam and made it difficult to validate the reconstruction results.  Therefore, in the first and third experiments, the microwave sources were off, and only the belt speed factor was examined. Figure 14 shows the 2D reconstructions at nine different time instants, in which each row of the sample foam was precisely in the middle of the electrode planes. As the electrode plane had a 100 mm length, there were several time instants when each cross-section of the foam was under this plane. In this figure, only the middle cross-section is demonstrated, and the rest are not shown. The time variable, t, shows the time passed from the beginning of the experiment. Here, t = 0 is when the foam just entered the sensor frame. As in the stationary case, the red rectangles indicate the actual locations of the pieces. Since the foam was moving on the conveyor belt in the y-direction, there were some small movements to the sides in the x-direction, resulting in small errors between the actual and estimated locations of the pieces. All the 2D reconstructions from the whole experiment were stacked together to create a 3D visualization of these experiments, as shown in Fig. 15. Since the pieces in this experiment had different moisture levels, four thresholds in the estimated moisture distribution were selected to show the variation in the moisture estimates more clearly. The location, moisture content, and the size of the pieces in the sample foam were the three factors that their effects were studied on the reconstructions.
The first factor to study was the sizes of the pieces in the sample foam. The pieces were in two different sizes. The ones on the odd rows were 50 mm in width, while the pieces on the even rows were 80 mm in width. The length and the thickness of all the pieces were 50 mm and 30 mm, respectively. As the reconstruction in Fig. 15 shows, the ECT sensor can identify moisture in both sizes. Since the wavelength of the microwaves in our application is 120 mm, a spatial resolution comparable to the half wavelength, 60 mm, is sufficient for process control. Therefore, the ECT sensor can identify the moisture in any reachable location in this application.
The second subject to study was the distance between the wet pieces. As seen in Fig. 9, two pieces are in each even row, and different distances are considered between these pieces to evaluate the sensor resolution. The idea was to see if the ECT sensor can detect these two pieces in separate locations or see them as a single moisture object. The label of the pieces located in each even row and their distance from each other are given in Table II. The pieces in Row 2 had the least distance, while at the same time, they had the most amount of moisture compared to the other pieces. Based on the reconstructions in Fig. 15, although there is some reconstructed moisture in the connecting domain of these two pieces, the ECT sensor has identified two separate moisture locations on this row. Figure 14b also shows the separate reconstructed moisture locations clearly. Identifying moisture in the connecting domain was because of spreading water from the wet pieces to the neighboring area.  The resolution of the ECT sensor and the smoothness assumption in the reconstruction algorithm might be the other reasons for the moisture reconstruction in the adjacent regions. Edge preserving priors could reduce this effect; however, the moisture locations do not have sharp edges in practice. In all the other even rows, the pieces are also identified in entirely separate places. In conclusion, it can be said that if the moisture locations are almost 50 mm apart, the ECT sensor can detect them as separate locations. Considering the microwave wavelength, this is an acceptable and sufficient distance.
The third factor to study in this experiment was the moisture content of the sample foam pieces. This experiment evaluated the ECT sensor sensitivity to different amounts of moisture contents. The added water to the pieces was decreased from the first row to the last row, as can be read from Table III. The moisture values in this table are approximately correct as the water starts to evaporate during the experiment, and there will be slightly less moisture than at the beginning.
The reconstruction in Fig. 15 clearly shows the different moisture levels in all 13 pieces. The last piece, P13, had the least amount of moisture, and only the minimum level among the four chosen thresholds of the estimated moisture values can be seen in this location. The first three pieces in the sample foam, on the other hand, had the largest moisture content, which is also shown in the reconstruction. The average estimated moisture and the moisture estimation error for all the 13 pieces are noted in Table III. The estimation errors for several pieces were adequately small while it was substantial for the rest of them. The large estimation error could be due to water moving to the neighboring area or small foam movements to the sides (x-direction). The average estimation error in this experiment was 8.9%. The results showed that the ECT sensor could identify the moisture amount from 17% to 70%. Although the detectable moisture range can be wider, it is far broader than the requirements of our application.
In the actual process, the ECT sensor is working quite close to the microwave oven. As it is an open oven, there is always some microwave leakage, possibly disturbing the measurements. Therefore, we needed to operate the ECT sensor while the microwave sources were on and study the effect on the moisture estimates. Experiment 2 evaluated the sensor performance with the same belt speed and the same sample foam as Experiment 1. The only difference was that the microwave sources worked with their 25% maximum power in this experiment. Since the actual foam moisture needed to stay constant in this study to validate the estimations, the microwave sources were activated only when the foam had already passed the oven and entered the microwave filter area where the microwave sources could not heat the foam. The results proved that the ECT sensor could work near the microwave oven without any visible effects on the reconstructions. Since the reconstruction results were similar to the reconstructions from Experiment 1, they have not been illustrated anymore.
In the last experiment, the effects of a different belt speed on the moisture estimates were studied. In this experiment, the belt speed was set to 20 cm/min. The 3D visualization from the results of this experiment is demonstrated in Fig. 16. Since this was the last experiment and took a long time as the belt speed was low, some of the foam moisture was already evaporated. Comparing Fig. 15 and Fig. 16, it can be seen that, for instance, P13 has less moisture in the last experiment compared to the first one. Nonetheless, all moisture locations are identified correctly, and the results show that the ECT sensor has good performance with both belt speeds of 20 cm/min and 40 cm/min.

VI. CONCLUSION
In this paper, we studied the performance of our designed ECT sensor in estimating the moisture distribution of polymer foam in two states of being stationary and moving on a conveyor belt. The reconstruction algorithm computes the permittivity change distribution of the foam. However, the material permittivity strongly correlates with its moisture, so using a calibration map, the moisture distribution was estimated in all experiments. First, three different stationary experiments were conducted, which showed the excellent performance of the ECT in detecting the moisture locations and distinguishing different moisture percentages. The average estimation error in the stationary experiments was 7.6%. Then, in the dynamic experiments, the measurements were done while the foam was moving on a conveyor belt. In these experiments, two different belt speeds were chosen, and the effect of the microwave power (without heating) was studied. The results showed very acceptable performance from the ECT sensor in the usual working belt speeds. In addition, the microwave power did not affect the ECT sensor signal and, therefore, the reconstructions.
In the dynamic experiments, the size of the moisture locations, the distance between them, and the moisture level in those locations were studied. The experimental results showed that the ECT sensor could easily detect small moisture objects with an area of 50 mm × 50 mm. The results also showed that the minimum distance in which the ECT sensor could distinguish two separate moisture locations was 50 mm. This distance was determined at a high-level moisture content (approximately 70%), while the distance can be smaller between the pieces with lower moisture content since the water moving to the surrounding area will be less. Moreover, the moisture percentages were estimated with reasonable accuracy. However, estimation error in some cases was large, and the average estimation error in the dynamic experiments was 8.6%.
The moisture estimation error should be reduced to nearly 5% so that the moisture estimates will be useful for moisture control. One solution to reduce the estimation error is to enhance the conveyor belt equipment and prevent foam from moving to the sides. It also should be noted that in practice, the foam moisture content after the drying process is lower than the moisture levels studied in our experiments. Removing the higher level moisture data and increasing the number of samples with the lower moisture level in the calibration may also reduce the moisture estimation error.
The experimental results, in general, proved that the accuracy and the resolution of the ECT sensor are satisfactory, and this sensor is a suitable candidate for process control, which is one of the motivations of this paper. The measurement time is short enough (in this study, 720 ms), and the reconstruction time also takes less than a second. Therefore, the measurements can be easily used in a closed-loop moisture control as the foam moisture feedback. Marzieh Hosseini received the M.Sc. degree in electrical engineering-control systems from the Qazvin Islamic Azad University, Qazvin, Iran, in 2015. She is currently pursuing the Ph.D. degree with the Department of Applied Physics, University of Eastern Finland. She is with the TOMOCON Program, a Marie Skłodowska-Curie European training network studying the innovative idea of combining tomographic sensors into control systems. Her research interests include optimal control, process tomography, and system identification.
Anna Kaasinen received the Ph.D. degree in applied physics from the University of Eastern Finland, Kuopio, Finland, in 2013. She is currently a University Lecturer in mathematics with the Department of Applied Physics, University of Eastern Finland. Her research interests include optimal control, process control, and process tomography.