Coal rock image recognition method based on improved CLBP and receptive field theory

Abstract

Rapid coal‐rock identification is one of the key technologies for intelligent and unmanned coal mining. Currently, the existing image recognition algorithms cannot satisfy practical needs in terms of recognition speed and accuracy. In view of the evident differences between coal and rock in visual attributes such as color, gloss and texture, the complete local binary pattern (CLBP) image feature descriptor is introduced for coal and rock image recognition. Given that the original algorithm oversimplifies local texture features by ignoring imaging information from higher‐order pixels and the concave and convex areas between adjacent sampling points, this paper proposes a higher‐order differential median CLBP image feature descriptor to replace the original CLBP center pixel gray with a local gray median, and replace the binary differential with a second‐order differential. Meanwhile, for the high dimensionality of CLBP descriptor histogram and feature redundancy, deep learning perceptual field theory is introduced to realize data nonlinear dimensionality reduction and deep feature extraction. With relevant experiments conducted, the following conclusion can be drawn: (1) Compared with that of the original CLBP, the recognition accuracy of the improved CLBP algorithm is greatly improved and finally stabilized above 94.3% under strong noise interference; (2) Compared with that of the original CLBP model, the single image recognition time of the coal rock image recognition model fusing the improved CLBP and the receptive field theory is 0.0035 s, a reduction of 71.0%; compared with the improved CLBP model (without the fusion of receptive field theory), it can shorten the recognition time by 97.0%, but the accuracy rate still maintains more than 98.5%. The method offers a valuable technical reference for the fields of mineral development and deep mining.

INTRODUCTION

Intelligent and unmanned mining is an important development direction of coal mining enterprises in China (Kang, 2021; Shan et al., 2019; Wang et al., 2020). In this case, coal-rock recognition is the core technology to realize intelligent shearer, which has become an urgent technical problem in the field of coal mining (McBeck et al., 2020; Zha et al., 2020).

To effectively solve the bottleneck of coal-rock identification technology, scholars both at home and abroad have made great efforts on the active feature extraction coal-rock identification method based on coal-rock image (color, texture, shape, etc.) feature descriptors and machine learning classifier. Using a plain Bayesian classifier, Hao et al. (2015) proposed automatic recognition of coal rock images with wavelet-transformed energy distribution dispersion in each frequency band as a feature vector. Based on differences in coal rock texture features, Meng and Li (2016) put forward a GLCM and BPNN-based coal rock interface identification method. Wu and Tian (2016); Wu, Zhang (2017) proposed a coal rock classification and recognition method based on K-SVD dictionary learning, curvelet domain compressed sensing, weighted fusion classification, distance metric learning, and sparse coding maximum pooling. Sun and She (2013); Sun and Su (2012); Sun and Chen (2016, 2017) successively proposed the coal rock image feature extraction method based on the combination of wavelet transform and GLCM, the coal rock interface detection method based on the GLCM salient-indigenous clustering feature, the coal rock image feature extraction and recognition method based on the combination of sparse representation and BCDTM statistical feature, and the coal rock recognition method based on the complete local binary pattern (CLBP) and discriminant dictionary learning. However, due to the harsh underground environment, the imaging quality of coal-rock images is generally low (Sun et al., 2015; Cao et al., 2015). Thus, it remains highly difficult to design coal rock feature descriptors. At the same time, the classification efficiency of the classifier based on the traditional machine learning algorithm (Yao & Sun, 2020) is low, resulting in a long time-consuming recognition process. Accordingly, both the accuracy and efficiency should be improved.

In recent years, the deep learning algorithm has been introduced into the research of coal and rock intelligent recognition (Si, Xiong, et al., 2020). Zhang et al. (2018) did a preliminary study on coal rock recognition using a convolutional neural network. Hua et al. (2019) used Faster R-CNN method to study the recognition and location of coal seams and strata. Zhang et al. (2020) combined YOLOv2 with linear imaging model for intelligent recognition and positioning of coal and rock images collected underground; and the recognition success rate reached up to 78%. Si et al. (2021) proposed a coal rock image recognition method based on CNN and improved U-Net network model. Wang et al. (2021) developed the Var-Con Sin GAN model and constructed the sample generation and feature migration framework to solve the problem of coal rock image data shortage. Sun et al. (2021) established a new evaluation index of coal rock interface recognition accuracy according to the continuous and penetrating characteristics of coal-rock interface. The coal rock interface recognition method was combined with improved YOLOv3 and cubic spline interpolation so as to obtain the near real coal-rock interface curve.

Deep learning is a gradual abstraction and conceptualization process of image features from a low level to a high level. The coal-rock recognition method based on deep learning can learn high-order feature information that cannot be observed by human eyes. This method is highly useful to the improvement of coal rock interface recognition accuracy, but admittedly, it also suffers from the following shortcomings: (1) It cannot be interpreted. The deep learning network model is a black box system which cannot model specific features of the image. (2) It raises high-quality requirements for the training set. To achieve a good recognition effect, a sufficient number of positive and negative samples should be included in the training set, and the proportional balance of positive and negative samples should be maintained. In the actual production process, the emergence of some negative samples sounds good for the construction of the training set but frustrating for the production. Thus, constructing an adequate training set becomes difficult. In addition, the training and prediction process of large-scale deep learning networks and data sets is usually time-consuming, which is not conducive to the improvement of recognition efficiency and requires rigorous computer computing power performance.

Balancing the accuracy and efficiency of coal and rock identification is worthy of further discussion. According to the differences between coal and rock in color, gloss, texture, and other visual attributes, a CLBP image feature descriptor for coal and rock image recognition is introduced based on active features; and it is different from the “black box” recognition strategy of depth. The high-order differential median CLBP image feature descriptor is proposed to improve the insufficient recognition accuracy caused by ignoring the imaging information of high-order pixels and concave-convex regions between adjacent sampling points in the original CLBP; deep learning receptive field and maximum pooling method are introduced to improve the recognition efficiency while ensuring accuracy.

COAL ROCK IMAGE RECOGNITION METHOD BASED ON IMPROVED CLBP AND RECEPTIVE FIELD THEORY

Analysis of texture characteristics of coal and rock images

Coal and rock surfaces have some texture features such as continuous repetition of local sequences, nonrandom arrangement, and roughly uniform unity in texture regions (Sun, 2018; Sun et al., 2018) (as shown in Figure 1). Moreover, through the comparison of Figure 1a,b, it is found that the coal rock has evident differences in visual properties, such as texture and gloss. For coal, the texture is rough, mostly long strip, and the distribution of metal luster area is uniform; for rock, the texture is more delicate, isotropic on the image with occasional metallic gloss. Evidently, these characteristics of coal-rock images can be used to construct image feature descriptors from the perspective of texture characteristics as the discriminant basis for coal-rock classification.

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CLBP feature descriptor

CLBP (Guo et al., 2010), an improvement of Local Binary Pattern (LBP), which incorporates structural information of texture primitives and statistical feature extraction methods, has shown strong descriptive power for coal rock images. The CLBP feature descriptor consists of the pixel value difference sign feature ($$\text{CLBP\_S}$$), the pixel value difference magnitude feature (CLBP_M), and the magnitude feature of the local central pixel value versus the global pixel mean (CLBP_C). The calculation formulas are expressed as follows (1)–(3): 1$$\text{CLBP\_}{{\rm{S}}}_{n,r}=\sum _{k=0}^{n-1}\text{sgn}[g(k)-{g}_{{\rm{c}}}]{2}^{k},$$ 2$$\text{CLBP\_}{{\rm{M}}}_{n,r}=\sum _{k=0}^{n-1}t[m(k),C],$$ 3$$\text{CLBP\_}{{\rm{C}}}_{n,r}=\text{sgn}({g}_{{\rm{c}}}-I),$$where $$n$$ represents the number of neighborhood sampling points; $$r$$ denotes the neighborhood radius; $${g}_{{\rm{c}}}$$ represents the gray value of the central pixel point; $$g(k)$$ represents the gray value of the neighborhood pixel $$k$$, $$k=0,1\,,\text{\unicode{x02026}},{n}-1$$; $$\text{sgn}(x)$$ and $$t(x,{b})$$ are sign functions, as shown in (4) and (5); $$m(k)$$ denotes the absolute value of the gray difference between the $$k-\text{th}$$ pixel point and the central pixel point in the neighborhood, as shown in Equation (6); C represents the mean on the image $$m(k)$$, as shown in Equation (7); I refers to the average gray level of the whole image. 4$$\text{sgn}(x)=\left\{\begin{array}{c}1,(x\ge 0)\\ 0,(x\lt 0)\end{array}\right.,$$ 5$$t(x,b)=\left\{\begin{array}{c}1,(x\ge b)\\ 0,(x\lt b)\end{array}\right.,$$ 6$$m(k)=|g(k)-{g}_{{\rm{c}}}|,(k=0,1,\text{\unicode{x02026}},n-1),$$ 7$$C=\frac{1}{n}\sum _{k=0}^{n-1}m(k),(k=0,1,\text{\unicode{x02026}},n-1).$$

A local sampling approach with a sampling radius of 1 and 8 sampling points is shown in Figure 2, where the sampling radius is defined as the size of one pixel in the plot.

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The CLBP_S and CLBP_M features are encoded and combined with CLBP_C features. The final result of the joint feature is a one-dimensional vector feature formed by combining the components in series to describe the texture structure of the image. The algorithm flow is shown in Figure 3.

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Improved CLBP feature descriptor

Formulas (1)–(3) show that CLBP extracts the gray difference $$(g(k) \mbox{-} {g}_{{\rm{c}}})$$ information between the central pixel and its neighborhood pixel.

The feature information is concentrated on the first-order static feature between adjacent pixels. Accordingly, CLBP would ignore the feature information of concave and convex regions between high-order pixels and adjacent sampling points. However, when the image is affected by illumination, it greatly affects the extracted gray difference results. The first-order static feature information is insufficient to deal with this situation. Therefore, it is necessary to add up the imaging information between the high-order pixels ignored by CLBP and the concave and convex regions between adjacent sampling points to the feature description. A pixel $${g}_{{\rm{c}}}$$ of a given gray image is set, and $$n$$ neighborhood points $${g}_{r}(k),({k}=0,1,\text{\unicode{x02026}},{n}-1)$$ on a circle centered at point $${g}_{{\rm{c}}}$$ and radius at point $$r$$ are uniformly collected, as well as $$n$$ neighborhood points $${g}_{r2}(k),({k}=0,1,\text{\unicode{x02026}},{n}-1)$$ on a circle centered on point $${g}_{{\rm{c}}}$$ and radius $$2r$$. Figure 4 shows the local sampling topology ($$r=1$$ radius and sampling point $$n=8$$) as an example.

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To extract the imaging information of concave and convex regions, the first-order sign-amplitude transformation of the original CLBP is adopted by the second-order difference, and the calculation expression is shown as formula (8): 8$$d(k)={g}_{{\rm{c}}}+{g}_{r2}(k)-2{g}_{r}(k),(k=0,1,\text{\unicode{x02026}},n-1),$$where $$d(k)$$ represents the local difference sign-magnitude transform (LDMT); $${g}_{r}(k)$$ and $${g}_{r2}(k)$$ denote the pixel value of the $$k\,-\text{th}$$ sampling pixel under the condition of the $$r,2r$$ radius.

The symbol and amplitude components of the improved CLBP feature can be further obtained from formula (8), as expressed in formulas (9)–(10). 9$$m(k)=|d(k)|,$$ 10$$s(k)=\left\{\begin{array}{c}1,d(k)\ge 0\\ -1,d(k)\lt 0\end{array}\right.,(k=0,1,\text{\unicode{x02026}},n-1),$$where $$s(k)$$ denotes symbol component; $$m(k)$$ refers to amplitude component.

In view of the harsh production environment in underground coal mines, coal rock images are constrained by the imaging environment, especially noise contamination, which is often difficult to avoid. For textures, the higher intensity noise contamination often has devastating and serious consequences. Unfortunately, CLBP feature descriptors are sensitive to noise. To mitigate the disturbance of noise, especially noise pollution, and to maximize the retention of coal rock image texture feature information, the improved CLBP feature descriptor is further processed by replacing the $$m(k)$$ mean C in the original CLBP descriptor with Equation (11). 11$$C=\mathrm{med}\{m(k)|k=0,1,\text{\unicode{x02026}},n-1\}.$$

Thus, the improved CLBP feature descriptor can be expressed as Equations (12)–(14). The general idea of improving CLBP algorithm is shown in Figure 5. 12$$\text{CLBP\_}{{\rm{S}}}_{n}=\sum _{k=0}^{n-1}{\rm{sgn}}[s(k)]{2}^{k}\,,$$ 13$$\text{CLBP\_}{{\rm{M}}}_{n}=\sum _{k=0}^{n-1}t(|{g}_{{\rm{c}}}+{g}_{r2}(k)-2{g}_{r}(k)|,\mathrm{med}\,\{m(k)|k=0,1,\text{\unicode{x02026}},n-1|\}){2}^{k}\,,$$ 14$$\text{CLBP\_}{{\rm{C}}}_{n}=\text{sgn}({g}_{{\rm{c}}}-I).$$

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In feature fusion, CLBP_S, CLBP_M and CLBP_C obtained by the original CLBP algorithm are cascaded to obtain CLBP_SMC features. The calculation method of CLBP_C operator in the improved algorithm is the same as that of the original CLBP algorithm, and the center pixels sampled are consistent. The improved CLBP feature descriptor only selects the extracted high-order pixel information, the symbol feature of pixel value difference, and the amplitude feature of pixel value difference to eliminate feature repetition and reduce the dimension of the final feature matrix; these features are cascaded with CLBP_SMC feature to obtain the final feature matrix.

Compared to the original LBP algorithm, which is overly simple and leads to incomplete information extraction, and the original CLBP algorithm, which ignores the higher-order information of the image, the improved CLBP algorithm extracts higher-order feature information and enhances some performance based on more comprehensive feature information than the original algorithm.

In summary, the improved CLBP algorithm strengthens the expression of coal rock image texture features in the following aspects:

• (1)

  The original CLBP is combined with the first-order static and second-order dynamic feature information of the improved algorithm, and the concave and convex region information are ignored by the original algorithm. However, the integrity of the low-order feature information is ensured;

• (2)

  The interference of destructive noise pollution is removed when extracting texture feature information.

Coal rock image recognition model based on improved CLBP and receptive field theory

The improved CLBP feature descriptor has a greater intensity in extracting texture feature information, but the following problems still remain:

• (1)

  The improved CLBP feature descriptor integrates high-order texture information, resulting in the high dimension of the feature matrix, which is 5/3 times that of the original CLBP feature matrix;

• (2)

  High-order feature matrix contains a large number of redundant information, which not only interferes with the improvement of recognition accuracy but also causes a sharp increase in computer space-time overhead, which limits the recognition speed and is not conducive to the practicability of the algorithm.

There is the concept of “receptive field” in the theory of biological visual cognition which is featured by layer-by-layer abstraction and iteration of visual information processing. The size of the receptive field changes with the neuron level. Deep learning is a machine learning method based on a deep network model. To be specific, inspired by the concept of “receptive field” in the biological community, it adopts a layer-by-layer abstraction mechanism to finally form high-level concepts in the case of low-level data objects. Obviously, the concept of “receptive field” is an effective method to remove information redundancy and reduce data dimension. To effectively improve the computational efficiency of the improved CLBP feature descriptor and enhance its practicability, this paper further integrates the improved CLBP feature descriptor with the receptive field theory.

A coal rock image recognition model based on improved CLBP and receptive field theory is established. Firstly, the improved CLBP feature descriptor is obtained by using the improved CLBP algorithm. Then the feature descriptor is fused into a feature matrix and input into the network. The loss function of the network model is selected as the cross entropy loss function. Each convolution layer is activated by the hyperbolic tangent function and operated by several receptive field modules. The feature information could be output by using Flatten operation. And finally, through the softmax operation, it can be determined whether the characteristic information is coal or rock and then the results are output. The model structure is shown in Figure 6.

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The receptive field module mapping model is shown in Figure 7, which consists of several convolution and pooling layers. The convoluted feature matrix is set as E and the convolution kernel is set as K. Then, the element $${O}_{i,{j}}$$ in row i and column j of the output feature after convolution can be expressed as follows: 15$${O}_{i,j}=\sum _{s=1}^{{h}_{{\rm{k}}}}\sum _{t=1}^{{w}_{{\rm{k}}}}{E}_{i+s-1,j+t-1}{K}_{s,t},$$where, $${h}_{{\rm{k}}}$$ and $${w}_{{\rm{k}}}$$ denote the height and width of convolution kernels, respectively; $${K}_{s,{t}}$$ is the s row and t element in the convolution kernel. $$s=1\,,2,\text{\unicode{x02026}},{h}_{{\rm{k}}}$$, $$t=1\,,2,\text{\unicode{x02026}},{w}_{{\rm{k}}}$$.

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Typically, the feature matrix should be pooled after several convolution operations to further abstract feature information. The pooling operation formula is shown as follows: 16$${O}_{i,j}^{l,m}=\mathop{\max }\limits_{h,w}[{O}_{(i-1)\times {h}_{s}+h,(j-1)\times {w}_{s}+w}^{l-1,m}],$$where $${O}_{i,{j}}^{l,{m}}$$ denotes the elements (i line and j column) of the m-th feature graph in the pooling layer l obtained by the pooling operation; h is the serial number of pooled nuclei, $$h=1\,,2,\text{\unicode{x02026}},{h}_{s}$$; $${h}_{s}$$ is the height of pooled nuclei; $$w$$ refers to the pooled kernel row number, $$w=1\,,2,\text{\unicode{x02026}},{w}_{s}$$; $${w}_{s}$$ is the width of the pooled kernel. Usually, $${h}_{s}=2,{w}_{s}=2$$.

A receptive field module can be formed by cascading N convolution operations (convolution kernel size $$k\times k$$) and 1 pooling operation (pooling kernel size $$2\times 2$$). It can be seen from Figure 7 and Equations (15) and (16) that, an element of the output feature matrix after operation through this module is the abstraction of the feature information of the original feature matrix $$R\times R$$ region. The calculation of R is shown in Equation (17). 17$$R=2[k+(N-1)(k-1)].$$

That is, after a receptive field operation module abstracts the original feature matrix, one element of the output feature matrix represents the original matrix $$4{\left([k+\left((N-1)\right)\left((k-1)\right)]\right)}^{2}$$ elements. This model consists of two receptive field modules: and the first one contains two convolution operations and one pooling operation; and the second one includes one convolution operation and one pooling operation. The convolution kernel size is $$3\times 3$$, and the pooling kernel size is $$2\times 2$$. Then one element of the output feature matrix corresponds to the information of 576 elements of the original feature matrix, and its data dimension reduction and redundancy reduction ability are highly satisfactory.

EXPERIMENTAL RESULTS AND ANALYSIS

Experimental scheme

The experimental scheme is as follows: first, to verify the feasibility and generalization performance of the improved CLBP feature descriptor; then, to verify the performance of the coal rock image recognition model fusing the improved CLBP with the perceptual field theory.

The main hardware experimental environment is as follows: Intel Corei5-4590k CPU, 8GB memory, Nvidia Quadro P4000 8GB GPU. The software environment is as follows: the operating system is 64-bit Window10, the development environment is Pycharm2020, the development language is Python3.6.0, and the configuration environment is Tensrflow2.0.

The coal rock database used in the experiment includes two categories of coal and rock, a total of 67 968 jpg format (256 level) gray coal rock images with a size of 200 × 200. The images were collected partly from coal mines such as Chongqing, Sichuan, and Shanxi, and partly from the Internet. The ratio of coal to rock images is 1:1, and some images are shown in Figure 8.

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Feasibility and generalization performance verification test

Due to the harsh imaging environment in coal mine, coal rock images often contain high-intensity noise such as Gaussian, salt, and pepper, which thereby seriously affects the recognition. The following comparative experiments were carried out to verify the feasibility and generalization performance of the improved CLBP algorithm. Firstly, 23 789 coal and rock images were randomly selected from the coal and rock database as the training sample set, and 10 195 remaining coal and rock images were selected as the test sample set. Then, the improved CLBP algorithm was used to extract the texture features of each image to investigate the accuracy of the model. Then, Gaussian noise and salt-and-pepper noise with different intensities were added to simulate the complex downhole imaging quality and observe the generalization performance of the model. Finally, the original LBP and CLBP algorithms were used to extract the features of these samples, and the generalization performances of the three were compared.

The experimental results are shown in Figure 9 and Table 1. Under the influence of Gaussian noise with different intensities, the recognition accuracy of the improved CLBP algorithm displays a small fluctuation. Although the overall accuracy shows a downward trend, the decline is rather mild, and the final recognition accuracy can be stabilized at more than 96%. Moreover, the recognition accuracy of the improved CLBP algorithm is superior to that of the original LBP and the original CLBP algorithms. Under the influence of salt and pepper noise with different intensities, the identification accuracy of the original CLBP algorithm is still low, but the floating degree is high and the noise is large. The improved CLBP algorithm displays higher recognition accuracy (more than 94%), and the accuracy fluctuates less with the noise intensity.

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Table 1 Comparison of correct recognition rates of different methods under different noise intensities

Noise type	Noise intensity	LBP method	CLBP method	Improved method
Gaussian noise	0	99.3%	99.7%	99.9%
0.005	97.7%	98.0%	99.6%
0.007	97.2%	98.2%	99.5%
0.009	95.9%	98.4%	99.5%
0.010	96.1%	98.2%	99.0%
0.030	87.1%	97.1%	98.0%
0.050	77.4%	96.2%	96.9%
Impulse noise	0.03	99.3%	99.9%	99.8%
0.04	99.2%	99.6%	99.7%
0.05	78.2%	96.2%	97.2%
0.06	99.0%	99.6%	99.9%
0.07	60.7%	86.3%	94.3%
0.08	97.1%	99.1%	99.8%
0.09	98.1%	99.2%	99.8%

As can be seen from Figure 9a, the accuracy rate decreases very significantly while the noise increases in that the LBP algorithm is more sensitive to noise. Also, due to the absence of median processing, the original CLBP algorithm is less accurate than the improved algorithm under the influence of different noises: meanwhile, in Figure 9b, it can be observed that the noise resistance of the LBP algorithm still fluctuates the most, and the fluctuation of the original CLBP algorithm still does not reach a high recognition accuracy rate due to the absence of median processing.

Coal rock image recognition model performance validation test

The hardware conditions and coal-rock data sets are used for a comparison test to verify the performance of the coal-rock image recognition model based on the fusion of improved CLBP and receptive field theory. The comparison algorithms are LBP and CLBP, and the classifier is a support vector machine (SVM).

• (1)

  The configuration of model and training parameters mainly includes iterative steps and learning rate settings. The input data include feature information extracted by the improved algorithm, and the Batch size is configured to 1. The loss function adopts the cross entropy loss function and introduces the Adam optimization algorithm. The learning rate can be smaller, at 0.001. The number of training steps can be set to 20. Class is the category, and the category label is encoded by exclusive coding.

• (2)

  When the model and training parameters are preset, the prepared coal rock image data set and the coal rock image data set with noise are input into the model for training.

• (3)

  When the model is trained, the test set is used to verify its performance, and the final coal rock recognition accuracy and the space-time overhead for single image processing are outputted.

The space-time overhead results of each model are shown in Figure 10, and the recognition accuracy is shown in Figure 11. As can be seen from Figure 10, compared with that of the original LBP model, the original CLBP model and the CLBP model with SVM as the classifier, the running time of the coal rock image recognition model based on the improved CLBP and the receptive field theory is greatly reduced; in addition, the space-time overheads are only 159%, 29%, and 2.7% of the original LBP, the original CLBP, and the improved CLBP and SVM classifier models, respectively. The time consumption is reduced by 59%, 71% and 97%. At the same time, Figure 11 shows that the coal-rock image recognition model based on the improved CLBP and receptive field theory can still maintain the recognition accuracy of more than 98.5% by saving such large space-time overhead.

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CONCLUSIONS

• (1)

  The improved CLBP algorithm contains both low-order feature information and higher-order feature information of textured concave and convex regions; the recognition accuracy and generalization ability are greatly improved compared with the original CLBP; and the recognition accuracy is finally stabilized at over 94.3% under strong noise interference.

• (2)

  The coal rock image recognition model incorporating improved CLBP and receptive field theory balances recognition accuracy and efficiency. The single image recognition time is 0.0035 s, which is 71% shorter than the original CLBP model and 97% shorter than the improved CLBP model (without the fusion of receptive field theory), while the accuracy rate still maintains at over 98.5%.

ACKNOWLEDGMENTS

The authors would like to thank the anonymous reviewers for their valuable revise opinion and suggestions in improving the technical presentation of this paper. We declare that we do not have any commercial or associative interest that represents a conflict of interest in connection with the work submitted. This study is supported by Shanxi Province Science Foundation for Youths (No. 201901D211249), and the Scientific and technological innovation project of colleges and universities in Shanxi Province (No. 2020L0294).

CONFLICT OF INTEREST

The authors declare no conflict of interest.

DATA AVAILABILITY STATEMENT

Our code is available at: .

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