非线性过程监控的局部加权典范相关分析资源-CSDN文库

需积分: 5 82 浏览量 2021-05-11 22:57:43 上传评论收藏 853KB PDF 举报

### 非线性过程监控的局部加权典范相关分析 #### 摘要与引言本研究提出了一种名为局部加权典范相关分析（Locally Weighted Canonical Correlation Analysis, LWCCA）的方法，旨在实现高效且准确的非线性过程监控。该方法的核心思想是通过构建多个局部线性的典范相关分析(Canonical Correlation Analysis, CCA)模型来近似描述非线性过程。在这些局部模型中，样本权重的确定成为关键步骤之一。如果权重下降过慢，则可能忽略局部行为；相反，若权重下降过快，则可能导致显著的误报。因此，研究提出了一种基于随机算法的方法来确定用于计算权重的可调参数，确保LWCCA模型能够在保证较低误报率的同时探索尽可能多的局部行为。 #### 方法论 LWCCA方法的具体实现步骤如下： 1. **数据预处理**：首先对采集到的过程数据进行必要的预处理，包括但不限于数据清洗、标准化等。 2. **样本权重计算**：采用一种基于随机算法的方法确定用于计算样本权重的可调参数。这一步骤对于确保LWCCA的有效性和可靠性至关重要。 3. **局部CCA模型建立**：根据样本权重划分不同的局部区域，并在每个区域内建立CCA模型，以此来表征输入与输出之间的关联性。 4. **故障检测残差生成**：一旦建立了局部CCA模型，就可以生成最优的故障检测残差。 5. **监控统计量建立**：基于这些故障检测残差，建立相应的监控统计量，用于在线监测过程中出现的异常情况。 #### 实验验证为了验证LWCCA方法的有效性，进行了两项实验研究。第一项研究采用了模拟数据集，该数据集包含了一系列典型非线性过程的特征，以检验LWCCA方法在不同条件下的性能表现。第二项研究则是在一个实际工业过程中进行的，具体为化工生产环境中的过程监控。通过这两项实验，不仅验证了LWCCA方法能够有效地识别过程中的异常状态，而且还展示了其相对于传统MVA方法的优势，尤其是在处理复杂非线性过程时的优越性。 #### 研究背景随着数据收集与传输技术的快速发展，现代生产工厂能够获取大量的过程数据。这些数据蕴含着丰富的过程信息，如何有效利用这些信息进行过程监控变得尤为重要。数据驱动的多元分析(Multivariate Analysis, MVA)方法在此背景下发挥着越来越重要的作用。经典的MVA监控方法通常包括离线建模与在线监控两个阶段。离线建模阶段利用多元数据分析技术探索变量间的相互关系并构建监控空间；在线监控阶段将待测样本映射到已建立的监控空间中，并依据监控统计量判断过程状态。 #### 基础MVA方法 - **主成分分析(Principal Component Analysis, PCA)**：主要用于降维和异常检测。 - **偏最小二乘(Partial Least Squares, PLS)**：适用于输入和输出变量间存在强线性关系的情况。 - **典范相关分析(Canonical Correlation Analysis, CCA)**：用于探索两组变量间的最大相关性，适用于输入输出变量之间存在较强相关性的场景。 #### 结论 LWCCA方法通过构建多个局部线性的CCA模型，能够有效地解决非线性过程监控的问题。这种方法不仅能够提高故障检测的准确性，还能减少误报率，从而为工业过程监控提供了一个强大而灵活的工具。未来的研究可以进一步探讨如何优化样本权重的计算方法以及如何扩展LWCCA方法的应用范围，以适应更广泛的过程监控需求。

资源推荐

资源详情

资源评论

Locally Weighted Canonical Correlation Analysis for Nonlinear

Process Monitoring

Qingchao Jiang and Xuefeng Yan*

Key Laboratory of Advanced Control and Optimization for Chemical Processes of Ministry of Education, East China University of

Science and Technology, Shanghai 200237, P. R. China

Supporting Information

ABSTRACT: A locally weighted canonical correlation analysis (LWCCA)

method is proposed to achieve eﬃcient nonlinear process monitoring.

The basic idea of the LWCCA is to approximate a nonlinear process

through several local linear canonical correlation analysis (CCA) models, in

which the determination of sample weights is a key step. Slowly decreasing

weights will ignore the local behaviors, whereas rapidly decreasing weights

will lead to signiﬁcant false alarms. A randomized algorithm-based approach

is proposed to determine the tunable parameter for calculating the weights.

Thus, the LWCCA model explores as much local behavior as possible with

the false alarm performance guaranteed. When a local CCA model that

characterizes the process input and process output correlation is estab-

lished, optimal fault detection residuals are generated, and monitoring sta-

tistics are established. Two experimental studies are conducted through

which the eﬃciency of the LWCCA method is veriﬁed.

■

INTRODUCTION

Process monitoring is crucial in maintaining the long-term safe

operation of a production plant. Rapid advancement of data

collecting and transmitting techniques has created an abundance

of process data that contain meaningful available process infor-

mation.

1−3

Especially, data-driven multivariate analysis (MVA)

methods play a more important role in process monitoring.

4−9

Generally, a classical MVA monitoring method follows oﬄine

modeling with online monitoring procedures. During the oﬄine

modeling, a multivariate data analysis technique is employed to

explore the relationship among variables and to construct the

feature spaces for monitoring. In the online monitoring proce-

dure, a query sample is projected into the monitoring spaces, and

the process status is determined according to monitoring

statistics.

Principal component analysis (PCA), partial least-squares

(PLS), and canonical correlation analysis (CCA) are the basic

MVA methods. PCA focuses on the variable relationships of the

entire process (without discriminating process input and

output).

10−12

It constructs a dominant subspace and a residual

subspace according to the features’ importance for reconstruct-

ing the original data. PLS focuses on the quality-related process

monitoring.

13−15

It constructs the quality-related subspace and

the residual subspace according to their relationship with

diﬃcult-to-measure quality variables. A fault in the quality-

related subspace is important, because the fault will generally

aﬀect the production quality. CCA explores the correlation

between two sets of variables. It is generally used in two diﬀerent

ways for process monitoring, as follows: one way focuses on the

relation between the process input and process output; and the

other way focuses on the relation between two coupled

units.

16−20

It is proven that the CCA generates optimal fault

detection residual when only one set of variables are aﬀected by a

fault.

Given the eﬃciency, PCA, PLS, and CCA-based moni-

toring methods have been intensively extended to solve various

monitoring problem. Other MVA-based monitoring methods

were also proposed and eﬃciency has been reported.

21−23

How-

ever, these methods generally assume that the measured vari-

ables are linearly related, which limits their applications in

nonlinear processes.

For nonlinear process monitoring, the neural networks (NN)-

based methods,

24,25

the kernel learning methods,

26−28

and the

just-in-time learning methods

29,30

are the basic ones. The

NN-based methods extract features through nonlinear mapping,

which is relatively sophisticated and generally requires a large

amount of computation. Moreover, the structure and parame-

ters should be determined in designing an NN for monitoring,

which remains a challenge. The kernel-based methods replace

the nonlinear mapping through kernel functions and then

extract features in the high-dimension space. Although eﬃciency

is shown, the selection of related parameters and kernel func-

tions is subjective, which signiﬁcantly aﬀects monitoring results.

Recently, just-in-time learning (JITL) approaches have been

developed for nonlinear process modeling and monitoring.

29−31

The basic idea of a JITL method is to establish several local

Received: April 26, 2018

Revised: August 7, 2018

Accepted: September 13, 2018

Published: September 13, 2018

Article

pubs.acs.org/IECR

Cite This: Ind. Eng. Chem. Res. 2018, 57, 13783−13792

Ind. Eng. Chem. Res. 2018, 57, 13783−13792

Downloaded via EAST CHINA UNIV SCIENCE & TECHLGY on December 30, 2018 at 07:25:16 (UTC).

See https://pubs.acs.org/sharingguidelines for options on how to legitimately share published articles.

linear models to represent a nonlinear process.

Although the

method is eﬃcient, there are still some problems that need to be

addressed. First, locally weighted PCA (LWPCA) and locally

weighted PLS (LWPLS), which are extensions of PCA and PLS,

are proposed for modeling nonlinear processes.

29,30

However,

the process input and output relationship is not well charac-

terized by the PCA and PLS-based methods. Extensions of CCA

to the nonlinear form are necessary. Second, determination

of the tunable parameter in calculating the sample weights

remains a challenge. The importance of far-away samples is not

distinguishable from that of nearer samples when too-slowly

decreasing weights are used. This situation will ignore the local

behaviors. Using too-rapidly decreasing weights will highlight

only a few of the nearest samples, which leads to deviation in the

estimation of the covariance matrix and create signiﬁcant false

alarms (FAs).

In this paper, we proposed a JITL-locally weighted CCA

(LWCCA) monitoring scheme for nonlinear processes. First,

the tunable parameter for calculating the weights is determined

through a randomized algorithm (RA). This allows the model to

explore as much local behavior as possible with the false alarm

performance protected. Second, LWCCA is established to char-

acterize the process input and process output correlation. Then,

fault detection residuals are generated and monitoring statistics

are established. The rest of this article is organized as follows.

Section 2 introduces the CCA and RA basics. Motivations for

establishing a JITL-LWCCA model are presented. Section 3

details the LWCCA monitoring scheme. In section 4, two

experimental studies are presented. Conclusions are provided in

section 5.

2. PRELIMINARIES AND MOTIVATIONS

2.1. CCA Fault Detection Basics. CCA is a classical MVA

technique which is used to explore the correlation between two

sets of random variables. Let

∂

∂∂∏∂

xx x

...

nn np

11 12 1

21 22 2

(n samples, p variables) and

∂

∂∂∏∂

yy y

...

nn nq

11 12 1

21 22 2

(q variables) be zero-mean process input and output data. CCA

tries to ﬁnd projection vectors J and L such that the J

and

are most correlated, as follows:

4,33

ΣΣ

=JL

JJ LL

(

, ) arg max

()( )

(, )

T 1/2 T 1/2

(1)

where Σ

(·)

is the covariance. To obtain the solution to eq 1,a

matrix K is constructed. Then singular value decomposing is

performed on K as follows

4,33

ΣΣΣ Σ==

−−

KRV

XXYY

1/2 1/2

(2)

where

σσ

=∈

diag( , ..., )

and l = rank(Σ). Then,

we have

4,33

−

1/2

(3)

For samples

9∈

p 1

and

9∈

q 1

, the following residual

vector is generated

16,18

Σ=−

Jx Ly

(4)

where

Σ=− =rJx LyEE E

() () ()

(5)

ΣΣ=−I

(6)

Then, the T

statistic for the residual is established as

16,18

Σ=

−

(7)

With Gaussian assumption, the threshold of the T

is deter-

mined as T

= χ

), where m

= rank (Σ

), given a level of

signiﬁcance α. We assume that the x and y are related as A(x + ε)

= By, where ε is process noise. Under the Gaussian assumption,

this T

statistic is optimal for detecting a fault that aﬀects only

16,18

Similarly, the T

statistic for detecting a fault that aﬀects

variables in y can be established.

2.2. RA. Let ω be a random variable with density D(ω).

Let D

be the support of ω. Let ε be the accuracy level.

RA delivers an estimated p



(γ)ofp(γ)=prob(J(ω) ≤ γ),

which satisﬁes p(γ)<p



(γ)+ε with probability of at least

1−δ.

34,35

The p



(γ) is calculated based on the generated N

independent identical distributed random samples ω

(1)

,···,ω

(N)

⊂ D

as follows:

34,35

∑

γωω



∈

γγ

()

I(),I()

1, if

0, otherwise

()

(8)

where D

is the support of γ. N determines the reliability of the

estimate p



(γ), as stated in the following Theorems 1 and 2.

34,35

Theorem 1: (Hoeﬀding inequality) If we let z

∈ [a

]

(i =1,···,N) be an independent random variable, then for any ε >0,

we have

34,35

∑∑

−≥≤−

∑

−

−≤−≤−

∑

−

{

zE z

prob exp

()

prob exp

()

(9)

We further assume [a

] = [0,1]. The following Theorem 2 is

obtained:

Theorem 2. For any ε ∈ (0,1) and δ ∈ (0,1), N satisﬁes the

one-sided Chernoﬀ bound

34,35

≥

(10)

derives p(γ)<p



(γ)+ε with probability prob(p(γ)<p



(γ)+ε)>

1−δ. Theorem 2 provides guidance on the selection of a proper

N to obtain a reliable estimate p



(γ) of a real probability p(γ).

Industrial & Engineering Chemistry Research Article

DOI: 10.1021/acs.iecr.8b01796

Ind. Eng. Chem. Res. 2018, 57, 13783−13792

13784

剩余9页未读，继续阅读

评论收藏

内容反馈

weixin_38628150

粉丝: 4
资源: 936

非线性过程监控的局部加权典范相关分析

利用典范相关分析对过程和质量故障进行并发监测和诊断

使用依赖于数据的内核全局-局部保留投影进行非线性过程监控

基于遗传算法正则相关分析的大型过程数据驱动分布式局部故障检测

实战（python）局部加权线性回归

局部加权的线性回归的matlab实现

非线性过程系统的分析与控制

matlab开发-线性和非线性数据增强的低局部加权散射图平滑

LOWESS，线性和非线性数据的局部加权散点图平滑（增强）：LOWESS，像 LOWESS 这样的稳健回归允许检测趋势，否则方差太大-matlab开发

CAE线性分析与非线性分析的区别.pdf

局部加权法MATLAB实现

ansys非线性分析

【ANSYS Workbench仿真】非线性静力学分析(三)：材料非线性分析

相分配用于非线性批处理过程监控

混凝土非线性分析讲义+ANSYS分析ANSYS分析实例与工程应用+ANSYS分析实例集+钢筋混凝土结构非线性有限元理论与应用+钢筋混凝土结构非线性有限元分析

哈默斯坦非线性时变系统的加权学习辨识方法.docx

非线性泛函分析引论,1998版,钟承奎

非线性动力学系统matlab程序分析.pdf

matlab开发-带绘图仪的加权非线性曲线

钢筋混凝土结构非线性有限元分析_江见鲸.pdf

matlab 非线性光学模拟

基于Matlab的多模型加权自适应控制策略：提升非线性时变工业过程的控制效果,基于Matlab的多模型加权自适应控制程序：优化非线性时变工业过程的控制效果,65.基于matlab的多模型加权自适应控制

基于Matlab的多模型加权自适应控制程序：非线性时变工业过程的优化控制策略,基于Matlab的多模型加权自适应控制程序：提升非线性时变工业过程控制效果,65.基于matlab的多模型加权自适应控制器

多元非线性回归分析源代码

非线性高阶共振非局部边值问题

非线性系统 第三版 课后答案.pdf

Labview非线性拟合

logistic回归和局部加权回归

最新资源

非线性系统第三版课后答案.pdf