A BiLSTM-based soft sensing modeling method with distributed nonlinear mapping and parallel inputs

doi:10.11949/0438-1157.20241514

Abstract

Abstract:

Actual chemical industry process data often have multiple characteristics such as multicollinearity and high nonlinearity, which will seriously affect the prediction accuracy of traditional soft sensor models for key quality variables. To address these limitations, this study proposes a novel soft-sensing model based on distributed nonlinear mapping and parallel input bidirectional long short-term memory (DNMPI-BiLSTM). In the proposed approach, mutual information and maximum relevance minimum redundancy methods are first employed to differentiate and select input datasets, thereby elucidating the relationships between process variables and quality indicators. Subsequently, to capture the highly complex nonlinear relationships inherent in industrial processes, the hidden layers of a deep extreme learning machine are utilized to perform nonlinear mappings of subprocess variable spaces into high-dimensional spaces. The nonlinear mapping results of three categories of data are then processed in parallel to establish the DNMPI-BiLSTM model with distributed nonlinear mapping and parallel inputs. This model enhances the predictive capability for quality indicators in complex industrial processes. The effectiveness of the proposed method was validated through three industrial case studies. Simulation results demonstrate that the proposed BiLSTM-based soft sensing modeling approach, which incorporates distributed nonlinear mapping and parallel input, achieves superior prediction accuracy compared to other advanced models.

Key words: bidirectional long short-term memory, soft sensor, deep extreme learning machine, distributed input, nonlinear mapping

摘要：

实际化工工业过程数据往往存在多重共线性、高度非线性等多重特性，这会严重影响传统软测量模型对关键质量变量的预测精度。针对这一局限性，提出了一种分布式非线性映射和并行输入的双向长短记忆（distributed nonlinear mapping and parallel input bidirectional long short-term memory，DNMPI-BiLSTM）软测量模型。在所提策略中，首先为了阐述过程变量与质量变量之间的关联性，采用互信息以及最大相关最小冗余方法对输入数据集进行分类。随后，为了充分挖掘工业过程内部所包含的高度复杂的非线性关系，利用深度极限学习机的隐藏层对子过程变量空间进行非线性映射到高维空间。最后，将三类数据的非线性映射结果并行，建立了基于分布式非线性映射和并行输入的DNMPI-BiLSTM软测量模型，以提升模型对复杂工业过程质量变量的预测能力。通过三个工业案例验证所提方法的有效性，仿真结果表明，所提出的基于分布式非线性映射和并行输入的BiLSTM软测量建模方法的预测精度优于其他先进模型。

关键词: 双向长短期记忆, 软测量, 深度极限学习机, 分布式输入, 非线性映射

CLC Number:

TP 273

Yihan LIU, Yan WANG, Hao MA, Tuanjie WANG, Cuihong DAI. A BiLSTM-based soft sensing modeling method with distributed nonlinear mapping and parallel inputs[J]. CIESC Journal, 2025, 76(7): 3373-3387.

刘翌晗, 王艳, 马浩, 王团结, 戴翠红. 基于分布式非线性映射和并行输入的BiLSTM软测量建模方法[J]. 化工学报, 2025, 76(7): 3373-3387.

Figures/Tables 18

Fig.1 DNMPI-BiLSTM soft sensing model

Fig.2 Structure of the DELM

Fig.3 Structure of the BiLSTM

Table 1 Description of the variables for the DC

输入	变量描述
$x 1$	顶部温度
$x 2$	顶部压强
$x 3$	回流流量
$x 4$	流向下一工艺的流量
$x 5$	第6层板的温度
$x 6$	底部温度A
$x 7$	底部温度B

Table 1 Description of the variables for the DC

输入	变量描述
$x 1$	顶部温度
$x 2$	顶部压强
$x 3$	回流流量
$x 4$	流向下一工艺的流量
$x 5$	第6层板的温度
$x 6$	底部温度A
$x 7$	底部温度B

Table 2 Prediction performance of six soft sensing models in the DC dataset

模型	MAE	RMSE	$R 2$
GRU	0.04439	0.0621	0.887
LSTM	0.04099	0.0525	0.921
BiLSTM	0.03353	0.0465	0.938
PSO-BiLSTM	0.03172	0.0448	0.942
NM-BiLSTM	0.01867	0.0280	0.977
DNMPI-BiLSTM	0.00581	0.0088	0.997

Table 2 Prediction performance of six soft sensing models in the DC dataset

模型	MAE	RMSE	$R 2$
GRU	0.04439	0.0621	0.887
LSTM	0.04099	0.0525	0.921
BiLSTM	0.03353	0.0465	0.938
PSO-BiLSTM	0.03172	0.0448	0.942
NM-BiLSTM	0.01867	0.0280	0.977
DNMPI-BiLSTM	0.00581	0.0088	0.997

Fig.4 Predicted results of the six soft sensing models in the DC

Fig.5 Predicted errors of the six soft sensing models in the DC

Fig.6 Predicted error box plot of the six soft sensing methods in the DC

Table 3 Description of the variables for the SRU

输入	变量描述
$x 1$	MEA气体流量
$x 2$	MEA一次气流
$x 3$	MEA二次气流
$x 4$	SWS气体流量
$x 5$	SWS气流
$y$	SO₂浓度

Table 3 Description of the variables for the SRU

输入	变量描述
$x 1$	MEA气体流量
$x 2$	MEA一次气流
$x 3$	MEA二次气流
$x 4$	SWS气体流量
$x 5$	SWS气流
$y$	SO₂浓度

Table 4 Prediction performance of six different soft sensing models in the SRU dataset

模型	MAE	RMSE	$R 2$
GRU	0.01612	0.0221	0.856
LSTM	0.01233	0.0178	0.905
BiLSTM	0.01059	0.0170	0.914
PSO-BiLSTM	0.00959	0.0166	0.918
NM-BiLSTM	0.00792	0.0145	0.938
DNMPI-BiLSTM	0.00503	0.0135	0.946

Table 4 Prediction performance of six different soft sensing models in the SRU dataset

模型	MAE	RMSE	$R 2$
GRU	0.01612	0.0221	0.856
LSTM	0.01233	0.0178	0.905
BiLSTM	0.01059	0.0170	0.914
PSO-BiLSTM	0.00959	0.0166	0.918
NM-BiLSTM	0.00792	0.0145	0.938
DNMPI-BiLSTM	0.00503	0.0135	0.946

Fig.7 Predicted results of the six soft sensing models in the SRU

Fig.8 Predicted errors of the six soft sensing models in the SRU

Fig.9 Predicted error box plot of the six soft sensing methods in the SRU

Fig.10 Process flow diagram for honeysuckle extracting process

Table 5 Prediction performance of six soft sensing models in the extraction process of honeysuckle

模型	MAE	RMSE	$R 2$
GRU	0.02610	0.0353	0.856
LSTM	0.02021	0.0282	0.921
BiLSTM	0.01819	0.0268	0.929
PSO-BiLSTM	0.01702	0.0254	0.936
NM-BiLSTM	0.01379	0.0190	0.964
DNMPI-BiLSTM	0.01149	0.0162	0.974

Table 5 Prediction performance of six soft sensing models in the extraction process of honeysuckle

模型	MAE	RMSE	$R 2$
GRU	0.02610	0.0353	0.856
LSTM	0.02021	0.0282	0.921
BiLSTM	0.01819	0.0268	0.929
PSO-BiLSTM	0.01702	0.0254	0.936
NM-BiLSTM	0.01379	0.0190	0.964
DNMPI-BiLSTM	0.01149	0.0162	0.974

Fig.11 Predicted results of the six soft sensing models in the extraction process of honeysuckle

Fig.12 Predicted errors of the six soft sensing models in the extraction process of honeysuckle

Fig.13 Predicted error box plot of the six soft sensing methods in the extraction process of honeysuckle

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