Fault detection using hierarchical variational Gaussian mixture model and principal polynomial analysis

doi:10.11949/0438-1157.20200793

Abstract

Abstract:

Aiming at the problem that the number of modes is difficult to determine in multi-modal industrial processes, a hierarchical variational Gaussian mixture model (HVGMM) is proposed. Based on this, principal polynomial analysis (PPA) was used for multimode nonlinear processes fault detection. Firstly, the variational Bayesian Gaussian mixture model (VBGMM) was used as the initial model to decompose the process data to obtain the initial number of condition modes, and the process was decomposed into sub-blocks according to the initial number of modes. Secondly, the VBGMM containing multiple local models was used to decompose each sub-block into subsidiary sub-blocks, and the information such as mean and precision matrix of subsidiary sub-blocks was used to reconstruct the VBGMM. After that, the reconstructed VBGMM was used again as the initial model to decompose the original process data, and the above steps are repeated until the reconstructed VBGMM cannot decompose each sub-block. Finally, multiple local PPA models were established in each sub-block, and T² and SPEstatistics were calculated in each local model for fault detection. Through a numerical example and the Tennessee Eastman (TE) process, the simulation result demonstrates that HVGMM-PPA outperformed conventional PCA and PPA techniques in the monitoring rate.

Key words: principal component analysis, variational Bayesian Gaussian mixture model, fault detection, process control, multimode processes, parameter estimation

摘要：

针对多模态工业过程中模态数量难以确定问题，提出一种层次变分高斯混合模型（hierarchical variational Gaussian mixture model， HVGMM）。在此基础上，使用主多项式分析（principal polynomial analysis， PPA）用于多模态非线性过程故障检测。首先，变分贝叶斯高斯混合模型（variational Bayesian Gaussian mixture model， VBGMM）作为初始模型用于分解过程数据得到工作模态的初始数量，将过程按初始数量分解为多个子块；其次，应用包含多个局部模型的VBGMM将各子块分解为附属子块，并利用附属子块的均值、精度等信息对VBGMM进行重构；然后，将重构后的VBGMM作为初始模型再次用于分解原始过程数据，重复上述步骤直至重构VBGMM无法分解各子块时停止；最后，分别在各附属子块中建立局部PPA模型，并在每个局部模型中计算T²和SPE统计量进行故障检测。将该方法应用于数值例子和Tennessee Eastman（TE）化工过程，并将仿真结果与主元分析（principal component analysis， PCA）、PPA进行对比，验证了所提出方法的有效性。

关键词: 主元分析, 变分贝叶斯高斯混合模型, 故障检测, 过程控制, 多模态过程, 参数估值

CLC Number:

LI Yuan, YANG Dongsheng, ZHAO Liying, ZHANG Cheng. Fault detection using hierarchical variational Gaussian mixture model and principal polynomial analysis[J]. CIESC Journal, 2021, 72(3): 1616-1626.

李元, 杨东昇, 赵丽颖, 张成. 层次变分高斯混合模型与主多项式分析的故障检测策略[J]. 化工学报, 2021, 72(3): 1616-1626.

Figures/Tables 21

References 32

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模态	G/H比例	生产率
1	50/50	7038 kg/h G 和7038 kg/h H
2	10/90	1408 kg/h G 和12669 kg/h H
3	90/10	10000 kg/h G 和1111 kg/h H
4	50/50	Maximum
5	10/90	Maximum
6	90/10	Maximum

模态	G/H比例	生产率
1	50/50	7038 kg/h G 和7038 kg/h H
2	10/90	1408 kg/h G 和12669 kg/h H
3	90/10	10000 kg/h G 和1111 kg/h H
4	50/50	Maximum
5	10/90	Maximum
6	90/10	Maximum

No.	变量	No.	变量
X₁	A物料流量	X₁₈	汽提塔温度
X₂	D物料流量	X₁₉	汽提塔蒸汽流量
X₃	E物料流量	X₂₀	压缩机工作功率
X₄	A、C混合物料流量	X₂₁	反应器冷却水出口温度
X₅	回收流量	X₂₂	分离器冷却水出口温度
X₆	反应器进料率	X₂₃	D流量
X₇	反应器压力	X₂₄	E流量
X₈	反应器液位	X₂₅	A流量
X₉	反应器温度	X₂₆	AC混合流量
X₁₀	放空率	X₂₇	压缩循环阀控制量
X₁₁	产品分离器温度	X₂₈	放空阀控制量
X₁₂	产品分离器液位	X₂₉	分离器液体流量
X₁₃	产品分离器压力	X₃₀	汽提塔液体流量
X₁₄	产品分离器出口流量	X₃₁	汽提塔蒸汽阀控制量
X₁₅	汽提塔液位	X₃₂	反应器冷凝水流量
X₁₆	汽提塔压力	X₃₃	冷凝器冷却水流量
X₁₇	汽提塔出口流量

No.	变量	No.	变量
X₁	A物料流量	X₁₈	汽提塔温度
X₂	D物料流量	X₁₉	汽提塔蒸汽流量
X₃	E物料流量	X₂₀	压缩机工作功率
X₄	A、C混合物料流量	X₂₁	反应器冷却水出口温度
X₅	回收流量	X₂₂	分离器冷却水出口温度
X₆	反应器进料率	X₂₃	D流量
X₇	反应器压力	X₂₄	E流量
X₈	反应器液位	X₂₅	A流量
X₉	反应器温度	X₂₆	AC混合流量
X₁₀	放空率	X₂₇	压缩循环阀控制量
X₁₁	产品分离器温度	X₂₈	放空阀控制量
X₁₂	产品分离器液位	X₂₉	分离器液体流量
X₁₃	产品分离器压力	X₃₀	汽提塔液体流量
X₁₄	产品分离器出口流量	X₃₁	汽提塔蒸汽阀控制量
X₁₅	汽提塔液位	X₃₂	反应器冷凝水流量
X₁₆	汽提塔压力	X₃₃	冷凝器冷却水流量
X₁₇	汽提塔出口流量

No.	PCA		PPA		HVGMM-PPA
No.	T²	SPE	T²	SPE	T²	SPE
IDV1	0.5	0.99	0.6	0.99	1	1
IDV2	0.48	0.57	0.15	0.64	0.89	0.99
IDV3	0.01	0.01	0.01	0.02	0.04	0.03
IDV4	0.5	1	0.04	1	0.95	1
IDV5	0.04	0.48	0.4	0.48	0.51	0.52
IDV6	0.52	1	0.98	1	1	1
IDV7	0.37	0.22	0.03	0.91	1	1
IDV8	0.41	0.94	0.82	0.93	0.98	0.99
IDV9	0.01	0.04	0.03	0.05	0.1	0.13
IDV10	0.02	0.04	0.04	0.04	0.72	0.92
IDV11	0.19	0.45	0.12	0.46	0.71	0.93
IDV12	0.16	0.51	0.47	0.53	0.68	0.72
IDV13	0.3	0.9	0.85	0.85	0.93	0.93
IDV14	0.38	0.67	0.02	0.79	0.71	1
IDV15	0.02	0.01	0.01	0.01	0.04	0.05
IDV16	0.01	0.01	0.01	0.01	0.03	0.03
IDV17	0.21	0.69	0.08	0.74	0.87	0.94
IDV18	0.2	0.49	0.47	0.44	0.76	0.86
IDV19	0.03	0.5	0.26	0.35	0.94	1
IDV20	0.29	0.84	0.72	0.79	0.89	0.95
IDV21	0.01	0.01	0.01	0.01	0.02	0.02