A Sensor-Based Magnetite Ore Sorting System Integrating Empirical Mode Decomposition and Convolutional Neural Network

Abstract

To address the challenge of poor separation performance exhibited by conventional magnetic separation equipment when processing coarse-grained, low-grade magnetite ore, this paper proposes a novel ore recognition method that integrates empirical mode decomposition (EMD) with a convolutional neural network (CNN). First, the original signal undergoes standardization to suppress sensor baseline drift. Then, it is decomposed by using EMD to obtain a series of intrinsic mode functions (IMFs). Subsequently, based on scaling exponents and kurtosis values, IMFs containing significant feature information are selected and fused, resulting in a reconstructed signal with substantially reduced noise. To preserve effective features, the absolute values of the reconstructed signal are taken, followed by normalization and dimensional transformation to convert it into a two-dimensional matrix format, thereby constructing training, validation, and test sets. Finally, a CNN is designed and optimized to automatically extract discriminative features from the preprocessed samples, enabling accurate classification of magnetite ore grades. Experimental results demonstrate that the proposed comprehensive identification method achieves effective and stable classification performance across different ore grades. Specifically, the implementation of standardization and EMD-based denoising has been demonstrated to enhance the accuracy of CNNs in recognizing diverse ores.

1. Introduction

Iron ore is one of the most essential raw materials in modern industrial systems, playing a crucial role in construction, manufacturing, energy, and numerous other sectors. With the sustained growth in global steel demand, high-grade iron ore resources have become increasingly depleted, making them insufficient to meet market requirements. Consequently, the exploitation and utilization of low-grade iron ore have escalated dramatically. However, low-grade iron ore must undergo beneficiation to increase its iron content to a level suitable for blast furnace or direct reduction processes. This typically involves multi-stage grinding and separation operations. Existing studies have shown that grinding accounts for the largest proportion of energy consumption and operational costs in the entire beneficiation process [1]. Therefore, implementing pre-concentration to discard waste rock at an early stage significantly reduces the volume of material entering subsequent grinding circuits, thereby lowering energy consumption and processing costs [2].

Since the early 21st century, ore pre-concentration technology has advanced from manual hand-sorting to sophisticated sensor-based sorting (SBS). Sensor-based sorting encompasses a range of automated techniques that detect individual particles using sensor-acquired data and subsequently separate them through mechanical, hydraulic, or pneumatic actuation. SBS has been widely adopted across various industries, including food and agricultural product processing, waste recycling, and mining. In agriculture, SBS is used to identify defects, shriveled or broken kernels, and pathogens in crops such as maize, rice, and wheat [3,4,5]. In recycling, it facilitates the classification of glass by color purity [6,7], the recovery of metals based on conductivity or magnetic permeability [8,9], and the sorting of construction and demolition waste through multi-sensor fusion [10,11,12,13,14,15]. In mining, SBS leverages differences in physical and chemical properties (e.g., color, reflectivity, conductivity, magnetic susceptibility, or atomic density) to separate valuable minerals from gangue. Representative techniques include X-ray transmission and dual-energy X-ray transmission sorting [16,17], magnetic resonance, and prompt gamma neutron activation analysis for copper ore grade detection [18], visible-range machine vision for gold-silver ore classification [19], and visible-near-infrared to short-wave infrared hyperspectral imaging for tin and copper ores [20]. Further applications of SBS in mining are comprehensively reviewed in [21,22,23].

Magnetite ore, a typical example of disseminated mineralization, contains intergrown valuable minerals and gangue. X-ray transmission imaging (Figure 1) shows that variations in iron grade do not produce distinct radiographic contrasts, while surface characteristics such as geometry and color are similarly indistinguishable between ore and gangue. Consequently, conventional SBS technologies have not been widely adopted for iron ore pre-concentration in industrial applications. However, magnetite exhibits strong magnetic susceptibility, which has led to the predominant use of magnetic separation in the iron ore industry. Magnetic separation exploits differences in magnetic susceptibility under controlled magnetic field intensity and gradient to achieve mineral separation. Coarse-grained magnetite ore typically undergoes dry or wet low-intensity magnetic separation before fine grinding. Numerous studies have focused on improving magnetic separator design and performance [24,25,26,27,28]. Despite these advances, conventional magnetic separators show limited effectiveness when processing coarse-grained, low-grade magnetite feeds, especially those with weakly magnetic or complex intergrowth characteristics. Furthermore, the production of high-performance permanent magnets requires substantial quantities of rare-earth elements (e.g., neodymium–iron–boron), and the separation process itself is both water- and energy-intensive, which conflicts with the principles of green and sustainable beneficiation. Against this background, conventional SBS technology has emerged as a pivotal research direction in intelligent mineral processing [2,22], providing valuable inspiration for the present study. This paper proposes a novel SBS method specifically tailored for magnetite ore (with potential applicability to other magnetic minerals). The underlying principle aligns with established SBS paradigms (e.g., X-ray transmission- or vision-based systems): a sensor acquires characteristic signals from individual particles, a deep learning model performs grade prediction and classification, and high-pressure air jets execute physical separation. In contrast to conventional methodologies, a novel detection approach has been adopted that utilizes the magnetic properties of magnetite. Specifically, Hall sensors are employed to directly measure the changes in the magnetic field induced when magnetite particles pass through an external magnetic field. This modification offers a more intuitive representation of the ore grade.

Convolutional neural networks (CNNs), first proposed by LeCun et al. [29] in 1998, represent one of the most influential deep learning architectures and have achieved remarkable success in computer vision, speech recognition, and natural language processing [30]. Due to their exceptional capability for hierarchical feature extraction and high classification efficiency, CNNs have been increasingly adopted in SBS systems to enable rapid and accurate material recognition. In recent years, several studies have explored CNN-based approaches for mineral and rock classification, predominantly using two-dimensional inputs such as optical images, X-ray radiographs, or spectral data. Liu et al. [31] combined CNNs with transfer learning to classify 12 rock and mineral types, achieving an overall accuracy exceeding 70%, although the accuracy for magnetite remained below 60%. Pu et al. [32] applied a similar transfer-learning CNN framework to coal/gangue separation, attaining 82.5% accuracy. Zhou et al. [33] developed a CNN integrated with Squeeze-and-Excitation (SE) blocks to identify seven ore types, reaching 96% classification accuracy. More recently, Qiu et al. [34] employed CNN and Transformer models for photofluorescent uranium ore recognition, both surpassing 90% accuracy. Chen et al. [35] fused CNN with long short-term memory networks to extract spectral features of iron ore, achieving 91.67% recognition accuracy, while Yu et al. [36] utilized an improved YOLO architecture on UV-induced fluorescence images of spodumene, obtaining 90.2% accuracy. Despite these advances, existing CNN-based ore sorting methods have focused almost exclusively on two-dimensional visual or spectral data, whereas the classification of one-dimensional sensor signals—particularly magnetic induction signals—has received little attention.

To bridge this gap, this study proposes a CNN-based classification framework that directly processes one-dimensional magnetic induction signals acquired via Hall sensors mounted on a laboratory-scale magnetite separation device. To enhance signal quality and improve classification robustness, empirical mode decomposition (EMD) is employed for adaptive denoising before CNN input. The denoised signals are then reconstructed, transformed into two-dimensional representations, and fed into an optimized CNN for multi-class grade prediction. Finally, the reliability of the proposed classification method is validated through chemical assays of the sorted products. Although currently at the laboratory proof-of-concept stage and lacking evaluation of industrial-scale throughput or rejection rates, this work demonstrates the feasibility of intelligent magnetic-based sorting and offers a promising new paradigm for the pre-concentration of magnetite and other magnetic minerals. The subsequent sections are organized as follows: Section 2 establishes a magnetite ore sorting system based on Hall sensors, Section 3 introduces the acquisition and processing of the magnetic field signal, Section 4 disscusses the issue of magnetite ore identification, Section 5 conducts magnetite ore recognition experiment, and finally Section 6 concludes this paper.

2. Magnetite Ore Sorting System Based on Hall Sensors

2.1. Magnetite Ore Sorting Principle

Any mineral exhibits a certain degree of magnetism when subjected to an external magnetic field, a phenomenon known as magnetization. Based on magnetic susceptibility, ores can be classified as either strongly magnetic or weakly magnetic, with magnetite belonging to the former category. Previous studies have shown that, under specific conditions, the magnetization of magnetite increases with increasing external magnetic field strength, and this relationship can be described by the following equation [37]

$$\left\{\begin{array}{cc}\hfill \mathit{B}& ={\mu }_0(\mathit{H}+\mathit{M})\hfill \\ \hfill \mathit{M}& =ϵ\mathit{H}\hfill \end{array},\right.$$

(1)

where $\mathit{B}$ is the total magnetic field intensity, $\mathit{H}$ is the external magnetic field intensity, $\mathit{M}$ is the magnetization intensity of ore, ${\mu }_0$ is the relative permeability, and $ϵ$ is the specific magnetic coefficient.

When magnetite is placed in an external magnetic field, the total magnetic field intensity consists of the applied external field and the magnetic field induced within the ore. If the external magnetic field remains constant, variations in the total magnetic field intensity are solely determined by changes in the ore’s magnetic intensity. For a given ore particle entering the magnetic field, the induced magnetic intensity is fixed, resulting in a corresponding fixed variation in the total magnetic field intensity. Therefore, any change in this variation indicates the presence of additional ore particles within the magnetic field. Moreover, greater variations in the total magnetic field intensity correspond to stronger magnetism and, consequently, higher ore grades. Therefore, magnetic sensors can be used to detect these variations, providing a quantitative basis for evaluating ore grade and enabling effective sorting of ore and gangue.

A Hall sensor is a magnetic field sensor that operates based on the Hall effect and is capable of measuring variations in magnetic field intensity. As previously discussed, when a Hall sensor is exposed exclusively to an external magnetic field, the detected magnetic field intensity remains constant, provided the external field does not change. Minor fluctuations in the sensor output may occur due to factors such as signal transmission, thermal effects, and mechanical vibrations of electronic components; however, these fluctuations are considered negligible and are treated as a constant background. When magnetite passes through the sensing region, the magnetic field intensity detected by the Hall sensor changes relative to the background external magnetic field. Figure 2 illustrates the magnetic field variations produced by ores with different magnetic intensities under an external magnetic field. These variations correspond to the induced magnetic intensity of magnetite and serve as the fundamental feature for ore grade identification.

2.2. Magnetite Ore Sorting Device

Based on the principle of magnetite sorting, this study designs a Hall-sensor-based magnetite sorting device, as illustrated in Figure 3. The device comprises the following components: (1) a vibrating feeder, (2) a conveyor belt, (3) a permanent magnet assembly, (4) a Hall sensor detection unit, (5) a signal acquisition unit, (6) a signal processing and recognition unit, (7) a compressed air supply unit, (8) a separation unit, (9) a concentrate hopper, and (10) a tailings hopper. The Hall sensor is installed in close proximity to the surface of the conveyor belt due to the fact that magnetite functions as a magnetic source, thereby generating a divergent magnetic field. The magnetic field strength at a given point decreases exponentially with distance from the magnetic source. The permanent magnet assembly is installed in a position above the sensor, the purpose of which is to generate an external magnetic field.

Figure 2. Changes of magnetic field intensity.

Figure 2. Changes of magnetic field intensity.

Figure 3. Magnetite sorting device.

Figure 3. Magnetite sorting device.

The sorting process operates as follows. Ore particles are first dispersed and uniformly distributed onto the conveyor belt by the vibrating feeder. As the particles pass through the detection zone, the Hall sensor measures variations in the magnetic field and transmits the acquired signals to the signal processing and recognition unit via the signal acquisition unit. A pre-trained CNN model is then employed to predict and classify the magnetic field signals. The classification results are sent to a solenoid valve controller, which regulates the air nozzle based on the received commands to separate ores of different grades, directing them into either the concentrate hopper or the tailings hopper.

The main operating parameters of the sorting device are as follows: the Hall sensor sensitivity is 50 mV/Gs, the data acquisition card has a 16-bit resolution, the maximum sampling rate is 1000 Hz, the external magnetic field intensity in the sensor detection region is approximately 50 Gs, and the conveyor belt speed is 0.1 m/s.

3. Signal Acquisition and Processing

As shown in Figure 2, the magnetic field signals detected by the Hall sensor fluctuate within a certain range due to external disturbances; these fluctuations are referred to as noise. It can be observed that the magnetic field intensity generated by low-grade ores is comparable in magnitude to the noise level, making it difficult to distinguish and thereby adversely affecting the accuracy of system judgment. Therefore, before CNN-based recognition of ore magnetic field signals, the acquired signals must be preprocessed to suppress noise and enhance discriminative features. The preprocessing procedure applied to the collected signals is illustrated in Figure 4.

3.1. Signal Acquisition and Standardized Processing

The magnetic field signal of the ore is acquired using a Hall sensor (Guangzhou Longge Electronic Technology Co., Ltd., Guangzhou, China) to obtain the raw data, as shown in Figure 4a. Hall sensors are vulnerable to external interferences, including temperature and electromagnetic noise. These interferences can lead to baseline drift in the detected signals. Consequently, signals are captured on varying baselines across different acquisitions. Furthermore, the baseline of the signal generally represents invalid information and may even mask weak valid signals. Therefore, in this study, we mitigate the effect of baseline drift by removing the direct current (DC) component from the raw signal. This approach highlights the dynamic variations in the magnetic field signal, as illustrated in Figure 4b. The underlying calculation principle is described as

$$S_{ij}=V_{ij}-Mean\left(V_i\right),$$

(2)

where $S_{ij}$ denotes the variation at the j-th sampling point of the i-th ore, $V_{ij}$ represents the amplitude at the j-th sampling point of the i-th ore, and $Mean\left(V_i\right)$ corresponds to the direct-current component of the signal associated with the i-th ore.

3.2. EMD Decomposition and Reconstruction

EMD is well-suited for processing non-stationary and nonlinear signals because it can adaptively decompose a signal into several intrinsic mode functions (IMFs) components and a residual component [38]. Each IMF must satisfy two specific conditions:

$\left(1\right)$

Given the original signal $x\left(t\right)$, all local extrema are first identified. The upper envelope $E_1$ and lower envelope $E_2$ are then constructed using cubic spline interpolation of the local maxima and minima, respectively.

$\left(2\right)$

The mean envelope $M_1$ is calculated from $E_1$ and $E_2$, and the first component $H_1$ is obtained by subtracting $M_1$ from the original signal.

Based on the above conditions, the EMD procedure for the original signal $x\left(t\right)$ can be summarized as follows:

Step 1: For the original signal $x\left(t\right)$, all local extrema are first identified, and the upper envelope $E_1$ and lower envelope $E_2$ are then constructed using cubic spline interpolation.

Step 2: Calculate the mean value $M_1$ of the upper and lower envelopes, and determine the first component $H_1$ by using the following equation

$$H_1=x\left(t\right)-M_1.$$

(3)

Step 3: Determine whether $H_1$ satisfies the two conditions required for an IMF component. If it does, $H_1$ is the first IMF component of $x\left(t\right)$; otherwise, treat it as the new original signal and repeat Step 1 and Step 2. Suppose the IMF component conditions are satisfied for the k-th time; then the first IMF component $C_1$ can be obtained according to the following equation

$$C_1=H_{1k}\left(t\right)=H_{1(k-1)}-M_{1k}\left(t\right).$$

(4)

Step 4: Separate $C_1$ from $x\left(t\right)$ to obtain the residual component $R_1$ by

$$R_1=x\left(t\right)-C_1.$$

(5)

Step 5: Treat $R_1$ as the new original signal and repeat Step 1 through Step 4 for n times to obtain the n-th IMF component $C_n$ by

$$R_2=R_1-C_2,\cdots ,R_i=R_{i-1}-C_i,\cdots ,R_n=R_{n-1}-C_n.$$

(6)

Step 6: The decomposition process terminates when $R_n$ becomes a monotonic function and can no longer be decomposed further.

Finally, the standard signal can be represented as

$$x\left(t\right)=\sum _{i=1}^n{C}_i+R_n.$$

(7)

The standardized signal was decomposed using EMD to extract multiple IMFs at different frequency levels, as illustrated in Figure 4c. These IMFs contain both the ore’s magnetic field signal and various noise components. Notably, the ore’s magnetic signal is weaker in the higher-frequency IMFs but becomes more distinct in the lower-frequency IMFs. The boundary between the high- and low-frequency bands was determined using detrended fluctuation analysis (DFA) [39].

If all high-frequency IMFs were discarded, the magnetic signal from the ore would be significantly attenuated. To address this, the kurtosis—a statistic reflecting the peakedness and tail weight of the signal distribution—is calculated for each high-frequency IMF. Notably, under identical experimental conditions, the external interference affecting each acquired signal remains within a stable range, resulting in a largely consistent number of high-frequency IMFs distinguished by DFA. In the experiments conducted in this study, the vast majority of signals yielded three high-frequency IMFs after EMD. Therefore, the two IMFs with the lowest kurtosis values are removed, and the remaining IMFs are combined to reconstruct the denoised signal, as shown in Figure 4d.

The kurtosis K is calculated according to the following equation

$$K={\displaystyle \frac{\frac{1}{n}{\sum }_{i=1}^n{(x_i-\overline{x})}^4}{{\left[\frac{1}{n}{\sum }_{i=1}^n{(x_i-\overline{x})}^2\right]}^2}},$$

(8)

where $x_i$ denotes the i-th sample point of an IMF component and $\overline{x}$ is the mean value of an IMF component.

3.3. Establishment of Sample Set

To fully leverage the CNN’s ability to extract discriminative features from the ore’s magnetic field characteristics, the reconstructed signal undergoes inversion, normalization, and dimensionality transformation. The processed signal is then used as input to the CNN.

3.3.1. Inversion Processing

Magnetite, a ferrimagnetic material, demonstrates not only high magnetic susceptibility but also possesses remanent magnetization, which is defined as inherent magnetism. When magnetite is subjected to an external magnetic field, the direction of its remanent magnetization must align with the external field for the total magnetic field to be enhanced; conversely, the total magnetic field is weakened. Consequently, the magnetic field signal in the waveform may manifest as an increase or decrease in amplitude, and the variation in amplitude serves as the key characteristic for identifying magnetite in this study. Subsequent to the elimination of the DC component from the acquired signal, positive and negative oscillations manifest. While the direction of the signal carries physical significance, the effectiveness of the CNN feature extraction adopted in this study primarily relies on the amplitude information of the signal rather than its direction. However, the rectified linear unit (ReLU) activation function employed in this study defaults to setting all negative values to zero, which would directly discard the amplitude information carried by the negative part. To address this, an absolute value preprocessing step is applied to the acquired signals before inputting them into the network. This guarantees that the amplitude information of all oscillations, irrespective of their sign, is fully retained and converted into non-negative values. Consequently, this prevents the subsequent ReLU processing from losing critical amplitude information. As illustrated in Figure 4e, the outcomes resulting from the implementation of the absolute value transformation are evident. The calculation principle of the inversion process is described as

$$P_{ij}=Abs\left(S_{ij}\right).$$

(9)

3.3.2. Normalization Processing

The magnetic field signals exhibited by high-grade ores are distinctly different from those manifested by waste ores or low-grade ores. This discrepancy may cause the model to be dominated by features with larger numerical values, potentially overlooking features with smaller values that could be equally important. Additionally, data exhibiting substantial variations in feature scales has the potential to influence the model’s convergence speed. Therefore, this paper proposes the implementation of a normalization process on the inverted signals, with the objective of ensuring that all data falls within a consistent range, as shown in Figure 4f. The normalization is performed by the following equation

$$O_{ij}={\displaystyle \frac{P_{ij}-Min\left(P_{all}\right)}{Max\left(P_{all}\right)-Min\left(P_{all}\right)}},$$

(10)

where $O_{ij}$ denotes the normalized value at the j-th sampling point of the i-th ore sample. Here, $Max\left(P_{all}\right)$ and $Min\left(P_{all}\right)$ represent the maximum and minimum values of all sampling points across the entire dataset, respectively.

3.3.3. Dimensionality Transformation

To enhance the processing efficiency and feature extraction capability of CNN, this study converts the one-dimensional ore signals (with a size of $1\times n$) collected by Hall sensors into a two-dimensional structure. The one-dimensional signals are essentially temporal manifold data characterized by strong sequential dependencies and high redundancy. When processed with CNN, the extraction of features is only possible by sliding along a single direction, frame by frame. This operation not only restricts the receptive field but also leads to low computational efficiency due to the inability to capture long-range dependencies in parallel. Conversely, two-dimensional signals exhibit discernible spatial topological relationships, enabling the sequential correlations inherent in the original signals to be mapped into local and global structures on a plane. By reconfiguring the signals into a two-dimensional form, CNN can perform convolutions simultaneously along two orthogonal directions—horizontal and vertical—thereby efficiently extracting multi-scale spatial features over a broader scope. This transformation essentially converts the structural complexity of the time series into regular patterns in the spatial domain that are more easily captured by convolutional operations. This approach has been demonstrated to markedly reduce the computational demands associated with processing extensive sequence data while concurrently augmenting the richness and discriminatory capability of feature representations. The conversion method entails the sequential arrangement of the $1\times n$ signal from left to right and top to bottom into a $\sqrt{n}\times \sqrt{n}$ two-dimensional matrix. In this context, “$\sqrt{n}$” denotes an integer, the value of which is determined by the system’s sampling rate, conveyor belt speed, and the particle size of the ore selected for analysis, as illustrated in Figure 4g.

4. Magnetite Ore Identification

After completing the input data preprocessing, a CNN is employed to extract discriminative features and classify the ore signals, as illustrated in the Feature Extraction and Classification modules shown in Figure 5.

4.1. CNN Principle

The CNN is a deep learning model derived from artificial neural networks and can be considered a specialized form of a multilayer perceptron. Its core principle involves constructing multiple learnable filters to automatically extract representative features from input data. A typical CNN architecture consists of convolutional layers, pooling layers, and fully connected layers. By alternately applying convolution and pooling operations, discriminative features are extracted from magnetic induction signals, which are then classified and output by the fully connected layers.

4.1.1. Convolution Layer

The convolutional layer comprises multiple convolutional kernels, whose primary function is to extract features from the input matrix through local connectivity and weight-sharing mechanisms. The computational principle underlying the convolution operation is described as

$$\mathit{X}(i,j)=\sum _m\sum _n\mathit{I}(m,n)\mathit{K}(i-m,j-n),$$

(11)

where i and j denote the spatial indices of the output matrix, m and n represent the spatial indices of the input matrix, $\mathit{X}$ represents the output of the convolution operation, $\mathit{I}$ denotes the input matrix, and $\mathit{K}$ denotes the convolution kernel parameter matrix.

To enhance the nonlinearity of the network, an activation function is typically applied after the convolution operation. Consequently, the final output of the convolutional layer can be expressed as

$$\mathit{A}=f(\mathit{X}+\mathit{b}),$$

(12)

where $f(·)$ denotes the activation function, $\mathit{X}$ is the output of the convolution operation, $\mathit{b}$ represents the bias matrix, and $\mathit{A}$ is the final output of the convolutional layer.

4.1.2. Pooling Layer

A pooling layer is connected after each convolutional layer. The primary function of pooling is downsampling, which compresses the output features of the preceding layer while retaining the most salient information. In practice, max-pooling is commonly used to extract the maximum value within a local neighborhood of the input feature map. The pooling operation can be expressed as

$$\mathit{P}=\underset{s\times s}{Max}\left(\mathit{A}\right),$$

(13)

where $\mathit{P}$ denotes the output of the pooling layer, $s\times s$ is the pooling window size, and $\mathit{A}$ is the output matrix of the convolutional layer.

4.1.3. Full Connection Layer

Before the features extracted from the final convolutional or pooling layer are fed into the fully connected layer, they are first flattened to match the input format expected by the fully connected layer. Each neuron in the fully connected layer is connected to every element of the flattened feature vector, enabling the integration of local features to perform identification and classification of the input samples. This operation can be expressed as

$$\mathit{O}=f(\mathit{\omega }\mathit{F}+\mathit{b}),$$

(14)

where $\mathit{O}$ denotes the output of the fully connected layer, $\mathit{\omega }$ and $\mathit{b}$ represent the weight matrix and bias vector, respectively, and $\mathit{F}$ is the flattened feature vector.

The final fully connected layer functions as the classification layer and contains the same number of neurons as there are ore classes. For multi-class classification tasks, the SoftMax function is commonly used to convert the output values into a probability distribution ranging from 0 to 1, with the sum of all probabilities equal to 1. This operation can be expressed as

$$SoftMax(z_i={\displaystyle \frac{e^{z_i}}{{\sum }_{c=1}^C{e}^{z_i}}}),$$

(15)

where $z_i$ is the output of the i-th node, and C is the total number of output nodes, corresponding to the number of categories.

4.1.4. Activation Function

Activation functions are applied after convolutional and fully connected layers to reduce structural risk and enhance the network’s nonlinear representation capabilities. Common activation functions include Sigmoid, Tanh, and ReLU. ReLU is widely used in CNNs due to its advantages in mitigating the vanishing gradient problem and accelerating network convergence. The ReLU function is defined as

$$f\left(x\right)=Max(0,x),$$

(16)

where $Max(0,x)$ indicates that if $x>0$, then $f\left(x\right)=x$; otherwise, $f\left(x\right)=0$.

4.2. CNN Structure Design and Training

Based on the LeNet-5 architecture [29], the CNN framework proposed in this study is illustrated in Figure 5. The input layer receives image signals of size 32 × 32 × 32. The feature extraction and classification components consist of three convolutional-pooling layers and two fully connected layers, respectively. Guided by empirical knowledge and the input size, the number of convolutional kernels is set to 32, 64, and 128 for the three convolutional layers, each with a kernel size of 3 × 3 and a stride of 1. Both max pooling and average pooling can be employed; however, since the magnetic field intensity of the ore is the primary recognition feature, max pooling is adopted. The pooling window is set to 2 × 2 with a stride of 1.

The fully connected layers perform recognition and classification of the extracted features. Before entering these layers, the feature maps obtained from the convolutional and pooling operations are flattened and processed using the Dropout technique [40] with a dropout rate of 0.5 to prevent overfitting. Based on the number of parameters after flattening, the first fully connected layer is configured with 64 neurons. The second fully connected layer is responsible for feature classification and outputs the ore categories. In this study, ores are classified into four categories: waste ore, low-grade ore, medium-grade ore, and high-grade ore. Therefore, the second fully connected layer contains four neurons and employs the SoftMax activation function. Representative sensor signals collected from ores of different grades are shown in Figure 5a–d. Detailed parameters for each layer are summarized in

Table 1. Parameters of each layer of CNN.

Structure	Size	Number	Strides	Padding	Activity Function
C1	3 × 3	32	1	Same	ReLU
P1	2 × 2	32	1	-	-
C2	3 × 3	64	1	Same	ReLU
P2	2 × 2	64	1	-	-
C3	3 × 3	128	1	Same	ReLU
P3	2 × 2	128	1	-	-
Flatten	-	-	-	-	-
Dropout	-	-	-	-	-
FC1	-	64	-	-	ReLU
FC2	-	4	-	-	SoftMax

.

5. Experiment and Analysis

All experiments were conducted on a computer running the Windows 11 platform, equipped with a 12th Gen Intel(R) Core(TM) i5-12500 processor (2.50 GHz) and 16.0 GB of RAM. The proposed model was trained and tested using Python 3.11 and Keras 3.5.0.

5.1. Input Data Preprocessing

The magnetite ore sorting system, constructed as shown in Figure 3, is depicted in Figure 6. The data acquisition card was configured with a sampling rate of 1000 Hz, and the conveyor belt operated at a speed of 0.1 m/s. A total of 1000 ore samples, with particle sizes ranging from 10 to 50 mm, were collected from a concentrator in northwestern China. These samples included 250 each of waste ore, low-grade ore, medium-grade ore, and high-grade ore. Generally, ores with a grade below 20% are considered waste ore, while those above this threshold are classified as qualified ore. Since this study focuses on the classification performance of a CNN for ores of different grades, the qualified ores were further divided into three categories: low grade (20%∼30%), medium grade (30%∼40%), and high grade (above 40%). Each category of ore was randomly selected from the corresponding grade stockpile, as shown in Figure 7. The magnetic field signals of these ores were then individually collected using a sorting system to create a dataset. Each category of the dataset was randomly split into training and testing sets in an 80/20 ratio. The sample distribution is summarized in

Table 2. Sample distribution.

Sample Set	Grade	Label	Training Set	Test Set	Sum
Waste ore	≤20%	0	200	50	250
Low-grade ore	20%∼30%	1	200	50	250
Medium-grade ore	30%∼40%	2	200	50	250
High-grade ore	≥40%	3	200	50	250
Sum	-	-	800	200	1000

.

Preliminary calculations, based on the set sampling rate, conveyor belt speed, and ore particle size, indicate that a minimum of 0.5 s is necessary to adequately capture the magnetic signal of a solitary ore fragment. However, in actual working conditions, not all ore particles are smaller than 50 mm, and the magnetic fields between adjacent ores interfere with each other. Furthermore, the conversion of a one-dimensional signal into a two-dimensional signal that is not square in shape would result in an increase in computational costs. Therefore, to circumvent the aforementioned issues, the value of n was set to 1024 in this experiment.

Data preprocessing was conducted on the sample set, and the processed data were used as input for the CNN. In this study, one ore sample was randomly selected from each ore category—waste ore, low-grade ore, medium-grade ore, and high-grade ore—designated as WR, LR, MR, and HR, respectively. These four samples were processed according to the procedure outlined in Figure 4. The raw signals acquired by the Hall sensor from the processed samples are shown in Figure 8. Subsequently, the raw signals were standardized and decomposed using EMD to obtain the IMF component of various orders.

DFA is a method used to analyze long-range correlations in time series data. Its scaling exponent, $\alpha$, characterizes the autocorrelation properties of the series: when $\alpha$ < 0.5, the series exhibits long-range anti-correlation; when $\alpha$ = 0.5, the series is uncorrelated (i.e., it shows no long-range correlation), and when $\alpha$ > 0.5, the series exhibits long-range positive correlation [41]. In this study, the physical interpretation of $\alpha$ is not the primary focus; rather, it is employed to distinguish high-frequency IMFs from low-frequency IMFs. Specifically, IMF components with $\alpha$ ≤ 0.5 are classified as high-frequency, whereas those with $\alpha$ > 0.5 are considered low-frequency. For the IMF components of WR, LR, MR, and HR, the DFA subinterval lengths u were set to [4, 8, 16, 32, 64, 128, 512]. The resulting scaling exponents $\alpha$ for each IMF component are listed in

Table 3. Scaling exponents of IMFs.

Ore Types	IMF0	IMF1	IMF2	IMF3	IMF4	IMF5	IMF6	IMF7
WR	0.069	0.156	0.372	0.755	1.180	1.622	1.931	-
LR	0.053	0.183	0.424	0.742	1.249	1.629	1.858	2.036
MR	0.061	0.195	0.428	0.982	1.296	1.738	1.841	-
HR	0.098	0.214	0.479	0.905	1.458	1.669	1.892	2.013

.

As shown in Table 3, for the WR, LR, MR, and HR samples, IMF0 through IMF2 are classified as high-frequency components, while the remaining IMFs correspond to low-frequency components. Consequently, the kurtosis values of IMF0 through IMF2 are calculated, and the two IMFs with the lowest kurtosis values are removed. The kurtosis values for each IMF order are listed in

Table 4. Kurtosis of IMFs.

Ore Types	IMF0	IMF1	IMF2	IMF3	IMF4	IMF5	IMF6	IMF7
WR	3.85	3.03	2.89	2.88	2.32	2.58	1.75	-
LR	3.29	3.17	3.15	4.81	5.47	3.08	1.70	1.38
MR	3.45	3.19	2.81	6.46	2.23	3.40	1.96	-
HR	5.61	3.18	3.17	7.49	7.62	3.53	1.71	1.72

. Under these conditions, IMF1 and IMF2 are discarded. The reconstructed signal is then obtained by combining IMF0 with the low-frequency components, as illustrated in Figure 9.

To optimize the sample structure and reduce the computational complexity of the CNN, the reconstructed signals undergo inversion, normalization, and image processing. The resulting representations are shown in Figure 10. The same preprocessing procedure is applied to the entire sample set using the method described above.

5.2. Feature Extraction

In order to facilitate the CNN model’s comprehensive learning of the characteristics of diverse samples and enhance its generalizability, a 5-fold cross-validation approach was employed during the training process. Specifically, the samples of each class in the original training set were randomly shuffled and evenly divided into five parts. Subsequently, a proportion of each class was extracted and amalgamated to constitute a complete subset. The final dataset comprised five subsets, labeled A through E, each containing an equal number of samples per class. The total number of training and validation rounds was five. In each round, one subset was selected as the validation set, and the remaining four subsets were combined as the training set. The training parameters remained constant for each iteration. The sample distribution is shown in

Table 5. Sample distribution and validation accuracy.

Fold	Train Set	Validation Set	Total	Validation Accuracy
1	640(BCDE)	160(A)	800	93.38%
2	640(ACDE)	160(B)	800	97.75%
3	640(ABDE)	160(C)	800	96.12%
4	640(ABCE)	160(D)	800	95.75%
5	640(ABCD)	160(E)	800	94.63%
Mean	-	-	-	95.53%
Standard	-	-	-	1.47%

.

Based on empirical experience, satisfactory training performance can be achieved when the number of training epochs exceeds 100 and the learning rate is set below 0.2. Accordingly, the model is trained for 100 epochs using the error backpropagation algorithm based on gradient descent. To accelerate convergence, the Adam optimizer is employed, with the learning rate set to 0.001 for the first 75 epochs and reduced to 0.0001 for the remaining 25 epochs. The cross-entropy loss function is used as the training objective.

The ensuing training loss and accuracy curves are displayed in Figure 11, while the validation accuracy for each fold is presented in Table 5. The findings indicate that the model attained accuracies of 93.38%, 97.74%, 96.12%, 95.75%, and 94.63%, respectively, with a mean accuracy of 95.53% ± 1.47%. The fold accuracies for all models exceeded 93%, suggesting that the model consistently achieves high classification accuracy across various data subsets. The standard deviation of 1.47% indicates minimal variability in performance, indicative of stability and robustness. While the highest accuracy was observed in the second fold (97.74%), and the lowest in the first fold (93.38%), the overall distribution remains concentrated, thereby demonstrating the model’s reliable generalization performance. Consequently, this study retrained the model using the complete original training set of 800 samples and subsequently evaluated it on the test set.

5.3. Result Analysis

To ascertain the model’s reliability, the test set was methodically partitioned into five equal segments, with each segment comprising an equal number of samples from each category. Subsequently, the model was evaluated on these subsets. To further illustrate the model’s classification efficacy for each category, a confusion matrix was employed to conduct a detailed analysis of the prediction results for each subset, as depicted in Figure 12. The analysis indicates that the model’s recognition accuracy for all four ore categories exceeds 80%. Specifically, the average recognition rates for waste rock, low-grade ore, medium-grade ore, and high-grade ore reached 84%, 90%, 98%, and 96%, respectively. The comparatively elevated recognition rates for medium-grade and high-grade ores can be ascribed to their augmented magnetic properties and more pronounced magnetic field characteristics. Conversely, the slightly lower recognition rate for waste rock is due to the similarity of magnetic features between waste rock and low-grade ore, leading to the misclassification of some waste rock as low-grade ore.

To illustrate the feature-learning capabilities of each convolution–pooling layer in the CNN model, the t-distributed stochastic neighbor embedding (t-SNE) nonlinear dimensionality reduction algorithm is employed to project the high-dimensional feature vectors output by each layer into a two-dimensional space for visualization [42], as shown in Figure 13. The input-layer visualization represents the distribution of the original samples. Due to the inherent redundancy of the magnetic induction signals, samples from adjacent categories are difficult to distinguish at this stage, as shown in Figure 13a. Figure 13b–d shows the feature distributions after the first through third convolution-pooling layers, respectively. As the network depth increases, most samples become progressively more dispersed and cluster according to their respective categories; however, a small number of samples remain intermixed between adjacent classes. After processing by the fully connected layers, samples from different categories are clearly separated, as illustrated in Figure 13e, demonstrating the effectiveness of the proposed CNN in extracting discriminative features.

5.4. Comparative Analysis

In this paper, five preprocessing methods—standardization, EMD denoising, inversion, normalization, and dimensionality transformation—were applied to the raw data. To evaluate the effectiveness of these methods in improving the CNN model’s recognition accuracy, three preprocessing combinations were designed: “normalization + dimensionality transformation”, “standardization + normalization + dimensionality transformation”, and “standardization + EMD denoising + normalization + dimensionality transformation”. The CNN model was subsequently trained and tested using data processed by each of these approaches. Throughout the experiments, the dataset partitioning, CNN model architecture, and training and prediction procedures remained consistent with those described earlier in this paper. It is important to note that “normalization” and “dimensionality transformation” primarily accelerate model convergence and improve training efficiency, with minimal impact on the CNN model’s recognition performance; therefore, they are considered and thus regarded as common processing steps. The prediction results for each method are presented in

Table 6. Prediction result.

Method	WR	LR	MR	HR	Average
D + E	$74\%$	$86\%$	$80\%$	$68\%$	$77\%$
A + D + E	$86\%$	$84\%$	$92\%$	$86\%$	$87\%$
A + B + D + E	$88\%$	$90\%$	$92\%$	$96\%$	$91.5\%$
A + B + C + D + E	$84\%$	$90\%$	$98\%$	$96\%$	$92\%$

, where “A”, “B”, “C”, “D”, and “E” correspond to “standardization”, “EMD denoising”, “inversion”, “normalization”, and “dimensionality transformation”, respectively.

From the perspective of recognition performance for each type of ore, after incorporating standardization and EMD denoising, the model’s recognition accuracy for WR improved from 74% to 86%, and then to 88%. For HR, accuracy increased from 68% to 86%, and subsequently to 96%. The performance for LR remained relatively stable across the four preprocessing methods, while for MR, accuracy showed a gradual upward trend, reaching a maximum of 98%. Overall, the average recognition rate consistently improved with the addition of preprocessing techniques, achieving the highest value of 92% under the comprehensive method (A + B + C + D + E) proposed in this paper.

5.5. Ore Grade Assay

The sorted ore samples were sent to Slon Magnetic Separator Co., Ltd. (Ganzhou, China). for grade determination. The testing procedure consists of two stages—sample preparation and assay—as illustrated in Figure 14. During the sample preparation stage, every step—from selecting the raw ore samples, crushing, and grinding to preparing samples ready for chemical testing—involved sample reduction using the quartering method. Specifically, the sample was thoroughly mixed, divided into four equal parts, and two diagonal quarters were combined to form a new sample, while the remaining two quarters were discarded. During the chemical testing stage, the ore powder was first subjected to oxidation and reduction treatments using reagents such as sulfuric-phosphoric mixed acid, hydrochloric acid (HCI), stannous chloride (SnO₂), sodium tungstate (Na₂WO₄), and sodium diphenylamine sulfonate (C₁₂H₁₀NNaO₃S). The reacted solution was then titrated with a standard potassium dichromate solution (K₂Cr₂O₇). Finally, the ore grade was calculated based on the sample mass and the volume of K₂Cr₂O₇ consumed during the titration.

The grade calculation is expressed as $\omega =C\times B/A$, where $\omega$ denotes the ore grade, C is the titer, a constant equal to 0.22047, B is the volume of K₂Cr₂O₇ consumed, and A is the mass of the sample. The study’s methodology was based on the principle of quartering and involved preparing 10 g test samples from each of the four systematically classified raw ore types. Subsequently, 0.1 g of each sample was weighed for grade determination and chemical analysis. The measured grades of the four ore types—WR, LR, MR, and HR—were 23.66%, 28.24%, 38.25%, and 46.23%, respectively. A comparison of the measured grade of WR with the target grade ranges listed in Table 2 shows that it slightly exceeds its preset acceptable range. In contrast, the grades of the other three ore types fall within their respective target intervals. A synthesis of the discussion in Section 5.3 and the experimental findings reveals a misclassification of low-grade ore as waste ore during the systematic classification process. This misclassification led to an overall increase in the grade of waste ore. The primary reason for this phenomenon is the limited sensor precision, which creates significant challenges in accurately distinguishing the signal characteristics of waste ore from those of low-grade ore. Consequently, the mean assay results of waste ore and low-grade ore were used as the minimum effective processing grade of 25.95% for the methodology described in this study.

6. Summary and Conclusions

The proposed magnetite ore sorting device, which is based on Hall sensor detection, is currently at the laboratory stage and has not yet been tested or deployed in industrial mineral processing environments. However, experimental findings demonstrate the feasibility of magnetite sorting using SBS technology. The present study corroborates the hypothesis that the magnetic characteristics of magnetite can be effectively detected by Hall sensors. Furthermore, it is demonstrated that magnetite ores of different grades exhibit distinguishable magnetic signatures. The exploitation of this property resulted in the installation of Hall sensors beneath a conveyor belt, with the purpose of capturing the magnetic field variations induced by passing magnetite particles. The acquired signals were subsequently processed by a trained CNN model for identification and classification. Ore-gangue separation was ultimately achieved using a pneumatic sorting mechanism. The findings suggest that higher-grade magnetite generates more pronounced magnetic responses, which in turn results in higher recognition accuracy by the CNN model.

The efficacy of the proposed method is contingent upon the sensor’s sensitivity and spatial configuration. Higher sensitivity sensors have been shown to detect weaker magnetic signals associated with low-grade ores. This capability enables the classification of a broader range of ore grades. Furthermore, the configuration of the sensor has been demonstrated to exert a substantial influence on the precision of grade measurement. The present study employed a single-row matrix array, which possesses limited capacity to capture multi-directional magnetic information. Conversely, the integration of appropriate data preprocessing prior to the CNN-based recognition stage has been demonstrated to enhance classification accuracy, with standardization and EMD denoising contributing most significantly to performance enhancement. The method outlined in this paper attained a recognition rate of over 90% for low-grade and higher ores, with an effective processing grade of 25.95%, thereby expanding the processing range by approximately 5% in comparison to conventional magnetic separation equipment

In follow-up research, multi-row sensor matrix configurations will be explored to achieve comprehensive detection from multiple positions and angles, thereby enhancing the correlation between the captured signals and ore grades. Simultaneously, data preprocessing and CNN model construction methods will be further optimized to improve overall recognition performance. This study applies to general magnetic ores and offers a novel approach to magnetic mineral separation. It also underscores the potential for collaboration between sensor manufacturers and mining enterprises, which could jointly advance the development of intelligent magnetic ore sorting technologies.