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Article

The RF–Absolute Gradient Method for Localizing Wheat Moisture Content’s Abnormal Regions with 2D Microwave Scanning Detection

1
College of Engineering, China Agricultural University, Beijing 100083, China
2
School of Electrical and Information Engineering, Jiangsu University, Zhenjiang 212013, China
3
Beijing Key Laboratory of Optimized Design for Modern Agricultural Equipment, Beijing 100083, China
4
College of Engineering and Technology, Tianjin Agricultural University, Tianjin 300384, China
*
Author to whom correspondence should be addressed.
Agriculture 2025, 15(15), 1649; https://doi.org/10.3390/agriculture15151649
Submission received: 2 July 2025 / Revised: 28 July 2025 / Accepted: 29 July 2025 / Published: 31 July 2025
(This article belongs to the Section Agricultural Product Quality and Safety)

Abstract

High moisture content (MC) harms wheat storage quality and readily leads to mold growth. Accurate localization of abnormal/high-moisture regions enables early warning, ensuring proper storage and reducing economic losses. The present study introduces the 2D microwave scanning method and investigates a novel localization method for addressing such a challenge. Both static and scanning experiments were performed on a developed mobile and non-destructive microwave detection system to quantify the MC of wheat and then locate abnormal moisture regions. For quantifying the wheat’s MC, a dual-parameter wheat MC prediction model with the random forest (RF) algorithm was constructed, achieving a high accuracy (R2 = 0.9846, MSE = 0.2768, MAE = 0.3986). MC scanning experiments were conducted by synchronized moving waveguides; the maximum absolute error of MC prediction was 0.565%, with a maximum relative error of 3.166%. Furthermore, both one- and two-dimensional localizing methods were proposed for localizing abnormal moisture regions. The one-dimensional method evaluated two approaches—attenuation value and absolute attenuation gradient—using computer simulation technology (CST) modeling and scanning experiments. The experimental results confirmed the superior performance of the absolute gradient method, with a center detection error of less than 12 mm in the anomalous wheat moisture region and a minimum width detection error of 1.4 mm. The study performed two-dimensional antenna scanning and effectively imaged the high-MC regions using phase delay analysis. The imaging results coincide with the actual locations of moisture anomaly regions. This study demonstrated a promising solution for accurately localizing the wheat’s abnormal/high-moisture regions with the use of an emerging microwave transmission method.

1. Introduction

As the world’s population grows, there is an increasing demand for a stable supply of high-quality food. The population is expected to grow to 9.1 billion by 2050, requiring approximately 70% of additional grain production to be supplied [1,2,3]. However, globally, about one-third of grain is lost yearly during post-harvest operations [4], placing greater demands on loss reduction in grain storage and processing regions. Moisture content (MC) is vital for evaluating grain quality and monitoring during production and processing. Both over-drying and high MC can lead to severe post-harvest grain losses. The over-drying of grains reduces the amount of moisture in the grain kernels and produces large amounts of grain crushing in processing, which leads to grain losses [5,6]. The lower resulting weight due to over-drying also harms costs. The excessive MC of grains makes grain liable to mildew during storage [7]. Therefore, real-time rapid detection of grain and other products is needed to reduce the occurrence of the above situations in grain storage, grain processing, and other agricultural products. Conventional direct measurement methods (including the drying method and Karl Fischer titration) [8] applied for MC detection are impractical for real-time online detection as they are destructive to the measured material and are complex and time-consuming. In some studies, indirect measurement methods by detecting variable parameters related to the measured material’s MC of the material have been applied to detecting grain MC (including the infrared method [9], the capacitance method [10], the resistance method [11], and microwave method [12]). The capacitance method uses two metal electrode plates to form a capacitor and detects the MC by measuring the effect of the sample on the capacitance signal when it is used as a medium [13]. Chen et al. [14] fixed two planar electrodes in the grain bin sampling device of the harvester to achieve online MC monitoring during the grain-harvesting process. The resistance method measures the change in the conductivity or resistivity of the medium and establishes a fitting model between it and the MC to estimate the MC [11]. Near-infrared spectroscopy (NIR) is based on the absorption characteristics of a substance to light of a specific wavelength for detection [15]. Jiang et al. [16] developed an in situ detection device for corn cob moisture based on the 410–940 nm band spectrum and constructed a corresponding moisture prediction model. However, the capacitance method requires the material to fill two capacitor plates to minimize gaps [17], which adds significant testing time. The infrared method can only measure the material’s surface. The in-depth MC of most agricultural crop materials, such as grains, is not uniform. It is difficult for the infrared method to depict the internal MC of the samples [18,19]. The resistance method is mainly used to detect the MC of a single grain or a small number of grains [20]. Therefore, a non-contact, penetrative, non-destructive testing technique is needed to meet rapid online inspection needs for grain storage and processing.
Microwave detection is a non-destructive testing (NDT) method that transmits electromagnetic waves to interact with the material to be tested. The microwave method sensor does not require contact with the sample. It has a penetration depth far beyond that of the infrared method. The microwave-based NDT method has been applied to indoor target localization or obstacle identification [21,22,23], concrete structure quality inspection [24], steel surface quality inspection [25], ground-penetrating radar (GPR) detection [26], and other fields. Meanwhile, microwave detection is suitable for rapid online detection of grain MC. The microwave detection of grain MC mainly includes the transmission line, resonant cavity, and free-space methods. Among them, the microwave free-space transmission method has been employed for MC detection of agricultural products such as grain with the advantages of non-contact, extensive measurement range, and strong anti-interference ability. Trabelsi et al. [27] independently determined the MC of two hard red winter wheat varieties by measuring complex relative permittivity using the microwave transmission method. Okamura et al. [28] investigated microwave free-space technology, using it to build a transmissive microwave acquisition system with a vector network analyzer (VNA), and established a fitting equation between microwave phase shift and wood MC. As known, in the transmission process, when the microwave interacts with the material, the microwave attenuation describes the dielectric loss caused by the water molecules in the material, and the microwave phase shift reflects the change in the wave speed effected by the water in the material. However, in early research, the relationship between microwave signals and the material’s MC was only established by single-parameter attenuation or single-parameter phase shift. As a consequence, the detection range and accuracy of the detection were limited, so it was challenging to find the true MC.
Recent advancements in artificial intelligence, particularly in machine learning and deep learning [29], have driven their widespread adoption and advancement across diverse disciplines. Concurrently, there has been a notable increase in applying these data-driven methodologies to microwave-based MC research. This integration aims to leverage the powerful nonlinear mapping capabilities of deep architectures to significantly enhance the performance of microwave moisture detection systems. Guo et al. [30] used the microwave transmissive method to detect the wheat’s MC, exploring the effects of frequency, temperature, MC, and bulk density on the dielectric constant of wheat. The research also built an MC prediction model with a single frequency, multiple frequencies, and full frequency based on support vector machine (SVM) algorithms. Wu et al. [31] applied four hybrid-based ant colony optimization algorithms for microwave–tea interaction signals. Based on the features of these optimizations, three primary models—support vector regression, extreme gradient boosting, and multilayer perception—and one secondary model were constructed for tea MC prediction. Yigit et al. [32] constructed a detection system (signal frequency from 1 GHz to 2.48 GHz) using VNA and a horn antenna to measure the reflection and transmission coefficients of three materials, including crushed wheat, hard corn kernels, and corn stover. The study used the k-fold cross-validation (k-CV) technique to train and test the machine learning algorithms and utilized five different evaluation metrics to assess the algorithm’s performance. The study modeled and predicted the MC of the abovementioned materials using K-nearest neighbor (KNN), support vector regression (SVR) and artificial neural network (ANN) algorithms. Azmi et al. [33] measured the radio wave signals of rice placed in a stationary holder using a radio frequency identification (RFID) sensor-based system (with the RFID system operating in the 915 MHz range and the WSN operating in the 2.4 GHz range). They estimated the MC by using ML algorithms. Bartley et al. [34] established a microwave detection system (containing eight frequencies from 10GHz to 18GHz) and estimated red wheat’s MC using an artificial neural network (ANN). Zhang et al. [35] used a free-space measurement system (containing 41 frequencies from 2.60 to 3.00 GHz) to collect transmittance measurements of sweet corn in a fixed sampler holder and used a deep neural network to perform the feature extraction for determining the corn’s MC.
In addition, in most of the existing grain MC detection studies based on the microwave free-space principle, the samples’ moisture was uniformly distributed. Moreover, most of these studies focused on measurement accuracy. However, they ignored or lacked the high-moisture region in the samples. Water corrosion or other artificial reasons generate a localized high-MC region in wheat. Such a small abnormal MC region will further induce mildew, thus affecting the wheat quality and impeding grain processing. Therefore, monitoring and localization techniques for high-MC regions in grains are extremely important for safely managing grain transportation and storage. Microwave non-destructive testing methods can move the antenna to scan the whole domain of the target and identify the abnormal regions inside the target according to the microwave signal responses at different spots. In the present study, a transceiver antenna moving module is added to the traditional microwave transmission detection system, which also simulates the relative movement of grain and antenna for grain conveyance and transportation processes. A preliminary study is carried out on the feasibility of detecting and identifying the high-MC region of wheat using the microwave transmission method, which is of great importance for advancing and developing highly automated online MC detection for grain transportation and processing.
This paper is different from most previous studies that only focus on the overall moisture uniformity of samples and detection accuracy. For the first time, this study focuses on the identification and location of local high-MC areas in wheat and realizes spatial scanning and identification of abnormally high-MC areas. In summary, the main work of this study is as follows.
(1)
Research on an accurate microwave detection method for grain moisture: This study aims to establish an accurate grain moisture detection model, associate microwave signals with two microwave parameters of the material, and realize effective detection of MC.
(2)
Detection of abnormal moisture regions: A mobile antenna scanning system was designed to identify and detect abnormal moisture regions in grain samples. Using CST software, a physical model for microwave detection was established and tested, and an effective method for identifying the boundary of moisture abnormal regions was proposed. Combined with the prediction model, the MC of different samples in the one-dimensional mobile detection process was effectively detected.
(3)
Based on the two-dimensional mobile scanning detection of the antenna, the effective detection of the positional information of the high-moisture region was realized based on the phase delay analysis imaging method.

2. Materials and Methods

2.1. Principle of Transmissive Microwave Detection

The transmissive microwave method of detecting the MC of wheat and other objects is based on the microwave propagation properties in the object medium and mainly on the interaction between microwaves and water molecules. Microwave propagation in wheat is affected by wheat’s dielectric properties, which are usually characterized by the relative complex dielectric constant ε = ε + j ε , where ε denotes the dielectric constant and ε denotes the dielectric loss [36]. The dielectric constant reflects the ability of the medium to store electrical energy in an electric field. The relative dielectric constant of water at room temperature is 30–77, and most of the dry matter (the state of the material once moisture has been removed) has a relative dielectric constant of 1–5. The dielectric loss reflects the ability of a medium to convert electrical energy into thermal energy in an electric field, and it is also higher for water than for dry wheat. When microwaves transmit through wheat samples, moisture in wheat significantly affects microwave propagation due to its high dielectric constant and dielectric loss characteristics. Moisture absorbs and attenuates microwave energy as well as causing a phase change in the microwave signals. These attenuations and phase changes highly relate to the MC in the wheat samples. In practical studies, a source transmits a steady beam of microwaves to a wheat sample via a transmitting antenna. After passing through the sample, the receiving antenna captures the microwave signal, and the signal’s attenuation and phase changes are measured. In this study, by analyzing the microwave signals’ two characteristic changes (attenuation and phase shift) and combining them with the experimental calibration process, a model correlating attenuation, phase shift, and MC was developed so that the MC of wheat could be predicted.
Based on the above principle, this study measures the S-parameter (transmission coefficient S21) of a wheat sample and obtains the corresponding attenuation value A and phase value φ by using a vector network analyzer (VNA) and a pair of waveguide antennas as a microwave signal transceiver device. The working schematic of the system is shown in Figure 1.
During the microwave measurement process, the scattering influence due to the empty sample container must be eliminated. Therefore, Equations (1) and (2) are used to calculate the attenuation and phase shift value. The attenuation difference ΔA and phase shift value Δφ are obtained by subtracting the empty container results from the experimental ones.
Δ A ( d B ) = A Y A N
Δ φ ( d e g r e e ) = φ Y φ N 360 n
where AY and φY denote the microwave signal’s attenuation and phase values after filling the container with wheat, and AN and φN denote the microwave signal’s attenuation and phase values when the container is empty, respectively. The unit of signal attenuation is dB, and the unit of phase shift is degree; n = 1, 2, … denotes the phase shift correction coefficient determined by MC and detection frequency in this study.

2.2. Design of Microwave MC Detection System

In this study, based on the detection principle of the microwave transmission method, a microwave MC detection system is designed and constructed to realize the static detection of wheat MC as well as the synchronous movement of the antenna. Figure 2 shows the detection system, including four important components. First, the system has a microwave detection platform (which forms an electromagnetic shielding test bench covered by wave-absorbing materials to reduce the signal reflection interference and radiations) and an acrylic container for different experiments. Second, the system has mobile transceiver antenna equipment, including six groups of ball screw sliding modules, two groups of miniature sliding platforms, stepper motors and drives, linear encoders, limit switches, and a measurement and control device. The ball screw sliding module mainly controls the antenna movement over a plane. The miniature sliding platforms adjust the distance between two antennas. The linear encoders read and give real-time feedback on the antenna’s moving positions. The switches limit the excessive movement of the guide rail. The device comprises a signal acquisition board and LabVIEW-based measurement and control software. Third, the system has a signal transmitting–receiving unit, including the VNA (PicoVNA 108, Pico Technology Company, St Neots, UK), coaxial cable, and a pair of rectangular antennas. This study uses standard gain waveguide antenna manufactured by Talent Microwave, Inc., namely, the TL-159SHAN15 model. This antenna operates within the frequency range of 4.64 GHz to 7.05 GHz, providing a gain of 15 dB. PicoVNA 108 needs to perform channel signal calibration before the experiment. The calibration model is TA344. The short, open, load, and through steps are performed after loading the basic file. The calibration process uses the official PicoVNA software (PicoVNA 3 v3.3) to set the signal transmission and reception characteristics according to the antenna frequency range and gain, and the calibration file is saved for use in similar experiments. Fourth, the system incorporates a signal acquisition and processing unit, which requires the VNA software platform to debug the equipment parameters and acquire the parameters, including the transmittance coefficient S21 (attenuation value and phase value). All the data are processed later and then imported into the MC model.
In this study, the microwave detection system supports three types of experiments: ① static detection experiments; ② abnormal moisture region detection experiments; ③ and imaging analysis of abnormal regions by two-dimensional mobile scanning on the plane. The static experiments are for the calibration and analysis of the effects of wheat MC changes on the microwave characteristic parameters, aiming to obtain data and build the MC prediction models. In the abnormal MC region experiments, the system continuously scans the whole domain of a rectangular container full of low-MC wheat with antennas. It can detect the width of an abnormal region with high MC over the whole container.

2.3. Sample Preparation and Experimentation

The wheat used in the experiments was selected from the National Precision Agriculture Research and Demonstration Base in Xiao Tangshan, Beijing, with the model number “Jing Mai 11”. The experiment was conducted in May 2024 at the College of Engineering, China Agricultural University, in an environment with an average temperature of about 26 °C and a relative humidity of 61RH%. Before sample preparation, the wheat was uniformly dried, manually screened, and de-hybridized to reduce extraneous interference. The samples were prepared separately for two types of microwave detection experiments. The static detection experiment prepared 30 groups (NMC.01~NMC.30) of wheat samples with different MCs, while the other type of experiment implemented two groups of samples with abnormal moisture regions. In the static detection experiment, the group NMC.01 was the initial MC of wheat. The remaining samples were added with different qualities of deionized water, stirred uniformly, and put into a sealed bag for 3–4 days of storage. The sealed bag was also shaken regularly for uniform and full absorption. The samples were then dried using the standard drying method [37] to obtain the true MC value of wheat. Three portions of 100 g per each were taken from every group of samples. The samples were dried and weighed in a drying oven until they reached a constant weight. Eventually, 30 wheat groups were obtained, with MC ranging from 5.038% to 40.130% (NMC.01 = 5.038%). The samples for the abnormal moisture region detection experiment had No.A (MCNOR = 10.563% and MCABN = 20.67%), and No.B (MCNOR = 15.124% and MCABN = 20.67%). In the two-dimensional imaging detection experiment, the MC in the high-MC region of the wheat was measured at 30.260%, while the MC in the remaining normal wheat regions was 5.762%.
In this study, microwave transmission scanning was performed in the frequency range of 4.7~7 GHz to obtain data at 401 frequency points. ① In the static detection experiment, all samples used in the wheat MC prediction model fell freely into a container (the container size was 280 × 140 × 200 mm). Some 30 groups of wheat samples with different MC and 1 group of empty container tests were measured in the microwave scanning mode, and a total of 62 groups of S21 parameters (including attenuation and phase) with a total of 24,862 raw data at different frequencies were obtained. ② In the abnormal moisture region detection experiment, the inner cavity size of the sample container was 300 × 100 × 700 mm (as shown in Figure 3a). The antenna was controlled by the measurement and control system to collect data every time it moved 15.45 mm. A total of 2 groups of wheat samples and 1 group of empty containers were measured, and 102 groups of S21 parameter raw data with a total of 40,902 different frequencies were obtained. The experimental data sets of all wheat samples were used to calculate the final attenuation value and phase shift value of the signal using Equations (1) and (2). ③ The inner cavity dimensions of the sample container used in the imaging scanning experiment were 600 × 100 × 700 mm (length × width × height), with the high-MC region measuring approximately 100 × 100 mm. As illustrated in Figure 3b, the system controlled the antenna to move horizontally, collecting data at intervals of 9.2 mm. Simultaneously, the vertical guide rail moved upward in 15 mm increments to enable horizontal scanning at different heights. A total of 24 rows of equally spaced horizontal scans were conducted, with each row comprising 51 evenly spaced scanning points, resulting in a total of 1224 uniformly distributed microwave sweep data points.

3. Data Analysis and Model Construction

3.1. Preprocessing of Dataset

In response to the measurement errors and noises that may occur during the data collection process of high MC, this study adopts a comprehensive method of outlier detection and data preprocessing to provide a stable and reliable dataset for subsequent data analysis and modeling. Figure 4a first uses a box plot to preprocess the overall data distribution of the attenuation spectrum (A). The observed outliers will affect feature analysis and provide inaccurate MC prediction models. The Hampel filter [38] checks the data point significantly different from its surrounding points based on a sliding window Kalman filter [39], which is an efficient precursor (autoregressive filter) that estimates the state of a dynamic system with a series of incomplete measurements and noises. In this study, Kalman filtering assesses the joint distribution of various measurement values with continuous frequencies and then generates estimates of absent values. The Hampel method was used to remove detected outliers and replaced abnormal values in the data, and the Kalman filtering algorithm smoothed the processed data, effectively suppressing noise interference and making the data more stable, as shown in Figure 4b.
In the process of establishing a regression prediction model for MC, the model input is composed of dual feature parameters of attenuation (ΔA) and the phase shift value (Δφ). A min–max normalization was selected for further data processing to reduce the dimensional influence between different features, improve the training efficiency, and increase model prediction accuracy.
This study uses an outlier detection and data preprocessing method to address measurement errors and noises in the original dataset, yielding a more stable and reliable dataset for further analysis and modeling. Figure 4a observes the overall data distribution of the ΔA and Δφ frequency spectra using a box-and-line plot. These outliers will impact the feature analysis and deliver an inaccurate MC prediction model. Therefore, Hampel removal of outliers and the Kalman filtering algorithm are used synergistically on the dataset to solve outlier interference (Figure 4b). The dual parameters (ΔA and Δφ) are further standardized to reduce the significant magnitude difference before importing them into the MC regression models.

3.2. Construction of the MC Prediction Model

Considering the complex nonlinear relationship between numerous microwave characteristic parameters, frequencies, and corresponding actual MC, this study integrates machine learning algorithms to establish MC prediction models from the dataset of static detection experiments. The dataset is divided into training and test sets and preprocessed. Six regression models—support vector regression (SVR) [40], BP neural network (BPNN) [41], light gradient boosted regression (LightGBM) [42], random forest regression (RF) [43], multivariate linear regression (MLR) [44], and Lasso regression [45]—are chosen for MC prediction and comparison. This study analyzes the difference and degree of conformity between prediction results and true MC values to assess the applicability displayed by each regression prediction model. Moreover, this study uses R2, RMSE, and MAE to evaluate the model performance. It also uses comparative analysis to determine which regression model is most appropriate for microwave MC prediction. The following formula is used to obtain the evaluation indices:
R 2 = i = 1 N ( y ^ i y ¯ ) 2 i = 1 N ( y i y ¯ ) 2
M S E = i = 1 N ( y i y ^ i ) 2 N
M A E = i = 1 N y i y ^ i N
where N is the total number of sample data points, y ^ i denotes the predicted MC, y ¯ i is the average of the true MC values, and y i is the true value of MC.

3.3. CST Modeling of Microwave Detection of Abnormal Moisture Regions

This section proposes a microwave transmission model using the three-dimensional electromagnetic simulation software CST (CST Studio Suite 2020.00) to simulate the transmissive microwave detection of abnormal moisture regions in rectangular wheat samples and investigate its viability. The model employs the hor2n antenna TL-159SHAN15 in CST, which operates within the frequency range of 4.64~7.05 GHz and gathers 401 frequency points, the same as in experiments. Reference [46] provided information on the electromagnetic parameters of microwave sensing of wheat with varying MCs in the 4.7~7.0 GHz range.
The geometric setup of the CST model constructs the sample with an abnormal moisture region, as shown in Figure 5. The size of the wheat sample is 300 × 100 × 700 mm. The sample container is ignored in the simulation model because the acrylic container in the test on the microwave transmittance is almost transparent compared to that of the wheat, using the S21 amplitude (ΔA) parameter for simulation analysis. Figure 5 demonstrates the coordinate system, where the x-axis is 50 mm from the edge of the sample, the y-axis is 113.5 mm from the edge of the sample, and the center of the abnormal MC region is (289, 0). The antenna moves along the positive x-axis and collects S21 parameters every 10 mm, leading to a total of 52 microwave-receiving signals. The distance between the antenna aperture and the sample is 28 mm. Once modeling and parameter setting are finished, the model is divided into a discrete structure of hexahedral meshes to solve Maxwell’s equations. The boundary conditions of the simulation are configured as open boundaries to imitate the ideal environment of free space.
The simulation employs two groups of wheat samples for the microwave scanning test (sample number: No.A and No.B). The simulation results are then compared to the actual test to verify the feasibility of the simulation analysis. We then perform a series of simulations to analyze the change in the S21 amplitude of the abnormal moisture region along the antenna moving direction and calculate the abnormal region width.

3.4. Phase Delay Analysis Imaging

This paper proposes a phase delay analysis imaging method based on a scanning detection approach. The method calculates the signal propagation delay by measuring phase changes in microwave signals within wheat samples, enabling imaging detection of high-MC regions inside the samples. The MC in the sample influences the microwave signal’s propagation speed, causing phase changes and propagation time delays. These variations are used to construct a distribution image of high-MC regions within the wheat sample.
The propagation time delay τ of a microwave signal can be determined from the phase change φ and the signal frequency f. The relationship between these parameters is expressed in Equation (6), where f is in Hz and τ is in s.
τ = φ 2 π f

4. Results and Discussion

4.1. Analysis of Microwave Characteristic Parameters

Figure 6 plots various MCs’ ΔA and Δφ curves from the static detection experiment. The spectrograms of the ΔA and Δφ differences of wheat samples with varying water concentrations (with 30 groups in which MC ranges from 5.04% to 40.13%) are displayed in Figure 6a,b. The plots demonstrate how ΔA and Δφ (absolute values) progressively vary as frequency increases, and it was found that the attenuation and phase shift values do not increase linearly with frequency but have certain fluctuations with different frequencies, which is consistent with the results of other scholars [17,31]. Frequency plays a pivotal role in the microwave propagation ability in a medium. The microwave signal is subject to more ΔA and Δφ when the frequency is high, since the corresponding interaction between high-frequency radiation and water molecules increases. Similarly, when wheat’s MC rises, more water molecules cause the microwave signal to polarize strongly and absorb more energy, which causes more signal ΔA and Δφ.
Figure 6 illustrates that for the water MC interval B (sample number: NMC.21~NMC.30), the ΔA curve and Δφ curve fluctuations of the samples increase when the frequency is between 5.0 GHz and 7.0 GHz; the ΔA value and Δφ value between the samples decrease significantly when the frequency is between 5.6 GHz and 7 GHz. Figure 7 shows the absolute mean deviation (MAD) of the Δφ-frequency spectral rate data. The MAD displays the degree to which each data point in the dataset deviates from the mean value. Additionally, MAD values over frequencies associated with MC interval A (for sample number NMC.01 to NMC.20) and MC interval B (sample number NMC.21 to NMC.30) are compared. The phase shift for various MCs at around 5 GHz shows no obvious fluctuation, and the value rises steadily with the MC increase.
As observed in Figure 6b and Figure 7, when frequency increases (f > 5 GHz), the MAD of MC interval A gradually increases, representing the increasing phase shift deviations between those samples. On the contrary, the MAD of MC interval B decreases for the smaller gaps between corresponding samples. Using the degree of dispersion, it can be observed that the difference in phase shift values between samples with high MC and a high frequency range significantly decreases. At high frequencies, as the sample’s MC increases, the ΔA value and Δφ values increase at first then lead to minor change and finally tend to become stable. The reason for this observation is that the absorption capacity of the medium may be close to saturation, which reduces the penetration of microwaves when the MC and frequency are too high. The absorption of microwave signals by additional moisture molecules can no longer increase significantly, and the signal ΔA value increases slowly to a certain extent. The change in the Δφ values is also the same. Figure 7 shows that the dielectric constant does not always increase accordingly. Such a saturated trend demonstrates the impact of the dielectric properties of the medium on its microwave signals with respect to frequency. The Maxwell–Wagner effect properly explains the relationship between the dielectric constant, MC, and frequency by utilizing an intervening variable, i.e., the medium’s polarization ability. When MC increases, the number of water molecules becomes sufficiently large, and the polarization effect approaches saturation; thus, the increase in the dielectric constant becomes negligible.

4.2. Comparative Analysis of MC Prediction Models

Figure 8 compares the prediction results of the six wheat MC regression models to the true values. The dataset for producing the prediction models is selected from the original dataset associated with a frequency of 5.850 GHz. The training and test datasets are in a ratio of 7:3, having 42 and 18 sets, respectively. The ΔA and Δφ values are dual feature inputs for training models, and the corresponding true MC value is the feature output.
As shown in Figure 8, the six regression models exhibit dramatically different performance. Generally, the water MC interval B contributes to the majority of errors in which the predicted values are always lower than the true values. Five regression models—namely, SVR, BPNN, LightGBM, MLR, and Lasso—perform poorly at a high MC, especially when the MC is greater than 30%. The LightGBM model produces even poorer predictions in the low-MC interval. As the dot–line graph in Figure 8d illustrates, the RF-based MC prediction model performs better than the others, demonstrating superior prediction performance and adaptability in the high-MC region. Additionally, the test dataset evaluates and compares the models’ MC prediction results with three metrics (R2, MSE, and MAE). The RF model demonstrates the best prediction performance, with R2 = 0.9846, MSE = 0.2768, and MAE = 0.3986. The LightGBM model performs the worst, with the lowest coefficient of determination (R2 = 0.7998) and the highest MSE and MAE (MSE = 22.6823 and MAE = 4.1770). The other four models yield similar predictive performance, which is worse than that of the RF model.

4.3. Localization and Analysis of Abnormal Moisture Regions

4.3.1. MC Prediction in Regions with Abnormal Moisture

The RF prediction model of wheat MC enabled the detection of wheat MC at different collection points during the mobile detection process of the waveguide, as illustrated in Figure 9. The red dotted line marks the interface between wheat regions with different MCs. A transition in attenuation values and phase shift values is observed in this region. Therefore, the points within the yellow dotted line area are considered the effective and actual MC prediction values. The statistical results of the MC predictions are shown in Table 1.
In the experiment with sample group NO.A, the average predicted MC in the normal-MC wheat region was 10.344%, while the high-MC region had an average prediction of 20.105%. For sample group NO.B. The average predicted MC in normal wheat regions was 14.645%, while the predicted MC in high-moisture regions was 20.158%. Across both experiments, the maximum absolute error between the predicted and true values of MC was 0.565%, and the maximum relative error was 3.166%. These results demonstrate that the prediction accuracy of MC is relatively high. This study highlights that the combination of waveguide antenna mobile detection and the MC prediction model effectively enables the detection of wheat MC at various locations.

4.3.2. Analysis of CST Simulation for Abnormal Moisture Regions

Figure 10 plots the simulated S21 amplitude curve with antenna positions at various frequencies. The curve derived from the simulation satisfies the experimental observations that the S21 amplitude value (the increase in S21 amplitude in this analysis refers to its absolute value magnitude) dramatically increases with higher frequencies and MCs. When the antenna detects the normal-MC regions, the S21 amplitude values negligibly change and stabilize at the same level. When the antenna is close to the sample edges, the curve fluctuates slightly due to the diffraction effect of the received electromagnetic waves. Moreover, the curve on the right edge (scanning end) fluctuates more than the left side (scanning start). The reason for this is that the antenna starts to scan 113.5 mm from the left edge of the sample and ends at 73.5 mm to the right edge. Thus, the antenna receives more diffractions when it moves to the end.
When the antenna approaches the center of the high-MC region (289, 0), the S21 amplitude exhibits a notably high value compared to that of the normal-MC regions. The high S21 amplitude of the microwave signal indicates more electromagnetic energies consumed due to more water molecular polarization and, thus, higher MC. Furthermore, as the microwave frequency rises, the S21 amplitude value also rises. Such an increase in S21 amplitude is because the frequency increase also contributes to the polarization of water molecules. Moreover, it is seen that the S21 amplitude increase correlates with an increase in the abnormal MC region’s width.
The highest S21 amplitude is located unexpectedly near the interface between the normal and abnormal MC regions but not at the center of the abnormal MC region. The evidence is found in the simulation results of Figure 10a for 175 mm and 200 mm, Figure 10b for 175 mm and 200 mm, and Figure 10c. These figures present a similar curve exhibiting two sharp points. The S21 amplitude value increases accordingly when the antenna approaches the medium’s interfaces. The S21 amplitude value decreases after the antenna crosses the interface over a certain distance. The S21 amplitude curve flattens out when the antenna moves to the center of the high-MC region. At the interfaces, a considerable part of the incident electromagnetic waves is reflected and refracted because the radiation of the horn antenna in the near field (the Fresnel zone) approximates a spherical wave rather than a uniform plane wave. The horn antenna contributes to an apparent S21 amplitude and produces two valleys in the microwave signals. The amplitude of curve S21 reduces as the abnormal region grows wider, and the widths of the two valleys also increase synchronously. Therefore, this paper explores the location and width information of anomalous water regions in wheat (high-MC regions) through two aspects: the change in the attenuation value curve and the rate of curve change.
Firstly, from the perspective of changes in the magnitude of attenuation values, the signal S21 amplitude curves share a similar trend in fewer oscillations at the frequencies of 4.7 GHz, 5.275 GHz, 5.850 GHz, and 6.425 GHz; however, the curves show violent oscillations when microwave radiation is at 7.000 GHz. Therefore, the CST simulation demonstrates the feasibility of the microwave antenna scanning method in distinguishing the width of the high-MC wheat region (LABN). Table 2 provides the statistical results of the remarkable S21 amplitude values indicating the abnormal region width. XC denotes the center, XL denotes the left remarkable S21 amplitude point, and XR represents the right point. Examining these remarkable S21 amplitude points can suggest the breadth of abnormal moisture regions in wheat samples (LLR). In order to evaluate the prediction of an abnormal region, two errors are used, including the error of the center position of the abnormal region (ECENTER) and the error of the width of the abnormal region (EWIDTH). After calculation, when the region width of the simulation model LABN = 125 mm, the ECENTER = 1 mm, and the EWIDTH = 115 mm. Based on the S21 amplitude value, the center coordinate error is relatively small, but the region width detection error is relatively large.
Given the non-obvious nature of the S21 amplitude value’s change at low frequencies and its drastic fluctuation at high frequencies, this study selects an intermediate frequency of 5.85 GHz for extracting the S21 amplitude curve of the antenna measuring positions. Therefore, this study investigates the S21 amplitude value’s rate of change in order to investigate the abnormal width of the moisture region. This work derives the gradient of the S21 amplitude value and then takes the absolute value of the gradient. Figure 11 processes and displays the gradient of the S21 amplitude curves corresponding to various normal moisture levels and widths of the abnormal moisture region.
The main goal is to find remarkable points that can infer the locations of two interfaces of the abnormal MC region. As shown in Figure 11, two significantly large values (peaks) appear on both sides of the S21 amplitude–gradient curve. These points are readily identifiable and effectively denote the targeted region’s boundaries. We select the first peak of the S21 amplitude gradient curve along the positive scanning direction as the left remarkable point and choose the corresponding coordinate X1. The right remarkable point and coordinate X2 are selected by checking the negative scanning direction. The study assigns a threshold that is twice the mean of the absolute gradient value to filter out the signal fluctuations around the antenna’s beginning and end spots and efficiently extract two remarkable points. Thus, the breadth of the abnormal MC region is calculated using two-point coordinate spacing (L12), where Table 3 displays the relevant statistical data. Compared with the width, LLR, which is calculated based on the previous attenuation value, the width L12 of the abnormal moisture region calculated by the new calculation method is closer to the actual width of the abnormal moisture region. For example, when the region width LABN of the simulation model is 125 mm, the minimum region width error calculated by the method shown in Figure 11 is only EWIDTH = 15 mm (for different MCs). Moreover, the center coordinates (XC) in the following three sets of simulation results with varying normal MCs are essentially the same as the actual center coordinates (289, 0).

4.3.3. Analysis of the Experiment for Localizing the Abnormal MC Region

In this study, we perform two experiments to verify the localization of the abnormal region with an MC of 20.67% and a width of 125 mm outside of the normal region, which has an MC of 10.563% and 15.124%, respectively. Figure 12a,b display the ΔA curves with five frequencies corresponding to two experimental settings. In the figures, the acquired data are compensated for by the background signals of the empty container, aiming to remove the interference of the test environment. The ΔA values signified by the frequency of 5.85 GHz are extracted to predict the abnormal MC region’s center position and width. Using the center and width detected by the amplitude change method, Table 4 compares the statistical results (XL, XR, XC, LLR) between the predictive and actual values for the two experiments. As seen, the predicted center position for the abnormal MC (high-MC) region slightly deviates from the actual position of 289 mm. After calculation, the ECENTER = 4.7 mm and the EWIDTH = 122.3 mm when the normal region’s MC is MCNOR = 10.563% (Figure 12a). The ECENTER = 3.1 mm and the EWIDTH = 106.8 mm for the condition of MCNOR = 15.124% (Figure 12b).
Furthermore, in the study, we employ the absolute gradient method to predict the abnormal MC region’s size. The ΔA values at a frequency of 5.85 GHz are extracted. Figure 12c,d demonstrate the absolute ΔA gradient curves of the absolute gradient method, where a chosen threshold filters out the two remarkable peaks of the curves. Table 5 also displays the statistical information (X1, X2, XC, L12) regarding the resulting curves. This methods achieves the prediction of the center position and width of the abnormal MC regions, yielding errors of ECENTER = 10.8 mm, EWIDTH = 1.4 mm for the sample of MCNOR = 10.563% and ECENTER = 11.2 mm, EWIDTH = 30.4 mm for the MCNOR = 15.124% sample. The comparison demonstrates an addition of error when the MC contrast between the abnormal and normal region is smaller. Although the width detection error of sample group NO. B increases, the actual peak point is located between the left peak point (X1) and its next adjacent point, which indicates a more accurate prediction of the abnormal region’s width when the sampling rate increases. Therefore, we can deliver a reasonable hypothesis that conducting multiple sample experiments and increasing the sampling rate enhances prediction accuracy. This study concludes that the absolute gradient method, by taking the ΔA gradient, performs considerably better than the method employing the attenuation value.
In summary, this study preliminarily investigates the feasibility of localizing high-MC regions in wheat by performing antenna mobile detection experiments and CST modeling and simulation analysis. A two-peak point distance localization method based on the gradient of the absolute attenuation value is proposed and validated for its efficacy in finding the center and width of the target.

4.3.4. Two-Dimensional Imaging Results of the Anomalous Region

In order to clearly visualize the two-dimensional plane position of anomalous moisture regions in wheat, this study conducts a two-dimensional imaging experiment using the phase delay analysis imaging method, aiming to localize and clearly visualize the two-dimensional plane of wheat’s anomalous MC regions. First, the phase matrix ϕ (n,m) is constructed by synchronously organizing the phase data of the scanning points, where n and m represent the phase values of the scanning points at different positions in the horizontal and vertical directions, respectively. Figure 13a illustrates the three-dimensional distribution of phase delay across 24 rows × 51 columns. In this figure, the Z-axis represents the phase delay value, while the X-axis and Y-axis represent the positions of the scanning points.
The delay time at each point is calculated using a predefined formula, resulting in a two-dimensional matrix τ (n,m) for time delay distribution imaging, as shown in Figure 13b. Based on the time delay distribution, a threshold is set using the mean delay value plus the standard deviation. Specifically, t h r e s h o l d = μ τ + σ τ and μ τ denote the average values of all time delay data, while σ τ represents the standard deviation. Any scanning point of τ (n,m) >k*threshold (where k is a constant) exceeding the threshold is determined as a potential high-MC region, as depicted in Figure 13c. The phase delay distribution imaging effectively identifies high-MC regions within the actual size and position range of the target region, as observed in Figure 13b. Within the actual monitoring point range of the high-MC area (X: 20–31, Y: 10–16.5), the high-MC area measured by the scanning monitoring imaging point probe has an overlap result of over 95%, proving that the imaging of the anomalous moisture area has a high degree of spatial consistency with the actual area. This approach successfully achieves two-dimensional imaging for detecting the positional information of high-MC regions.

5. Conclusions

The present study analyzed the spectra of microwave signals’ magnitude attenuation and phase shift and established an accurate wheat moisture prediction model. Based on this, our study further explored the applicability and effectiveness of a non-destructive method for detecting wheat moisture abnormality. The specific conclusions were as follows.
(1)
The overall trend of magnitude attenuation and phase shift of wheat hydration positively correlated with microwave frequency. Six regression methods based on selective machine learning (SVR, BP, LightGBM, RF, MLR, and Lasso algorithm) were used to construct an MC prediction model with dual-parameter inputs. Among them, the RF model, with an impressive prediction as R2 = 0.9846, MSE = 0.2768, and MAE = 0.3986, emerged as the accurate and stable model for wheat’s MC prediction. After experimental validation, the RF-based MC prediction model yielded a maximum absolute error between the prediction and the true value of 0.565%, and the maximum relative error was 3.166%.
(2)
The feasibility of localizing and visualizing the distribution of wheat’s abnormal (high-MC) regions was assessed in both CST modeling and experimental validation. Additionally, two methods, absolute and gradient methods, were developed and employed for the signal attenuation ΔA. Both results implicitly showed the better performance of the absolute gradient method through its lower prediction error on center position and width. Specifically, the predictive center error was less than 12 mm, while the width error was 1.4 mm for the sample with the normal MC (10.563%) and 30.4 mm for a MC of 15.124%, respectively. Still, the prediction can be further improved by more sampling with the indicated evidence.
(3)
Further, this study employed the phase delay analysis method to realize effective imaging and visualization of high-moisture regions. According to the exploration and investigation provided above, this study indicates a bright future and the high possibility of accurately locating and presenting water distribution in order to provide early warnings of high-MC regions in wheat storage.

Author Contributions

Conceptualization, D.D. and X.M.; methodology, D.D., H.H. and Y.L.; software, D.D. and Y.L.; validation, D.D., H.H. and H.L.; formal analysis, D.D. and Y.L.; investigation, D.D. and H.H.; resources, X.M., D.C. and Z.W.; data curation, D.D. and H.H.; writing—original draft preparation, D.D., H.H. and H.L.; writing—review and editing, D.D. and X.M.; project administration, X.M., Z.W. and D.C.; funding acquisition, X.M. and D.C. All authors have read and agreed to the published version of the manuscript.

Funding

This work was financially supported by the Jiangsu Province and Education Ministry Cosponsored Synergistic Innovation Center of Modern Agricultural Equipment (XTCX2005), the National Natural Science Foundation Project (32201687), and the National Key Research and Development Program of China (Grant No. 2023YFD200090202).

Institutional Review Board Statement

Not applicable.

Data Availability Statement

Dataset available on request from the authors.

Conflicts of Interest

The authors declare no conflicts of interest.

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Figure 1. Schematic diagram of the experiment detecting wheat MC via the microwave transmission method.
Figure 1. Schematic diagram of the experiment detecting wheat MC via the microwave transmission method.
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Figure 2. Design and experiment using the wheat MC detection system.
Figure 2. Design and experiment using the wheat MC detection system.
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Figure 3. Experimental scheme for detecting abnormal moisture regions’ movement in wheat. (a) One-dimensional horizontal movement detection. (b) Two-dimensional scanning imaging detection.
Figure 3. Experimental scheme for detecting abnormal moisture regions’ movement in wheat. (a) One-dimensional horizontal movement detection. (b) Two-dimensional scanning imaging detection.
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Figure 4. Example of data preprocessing: (a) box plot of data distribution; (b) outlier removal and smoothing.
Figure 4. Example of data preprocessing: (a) box plot of data distribution; (b) outlier removal and smoothing.
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Figure 5. Schematic diagram of simulation detection of the region of moisture abnormality: (a) schematic diagram of antenna and detection target during the simulation process; (b) simulation software model establishment.
Figure 5. Schematic diagram of simulation detection of the region of moisture abnormality: (a) schematic diagram of antenna and detection target during the simulation process; (b) simulation software model establishment.
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Figure 6. Effect of signal frequency on ΔA and Δφ under different wheat MCs.
Figure 6. Effect of signal frequency on ΔA and Δφ under different wheat MCs.
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Figure 7. Mean absolute deviation (MAD) of phase shift spectrum data.
Figure 7. Mean absolute deviation (MAD) of phase shift spectrum data.
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Figure 8. Prediction results of six regression models: (a) SVR model; (b) BPNN model; (c) LightGBM model; (d) RF model; (e) MLR model; and (f) Lasso model.
Figure 8. Prediction results of six regression models: (a) SVR model; (b) BPNN model; (c) LightGBM model; (d) RF model; (e) MLR model; and (f) Lasso model.
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Figure 9. MC prediction results of different positions of waveguide synchronous movement.
Figure 9. MC prediction results of different positions of waveguide synchronous movement.
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Figure 10. Variation curves of S21 amplitude values with antenna position at different frequencies and in different regions of normal MC: (a) MCNOR = 9.007%; (b) MCNOR = 11.556%; (c) MCNOR = 14.833%. MCNOR represents the normal MC of wheat in the region. The yellow shaded region indicates the predicted width of the abnormal moisture region based on the S21 amplitude value. The red dashed line indicates the true boundary of the abnormal moisture region.
Figure 10. Variation curves of S21 amplitude values with antenna position at different frequencies and in different regions of normal MC: (a) MCNOR = 9.007%; (b) MCNOR = 11.556%; (c) MCNOR = 14.833%. MCNOR represents the normal MC of wheat in the region. The yellow shaded region indicates the predicted width of the abnormal moisture region based on the S21 amplitude value. The red dashed line indicates the true boundary of the abnormal moisture region.
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Figure 11. The absolute derivative of the attenuation value as a function of antenna position at a frequency of 5.85 GHz. The blue-shaded region indicates the predicted width of the abnormal moisture region derived using the attenuation gradient method (MCNOR = 14.883%). The red dashed line indicates the true boundary of the abnormal moisture region.
Figure 11. The absolute derivative of the attenuation value as a function of antenna position at a frequency of 5.85 GHz. The blue-shaded region indicates the predicted width of the abnormal moisture region derived using the attenuation gradient method (MCNOR = 14.883%). The red dashed line indicates the true boundary of the abnormal moisture region.
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Figure 12. Two sets of experimental analysis results show the variation curves of ΔA values and absolute derivative values with antenna position at different frequencies: (a) change in ΔA values (MCNOR = 10.563%); (b) change in ΔA values (MCNOR = 15.124%); (c) change in absolute derivative value (MCNOR = 10.563%); and (d) change in absolute derivative value (MCNOR = 15.124%). The yellow-shaded area indicates the predicted width of the abnormal moisture region using the ΔA method, and the red dashed line indicates the true boundary of the abnormal moisture region. The blue-shaded area indicates the predicted width of the abnormal moisture region using ΔA-gradient method. The red dashed line indicates the true boundary of the abnormal moisture region.
Figure 12. Two sets of experimental analysis results show the variation curves of ΔA values and absolute derivative values with antenna position at different frequencies: (a) change in ΔA values (MCNOR = 10.563%); (b) change in ΔA values (MCNOR = 15.124%); (c) change in absolute derivative value (MCNOR = 10.563%); and (d) change in absolute derivative value (MCNOR = 15.124%). The yellow-shaded area indicates the predicted width of the abnormal moisture region using the ΔA method, and the red dashed line indicates the true boundary of the abnormal moisture region. The blue-shaded area indicates the predicted width of the abnormal moisture region using ΔA-gradient method. The red dashed line indicates the true boundary of the abnormal moisture region.
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Figure 13. Imaging of high-MC regions in wheat based on phase delay analysis. (a) Three-dimensional distribution of time delay values. (b) Two-dimensional imaging of time delay analysis. (c) Delay distribution threshold to determine the location of high-MC regions. The purple rectangle in Figure 13b represents the actual boundary of high-MC wheat.
Figure 13. Imaging of high-MC regions in wheat based on phase delay analysis. (a) Three-dimensional distribution of time delay values. (b) Two-dimensional imaging of time delay analysis. (c) Delay distribution threshold to determine the location of high-MC regions. The purple rectangle in Figure 13b represents the actual boundary of high-MC wheat.
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Table 1. MC prediction performance index during waveguide movement detection.
Table 1. MC prediction performance index during waveguide movement detection.
Sample GroupTrue MC/%Average Predicted Value/%Absolute ErrorRelative Error
NO.A10.56310.3440.2192.070
20.67020.1050.5652.733
NO.B15.12414.6450.4793.166
20.67020.1580.5122.476
Table 2. Width of the region with increased S21 amplitude values (simulation data).
Table 2. Width of the region with increased S21 amplitude values (simulation data).
LABN/mmXL Coordinate/mmXR Coordinate/mmXC/mmLLR/mm
125170410290240
150150420285270
175140440290300
200120450285330
Table 3. Characteristic parameters of the absolute derivative of the S21 amplitude curve at a frequency of 5.85 GHz. (simulation data).
Table 3. Characteristic parameters of the absolute derivative of the S21 amplitude curve at a frequency of 5.85 GHz. (simulation data).
MC (%)LABN/mmX1 Coordinate/mmX2 Coordinate/mmXC Coordinate/mmL12/mm
9.007125230370300140
150190360275170
175200400300200
200170410290240
11.556125230380305150
150190360275170
175200400300200
200170410290240
14.883125220360290140
150210370290160
175190380285190
200180400290220
Table 4. Width of the area with increased ΔA values (experimental data).
Table 4. Width of the area with increased ΔA values (experimental data).
Sample GroupMCNOR/%XL Coordinate/mmXR Coordinate/mmXC/mmLLR/mm
NO.A10.563%170417.3293.7247.3
NO.B15.124%170401.8285.9231.8
Table 5. Characteristic parameters of the absolute derivative of the ΔA curve at a frequency of 5.85 GHz. (experimental data).
Table 5. Characteristic parameters of the absolute derivative of the ΔA curve at a frequency of 5.85 GHz. (experimental data).
Sample GroupMCNOR/%X1 Coordinate/mmX2 Coordinate/mmXC/mmL12/mm
NO.A10.563%216.4340278.2123.6
NO.B15.124%200.9355.5277.8155.4
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Dai, D.; Wang, Z.; Huang, H.; Mao, X.; Liu, Y.; Li, H.; Chen, D. The RF–Absolute Gradient Method for Localizing Wheat Moisture Content’s Abnormal Regions with 2D Microwave Scanning Detection. Agriculture 2025, 15, 1649. https://doi.org/10.3390/agriculture15151649

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Dai D, Wang Z, Huang H, Mao X, Liu Y, Li H, Chen D. The RF–Absolute Gradient Method for Localizing Wheat Moisture Content’s Abnormal Regions with 2D Microwave Scanning Detection. Agriculture. 2025; 15(15):1649. https://doi.org/10.3390/agriculture15151649

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Dai, Dong, Zhenyu Wang, Hao Huang, Xu Mao, Yehong Liu, Hao Li, and Du Chen. 2025. "The RF–Absolute Gradient Method for Localizing Wheat Moisture Content’s Abnormal Regions with 2D Microwave Scanning Detection" Agriculture 15, no. 15: 1649. https://doi.org/10.3390/agriculture15151649

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Dai, D., Wang, Z., Huang, H., Mao, X., Liu, Y., Li, H., & Chen, D. (2025). The RF–Absolute Gradient Method for Localizing Wheat Moisture Content’s Abnormal Regions with 2D Microwave Scanning Detection. Agriculture, 15(15), 1649. https://doi.org/10.3390/agriculture15151649

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