Interval Prediction Model of RF-ET-KDE Sintering Process Physical Index Based on Stacking Integration

doi:10.12068/j.issn.1005-3026.2024.10.001

Abstract

Abstract:

Due to the many uncertainties in the sintering process， the reliability of mechanism analysis and point prediction results is insufficient. Therefore， a random forest-extreme tree-kernel density estimation （RF-ET-KDE） algorithm is proposed to realize interval predictions for physical indicators， such as particle size and moisture. Firstly， data preprocessing and feature selection operations are adopted to screen out the most suitable feature variables for modeling. Secondly， the RF-ET algorithm based on Stacking is utilized to realize point predictions for the indicators. This algorithm makes the model with higher accuracy and generalization， and then the KDE algorithm is adopted to calculate the prediction error of the indicator. The distribution interval and interval prediction results under a certain confidence level are obtained. Finally， the proposed model is compared with the other combined models. The results show that the RF-ET algorithm has higher point prediction accuracy， and the KDE algorithm can quantify the error of the indicator very well， so that a higher credibility interval prediction result can be obtained.

Key words: sintering process, random forest-extreme tree （RF-ET）, kernel density estimation （KDE）, physical index, interval prediction

CLC Number:

TP 181

Zeng-xin KANG, Jin-chao CHEN, Jin-yang WANG, Zhao-xia WU. Interval Prediction Model of RF-ET-KDE Sintering Process Physical Index Based on Stacking Integration[J]. Journal of Northeastern University(Natural Science), 2024, 45(10): 1369-1378.

Figures/Tables 16

Table 1 Parameters of sintering process

钙石灰粉/（t·h^-1）

除尘矿/（t·h^-1）

燃料/（t·h^-1）

钒钛铁精粉/（t·h^-1）

自返矿/（t·h^-1）

高炉返矿/（t·h^-1）

烧结混合料质量百分数

全铁/%

五氧化二钒/%

氧化钙/%

二氧化硅/%

烧结机操作

圆辊速度/（r·h^-1）

机速九辊/（r·h^-1）

烧结机机速/（m·min^-1）

点火温度/oC

煤气流量/（m³·h^-1）

风机风量/（m³·h^-1）

一号风门开度/%

二号风门开度/%

机速板式转速/（r·h^-1）

环冷机机速/（m·min^-1）

助燃风流量/（m³·h^-1）

助燃风压力/kPa

烧结机状态

南烟道温度/oC

南烟道负压/kPa

北烟道温度/oC

27~40

41~54

北烟道负压/kPa

风箱废弃温度/oC

风箱负压/kPa

输出

水分的质量分数/%

粒度/%

Table 2 Original data of sintering

数据类型	单位时间原料下料量/（t·h^-1）						输出质量百分数/%
数据类型	钙石灰粉	除尘矿	燃料	焦粉	铁粉	钒粉	粒度	水分
均值	30.184	9.768	13.693	5.621	14.792	72.938	24.532	8.295
最小值	11.913	0	0	0	0	0	20.500	7.500
最大值	48.753	24.248	40.821	20.935	67.366	305.117	26.400	9.100

Fig.1 Box diagram

Fig. 2 Results of data processing

Table 3 Results of MIC

水分				粒度
工艺参数	M_IC	工艺参数	M_IC	工艺参数	M_IC	工艺参数	M_IC
风机风量	0.215 2	1号风箱真空度	0.101 1	风机风量	0.115 9	圆辊速度	0.062 6
11号风箱真空度	0.177 4	5号风箱真空度	0.099 9	钒钛铁精粉	0.105 4	20号风箱废气温度	0.061 9
钒钛铁精粉	0.158 8	高炉返矿	0.095 1	2号风门开度	0.102 8	5号风箱真空度	0.059 8
7号风箱真空度	0.132 0	1号风门开度	0.094 9	自返矿	0.084 1	21号风箱废气温度	0.059 1
钙石灰粉	0.126 3	1号风箱废气温度	0.093 2	1号风门开度	0.083 0	3号风箱废气温度	0.058 6
2号风门开度	0.116 5	烧结用白煤	0.091 6	7号风箱废气温度	0.071 6	除尘矿	0.058 1
20号风箱废气温度	0.113 6	9号风箱真空度	0.087 4	烧结用白煤	0.069 4	22号风箱废气温度	0.056 4
自返矿	0.106 0	9号风箱废气温度	0.086 9	钙石灰粉	0.065 1	1号风箱废气温度	0.055 7
7号风箱废气温度	0.104 9	11号风箱废气温度	0.085 3	13号风箱真空度	0.063 7	南烟道温度	0.055 2
2号风箱真空度	0.101 8	5号风箱废气温度	0.085 2	北烟道温度	0.063 1	高炉返矿	0.055 0

Fig. 3 Flowchart of RF algorithm

Fig.4 Framework of Stacking integration learning

Fig. 5 Flowchart of interval prediction model

Fig. 6 Prediction results of particle size Stacking model

Fig.7 Prediction results of moisture Stacking model

Table 4 Comparison results of particle size model

算法	M_AE	M_SE	R_MSE
LGBM	0.233 02	0.094 58	0.307 54
RF	0.222 21	0.090 15	0.300 25
ET	0.198 21	0.072 47	0.269 21
RF-ET	0.102 12	0.019 82	0.140 79

Table 5 Comparison results of moisture model

算法	M_AE	M_SE	R_MSE
LGBM	0.154 35	0.040 07	0.200 19
RF	0.144 80	0.038 52	0.196 27
ET	0.136 11	0.034 01	0.184 41
RF-ET	0.078 52	0.011 23	0.105 95

Fig. 8 PDF comparison of particle size and moisture

Table 6 Interval prediction comparison results of particle size

模型	置信水平	P_ICP	$W P I N A$	F
LGBM-KDE	95%	0.950 66	0.602 58	1.208 84
	90%	0.900 57	0.490 30	1.249 45
	85%	0.851 23	0.414 60	1.258 36
RF-KDE	95%	0.950 28	0.611 95	1.201 73
	90%	0.900 19	0.487 00	1.251 66
	85%	0.850 47	0.397 54	1.271 17
ET-KDE	95%	0.950 28	0.580 73	1.224 70
	90%	0.899 43	0.453 16	1.277 98
	85%	0.850 47	0.376 63	1.288 29
RF-ET-KDE	95%	0.951 80	0.288 44	1.493 56
	90%	0.902 85	0.228 38	1.497 02
	85%	0.851 23	0.188 96	1.466 57

Table 6 Interval prediction comparison results of particle size

模型	置信水平	P_ICP	$W P I N A$	F
LGBM-KDE	95%	0.950 66	0.602 58	1.208 84
	90%	0.900 57	0.490 30	1.249 45
	85%	0.851 23	0.414 60	1.258 36
RF-KDE	95%	0.950 28	0.611 95	1.201 73
	90%	0.900 19	0.487 00	1.251 66
	85%	0.850 47	0.397 54	1.271 17
ET-KDE	95%	0.950 28	0.580 73	1.224 70
	90%	0.899 43	0.453 16	1.277 98
	85%	0.850 47	0.376 63	1.288 29
RF-ET-KDE	95%	0.951 80	0.288 44	1.493 56
	90%	0.902 85	0.228 38	1.497 02
	85%	0.851 23	0.188 96	1.466 57

Table 7 Interval prediction comparison results of moisture

模型	置信水平	P_ICP	$W P I N A$	F
LGBM-KDE	95%	0.951 42	0.503 75	1.286 33
	90%	0.900 57	0.414 08	1.311 91
	85%	0.850 47	0.351 91	1.309 14
RF-KDE	95%	0.950 66	0.494 05	1.293 70
	90%	0.899 43	0.401 61	1.321 51
	85%	0.850 09	0.340 49	1.318 54
ET-KDE	95%	0.950 28	0.484 68	1.301 24
	90%	0.900 19	0.380 80	1.340 77
	85%	0.85123	0.319 98	1.338 02
RF-ET-KDE	95%	0.952 56	0.229 15	1.563 78
	90%	0.903 23	0.182 32	1.551 03
	85%	0.858 82	0.153 17	1.517 96

Table 7 Interval prediction comparison results of moisture

模型	置信水平	P_ICP	$W P I N A$	F
LGBM-KDE	95%	0.951 42	0.503 75	1.286 33
	90%	0.900 57	0.414 08	1.311 91
	85%	0.850 47	0.351 91	1.309 14
RF-KDE	95%	0.950 66	0.494 05	1.293 70
	90%	0.899 43	0.401 61	1.321 51
	85%	0.850 09	0.340 49	1.318 54
ET-KDE	95%	0.950 28	0.484 68	1.301 24
	90%	0.900 19	0.380 80	1.340 77
	85%	0.85123	0.319 98	1.338 02
RF-ET-KDE	95%	0.952 56	0.229 15	1.563 78
	90%	0.903 23	0.182 32	1.551 03
	85%	0.858 82	0.153 17	1.517 96

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