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

doi:10.11949/0438-1157.20230716

Abstract

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

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

CLC Number:

TQ 028.8

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.

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.

Figures/Tables 14

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

Fig.2 The absorption tower case

Fig.3 The reconstructed and predicted results for absorption case

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

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

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)	$7.00 × 10 - 4$	$3.68 × 10 - 2$	$1.12 × 10 - 2$	$5.03 × 10 - 2$	$5.66 × 10 - 2$

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)	$7.00 × 10 - 4$	$3.68 × 10 - 2$	$1.12 × 10 - 2$	$5.03 × 10 - 2$	$5.66 × 10 - 2$

Fig.6 The binary distillation tower case

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

Fig.7 The reconstructed and predicted results for distillation case

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)	$3.53 × 10 - 6$	$1.04 × 10 - 5$

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)	$3.53 × 10 - 6$	$1.04 × 10 - 5$

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

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

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)	$2.50 × 10 - 3$	$1.14 × 10 - 2$	$1.15 × 10 - 2$	$3.12 × 10 - 2$

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)	$2.50 × 10 - 3$	$1.14 × 10 - 2$	$1.15 × 10 - 2$	$3.12 × 10 - 2$

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

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