3.1

Direct orthogonal signal correction

The principle of the direct orthogonal signal correction¹⁰ method is to orthogonalize the spectral array with the concentration array before establishing the quantitative correction model, filter out the signals irrelevant to the concentration array, and then carry out a multivariate correction, to simplify the model and enhance the prediction ability of the model. The orthogonal mathematical method filters out the spectral signals independent of the concentration array, which can reduce the number of main factors used in establishing the model and improve the prediction ability and robustness of the correction model. The spectral curve of coal data processed by the direct orthogonal signal correction method is shown in Figure 2.

Figure 2.

Spectral curve of coal data after DOSC processing.

3.2

Principal component analysis

Principal component analysis (PCA) is not only a basic mathematical analysis method but also a method widely used to reduce dimension. The principle is to establish a few new variables as possible according to many variables with certain correlations, and these new variables are irrelevant. At the same time, these new variables can contain as much information as possible. In the DP_WTELM model, we mainly use PCA to reduce the dimension of data. Each spectral data has 1024 features. We set the cumulative contribution rate to 99% and extracted 9 principal components from the original data, as shown in Figure 3.

Figure 3.

Cumulative contribution rate of 9 principal components.

3.3

Whale optimization algorithm

Whale optimization algorithm (WOA) is an algorithm proposed by Mirjalili et al.¹¹ to simulate the humpback whale hunting strategy. In contrast to classical algorithms, WOA is superior to classical algorithms in both accuracy and speed.

3.4

Extreme learning machine

In contrast to the traditional neural network structure, extreme learning machine (ELM) has the advantages of less iterations and fast training speed. We choose the TELM network with two hidden layers as the infrastructure. TELM not only takes into account these advantages of ELM, but also has higher accuracy. In this paper, the WOA is used to find the optimal weight and bias parameters of TELM, and the DP-WTELM network model for detecting coal quality is obtained. Figure 4 is a schematic diagram of the TELM network structure.

Figure 4.

Network structure of TELM.

For any different N samples (x_i,t_i), here x_i =[x_i1,x_i2,…,x_in]^T∈Rⁿ,t_i=[t_i1,t_i2,…,t_im]^T ∈ R^m. According to the ELM algorithm, the output matrix H₁ of the first layer can be calculated and the output weight . Defining the expected output matrix of a second hidden layer as H_2E, this matrix is obtained by equation (1).

In the equation, is the Moore-Penrose generalized inverse matrix of β₁. Define a matrix W_H2=[B₂ W₂], where B₂,w₂ is the input deviation and input weight of the second hidden layer, then W_H2 is obtained from equation (2).

In the equation, M₂=[1 H₁]^T, vector 1 is a column vector composed of N scalars 1; is the Moore Penrose generalized inverse matrix of M₂, and the calculation method is the same as that of ; g^–1(x) is the inverse of the activation function g(x).

The output of the second hidden layer is defined as H_2A. It can be obtained by equation (3).

Then, the output weight of the second hidden layer can be calculated β₂.

In the equation, is the Moore Penrose generalized inverse matrix of H_2A, and the calculation method is the same as that of .

Finally, the actual output of the whole TELM network is represented by equation (5).

4.1

Preprocessing of coal spectral data

The spectral data of coal directly measured by spectrometer contains a lot of noise and the dimension is 1024 dimensions, if these data are directly input into the model, it will lead to problems such as complex model structure and long training time. Therefore, the DOSC and PCA are used to preprocess the data. After preprocessing, the data dimension is reduced from 1024 to 9, which greatly enhances the training speed of the model.

4.2

Coal quality test results

In the experiment, we collected 50 coal samples, of which 40 were used as training sets and 10 as test sets. Based on the coal spectral data, the coal quality detection model is established by using the DP_WTELM neural network algorithm. The test results are shown in Figure 5a.

Figure 5.

Prediction results of low calorific value based on different models.

Figure 5 shows the prediction results of the DP_WTELM model and ELM model on the low calorific value of coal respectively. It can be seen that the overall prediction effect of low calorific value of coal samples in figure 5a is

marvelous, while the prediction results of low calorific value of multiple coal samples in figure 5b have large errors. It can be seen that the DP_WTELM model can obtain more accurate results in predicting the low calorific value of coal than the ELM model. From the experimental results, the R2 value is 0.98885 and the RMSE value is 0.62748, which verifies that the DP_WTELM model has good prediction performance.