基于过采样结构的贝叶斯鲁棒辨识方法

doi:10.11949/0438-1157.20190880

摘要/Abstract

摘要：

在实际工业过程中，异常值的干扰是不可避免的，现有的处理异常值方法会导致模型估计有偏差，并且没有考虑潜在异常值的影响。针对上述缺点，利用学生分布噪声来处理潜在异常值，提出一种适用于学生分布噪声情况的贝叶斯鲁棒辨识方法，并且将其与过采样结构相结合，推出了基于过采样结构的贝叶斯鲁棒辨识方法。仿真实验表明：本文提出的算法，随着异常值影响的增加，仍然保持较小的辨识误差，而传统辨识方法已不再适用，同时，还克服了传统结构需添加额外测试信号所带来的巨额成本。因此，本文的算法更适合于实际工业过程辨识。

关键词: 异常值, 学生分布噪声, 贝叶斯变分法, 鲁棒辨识, 过采样结构

Abstract:

In the actual industrial process, the interference of outliers is inevitable. Existing methods of dealing with outliers can cause bias in model estimates and do not take into account the effects of potential outliers. In view of the above shortcomings, using student distributed noise to deal with potential outliers, this paper proposes a variational Bayesian method based on student distribution noise, and combines it with over-sampling structure to introduce a variational Bayesian method to robust identification based on over-sampling structure. The simulation experiments show when the outlier has a large influence, it still maintains a small identification error, while the traditional identification method is no longer applicable, and it also overcomes the huge cost of adding additional test signals to the traditional structure. Therefore, the algorithm in this paper is more suitable for practical industrial process identification.

Key words: outliers, student distributed noise, variational Bayesian method, robust identification, over-sampling structure

中图分类号:

TP 273

徐宝昌, 白振轩, 王雅欣, 袁力坤. 基于过采样结构的贝叶斯鲁棒辨识方法[J]. 化工学报, 2019, 70(12): 4673-4679.

Baochang XU, Zhenxuan BAI, Yaxin WANG, Likun YUAN. A variational Bayesian method to robust identification based on over-sampling structure[J]. CIESC Journal, 2019, 70(12): 4673-4679.

图/表 6

图1 过采样结构图

Fig.1 Oversampling structural diagram

图2 当Kp=0.05时贝叶斯变分法相对误差曲线

Fig.2 Relative error curve of Bayesian variational method when Kp=0.05

图3 当Kp=0.05时递推最小二乘法相对误差曲线

Fig.3 Relative error curve of RLS method when Kp=0.05

表1 当Kp=0.05时贝叶斯变分法与递推最小二乘法辨识结果

Table 1 Identification results of Bayesian variational method and recursive least squares method when Kp=0.05

Algorithm	$a Δ, 1$	$a Δ, 2$	$b Δ, 1$	$b Δ, 2$	$σ$ /%
VB	-0.9927	0.0943	0.0556	-0.0107	0.3023
RELS	-0.9893	0.1065	-0.1102	-0.1629	21.12
真值	-0.9937	0.0967	0.0267	-0.0027	—

表1 当Kp=0.05时贝叶斯变分法与递推最小二乘法辨识结果

Table 1 Identification results of Bayesian variational method and recursive least squares method when Kp=0.05

Algorithm	$a Δ, 1$	$a Δ, 2$	$b Δ, 1$	$b Δ, 2$	$σ$ /%
VB	-0.9927	0.0943	0.0556	-0.0107	0.3023
RELS	-0.9893	0.1065	-0.1102	-0.1629	21.12
真值	-0.9937	0.0967	0.0267	-0.0027	—

图4 当Kp=0.05时模型1与模型2重复性辨识实验相对曲线

Fig.4 Relative curves of model 1 and model 2 repeatability identification experiments when Kp=0.05

图5 当0.05≤Kp≤1时VB与RLS相对误差变化曲线

Fig.5 Relative error change curve of time VB and RLS when 0.05≤Kp≤1

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