缺失输出数据的Hammerstein系统：新颖EM识别方法

130 浏览量更新于2024-08-27 收藏 1.18MB PDF 举报

本文探讨了一种针对缺失输出数据的Hammerstein系统进行新颖估计的方法，发表在2020年4月的《IEEE Transactions on Industrial Informatics》第16卷第4期上。作者们针对实际系统中存在的非线性特性，提出了一个基于辅助模型的期望最大化（EM）识别算法，以扩展传统的EM方法，适应处理具有多个参数向量的模型。传统的Hammerstein系统识别通常依赖于完整的输入输出数据，但在许多实际应用中，数据可能会丢失或不完整。为解决这一问题，该研究者们设计了一个创新的EM算法，它不再严格要求单一参数向量的自回归模型，而是通过将问题扩展到一个更一般的模型框架中来应对。在迭代过程中，他们利用一个辅助模型来估算缺失的输出数据，并将其融入信息向量中，从而减轻了数据不足对参数估计的影响。新算法的关键在于其交互式优化策略，即在多参数向量的期望最大化过程中，逐步提升模型的拟合能力。这种方法的优势在于能够更好地处理复杂的非线性关系，同时对缺失数据的敏感度降低，提高了识别的稳健性和准确性。为了验证这个新颖EM方法的有效性，研究者进行了数值模拟。实验结果显示，相比于传统方法，该算法在面对缺失输出数据时，不仅能够更准确地估计 Hammerstein 系统的参数，而且在系统建模和预测性能上表现优异。这项工作对于处理实际工业系统中常见的数据缺失问题具有重要意义，为 Hammerstein 系统的在线参数估计提供了一种有效的解决方案。这对于提高工业过程控制、故障诊断以及系统优化等领域具有实用价值。未来的研究可以进一步探索如何将此方法推广到其他类型的复杂系统中，以及如何处理不同类型的数据缺失情况。

2500 IEEE TRANSACTIONS ON INDUSTRIAL INFORMATICS, VOL. 16, NO. 4, APRIL 2020

A Novel EM Identiﬁcation Method for

Hammerstein Systems With Missing Output Data

Dongqing Wang , Shuo Zhang , Min Gan , and Jianlong Qiu

Abstract—This article concerns a novel auxiliary-model-

based expectation maximization (EM) estimation method for

Hammerstein systems with data loss by extending the EM

method to estimate models with multiple parameter vectors.

The novel EM method relaxes the requirements on an au-

toregression model with one parameter vector, interactively

maximizes the expectation over multiple parameter vectors

in a more general model, and uses the output of an auxiliary

model to substitute the missing outputs in the information

vector in iteration processes. A numerical simulation is

employed to demonstrate the effectiveness of the proposed

novel EM method.

Index Terms—Data loss, expectation maximization (EM)

algorithm, Hammerstein systems, parameter identiﬁcation.

I. INTRODUCTION

UE TO the widespread nonlinear characteristics of actual

systems, a nonlinear model is a reasonable modeling

method for a natural complex system that is absolutely nec-

essary [1]–[5]. For decades, block-oriented nonlinear systems

are popular with their ability of elastic arrangement of functional

modules and elastic representation of each module. The thought

of block-oriented nonlinear systems is originated from the

innovative idea of dividing comprehensive problems into simple

small ones. A whole nonlinear dynamic structure can be divided

into static nonlinearities and linear dynamics, i.e., one com-

prehensive structure is parted into two or more simple blocks.

The investigated two-block-oriented Hammerstein system is the

simplest among the family of the block-oriented structure.

The identiﬁcation methods for the block-oriented system can

be classiﬁed into different types according to different aspects.

From the viewpoint of the basic identiﬁcation principle, the

identiﬁcation strategies can be divided into the least squares

methods [6], [7], the stochastic gradient methods [8], [9], the

probability-based maximum likelihood methods [10], [11], and

Manuscript received June 24, 2019; revised July 15, 2019; accepted

July 22, 2019. Date of publication July 29, 2019; date of current version

January 17, 2020. This work was supported in part by the National

Natural Science Foundation of China under Grant 61873138, Grant

61573205, Grant 61673155, and Grant 61877033, and in part by the

Taishan Scholar Project Fund of Shandong Province of China. Paper no.

TII-19-2677. (Corresponding author: D. Q. Wang.)

D. Q. Wang, S. Zhang, and M. Gan are with the College of Electri-

cal Engineering, Qingdao University, Qingdao 266071, China (e-mail:,

dqwang64@qdu.edu.cn; a3b412@163.com; aganmin@aliyun.com).

J. L. Qiu is with the School of Automation and Electrical Engineering,

Linyi University, Linyi 276000, China (e-mail:,qiujianlong@lyu.edu.cn).

Color versions of one or more of the ﬁgures in this article are available

online at http://ieeexplore.ieee.org.

Digital Object Identiﬁer 10.1109/TII.2019.2931792

the orthogonal matching pursuit identiﬁcation methods [12],

[13]. From the viewpoint of computational style, the identiﬁca-

tion strategies can be divided into the recursive estimation meth-

ods [14]–[16] and the iterative estimation methods [17]–[20].

From the viewpoint of the parameterization mode, there exist

the overparameterization estimation methods [21]–[24], the hi-

erarchical estimation methods [25]–[27], and the key-term sepa-

ration estimation methods [28]–[30]. From the viewpoint of the

assistant technique, there exist the ﬁltering technique [31], the

multi-innovation theory [33], and the auxiliary model idea [34].

In discrete-time systems, usually, the update of t he system

input and output at the same period, i.e., single-rate systems,

when the measurement technology is limited, or the system de-

lay or congestion appears, different input–output sampling rates

or missing output data are occurred [35]–[37], i.e., dual-rate,

multirate, or miss data systems.

Several identiﬁcation methods for missing data systems are

published. Through the polynomial transformation technique

[38], a dual-rate sampling system can be transformed into a

dual-rate regression model that does not involve the missing

output data; through the lifting t echnique, the multirate s ystems

can be reformulated into a lifted state space model with a

slow-rate sampling [39], [ 40]; and through the auxiliary model

idea, parameter estimation of the multirate systems can be

implemented by substituting the missing output with the output

of an auxiliary model [41].

Recently, the likelihood-function-based expectation maxi-

mization (EM) estimation methods have captured much atten-

tion in the estimation area of missing data [42]–[44]. Xiong

et al. investigated a likelihood-function-based EM algorithm for

a nonlinear block-oriented Wiener structure with missing output

data [42], Chen et al. explored a modiﬁed Bayesian-based EM

algorithm for a linear missing data system [43], and Zhang et al.

applied a likelihood-function-based EM algorithm to handle

missing data of a discrete distribution system [44].

Most EM algorithms like in papers [42]–[44] aim to transform

linear/nonlinear systems into a regression identiﬁcation model

with only one parameter vector, e.g.,

y(k)=Φ

where y(k) ∈ R is the system output, Φ ∈ R

is the measured

vector formed by observed data, and Θ ∈ R

is the parameter

vector [42]–[44]. The typical EM method is to maximize the

expectation of a logarithmic likelihood function of the complete

data over the parameter vector Θ to compute the parameter

estimates.

See http://www.ieee.org/publications

standards/publications/rights/index.html for more information.

下载后可阅读完整内容，剩余8页未读，立即下载

weixin_38547397

粉丝: 2
资源: 907

缺失输出数据的Hammerstein系统：新颖EM识别方法

最新资源