Soft Sensor Modeling Based on Adaptive Sparse Broad Learning System

doi:10.16182/j.issn1004731x.joss.24-0096

Abstract

Abstract:

To address the challenges posed by nonlinearity and the coupling of multiple features in complex industrial processes, resulting in increased model complexity and decreased performance, a soft sensor modeling method based on adaptive sparse broad learning system is proposed. Building upon the lateral enhancement transmission of features, the trace least absolute shrinkage and selection operator (LASSO) is further used to optimize the feature weights of the network, adaptively adjusting the penalty intensity based on the correlation between different variables to enhance the feature extraction capabilities of the model.The Dropout mechanism is introduced in the enhanced part, and the output weights are utilized by LASSO to sparsely optimize the model as a whole, eliminating excess nodes, and reducing redundant data in the calculation process. Experimental results show that the proposed method can effectively simplify the model structure and improve its prediction performance.

Key words: soft sensor, broad learning system, trace least absolute shrinkage and selection operator (LASSO), regularization, sparse model

CLC Number:

TP274

Du Kangping, Sui Lin, Xiong Weili. Soft Sensor Modeling Based on Adaptive Sparse Broad Learning System[J]. Journal of System Simulation, 2025, 37(6): 1449-1461.

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模型	预测变量	特征窗口数	各窗口特征节点数	增强节点数	特征层正则化参数	增强层Dropout率	输出层正则化参数
BLS	DBO-S	16	13	100	1^-4	—	2^-30
	DQO-S	7	14	263	1^-4	—	2^-30
	SS-S	13	12	118	1^-4	—	2^-30
L1BLS	DBO-S	16	13	100	1^-4	—	2^-2
	DQO-S	7	14	263	1^-4	—	2^-4
	SS-S	13	12	118	1^-4	—	2^-5
ENBLS	DBO-S	16	13	100	1^-4	—	2^-2, 2^-5
	DQO-S	7	14	263	1^-4	—	2^-4, 2^-5
	SS-S	13	12	118	1^-4	—	2^-5, 2^-5
TL-BLS	DBO-S	16	13	100	1^-4	0.05	2^-2
	DQO-S	7	14	263	1^-4	0	2^-4
	SS-S	13	12	118	1^-4	0.3	2^-5

模型	预测变量	RMSE		MAPE		R²		实际节点数
模型	预测变量	训练集	测试集	训练集	测试集	训练集	测试集	实际节点数
BLS	DBO-S	0.741 9	5.847 0	0.026 4	0.118 0	0.996 2	0.669 6	308
	DQO-S	<10^-4	8.078 1	<10^-6	0.038 4	1.000 0	0.941 3	361
	SS-S	2.009 8	40.678 1	0.059 9	0.670 9	0.983 5	-15.355 9	274
L1BLS	DBO-S	1.520 3	3.718 5	0.057 7	0.112 8	0.984 1	0.866 4	127
	DQO-S	1.231 3	4.140 1	0.010 8	0.030 8	0.999 0	0.984 6	262
	SS-S	3.385 9	5.374 8	0.104 0	0.201 6	0.953 3	0.714 4	260
ENBLS	DBO-S	1.716 7	3.976 7	0.065 5	0.133 6	0.979 7	0.847 2	136
	DQO-S	1.655 0	4.383 5	0.014 2	0.033 4	0.998 2	0.982 7	301
	SS-S	3.870 3	5.598 8	0.117 4	0.215 7	0.939 0	0.690 1	254
TL-BLS	DBO-S	1.891 9	1.676 6	0.072 6	0.068 7	0.975 3	0.972 8	166
	DQO-S	1.094 6	2.539 3	0.009 1	0.021 0	0.999 2	0.994 2	236
	SS-S	3.164 1	3.748 7	0.101 2	0.148 2	0.959 2	0.861 1	270

模型	预测变量	RMSE		MAPE		R²		实际节点数
模型	预测变量	训练集	测试集	训练集	测试集	训练集	测试集	实际节点数
无迹LASSO	DBO-S	1.896 5	2.389 5	0.073 6	0.095 4	0.975 2	0.944 8	168
	DQO-S	1.231 3	4.140 1	0.010 7	0.030 8	0.999 0	0.984 6	262
	SS-S	3.178 9	6.598 0	0.104 0	0.286 9	0.958 8	0.569 7	272
无Dropout	DBO-S	1.658 0	2.434 2	0.061 5	0.090 5	0.981 1	0.942 7	129
	DQO-S	1.094 6	2.539 3	0.009 1	0.021 0	0.999 2	0.994 2	236
	SS-S	3.067 0	7.296 6	0.095 7	0.219 8	0.961 7	0.473 7	254
无LASSO	DBO-S	3.102 2	3.445 4	0.116 7	0.122 2	0.933 7	0.885 3	308
	DQO-S	2.009 8	3.031 7	0.015 9	0.026 1	0.997 3	0.991 7	361
	SS-S	3.498 1	4.739 9	0.112 8	0.191 8	0.950 1	0.777 9	274
TL-BLS	DBO-S	1.891 9	1.676 6	0.072 6	0.068 7	0.975 3	0.972 8	171
	DQO-S	1.094 6	2.539 3	0.009 1	0.021 0	0.999 2	0.994 2	236
	SS-S	3.164 1	3.748 7	0.101 2	0.148 2	0.959 2	0.861 1	270

参数名称	MLP	RNN	LSTM
输入维度	30	30	30
网络隐含层数	1	1	1
隐含层节点数	10	10	128
输出维度	1	1	1
学习率	0.001	0.001	0.005
最大迭代次数	1 000	1 000	500

参数名称	BLS	L1BLS	ENBLS	TL-BLS
特征窗口数	8	8	8	8
各窗口特征节点数	8	8	8	8
增强节点数	224	224	224	224
特征层正则化参数	1^-4	1^-4	1^-4	1^-4
Dropout率	—	—	—	0.4
输出层正则化参数	2^-30	2^-5	2^-5, 2^-5	2^-5