基于动态模式分解的精馏吸收状态变量非设计条件下的重构与预测

doi:10.11949/0438-1157.20230716

化工学报 ›› 2023, Vol. 74 ›› Issue (10): 4229-4240.DOI: 10.11949/0438-1157.20230716

基于动态模式分解的精馏吸收状态变量非设计条件下的重构与预测

党青梅¹(), 李强²(), 丁晖殿², 贾胜坤³, 钱行¹(), 苑杨¹, 黄克谨¹, 陈海胜¹

^1.北京化工大学信息科学与技术学院，北京 100029
^2.中石化石油化工科学研究院有限公司炼油工艺与催化剂国家工程研究中心，北京 102299
^3.天津大学化工学院，化学工程联合国家重点实验室，天津 300350

收稿日期:2023-07-10 修回日期:2023-09-10 出版日期:2023-10-25 发布日期:2023-12-22
通讯作者: 李强,钱行
作者简介:党青梅（1999—），女，硕士研究生，2021210499@buct.edu.cn
李强（1973—），男，教授级高级工程师，liq.ripp@sinopec.com
基金资助:
炼油工艺与催化剂国家工程研究中心（中石化石油化工科学研究院有限公司）开放基金项目

Reconstruction and prediction of distillation or absorption state variables under off-design conditions based on dynamic mode decomposition

Qingmei DANG¹(), Qiang LI²(), Huidian DING², Shengkun JIA³, Xing QIAN¹(), Yang YUAN¹, Kejin HUANG¹, Haisheng CHEN¹

^1.College of Information Science and Technology, Beijing University of Chemical Technology, Beijing 100029, China
^2.National Engineering Research Center for Petroleum Refining Technology and Catalyst, RIPP, SINOPEC, Beijing 102299, China
^3.State Key Laboratory of Chemical Engineering, School of Chemical Engineering and Technology, Tianjin University, Tianjin 300350, China

Received:2023-07-10 Revised:2023-09-10 Online:2023-10-25 Published:2023-12-22
Contact: Qiang LI, Xing QIAN

摘要/Abstract

摘要：

精馏和吸收作为典型的非线性过程，其操作过程中存在大量描述系统特征的状态变量。为了对这些状态变量进行重构和预测，实现精馏吸收过程的实时数字孪生，通过动态模式分解算法（DMD）获取非线性系统的近似线性化模型，用于快速获取精馏吸收过程中各级浓度、流量、温度和持料量等状态变量。在此基础上，应用Kalman滤波器对DMD生成的线性模型进行实时校正，使得在非设计和有限测量条件下，也可以有效地预测吸收或精馏的状态变量，而无须重新训练模型。

关键词: 非线性系统, 吸收, 精馏, 动态模式分解算法, 近似线性化, 重构, 预测

Abstract:

Distillation and absorption, as typical nonlinear processes, have a large number of state variables that describe the characteristics of the system during their operation. In order to reconstruct and predict these state variables and realize the real-time digital twin of the distillation and absorption process, this paper obtains an approximate linearized model of the nonlinear system by the dynamic mode decomposition method (DMD), which is used to quickly obtain the state variables such as concentration, flow rate, temperature and holding capacity at each tray of the distillation and absorption process. Based on this, a Kalman filter is applied to correct the linear model generated by DMD in real time, which makes it possible to predict the state variables of absorption or distillation effectively without retraining the model even under off-design and limited measurement conditions.

Key words: nonlinear systems, absorption, distillation, dynamic mode decomposition method, approximate linearization, reconstruction, prediction

中图分类号:

TQ 028.8

党青梅, 李强, 丁晖殿, 贾胜坤, 钱行, 苑杨, 黄克谨, 陈海胜. 基于动态模式分解的精馏吸收状态变量非设计条件下的重构与预测[J]. 化工学报, 2023, 74(10): 4229-4240.

Qingmei DANG, Qiang LI, Huidian DING, Shengkun JIA, Xing QIAN, Yang YUAN, Kejin HUANG, Haisheng CHEN. Reconstruction and prediction of distillation or absorption state variables under off-design conditions based on dynamic mode decomposition[J]. CIESC Journal, 2023, 74(10): 4229-4240.

图/表 14

图1 基于Koopman算子的系统演进示意图

Fig.1 Schematic diagram of the evolution of the system based on the Koopman operator

图2 吸收塔案例

Fig.2 The absorption tower case

图3 吸收案例重构和预测结果

Fig.3 The reconstructed and predicted results for absorption case

图4 非设计条件下X(7)的响应曲线和进料变化曲线

Fig.4 The response curves of X(7) and the feed variation curves under off-design conditions

图5 吸收案例非设计条件下采用温度校正的预测结果

Fig.5 The prediction results with temperature correction under off-design conditions for absorption case

表1 不同情况下近似线性化模型预测的平均相对误差值

Table 1 Average relative error values of approximate linearized model predictions for different cases

状态变量	平均相对误差
状态变量	振幅减小10%	偏差减小10	振幅随机变化	添加噪声	输入随机变化
X(7)	$7.00 × 10 - 4$	$3.68 × 10 - 2$	$1.12 × 10 - 2$	$5.03 × 10 - 2$	$5.66 × 10 - 2$

表1 不同情况下近似线性化模型预测的平均相对误差值

Table 1 Average relative error values of approximate linearized model predictions for different cases

状态变量	平均相对误差
状态变量	振幅减小10%	偏差减小10	振幅随机变化	添加噪声	输入随机变化
X(7)	$7.00 × 10 - 4$	$3.68 × 10 - 2$	$1.12 × 10 - 2$	$5.03 × 10 - 2$	$5.66 × 10 - 2$

图6 二元精馏塔案例

Fig.6 The binary distillation tower case

表2 二元精馏塔温度控制器的调谐参数

Table 2 Controller tuning parameters of PI for the binary distillation column

控制器	被控变量	操纵变量	增益	积分时间/min
TC1	T₁₅	L	12.720	5.190
TC2	T₂₉	S1	6.280	10.920

图7 精馏案例重构和预测结果

Fig.7 The reconstructed and predicted results for distillation case

表3 近似线性化模型重构和预测的相对误差平均值

Table 3 Average relative errors of reconstruction and prediction of the approximate linearized model

状态变量	浓度校正相对误差平均值	温度校正相对误差平均值
X(109)	$2.69 × 10 - 5$	$2.88 × 10 - 5$
X(137)	$3.53 × 10 - 6$	$1.04 × 10 - 5$

表3 近似线性化模型重构和预测的相对误差平均值

Table 3 Average relative errors of reconstruction and prediction of the approximate linearized model

状态变量	浓度校正相对误差平均值	温度校正相对误差平均值
X(109)	$2.69 × 10 - 5$	$2.88 × 10 - 5$
X(137)	$3.53 × 10 - 6$	$1.04 × 10 - 5$

图8 非设计条件下系统输入的变化曲线

Fig.8 Variation curves of system inputs under off-design conditions

图9 精馏案例非设计条件下采用温度校正的预测结果

Fig.9 The prediction results with temperature correction under off-design conditions for distillation case

表4 不同情况下近似线性化模型预测的平均相对误差值

Table 4 Average relative error values of approximate linearized model predictions for different cases

状态变量	平均相对误差
状态变量	振幅减小10%	偏差减小1%	振幅随机变化	输入随机变化
X(109)	$1.90 × 10 - 3$	$2.89 × 10 - 2$	$1.23 × 10 - 2$	$6.15 × 10 - 2$
X(137)	$2.50 × 10 - 3$	$1.14 × 10 - 2$	$1.15 × 10 - 2$	$3.12 × 10 - 2$

表4 不同情况下近似线性化模型预测的平均相对误差值

Table 4 Average relative error values of approximate linearized model predictions for different cases

状态变量	平均相对误差
状态变量	振幅减小10%	偏差减小1%	振幅随机变化	输入随机变化
X(109)	$1.90 × 10 - 3$	$2.89 × 10 - 2$	$1.23 × 10 - 2$	$6.15 × 10 - 2$
X(137)	$2.50 × 10 - 3$	$1.14 × 10 - 2$	$1.15 × 10 - 2$	$3.12 × 10 - 2$

图10 非设计条件下采用温度校正的预测结果

Fig.10 The prediction results with temperature correction under off-design conditions

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基于动态模式分解的精馏吸收状态变量非设计条件下的重构与预测

Reconstruction and prediction of distillation or absorption state variables under off-design conditions based on dynamic mode decomposition

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