基于LVW-LM-QN算法的Wiener系统辨识

doi:10.12068/j.issn.1005-3026.2025.20240061

摘要/Abstract

摘要：

Wiener系统由线性动态子系统与静态非线性子系统串联组成，广泛应用于石油、化工等过程工业中，获得Wiener系统的模型具有重要意义.本文针对Wiener系统提出一种基于线性变化权重-列文伯格马夸尔特-拟牛顿(linear variable weight-Levenberg Marquardt-quasi Newton，LVW-LM-QN)算法的非线性系统辨识方法.将Wiener系统分成两个子系统分别处理，对于线性动态部分，采用规范变量分析(canonical variate analysis，CVA)算法的子空间识别方法进行参数估计；对于非线性静态部分，采用LVW-LM-QN算法进行辨识处理.最后通过数值例子和双储罐系统液位控制的应用案例来评估该方法，仿真结果验证了所提方法的有效性和精确性.

关键词: Wiener系统, 子空间方法, LVW-LM-QN算法, 神经网络, CVA算法

Abstract:

Wiener systems， consisting of a linear dynamic subsystem and a static nonlinear subsystem in series， find extensive application in process industries such as petroleum and chemical engineering. Obtaining the model of Wiener systems holds significant importance. A nonlinear system identification method based on the linear variable weight–Levenberg Marquardt–quasi Newton （LVW-LM-QN） algorithm for Wiener systems was proposed. The Wiener system was divided into two subsystems for separate processing. For the linear dynamic part， the subspace identification method with the canonical variate analysis （CVA） algorithm was used for parameter estimation， whereas for the subsequent nonlinear static part， the LVW-LM-QN algorithm was employed for identification. Finally， the method was evaluated through numerical examples and an application case of liquid level control in a two-tank system， and the effectiveness and accuracy of the proposed method were verified by the simulation results.

Key words: Wiener system, subspace method, LVW-LM-QN algorithm, neural network, CVA algorithm

中图分类号:

N 945.14

于淼, 汪万里, 魏永涛. 基于LVW-LM-QN算法的Wiener系统辨识[J]. 东北大学学报（自然科学版）, 2025, 46(10): 27-35.

Miao YU, Wan-li WANG, Yong-tao WEI. Identification of Wiener Systems Based on LVW-LM-QN Algorithm[J]. Journal of Northeastern University(Natural Science), 2025, 46(10): 27-35.

图/表 11

图1 Wiener 系统框图

Fig.1 Block diagram of Wiener system

图2 非线性子系统为神经网络的Wiener模型

Fig.2 Wiener model of nonlinear subsystem as a neural network

表1 Wiener系统LVW-LM-QN辨识算法 (for Wiener system)

Table 1 LVW-LM-QN identification algorithm

常量初始化：迭代最大值k_max，神经元权重 w₁， w₂，偏置参数b₁，b₂，算法停止标准e₁，e₂，学习率最值α_max，α_min， $μ$ 值,矩阵 B

found= $g (k) ∞ ≤ e 1$

While(not found)and(k $≤$ k_max)

k=k+1;

通过式(42)计算学习率

if method=LM

通过式(38)计算h_1m

初始化信赖域半径Δ

if $h 1 m ≤ e 2 w + e 2$

found=true

else

通过式(43)更新w

通过式(45)计算增益率 $ρ$

if $ρ$ $>$ 0

better=true

if连续3次迭代都满足式(47)，

则method切换到QN

end if

更新 $μ$ 值

end if

else if method=QN

通过式(40)计算

if $h q n ≤ e 2 w + e 2$

found=true

表1 Wiener系统LVW-LM-QN辨识算法 (for Wiener system)

Table 1 LVW-LM-QN identification algorithm

常量初始化：迭代最大值k_max，神经元权重 w₁， w₂，偏置参数b₁，b₂，算法停止标准e₁，e₂，学习率最值α_max，α_min， $μ$ 值,矩阵 B

found= $g (k) ∞ ≤ e 1$

While(not found)and(k $≤$ k_max)

k=k+1;

通过式(42)计算学习率

if method=LM

通过式(38)计算h_1m

初始化信赖域半径Δ

if $h 1 m ≤ e 2 w + e 2$

found=true

else

通过式(43)更新w

通过式(45)计算增益率 $ρ$

if $ρ$ $>$ 0

better=true

if连续3次迭代都满足式(47)，

则method切换到QN

end if

更新 $μ$ 值

end if

else if method=QN

通过式(40)计算

if $h q n ≤ e 2 w + e 2$

found=true

图3 所提辨识方法框图

Fig.3 Block diagram of proposed identification method

ξ（k）=（k）+0.3［（k）］2+0.4［（k）］3，

图4 Wiener系统的输入输出数据

Fig.4 Input and output data of Wiener system

图5 Wiener系统和不同方法的输出信号

Fig.5 Output signals of Wiener system and different methods

表2 不同识别方法的均方根误差及平均绝对百分比误差 (methods)

Table 2 RMSE and MAPE of different identification

方法	RMSE	MAPE
Subspace-based	10.574 6	7.377 9
LM	1.627 3	1.281 1
LVW-LM-QN	0.497 4	0.317 1

图6 双储罐系统的输入输出数据

Fig.6 Input and output data of two-tank system

图7 双储罐系统和不同方法的输出信号

Fig.7 Output signals of two-tank system and different methods

表3 不同识别方法的均方根误差及平均绝对百分比误差 (methods)

Table 3 RMSE and MAPE of different identification

方法	RMSE	MAPE
Subspace-based	0.116 6	0.627 7
LM	0.123 2	0.854 3
LVW-LM-QN	0.042 5	0.242 7

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