Research on Coal Calorific Value Prediction Based on K-Means Clustering and Ridge Regression Algorithm

doi:10.12096/j.2096-4528.pgt.23005

Abstract

Abstract:

Objectives The calorific value of coal is one of the important evaluation criteria for measuring coal quality, and is also the main basis for valuation of power coal. In order to realize high-precision and rapid prediction of coal calorific value while reducing prediction costs, a new prediction method is proposed. Methods The K-Means clustering algorithm is used to cluster similar coal types. The sample data comes from 4 269 entry testing information from a self-contained coal yard of a power plant in Shandong in the past 6 years. On the basis of clustering, Ridge regression models are established from industrial analysis data to received base calorific value, which is used as a prediction model for coal calorific value. Results The established K-Means clustering and Ridge regression hybrid model exhibits excellent prediction performance. Compared with the traditional multiple linear regression model, this hybrid model can reduce the mean absolute error by up to 30.525%, reduce the root mean square error by up to 60.054%, and increase the correlation coefficient by up to 2.320%. Conclusions The mixed model of K-Means clustering and Ridge regression reduces the prediction cost of coal calorific value, and also improves the accuracy and speed of prediction, providing a new idea for predicting coal calorific value.

Key words: coal-fired power plants, calorific value of coal, proximate analysis, prediction, K-Means clustering, Ridge regression

CLC Number:

TK 16

Shichao QIAO, Heng CHEN, Bo LI, Peiyuan PAN, Gang XU. Research on Coal Calorific Value Prediction Based on K-Means Clustering and Ridge Regression Algorithm[J]. Power Generation Technology, 2025, 46(1): 135-144.

Figures/Tables 14

Tab. 1 Basic information of the dataset

参数	最小值	最大值	平均值
收到基低位发热量Q_net，ar/(MJ⋅kg^-1)	14.14	28.18	21.13
收到基水分质量分数M_ar/%	2.15	29.09	9.55
收到基灰分质量分数A_ar/%	4.41	48.52	24.96
收到基固定碳质量分数F_C，ar/%	31.46	71.03	47.08

Fig. 1 Distribution of the sample data

Fig. 2 Elbow method to determine the optimal number of clustering

Fig. 3 Silhouette coefficient method to determine the optimal number of clustering

Fig. 4 Calinski-Harabasz index method to determine the optimal number of clustering

Fig. 5 Clustering results for the coal entered the yard

Tab. 2 Range of coal type parameters

煤种	M_ar	A_ar	F_C，ar
高固定碳煤	2.12~15.90	11.94~33.91	46.99~71.03
高灰分煤	3.63~19.51	18.14~48.52	31.46~49.76
高水分煤	9.12~29.03	4.40~23.58	34.17~54.95

Fig. 6 Division of the data set

Fig. 7 Comparison between the predicted heat value and actual heat value

Tab. 3 Model evaluation indicators corresponding to different regression algorithms

回归算法	回归方程	δ_MAE	δ_RMSE	R²
OLS回归	$Q n e t, a r = 26.569 84 - 0.337 03 M a r - 0.291 47 A a r + 0.103 11 F C, a r$	0.270 36	0.628 38	0.942 94
Lasso回归	$Q n e t, a r = 21.542 41 - 0.150 61 M a r - 0.222 05 A a r + 0.133 61 F C, a r$	0.464 60	0.792 84	0.909 16
Ridge回归	$Q n e t, a r = 26.569 15 - 0.337 01 M a r - 0.291 46 A a r + 0.103 12 F C, a r$	0.248 45	0.592 63	0.945 63
Elastic Net回归	$Q n e t, a r = 23.358 12 - 0.220 51 M a r - 0.247 72 A a r + 0.123 42 F C, a r$	0.358 70	0.696 54	0.929 89

Tab. 3 Model evaluation indicators corresponding to different regression algorithms

回归算法	回归方程	δ_MAE	δ_RMSE	R²
OLS回归	$Q n e t, a r = 26.569 84 - 0.337 03 M a r - 0.291 47 A a r + 0.103 11 F C, a r$	0.270 36	0.628 38	0.942 94
Lasso回归	$Q n e t, a r = 21.542 41 - 0.150 61 M a r - 0.222 05 A a r + 0.133 61 F C, a r$	0.464 60	0.792 84	0.909 16
Ridge回归	$Q n e t, a r = 26.569 15 - 0.337 01 M a r - 0.291 46 A a r + 0.103 12 F C, a r$	0.248 45	0.592 63	0.945 63
Elastic Net回归	$Q n e t, a r = 23.358 12 - 0.220 51 M a r - 0.247 72 A a r + 0.123 42 F C, a r$	0.358 70	0.696 54	0.929 89

Tab. 4 Variance inflation factors of input variables

输入变量	M_ar	A_ar	F_C，ar
VIF	6.095 27	9.974 05	16.879 13

Fig. 8 Process of building model

Tab. 5 Model evaluation indicators of regression models corresponding to different coal types after K-Means clustering

煤炭种类	回归方程	δ_MAE	δ_RMSE	R²
全部煤	$Q n e t, a r = 26.569 15 - 0.337 01 M a r - 0.291 46 A a r + 0.103 12 F C, a r$	0.248 45	0.592 63	0.945 63
高固定碳煤	$Q n e t, a r = 28.753 18 - 0.345 87 M a r - 0.315 47 A a r + 0.076 18 F C, a r$	0.172 61	0.236 73	0.967 57
高灰分煤	$Q n e t, a r = 24.843 48 - 0.301 57 M a r - 0.276 01 A a r + 0.125 64 F C, a r$	0.224 37	0.348 47	0.963 36
高水分煤	$Q n e t, a r = 28.329 07 - 0.404 50 M a r - 0.299 58 A a r + 0.089 79 F C, a r$	0.247 84	0.409 61	0.957 69

Tab. 5 Model evaluation indicators of regression models corresponding to different coal types after K-Means clustering

煤炭种类	回归方程	δ_MAE	δ_RMSE	R²
全部煤	$Q n e t, a r = 26.569 15 - 0.337 01 M a r - 0.291 46 A a r + 0.103 12 F C, a r$	0.248 45	0.592 63	0.945 63
高固定碳煤	$Q n e t, a r = 28.753 18 - 0.345 87 M a r - 0.315 47 A a r + 0.076 18 F C, a r$	0.172 61	0.236 73	0.967 57
高灰分煤	$Q n e t, a r = 24.843 48 - 0.301 57 M a r - 0.276 01 A a r + 0.125 64 F C, a r$	0.224 37	0.348 47	0.963 36
高水分煤	$Q n e t, a r = 28.329 07 - 0.404 50 M a r - 0.299 58 A a r + 0.089 79 F C, a r$	0.247 84	0.409 61	0.957 69

Fig. 9 Comparison between actual calorific value and predicted calorific value of different coal types after clustering

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