基于热扩散核密度确定密度峰值法的历史工况识别

doi:10.11949/0438-1157.20211615

摘要/Abstract

摘要：

在工业生产过程中，生产决策的调整或生产状况的变化会导致生产过程多模态化，常用的数据聚类方法进行工况识别时存在参数选取困难或需要先验知识等限制。基于此，提出一种将人工智能领域的热扩散核密度确定密度峰的技术与高斯混合模型相结合的方法，可有效克服目前方法的缺点。该方法首先利用热扩散核密度确定密度峰的技术估算每个数据点的密度及其与局部密度较大点的距离，获取数据集的聚类中心并完成聚类；其次，利用高斯混合模型获取不同工况的特征参数：平均值、协方差和先验概率，从而对多工况历史过程进行准确的描述；最后，利用文献中仿真数据和Tennessee Eastman过程两个案例进行验证，并与K-均值法和F-J改进的高斯混合模型进行比较，证明了本文提出方法可更加方便、有效地对历史工况进行准确识别。

关键词: 多模态, 聚类, 模型, 参数估值, 核密度估计

Abstract:

Adjustments in production decisions or changes from working statuses may lead to multi-modal production process. Commonly used data clustering methods have difficulty in parameter selection or need prior knowledge when recognizing multi-modal process. Therefore, a method is proposed that combines the kernel density estimation of heat diffusion determining density peak technology in the field of artificial intelligence with the Gaussian mixture model. It can effectively overcome the shortcomings of the current methods. The method first uses the kernel density estimation of heat diffusion determining density peak technology to estimate the local density of every data sample and its distance from higher local density to obtain the number of cluster centers and cluster the data set. Secondly, the characteristic parameters of different working conditions are obtained by using Gaussian mixture model: average, covariance and prior probability, so as to accurately describe the historical process of multiple operating conditions. Finally, two examples of Tennessee Eastman process and simulation data in literature were used for verification, and compared with K-means and Gaussian mixture model improved by F-J, it is proved that the proposed method can be more convenient and effective to accurately recognize the historical operating conditions.

Key words: multi-modal, clustering, model, parameter estimation, kernel density estimation

中图分类号:

TP 274.3

毕荣山, 韩智慧, 陶少辉, 孙晓岩, 项曙光. 基于热扩散核密度确定密度峰值法的历史工况识别[J]. 化工学报, 2022, 73(4): 1615-1622.

Rongshan BI, Zhihui HAN, Shaohui TAO, Xiaoyan SUN, Shuguang XIANG. Recognizing historical operating conditions by determining the density peaks at kernel density estimation of heat diffusion[J]. CIESC Journal, 2022, 73(4): 1615-1622.

图/表 9

参考文献 30

1	谭帅. 多模态过程统计建模及在线监测方法研究[D]. 沈阳: 东北大学, 2012.
	Tan S. Statistical modeling and online monitoring for multiple mode processes[D]. Shenyang: Northeastern University, 2012.
2	陈刚, 路殿坤. 黄金冶金原理与工艺[M]. 沈阳: 东北大学出版社, 1999.
	Chen G, Lu D K. Gold Metallurgy Principle and Technology [M]. Shenyang: Northeast University Press, 1999.
3	Jia R X, Wang J, Zhou J L. Fault diagnosis of industrial process based on the optimal parametric t-distributed stochastic neighbor embedding[J]. Science China Information Sciences, 2020, 64(5): 1-3.
4	Le Q H, Verheijen P J T, Mampaey K E, et al. Non-linear data reconciliation for a partial nitritation (SHARON) reactor[J]. IFAC-PapersOnLine, 2016, 49(7): 1139-1144.
5	李永明, 史旭东, 熊伟丽. 基于工况识别的污水处理过程多目标优化控制[J]. 化工学报, 2019, 70(11): 4325-4336.
	Li Y M, Shi X D, Xiong W L. Condition recognition based intelligent multi-objective optimal control for wastewater treatment[J]. CIESC Journal, 2019, 70(11): 4325-4336.
6	Yu J, Qin S J. Multimode process monitoring with Bayesian inference-based finite Gaussian mixture models[J]. AIChE Journal, 2008, 54(7): 1811-1829.
7	Zhao S J, Zhang J, Xu Y M. Performance monitoring of processes with multiple operating modes through multiple PLS models[J]. Journal of Process Control, 2006, 16(7): 763-772.
8	Cao Y, Jan N M, Huang B, et al. Multimodal process monitoring based on variational Bayesian PCA and Kullback-Leibler divergence between mixture models[J]. Chemometrics and Intelligent Laboratory Systems, 2021, 210: 104230.
9	Zhang Z, Deng X G. Anomaly detection using improved deep SVDD model with data structure preservation[J]. Pattern Recognition Letters, 2021, 148: 1-6.
10	Lee J M, Yoo C, Lee I B. Statistical process monitoring with independent component analysis[J]. Journal of Process Control, 2004, 14(5): 467-485.
11	Tan S, Wang F L, Peng J, et al. Multimode process monitoring based on mode identification[J]. Industrial & Engineering Chemistry Research, 2012, 51(1): 374-388.
12	Xie X, Shi H B. Multimode process monitoring based on fuzzy C-means in locality preserving projection subspace[J]. Chinese Journal of Chemical Engineering, 2012, 20(6): 1174-1179.
13	郭金玉, 袁堂明, 李元. 一种不等长的多模态间歇过程故障检测方法[J]. 化工学报, 2016, 67(7): 2916-2924.
	Guo J Y, Yuan T M, Li Y. Fault detection method for uneven-length multimode batch processes[J]. CIESC Journal, 2016, 67(7): 2916-2924.
14	Zhu J L, Ge Z Q, Song Z H. Distributed Gaussian mixture model for monitoring plant-wide processes with multiple operating modes[J]. IFAC Journal of Systems and Control, 2018, 6: 1-15.
15	Choi S W, Park J H, Lee I B. Process monitoring using a Gaussian mixture model via principal component analysis and discriminant analysis[J]. Computers & Chemical Engineering, 2004, 28(8): 1377-1387.
16	Dong J, Zhang C, Peng K X. A new multimode process monitoring method based on a hierarchical Dirichlet process—Hidden semi-Markov model with application to the hot steel strip mill process[J]. Control Engineering Practice, 2021, 110: 104767.
17	Zhang J X, Zhou D H, Chen M Y. Monitoring multimode processes: a modified PCA algorithm with continual learning ability[J]. Journal of Process Control, 2021, 103: 76-86.
18	Khediri I B, Weihs C, Limam M. Kernel k-means clustering based local support vector domain description fault detection of multimodal processes[J]. Expert Systems with Applications, 2012, 39(2): 2166-2171.
19	Huang T, Peng H, Zhang K. Model selection for Gaussian mixture models[J]. Statistica Sinica, 2017, 27(1): 147-169.
20	Karlis D, Xekalaki E. Choosing initial values for the EM algorithm for finite mixtures[J]. Computational Statistics & Data Analysis, 2003, 41(3/4): 577-590.
21	Figueiredo M A T, Jain A K. Unsupervised learning of finite mixture models[J]. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2002, 24(3): 381-396.
22	Paalanen P, Kamarainen J K, Ilonen J, et al. Feature representation and discrimination based on Gaussian mixture model probability densities—practices and algorithms[J]. Pattern Recognition, 2006, 39(7): 1346-1358.
23	Rodriguez A, Laio A. Clustering by fast search and find of density peaks[J]. Science, 2014, 344(6191): 1492-1496.
24	Mehmood R, Zhang G Z, Bie R F, et al. Clustering by fast search and find of density peaks via heat diffusion[J]. Neurocomputing, 2016, 208: 210-217.
25	Xiao J, Xu Q Q, Wu C L, et al. Performance evaluation of missing-value imputation clustering based on a multivariate Gaussian mixture model[J]. PLoS One, 2016, 11(8): e0161112.
26	Ma S, Sun S G, Wang B J, et al. Estimating load spectra probability distributions of train bogie frames by the diffusion-based kernel density method[J]. International Journal of Fatigue, 2020, 132: 105352.
27	Ge Z Q, Song Z H. Multimode process monitoring based on Bayesian method[J]. Journal of Chemometrics, 2009: 23(12):636-650.
28	解翔, 侍洪波. 多模态化工过程的全局监控策略[J]. 化工学报, 2012, 63(7): 2156-2162.
	Xie X, Shi H B. Global monitoring strategy for multimode chemical processes[J]. CIESC Journal, 2012, 63(7): 2156-2162.
29	Downs J J, Vogel E F. A plant-wide industrial process control problem[J]. Computers & Chemical Engineering, 1993, 17(3): 245-255.
30	Ricker N L. Optimal steady-state operation of the Tennessee Eastman challenge process[J]. Computers & Chemical Engineering, 1995, 19(9): 949-959.

项目	工况个数	每种工况的先验概率	每种工况下变量x₁, x₂, x₃的平均值	相对偏差
实际值	3	0.25	11.777,296.288,12.410	—
		0.25	20.467,192.899,354.307	—
		0.5	10.351,19.900,152.718	—
本文方法	3	0.25	11.777,296.288,12.410	0,0,0
		0.25	20.467,192.899,354.307	0,0,0
		0.5	10.351,19.900,152.718	0,0,0
K-均值法（K = 3）	3	0.25	11.777,296.288,12.410	0,0,0
		0.25	20.467,192.899,354.307	0,0,0
		0.5	10.351,19.900,152.718	0,0,0
K-均值法（K = 4）	4	0.25	11.777,296.288,12.410	0,0,0
		0.136	21.4211,209.428,388.063	4.66,8.57,9.53
		0.114	19.3326,173.233,314.144	5.54,10.2,11.34
		0.5	10.3508,19.900,152.718	0,0,0
GMM(F-J)法（K = 4）	4	0.25	11.777,296.288,12.410	0,0,0
		0.203	10.0372,15.8427,152.52	-2.84,-19.7,0.01
		0.25	20.467,192.899,354.307	0,0,0
		0.297	10.5662,22.6857,152.853	1.88,13.03,-0.05
GMM(F-J)法（K = 5）	4	0.25	11.777,296.288,12.410	0,0,0
		0.203	10.0372,15.8426,152.52	-3.03,-20.39,-0.13
		0.25	20.467,192.899,354.307	0,0,0
		0.297	10.5662,22.6857,152.853	2.08,14,0.09

项目	工况个数	每种工况的先验概率	每种工况下变量x₁, x₂, x₃的平均值	相对偏差
实际值	3	0.25	11.777,296.288,12.410	—
		0.25	20.467,192.899,354.307	—
		0.5	10.351,19.900,152.718	—
本文方法	3	0.25	11.777,296.288,12.410	0,0,0
		0.25	20.467,192.899,354.307	0,0,0
		0.5	10.351,19.900,152.718	0,0,0
K-均值法（K = 3）	3	0.25	11.777,296.288,12.410	0,0,0
		0.25	20.467,192.899,354.307	0,0,0
		0.5	10.351,19.900,152.718	0,0,0
K-均值法（K = 4）	4	0.25	11.777,296.288,12.410	0,0,0
		0.136	21.4211,209.428,388.063	4.66,8.57,9.53
		0.114	19.3326,173.233,314.144	5.54,10.2,11.34
		0.5	10.3508,19.900,152.718	0,0,0
GMM(F-J)法（K = 4）	4	0.25	11.777,296.288,12.410	0,0,0
		0.203	10.0372,15.8427,152.52	-2.84,-19.7,0.01
		0.25	20.467,192.899,354.307	0,0,0
		0.297	10.5662,22.6857,152.853	1.88,13.03,-0.05
GMM(F-J)法（K = 5）	4	0.25	11.777,296.288,12.410	0,0,0
		0.203	10.0372,15.8426,152.52	-3.03,-20.39,-0.13
		0.25	20.467,192.899,354.307	0,0,0
		0.297	10.5662,22.6857,152.853	2.08,14,0.09

项目	模态	G/H比例	产品生产率
第1组	1	50/50	7038 kg/h G和7038 kg/h H
第2组	2	10/90	1048 kg/h G和12669 kg/h H
第3组	3	90/10	10000 kg/h G 和1111 kg/h H
第4组	4	50/50	最大生产率
第5组	3	90/10	10000 kg/h G 和1111 kg/h H

项目	模态	G/H比例	产品生产率
第1组	1	50/50	7038 kg/h G和7038 kg/h H
第2组	2	10/90	1048 kg/h G和12669 kg/h H
第3组	3	90/10	10000 kg/h G 和1111 kg/h H
第4组	4	50/50	最大生产率
第5组	3	90/10	10000 kg/h G 和1111 kg/h H

项目	实际值	本文方法	K-均值法（K = 4）	K-均值法（K = 5）	K-均值法（K = 6）	GMM（F-J）法（K ≥ 4）
工况个数	4	4	4	5	6	无法得到参数
每种工况的先验概率	0.2	0.2	0.2	0.2	0.06	无法得到参数
	0.2	0.2	0.2	0.2	0.08
	0.4	0.4	0.4	0.106	0.06
	0.2	0.2	0.2	0.094	0.2
				0.4	0.4
					0.2