Assessing the capability of electrical capacitance tomography for monitoring chopped maize mass flow rates in field forage harvesters

Abstract

This study explores the potential and feasibility of Electrical Capacitance Tomography (ECT) for monitoring mass flow rates (MFR) of chopped maize in precision agriculture. The research, conducted using a stationary forage harvester stand, involved the analysis of whole Inagua maize samples weighing 5, 10, and 15 kg. These samples were further divided based on two moisture contents of 57% or 68%, and the geometric mean particle value was 9.39–12.69 mm, depending on the number of knives in the cutting unit. A 12-electrode capacitive sensor measured MFR, demonstrating less variation during calibration than a 6-electrode sensor. The study revealed a significant relationship between moisture content, particle size, and sensor capacitance, which was crucial for accurately converting capacitance measurements to MFR. The maximum mean value of the MFR was 3.18 kg·s^–1 ±0.93 kg·s^–1, compared to the theoretical 3.75 kg·s^–1. These findings have practical implications, highlighting the potential of ECT for precision agriculture applications. The study’s results could significantly impact the development of precision farming technologies, particularly forage harvester monitoring systems. By providing a more accurate and reliable method for measuring mass flow rates, the ECT system could enhance the efficiency and quality of crop production. The study also underscores the need for further research, particularly in technology improvement, to improve measurement accuracy and adapt the ECT system to the dynamic field conditions of precision farming.

Introduction

Advanced precision farming technologies use specialised machines equipped with sensors for monitoring and actuators and are supported by a computer system, which affects the change of rules in crop management¹. Software-supporting hardware systems enable accurate recording of data matrices that reflect the variability of crop yields and soil properties in spatial distribution². Using a set of current and historical data allows for the adjustment of the plant type, as well as precise fertilization and plant protection, taking into account the specific characteristics of individual soil conditions, plants, and their condition³. Precise agronomic technologies and the dosing of the right fertilizer ingredients for optimal crop protection are essential for achieving higher yields and better quality of cereals and maize⁴. The research results and conclusions contribute to creating a more comprehensive offer of new precision farming technologies by machine manufacturers, which depends on the accuracy of measuring systems, the precision of the sensors, their integration into work teams, and the quantity and quality of information they provide⁵.

One of the links in precision farming is the monitoring and mapping of yields, which takes place during the harvest of plants. Combine harvester manufacturers have offered a range of measurement kits such as the HarvestLab or the Crop Sensor. Sensor instrumentation equipment plays a crucial role in the real-time monitoring of yields and grain quality and provides farmers with valuable analytical information to optimise production techniques⁶.

The extensive experience and results from cereal harvesting have laid the foundation for developing yield monitoring systems for other crops, especially green plants. Initial tests conducted between 2000 and 2005 at the Warsaw University of Life Sciences (WULS) using a trailed forage harvester highlighted the necessity for refining methods to measure the MFR of material transported by the machine’s working units⁷. The first research in this domain was initiated in the early 1990s⁸. MFR monitoring tests, carried out to varying extents, involved measurements such as torque on the grinding drum and the chop projector⁸, the gap between smooth and crushing rollers positioned just ahead of the chopping unit⁹, the volume of the material stream in the discharge spout, the force exerted by the chaff stream on the strain gauge¹⁰, and the mass of the chaff on the trailer¹¹. Verification of the listed methods, also in interlaboratory studies, indicated varying measurement accuracy, depending on the technical advancement of the sensors used and the uniformity of the plant material distribution within the machine’s working units¹². Ensuring consistent thickness of compacted plants along the rollers’ length, uniform density of the chaff MFR within the discharge spout curve, and equal load on the measurement sensors was crucial.

Although yield monitoring technologies are readily available for crops like corn, soybeans, and cereals, they are less common for horticultural crops such as berries, field vegetables, and orchards. This gap is highlighted in the review article, discussing different approaches to measurement – near and far, direct and indirect¹³. The potential of using capacitive measurement methods, giving examples from the research results for sugar beet and potatoes¹⁴, chopped corn¹⁵, and hops¹⁶. However, further research is needed to understand and fully optimise this method for horticultural crops. The evaluations show that the shape of corn particles, moisture content, and temperature stability of the sensor are the three variable parameters affecting the accuracy of the developed system¹⁷.

With the development of measurement techniques in other technical and scientific fields, research has been undertaken to develop more advanced crop monitoring systems, especially for those crops for which current systems operate with unacceptable accuracy. This applies particularly to green plants harvested at variable spatial maturity, associated with material moisture content above 50%, e.g. maize. The primary criteria for evaluating these systems should be simplicity and reliability in field conditions. One such system is ECT. With its simplicity and cost-effectiveness, ECT proves to be well-suited for real-world applications as a non-intrusive method for monitoring plant material yield. The measuring elements must be positioned around the measuring area in a manner that does not disrupt the flow of plant material. ECT meets this requirement because it does not contain any moving mechanical components, which directly affects the increased durability and lifespan of the measuring device, especially in dynamic conditions in agricultural fields, providing certainty of its long-term use and operational reliability. ECT is employed for monitoring two-phase flows or in pneumatic transport, such as conveying bulk materials with uniform structures¹⁸. Recent advances in ECT technology have demonstrated its potential to overcome some traditional challenges faced in agricultural settings, such as non-uniformity in sensor readings due to variable crop densities and moisture levels¹⁹. Recently, the permissible accuracy of measurements using ECT has been confirmed, the method has been validated, and the reliability of the obtained data has been verified²⁰. Its use in agricultural engineering was indicated. Such studies convince potential users of the wide range of possibilities for using this technology in precision farming²¹. This method has been utilised to monitor combustion processes in industrial burners and aircraft engine chambers. The flame position and structure were visualised, and spatial resolution and signal level change for different flow conditions were determined²². Considering the use of top-class sensors and increasing the precision of measurements, ECT has a vast potential range of applications²³.

This identified knowledge gap was the impetus for adapting ECT within a forage harvester to measure the MFR of chopped maize plants intended for silage. The structure of the chopped material from whole maize plants and its higher moisture content than cereal grains present more significant challenges for researchers. Specifically within this research domain, studies on the measurement of cut corn throughput¹⁵ utilised a parallel plate capacitive sensor. Laboratory experiments have shown that the density of the cut corn material and its moisture content affect the accuracy of the measurement.

Although agriculture enjoys advanced technologies and computer support, new challenges in integrating crop monitoring methods are constantly emerging. Modern techniques such as machine vision and sensor fusion offer great opportunities for real-time monitoring of crop conditions. The development of digital technologies in agriculture creates a need for reliable and widely applicable crop monitoring systems, which is important for the sector’s future¹³.

The study focuses on applying ECT in agricultural engineering and sensor technology, presenting innovative solutions to identified problems in this field. The study aimed to evaluate the accuracy of MFR measurements of chopped maize plants with different particle sizes and moisture levels. The studies were conducted under controlled stationary conditions using a trailed forage harvester model. The test stand and the harvester were equipped with appropriate equipment to validate the ECT method. Adaptation of ECT to forage harvesters opens new possibilities for more accurate crop yield measurements, avoiding physical interference and typical wear problems associated with conventional sensors.

The research problem was formulated as a question. How can ECT be effectively adapted to measure the MFR of chopped maize plants in a forage harvester, overcoming challenges associated with the material’s high moisture content and variable density to improve real-time yield monitoring in precision agriculture?

Based on the context provided, here are two scientific hypotheses. These hypotheses were tested through a series of experiments and data analysis, which are detailed in the following sections.

Hypothesis 1

ECT technology, when adapted for use in a forage harvester, provides accurate measurements of MFR of chopped maize, regardless of variations in particle size and moisture content.

Hypothesis 2

Using an ECT sensor equipped with 12 electrodes in the chopper discharge chute enables reliable correlation of capacity changes with the actual mass flow of chopped corn, which confirms the effectiveness of this method in precise monitoring of green crop yields.

The key innovation in this study is using a 12-electrode ECT sensor, which is a significant improvement over initial attempts that used 6-electrode sensors. The introduction of 12 electrodes allowed for much better mapping and analysis of capacitance changes, resulting in more precise and reliable results. This study opens up new possibilities for ECT applications in precision agriculture, particularly in monitoring the yield of green crops. It offers the potential to improve measurement accuracy.

Materials and methods

Plant material

The research material, unique in composition, comprised whole maize plants of the Inagua variety, a medium-late variety (FAO number 230–240) cultivated explicitly for grain and silage. These maize plants were manually harvested using a brush cutter and transported to the WULS Institute of Mechanical Engineering via a volume trailer.

The moisture content of the plant material was meticulously determined using the dryer-weighing method²⁴. Randomly taken samples of 25 g were weighed on an electronic scale (WPS 600/C, Radwag, Radom, Poland) with an accuracy of 0.01 g, dried in a laboratory dryer (SLW 115, Pol-Eko Aparatura, Wodzisław Śląski, Poland) at 105° by 24 h, and weighed again after drying. The moisture content of the material was calculated based on the mass of wet matter. The particle size distribution was analysed for each combination of technical parameters under which the forage harvester operated, including a single sample, material moisture, and several knives. The particle size distribution of the chopped maize plants was conducted following the guidelines outlined in ASABE Standard S424.1, utilising an oscillating sieve separator²⁵. The resulting particle size distributions were then approximated using the Rosin-Rammler-Sperling-Bennett model²⁶, and their characteristics were evaluated based on distribution measures²⁷.

Measurement method

The concept of measurement in ECT revolves around analysing capacitance changes gathered from several to a dozen or so electrodes positioned around the research area (refer to Fig. 1). In this method, the capacitance changes values are significantly influenced by the distribution of dielectric constants of one medium within another, as per Eq. 1²⁸. This factor plays a crucial role in the accuracy of the ECT method.

$$\:{C}_{ij}=\frac{1}{{\phi\:}_{i}-{\phi\:}_{j}}{\int\:}_{\varOmega\:}^{\:}\epsilon\:\left(x,y\right)\nabla\:\phi\:\left(x,y\right)d\varOmega\:$$

(1)

where C_ij—represents the capacitance between electrodes i and j, F, φ_i—denotes the potential at electrode i, V, φ_j—refers to the potential at electrode j, V, ε(x,y)—stands for the distribution of electric permittivity, F·m^[–1, φ(x,y)—signifies the potential distribution, V, and (x,y)—the Cartesian coordinates, play a crucial role in understanding the Spatial distribution of the measurements, m.

Fig. 1

Diagram illustrating the concept of ECT: 1–4 represent measuring electrodes, while C₁₂–C₃₄ denote capacitances between electrodes.

The ECT system comprises three modules: sensors, a measurement system, and a computer (Fig. 2). The sensors consist of electrodes symmetrically positioned around the research area. Each pair of electrodes forms a distinct type of air capacitor. The measurement system is tasked with measuring the capacitance of each pair of electrodes. The computer with the free Python v. 3.11.5 software (https://www.python.org) serves crucial additional functions. Firstly, it oversees the operation of the measurement system, and secondly, it archives measurement data and analyses the results obtained.

Fig. 2

Components of the ECT system.

A critical component of an ECT system is its sensing electronics, which measure the minute inter-electrode capacitances. While several circuit designs can measure such low capacitance values²⁹, practical ECT applications demand that these circuits be immune to stray capacitance, straightforward, and responsive. The charge/discharge circuit meets these requirements and has been chosen for suitability. A vital benefit of this choice is the simplicity of the electronic components, allowing for straightforward integration, as demonstrated in Fig. 3.

Fig. 3

Simplified block diagrams of the charge/discharge (a) and AC-based circuits (b).

However, practical implementation of ECT demands a measuring circuit immune to stray signals, simple design, and quick response. The charge/discharge circuit, fulfilling these criteria, was thus adopted. A significant advantage of this charge/discharge-based ECT system lies in its electronic simplicity and cost-effectiveness, facilitating straightforward integration³⁰. The charge/discharge circuit is displayed in Fig. 4. Each complete cycle of operation consists of two phases: the charge phase and the discharge phase. During the charge phase, switches S2 and S4 are closed, and S1 and S3 are opened. The charge current flows from the voltage source V_e through the measured capacitance to operational amplifier A1 with resistance feedback Rf and capacitor Cf. Similarly, switches S1 and S3 are closed during the discharge phase, and switches S2 and S4 are opened. The charge stored in the measured capacitance discharges to the ground, and the right side draws current from operational amplifier A2. A differential amplifier A3 with a gain (depending on the combination of resistors R1 and R2) is used to sum these two signals, producing a DC measurement signal V_out proportional to the measured capacitance.

Fig. 4

Charge-discharge circuit; V_e—voltage source, S1–S4—switches, Cf—capacitor, Rf—resistance feedback, A1–A3—amplifiers, R1–R2—resistors, V_out—DC measurement signal.

The cornerstone of the system is the measurement system, comprising a series of capacitive-voltage converters, a multiplexing system, and an analog-to-digital converter. Capacitance change signals obtained from individual pairs of electrodes are sequentially multiplexed and processed in an analog-to-digital converter. The resulting digital signals are then transmitted to the computer, where the Python software, leveraging data collected from all pairs of electrodes, presents changes in the research space on the monitor screen.

The capacitance responses between electrode pairs are significantly influenced by the geometric configuration of the sensor electrodes, in addition to the permittivity distribution. This results in notable differences in magnitude and distribution profiles. Normalisation of the measured capacitances and sensitivities is essential before analysis to mitigate these effects and reduce systematic errors in the measurement system.

This comprehensive relationship for all electrode pairs is briefly represented in matrix form, as shown in Eq. 2³¹.

$$\:{C}_{n}={S}_{n}{\bullet\:K}_{n}$$

(2)

where: C_n is an m×1 matrix containing the normalised capacitances of the electrode pairs; m is the number of unique electrode pair combinations (e.g., 66 for a 12-electrode sensor); K_n is a k×1 matrix representing the normalised pixel permittivity; k is the number of pixels representing the sensor cross-section; S_n is an m×k matrix containing the normalised sensitivity matrices for each electrode pair.

Sensitivity distributions, also known as sensitivity maps, are crucial for image reconstruction and are typically derived from numerical solutions to the Laplace equation, as stated in Eq. 3³².

$$\frac{{{\partial ^2}\varphi }}{{\partial {x^2}}}+\frac{{{\partial ^2}\varphi }}{{\partial {y^2}}}=0$$

(3)

where: φ is the potential distribution.

Finite Element Methods are often employed because it is challenging to find analytical solutions for Eq. 3. In our studies, we use Ansys 2020 R2 software, https://www.ansys.com, (MESco, Bytom, Poland) to differentiate potential distributions between two electrodes, calculating electric field distributions E₁ and E₂ for source and detector electrodes, respectively.

The sensitivity of electrode pair i–j at a spatial location (x, y) is determined by dot-multiplying the two electric fields, as illustrated in Eq. 4³³.

$$\:{S}_{i-j}=-{\iint\:}_{{\Omega\:}}\frac{{\overrightarrow{E}}_{i}}{U}\cdot\:\frac{{\overrightarrow{E}}_{j}}{U}d{\Omega\:}$$

(4)

where: $\:{\overrightarrow{E}}_{i}$ and $\:{\overrightarrow{E}}_{j}$ represent the electric field distributions when electrodes i and j are the source electrodes, respectively, with an excitation voltage U applied, and Ω denotes the entire sensing region.

Each sensitivity matrix quantifies the response of an electrode pair to a stimulus within the sensor area, proportional to the change in inter-electrode capacitance caused by a pixel filled with high-permittivity material. In contrast, other pixels are filled with low-permittivity material. The presence of an object in different locations variably affects the same electrode’s capacitance, whereas the exact location can differentially influence various electrode capacitances.

As per our method, the sensitivity map for a specific electrode pair is normalised according to Eq. 5³³. Figure 5 illustrates typical sensitivity maps and their normalisations.

$$S{n_{i - j}}=\frac{{{S_{i - j}}}}{{\sum\nolimits_{{k=1}}^{N} {{S_{i - j}}(k)} }}$$

(5)

Fig. 5

Sensitivity map and normalised sensitivity map for electrode-pair 1–6 by using Ansys software.

The ECT system operates using precisely standardised values of dielectric permittivity and inter-electrode capacitance, which are always within the range (0.1). Such precision results from a careful calibration process of each sensor, which expresses the attention to detail in our work and guarantees the high accuracy of measurements performed by the system.

The first step in the calibration process involves using a sensor filled with a low-dielectric permittivity material (Fig. 6). The key here is the selection of air as the reference material, which has a dielectric permittivity of 1. This step establishes the interelectrode capacitance C_L values corresponding to the low dielectric permittivity value. The next step in calibration involves using a different reference material to determine capacitance values for higher dielectric permittivities. Equally important is the careful selection of this second material, which should ideally match the dielectricity of the object being tested, which allows the second set of interelectrode capacitance C_H values to be obtained. The scaling factor W_C concerning the transported polyethylene mass m_tp had a linear relationship; W_C = 0.1752m_tp, with the determination coefficient R² = 98.67%. Assuming linearity, an expression for the normalised capacitance value C_n can be Eq. 6³⁴.

$${C_n}=\frac{{{C_M} - {C_L}}}{{{C_H} - {C_L}}}$$

(6)

where: C_n – represents the normalised capacitance, C_M – denotes the capacitance of the plant material, F, C_L – signifies the capacitance corresponding to low dielectric permittivity, F, C_H – refers to the capacitance corresponding to high dielectric permittivity, F.

Fig. 6

Flowchart of the measuring steps of the calibration.

The sensor was calibrated using a material with a dielectric permittivity 2.6, corresponding to a normalised capacitance 1. If an object with a permittivity of 5.2 is placed, these values will double. In some measurements, the values exceeded 1. The calibration process is crucial as it directly affects the sensor’s performance, and any deviation from the expected values can impact the accuracy of the measurements.

An essential element of ECT technology is the appropriate selection of the number and size of electrodes. These two factors directly affect three critical aspects of the system: axial and radial resolution, measurement sensitivity, and data acquisition speed. Increasing the number of electrodes while maintaining the same device length, which reduces the size of individual electrodes and decreases measurement sensitivity, is a technical challenge. For each electrode configuration, it is necessary to maintain an appropriate balance between their number and size, as well as the resolution and sensitivity of the system. Another critical aspect is to ensure that the capacitance change values remain within acceptable noise levels of the measurement system.

It is reasonable to assume that axial resolution, and thus the length of the electrodes, will be of lesser importance, especially for processes that remain consistent along the sensor axis. The radial resolution is expected to improve with an increased number of electrodes. In existing ECT systems, sensor sets typically comprise 6, 8, or 12 electrodes. The measurement system’s sensitivity remains consistent for a smaller number of shorter and a more significant number of more extended electrodes, provided that the sensor dimensions remain constant. Tests conducted on a model stand using polyethylene granulation showed that the measurement accuracy increased with several electrodes. The variation of the W_C scaling factor, which is a measure of the sensor’s ability to accurately measure the mass of the transported polyethylene granulate, for 12 was smaller than for 6 sensor electrodes, and the evidence was a higher value of the linear regression determination coefficient, 98.67%, and 96.79%, respectively. Therefore, a sensor with 12 electrodes was used in the tests.

Measuring sensor

As part of the adaptation of the ECT system, a measurement 12 electrode sensor was designed and manufactured, the diagram of which is depicted in Fig. 7.

Fig. 7

Longitudinal section of the sensor: 1—steel sleeve, 2, 3—steel mounting flanges, 4, 11—mounting screws, 5—electrode, 6—steel threaded rod, 7, 8—insulating spacer sleeves, 9—SMB connectors, 10—distance sleeve, 12—resin layer.

The sensor design is centred around a steel sleeve (1) with an internal diameter of 183 mm and a wall thickness of 14.5 mm. The lower (2) and upper (3) steel collars were affixed to the sleeve using M8 screws (4), with holes drilled in these flanges to facilitate integration of the sensor with the forage harvester. Twelve electrodes (5) were fashioned from a steel pipe with an internal diameter of 169 mm and a thickness of 2 mm. The electrodes measured 120 mm in height and 36 mm in length, with each electrode having a 30 mm long M4 steel threaded rod (6) welded. Utilising spacer sleeves (7, 8), the electrodes were fastened to the chamber using an M4 nut. To establish connections between each electrode and the SMB connector (9), a specialised spacer sleeve (10) was crafted and secured to the chamber with four M3 screws (11). During the final construction phase, the void between the electrodes and the chamber was filled with resin (12) and subsequently shaped to achieve the desired diameter of 165 mm. The geometric model and perspective view of the 12-electrode sensor are presented in Fig. 8. In Fig. 8a, the view visually depicts the physical sensor, showing how the 12 electrodes are arranged in reality. It provides a schematic representation of the sensor’s key components. Figure 8b shows the structure of a 12-electrode sensor featuring visible electrodes and connectors for integration with the measurement system.

Fig. 8

Geometric model (a) and view (b) of the 12-electrode sensor; own elaboration.

Measuring stand

The adaptation of the ECT system was conducted under stationary conditions at the Department of Biosystems Engineering, WULS, utilising a model of a trailed forage harvester (Z 374, SIPMA, Lublin, Poland) powered by the power take-off (PTO) of an agricultural tractor (1234 Ursus, Warsaw, Poland) with an output of 85 kW. With a rotational speed of 1000 rpm, the tractor’s PTO drove the cutting disc shaft and, from it, a hydraulic pump that supplied oil to two hydraulic motors. The upper hydraulic motor propelled the upper drawing-compaction rollers, while the lower motor powered the lower drawing-compaction rollers and the adapter. Knives with a straight cutting edge were set at 5.9° to the radial cutting direction. The knife blade length was 373 mm, the blade angle was 25°, the clearance angle was 25°, and the gap between the knife blade and the edge of the counter blade was 0.2 mm. The grinding unit featured a corrugated bottom plate and straight projector blades with a sharp leading edge, with the working gap between these components set at 8 mm at the inlet and 2 mm at the outlet²⁵. The individual components of the measurement station are depicted schematically in Fig. 9, while the overall view of the station with the ECT sensor attached is presented in Fig. 10.

The forage harvester underwent appropriate modifications for the research and was outfitted with measuring instruments. Input samples of plant material were weighed using a decimal scale (WDO-150, Metalowiec, Średnica, Poland) with an accuracy of ± 0.2 kg. In contrast, the material was conveyed to the machine via a belt conveyor propelled by an electric motor through a V-belt transmission³⁵. The chopped chaff was gathered in a canvas container, with the metal frame of the container attached to a CLP 500/LC510 electronic scale (Radwag, Radom, Poland), boasting a capacity of up to 500 kg and an accuracy of 0.1 kg. The research material comprised maize plants of the Inagua variety intended for silage, sourced from the fields of the Agricultural Experimental Station in Wilanów-Obory, affiliated with WULS.

Fig. 9

Test stand: 1—agricultural tractor, 2—model of a trailed forage harvester, 3—electronic weighbridge with a forage tank, 4—discharge spout, 5—transport conveyor, 6—ECT sensor.

Fig. 10

View of the measurement station with a sample of corn plants evenly distributed on the transport conveyor and a 1234 Ursus tractor connected to the Z 374 forage harvester (a) and method of mounting the ECT sensor (b) on the discharge chute of the forage harvester, and a package of pressure and turbine oil flow sensors connected to the hydraulic system (c); own elaboration.

The course of the study

For varying weights of individual samples of maize plants (5, 10, 15 kg), different numbers of knives on the chopping unit of the forage harvester (5, 10), and varying moisture content of the maize material (68%, 57%), along with established technical parameters including the speed of the feeding belt conveyor at 1 m·s^–1 for plant material and the angular speed of the PTO at 104.7 s^–1 (rotational speed of 1000 rpm), the following physical quantities were measured: speed of the belt conveyor (measured by timing the 8 m distance travelled by the belt with a stopwatch); rotational speed and torque of the PTO (measured using an encoder with an accuracy of ± 6 rpm integrated with a torque sensor with an accuracy of ± 0.8 N·m, MTR 1000, Laboratory of Electronics, Poznań, Poland); rotational speed of the cutter disc shaft (measured using an incremental encoder with a roll 8.5802.1275.1000, with a resolution of 1000 rpm and accuracy of ± 6 rpm); pressure and absorbency of hydraulic motors driving the upper and lower feeding and compaction rollers, as well as hydraulic oil pressure at the exit from the hydraulic motors of the rollers (measured using piezo-resistive pressure sensors (PC-28) with a measuring range of 0–25 MPa ± 0.01 MPa, and turbine oil flow sensors (FT12) with a measuring range of 0–76 dm³·min^–1 and an accuracy of ± 0.1 dm³·min^–1 included in the set of FT12PM28KT42.TR sensors; APEK, Warsaw, Poland); rotational speed and torque of the shaft driving the lower drawing-compaction rollers (measured by an encoder with an accuracy of ± 5 rpm, integrated with an inductive torque gauge with an accuracy of ± 0.8 N·m, MT 500, Laboratory of Electronics, Poznań, Poland). An inductive sensor, CL-70-200, was employed to measure the thickness of the material layer between the rear compaction rollers, providing measurements with an accuracy of ± 1 mm. Additionally, a semiconductor thermometer was utilised to gauge the temperature of the hydraulic oil, measured from the combined output of the engines to the oil tank. Throughout the tests, the oil temperature was maintained at 30 ± 5 °C. Data were gathered at a sampling rate of 50 Hz on a personal computer overseeing the input/output (I/O) modules, utilising a high-speed Hottinger Baldwin DMCplus digital interface card and CATMAN v. 2.1 software, https://www.hbm.com (HBM, Darmstadt, Germany). These parameters were measured to assess the repeatability of technical settings in individual measurement tests.

For the most significant sample mass of maize plants, which was 15 kg, the theoretical material flow rate at the entrance to the forage harvester was 3.75 kg·s^–1. This relatively low value was necessary to safeguard the forage harvester’s feed unit against blockages caused by the maize plants and to ensure smooth material movement, thus minimising measurement errors. Following each test, a 25 g sample of plant material was extracted to determine its moisture content. The dryer-weighing method was employed for moisture measurement²³. The research encompassed recording signal changes using ECT for various precisely weighed samples of plant material, each with known moisture content and a specified number of knives in the chopping unit.

Preparation of research results and statistical analysis

The recorded data from the sensor set underwent processing using a third-order Butterworth high-pass filter³⁶. Further details are provided in subsection 3.2. The test results were analysed using the Statistica v. 13.3 program, https://www.statsoft.pl (StatSoft Poland Ltd., Cracow, Poland). This involved determining linear regression equations for a single variable and a nonlinear equation for the scaling factor containing two variables using the surface fitting module.

Research results and their analysis

Characteristics of plant material

The average plant moisture content varied depending on the moisture content of individual plant components. Grain kernels exhibited the lowest moisture content (33.70%), followed by the core (47.35%), leaves (62.11%), and stems (73.38%). The moisture content of the maize plant stems varied along its height, ranging from 70 to 80% in the lower part, abruptly decreasing to 40% at a height of 1.10 m, corresponding to the location of the maize cobs, then gradually increasing again to approximately 70% at a height of 1.40 m, before gradually decreasing to 10–60% at the top of the stem, depending on plant height and maturity level, influenced by soil conditions. The moisture content of chopped maize plant material ranged between (55.57% and 59.25%) and (65.53% and 70.17%), respectively, for 57% and 68% moisture levels.

The geometric mean particle size of chopped maize plant material varied between 9.39 mm and 12.69 mm, corresponding to the operation of the cutting disc with 10 and 5 knives, respectively. Particle sizes were more significant when cutting material with a lower moisture of 57% compared to a higher moisture of 68%, measuring 11.79 mm and 10.29 mm, respectively.

The particle size distributions exhibited right-skewness, with graphic skewness coefficients ranging from 0.22 to 0.29. They were also leptokurtic, indicating a distribution with density concentrated around the mean value, as evidenced by positive values of the graphic kurtosis coefficients ranging from 0.97 to 0.99.

Characteristics of measurement signals

The obtained waveforms of capacitance changes indicated a signal drift over time. Analysis revealed that this drift occurred due to moisture deposition on the sensor walls from water in the plant material. Further investigation showed that this issue predominantly affected measurements from pairs of electrodes positioned close to each other.

Initially, the recorded data underwent processing using a third-order Butterworth high-pass filter, followed by determining the absolute value of the function³⁶. Only data processed in this manner were utilised for subsequent analysis. This data processing procedure was applied to all recorded measurements, irrespective of the presence of drift. The individual steps of signal processing are illustrated in Figs. 11 and 12.

In the analysis of the results, Eq. 7 was employed to ascertain the scaling factor W_c (Fig. 13), utilising measurements of changes in sensor capacitance from individual pairs of electrodes.

$$\:{W}_{C}={\sum\:}_{{d}_{p}}^{{d}_{k}}\frac{{\sum\:}_{1}^{n}{C}_{i}}{{n}_{w}}$$

(7)

where: W_C—scaling factor, –, d_k—the final value of the interval, s, d_p—initial value of the interval, s, n_w—number of nodes representing the discretisation of the measurement area, n—number of measurements, Ci—normalised capacitance value from individual pairs of electrodes.

Fig. 11

The trend of changes in the average normalised capacitance values C_n in the time domain t for plant material with moisture MC = 67% and m = 3.6 kg without data processing (a) and with the application of a high-pass filter (b).

Fig. 12

The trend of changes in the average normalised capacitance values C_n in the time domain t for plant material with moisture MC = 67% and m = 3.6 kg with the absolute values of the function argument determined.

Based on the generated data, scaling factors were computed, and a graph illustrating the changes in the W_C value relative to the plant mass was plotted for different moisture levels and numbers of knives (Figs. 14 and 15). Table 1 summarises the W_C scaling factor values for various combinations of input variables: material moisture content MC and number of knives z.

Fig. 13

Graph depicting the method for determining the value of changes in the W_C value; C_n—normalised capacitance, t_i—time, d_p—initial value of the interval, d_k—the final value of the interval.

Table 1 W_C scaling factors for different moisture contents of plant material MC and number of knives z.

The computed values of the scaling factor Wc were utilised to approximate the correlation between the mass of plant material m_C derived from the capacitance measurement data and the weighed mass of plant material m (Figs. 16 and 17).

Fig. 14

Graph illustrating the variation of the W_C scaling factor concerning the transported plant mass m for moisture MC = 68% and the number of knives set to 5 (a) and 10 (b).

Fig. 15

Graph depicting the variation of the W_C scaling factor concerning the transported plant mass m for moisture MC = 57% and the number of knives set to 5 (a) and 10 (b).

Fig. 16

Graph illustrating the variation in the mass of plant material m_C derived from the capacitance measurement data against the mass of transported plants m, for moisture content MC = 68% and z = 5 (a), and z = 10 (b).

Fig. 17

Graph illustrating the variation in the mass of plant material m_C derived from the capacitance measurement data against the mass of transported plants m, for moisture content MC = 57% and z = 5 (a), and z = 10 (b).

The estimated mass values m_C were utilised to compute the relative error e_C for each set of decision variables, as per Eq. 8.

$$\:{e}_{C}=\left|\frac{{m}_{c}-m}{m}\right|\times\:100\%$$

(8)

where e_C—relative error, %, m—mass of the plant sample, as assumed, kg, m_c—estimated value of the plant mass from the capacitance measurement data, kg.

The absolute error values for the assumed forage harvester operational systems are depicted in Figs. 18 and 19.

Fig. 18

Graphs of relative error changes e_C with respect to plan sample mass m for moisture MC = 68% and z = 5 (a) and z = 10 (b).

Fig. 19

Graphs of relative error changes e_C with respect to plan sample mass m for moisture MC = 57% and z = 5 (a) and z = 10 (b).

For each configuration, dependencies were found for changes in the scaling factor W_c concerning the moisture of the plant material MC and the number of knives z. For this purpose, the Statistica v. 13.3 program used surface-fitting to obtain Eq. 9.

$$\:{W}_{C}=5.408-0.057MC-0.097z+0.001MCz$$

(9)

where: W_C—scaling factor, –, MC—plant material moisture content, %, z—number of knives in the chopped unit.

The graphical depiction of changes in the scaling factor based on the material moisture content and the number of knives in the chopping unit is illustrated in Fig. 20. Finally, Eq. 10 was derived for the instantaneous MFR of material q_C^t, considering the moisture of the plant material MC and the number of knives z.

$$\:{\varvec{q}}_{\varvec{C}}^{\varvec{t}}={\varvec{W}}_{\varvec{C}}\frac{{\varvec{n}}^{-1}\sum\:_{1}^{\varvec{n}}{\varvec{C}}_{\varvec{i}\left(\varvec{k}\right)}}{{\varvec{t}}_{\varvec{i}}}$$

(10)

where: q_C^t—MFR of plant material, kg·s^[–1, W_C—scaling factor, –, t_i—time, s, C_i—normalised capacitance value from individual pairs of electrodes, n—number of sensor measurements.

Fig. 20

Graph illustrating changes in the value of W_C relative to moisture MC and the number of knives z.

The proposed Eq. 10 enables the correlation of changes in normalised capacitance values to an actual representation of variations in the MFR of plant material over time. Examples of such variations in the MFR of plant material q_C^t are depicted in Fig. 21. The graph illustrates fluctuations in the MFR of plant material over time, as captured using a 12-electrode sensor. The dataset pertains to a 15 kg sample, with a material moisture content of 57%, and employing 10 knives. The mean value of the MFR was 3.18 kg·s^–1 with a standard deviation of 0.93 kg·s^–1, and the theoretical value for these parameters was 3.75 kg·s^–1. Thus, the error relative to the measurement was 15.2%. Through integral determination using the trapezoidal method, curve analysis provides insights into the total amount of plant material flowing at specific times.

During actual forage harvester tests, two issues were observed. In short-term evaluations, there was an issue with moisture condensing on the sensor walls. In contrast, the sensor became contaminated with minute plant material particles in long-term assessments, which distorted the measurement signal. Research conducted on a model measurement station indicated the method’s potential applicability. However, tests conducted under conditions resembling real-world scenarios using a forage harvester confirmed the design assumptions. Despite employing advanced signal processing techniques, the measurement error was approximately 30%. In contrast, other measurement methods achieved a more minor error of 10% ⁵. However, with its simplicity, non-intrusive measurement methodology, and low device cost, the ECT method remains a viable option for high-precision agriculture monitoring, particularly in crop management and processing applications³⁷. It offers non-intrusive and real-time imaging, which can significantly benefit soil analysis and crop health monitoring³⁸. With further enhancements in MFR measurement accuracy, the ECT method could solve the challenges in precision agriculture.

Fig. 21

Graphs depicting variations in the MFR of plant material q_c^t over time t, recorded using a 12-electrode sensor, with a sample mass of 15 kg, material moisture content of 57%, and utilising 10 knives.

Our research uniquely contributes to developing agricultural technologies and improving the efficiency of capacitance measurement systems. The analysis, supported by an extensive literature review, indicated a crucial parameter in these systems—the excitation frequency. This is a decisive element for the measurement signal, especially in monitoring material with higher moisture content³⁹. In the wood case, a parabolic relationship was identified between the sensor response and moisture content, where the increase in capacitance was more intense at higher moisture values⁴⁰. Similarly, for chopped corn, the nonlinear dependence of the sensor output signals on the bulk density and moisture content of the material significantly affects the measurements, which must be considered when calibrating capacitive flow sensors^13,15. Independent measurements of chopped corn moisture are essential for maintaining precision in practical conditions, and the increase in frequency leads to the linearisation of the relationship between capacitance and moisture, which allows for increased measurement accuracy. This unique finding, supported by the research of Zhang’s team⁴¹, has important practical implications, as it involves designing and constructing a new, modified measurement system.

The effect of moisture content and particle size on sensor capacitance is due to their direct impact on the dielectricity of the material, which is crucial for ECT measurements. Moisture increases the dielectricity of the material, which leads to an increase in the measured capacitance⁴². In turn, larger particles affect the uniformity of the electric field in the sensor, which can change local capacitance values. The interaction of these factors is essential for the accuracy of converting tonnage measurements to MFR, which is crucial in precision agriculture to monitor and optimise yields⁴³.

The current system operates at a frequency of 625 kHz. To minimize the measurement error resulting from moisture accumulation on the sensors, operating at a minimum frequency of 10 MHz is recommended. The optimal solution would be to develop an ECT system with a programmable excitation frequency. This approach aligns with the findings emphasising frequency control’s critical role in improving ECT systems’ reliability and accuracy under different conditions.

Electrostatic sensors are used in many industries for efficient and cost-effective measurements. They are used, among others, in the analysis of flow processes in pipelines, where techniques such as cross-correlation allow the measurement of flow velocities of solids and gases⁴⁴, and spatial filtering methods help study flow characteristics⁴⁵. In addition, ECT is used to map concentration profiles using process tomography⁴⁶, mass flow rate measurement⁴⁷, moisture content estimation⁴⁸, and average particle size determination⁴⁹. These applications demonstrate the versatility of ECT and its potential for precise monitoring and control of industrial processes. Each application demonstrates how ECT and electrostatic sensors contribute to technological advances by offering robust and evidence-based methods crucial for industrial production efficiency and quality⁵⁰.

This study has thoroughly investigated the characteristics of plant materials and measurement signals, which has expanded the knowledge of the capabilities of ECT in monitoring the yield of chopped maize. It demonstrates the significant influence of moisture and particle size on capacitance readings, which has important practical implications.

Advances in signal processing methodology have improved the accuracy of ECT systems in agriculture, paving the way for further research on developing this technology. Using ECT to measure the MFR of chopped corn is an excellent example of the effective integration of modern sensor technologies with traditional agricultural equipment, improving yield measurements’ precision and supporting long-term sustainable agriculture goals through better resource management and waste reduction. Furthermore, combining ECT with IoT technologies and cloud computing opens up new possibilities for precision farming, providing exciting development prospects for the future.

Conclusions

This study investigated the capabilities and effectiveness of ECT technology in monitoring the MFRs of chopped maize in the context of precision agriculture. On a stationary test bench with a self-propelled forage harvester, samples of Inagua maize were analysed with different weights (5, 10, 15 kg), which differed in moisture levels (57% or 68%) and particle size (9.39–12.69 mm), depending on the number of knives in the chopping unit. Using a 12-electrode capacitive sensor and a third-order Butterworth high-pass filter and the subsequent scaling factor calculation highlights the complex relationship between material properties and sensor performance, which is critical for an accurate performance estimate.

The findings of the study point to the potential benefits of adapting ECT technology to monitor maize yields. The hypothesis that ECT can precisely monitor the mass flow of chopped maize was confirmed, providing essential data regardless of changes in moisture and particle size, which is crucial for precision farming. Statistical analysis and new calibration methods have improved ECT measurements and practical usefulness. It also identified ways to minimise problems related to signal drift and sensor contamination by plant debris, which is crucial in field conditions. In addition, the innovative adjustment of the sensor’s excitation frequency enabled more precise measurements, which could be helpful for the further development of ECT technology in agriculture.

Moreover, the research has opened up exciting new possibilities for integrating ECT into precision farming systems, showcasing its potential for monitoring green crop yields. Looking ahead, the focus should be on optimising the design of ECT systems to accommodate higher operating frequencies, a development that could significantly enhance measurement accuracy and reliability. These results serve as a springboard for developing more reliable and flexible measurement systems that can effectively function in various agricultural conditions, inspiring hope for the future of ECT technology in agriculture.