基于时间片CCA的批处理关键操作单元的多元统计监控资源-CSDN文库

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现代的批处理过程的特点是规模庞大且有多个操作单元，因此必须对此类批处理过程的关键单元进行本地故障检测。提出了一种基于时分规范相关分析（CCA）的批处理关键操作单元多元统计监控方案。首先，将三路批处理数据展开为时间片数据。其次，在每个时刻都执行CCA建模，以探索关键单元与整个过程之间的相关性。然后，生成故障检测残差并构建监视统计信息。统计信息可区分过程状态和检测到的故障类型，即与其他单元相关或不相关的故障。通过数值实例和工业注塑Craft.io的案例研究，证明了所提出的故障检测方案的可行性和优越性。 ### 基于时间片CCA的批处理关键操作单元的多元统计监控 #### 摘要及背景本文介绍了一种新型的批处理关键操作单元的多元统计监控方法，该方法利用时间片规范相关分析（Canonical Correlation Analysis, CCA）来实现。随着化学、制药和半导体等行业对批处理过程的需求日益增长，对于这些复杂系统的监测变得尤为重要。传统的监控技术往往难以应对现代批处理过程中出现的大规模、多单元等复杂特性，因此，开发一种能够有效监测关键单元的多元统计方法显得十分必要。 #### 方法论概述 1. **数据预处理**：原始的三路批处理数据被转化为时间片数据。这一转换过程使得能够在特定的时间点上对数据进行更细致的分析。 2. **CCA建模**：在每个时间片内，采用CCA技术来探究关键操作单元与其他整个过程之间的相关性。这种方法不仅能够揭示单元间的内在联系，还能够帮助识别哪些单元的变化可能会影响到整个系统的运行。 3. **故障检测残差生成与统计量构建**：通过对模型预测值与实际观测值之间的差异计算得出故障检测残差，并进一步构建监控统计量。这些统计量能够有效地反映过程的状态以及是否出现了故障，并能区分故障是否与其他单元相关。 #### 监控统计量的作用 - **区分过程状态**：通过构建的统计量可以清楚地区分正常运行状态和异常状态。 - **故障类型的辨识**：能够准确地判断故障是否仅限于单个单元还是会影响整个系统，这对于及时采取纠正措施至关重要。 #### 实验验证 - **数值实例**：通过一个数值实例验证了该方法的有效性，结果显示在不同条件下都能够准确地检测到故障的存在。 - **工业应用案例**：在注塑成型工业过程中的应用进一步证明了该方法的实用价值。案例研究表明，即使在复杂的工业环境中，该方法也能够有效地监测关键操作单元的状态，并及时发现潜在的问题。 #### 结论本文提出了一种基于时间片CCA的批处理关键操作单元的多元统计监控方法，旨在解决大规模批处理过程中的本地故障检测问题。通过将三路批处理数据转化为时间片数据，并在每个时间点执行CCA建模，不仅能够探索关键单元与整个过程之间的相关性，还能有效生成故障检测残差及监控统计量。该方法的优势在于其能够区分不同的过程状态，并准确辨识故障类型，从而有助于快速定位问题所在并采取相应措施。通过数值实例和工业案例的研究，充分展示了该方法的可行性和优越性。对于提高现代批处理过程的稳定性和效率具有重要意义。

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This article has been accepted for inclusion in a future issue of this journal. Content is final as presented, with the exception of pagination.

IEEE TRANSACTIONS ON CONTROL SYSTEMS T ECHNOLOGY 1

Multivariate Statistical Monitoring of Key Operation Units

of Batch Processes Based on Time-Slice CCA

Qingchao Jiang , Member, IEEE, Furong Gao, Member, IEEE, Hui Yi, and Xuefeng Yan

Abstract— A modern batch process can be characterized by a

large scale and multiple operation units, and local fault detection

for the key units of such a batch process is imperative. A time-

slice canonical correlation analysis (CCA)-based multivariate

statistical monitoring scheme f or the key operation units of batch

processes is proposed. First, the three-way batch process data

are unfolded into the time-slice data. Second, CCA modeling is

performed at each time instant to explore the correlation between

the key units and the entire process. Then, a fault detection

residual is generated and monitoring statistics are constructed.

The statistics discriminate both the process status and the type of

a detected fault, a fault relevant or irrelevant to the other units.

The feasibility and superiority of the proposed fault detection

scheme are demonstrated by case studies on a numerical example

and an industrial injection molding process.

Index Terms— Batch processes, canonical correlation analy-

sis (CCA), key operation unit monitoring, multivariate statistical

process monitoring.

I. INTRODUCTION

ROCESS monitoring is gaining signiﬁcant attention in

process control and process system engineering com-

munities [1 ]–[5]. Batch processes play an impo r tant role in

chemical, pharmaceutical, and semiconductor industries, and

multivariate statistical batch process monitoring methods are

of p articular interests [6], [7], in which multiway principal

Manuscript received August 24, 2017; revised November 4, 2017; accepted

February 3, 2018. Manuscript receiv e d in ﬁnal form February 3, 2018.

This work was supported in part by the National Natural Science Founda-

tion of China under Grant 61603138 and Grant 61503181, in part by the

Guangdong Innova tive and Entrepreneurial Research Team Program under

Grant 2013G076, in part by Fundamental Research Funds for the Central

Uni versities under Grant 222201717006 and Grant 222201714027, in part

by Science Foundation of Jiangsu Pro vince under Grant BK20140953, and

in part by the Program of Introducing Talents of Discipline to Uni versities

(the 111 Project) under Grant B17017. Recommended by Associate Editor

A. Serrani. (Corresponding author: Furong Gao.)

Q. Jiang is with the Department of Chemical and Biomolecular Engineering,

Hong Kong University of Science and Technology, Hong Kong 999077,

and also with the Key Laboratory of Advanced Control and Optimiza-

tion for Chemical Processes of Ministry of Education, East China Uni-

versity of Science and Technology, Shanghai 200237, China (e-mail:

qchjiang@ecust.edu.cn).

F. Gao is with the Department of Chemical and Biomolecular Engineering,

The Hong Kong University of Science and Technology, Hong Kong 999077

(e-mail: kefgao@ust.hk).

H. Yi is with the College of Electronic Engineering and Control Sci-

ence, Nanjing University of Technology, Nanjing 211816, China (e-mail:

jsyihui@126.com).

X. Yan is with the Key Laboratory of Advanced Control and Opti-

mization for Chemical Processes of Ministry of Education, East China

Uni versity of Science and Technology, Shanghai 200237, China (e-mail:

xfyan@ecust.edu.cn).

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

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

Digital Object Identiﬁer 10.1109/TCST.2018.2803071

component analysis and multiway partial least squares are

the basic ones [8], [9]. Many extensions and applications of

the multivariate statistical batch process monitoring methods

have been reported [10]–[13]. However, most of these methods

focus on monitoring the entire plant but not on a speciﬁc key

operation unit.

A batch process can be characterized by a large scale and

multiple operation un its and the correlations among the entire

process are complex [14]–[16]. Some operation units play the

key role in guaranteeing process safety or product quality, and

therefore, they are fault sensitive. T hese key operation units

should be monitored emphatically and a fault with even a

small amplitude should be detected timely. However, the local

fault detection issue for a key operation unit has rarely been

discussed. Monitoring a key unit using only the measured

variables from the local unit will ignore the correlation with

the other un its, whereas involving the variables from other

units may cause monitoring redundancy and degrade the

monitoring performance. Efﬁcient fault detection methods, for

a key operation unit in a batch process, are under investigation.

Canonical correlation analysis (CCA) is a basic multivariate

analysis method which has been widely u sed for system identi-

ﬁcation as well as process monitoring [1], [17], [18]. Recently,

CCA-based fault detection methods under the residual genera-

tion framework are developed. Chen et al. [19], [20] proposes

a CCA-based fault d etection method, and then improves it

to deal with incipient multiplicative faults. More recently,

Jiang et al. [21] proposes a genetic algorithm-regularized

CCA (GAR-CCA) monitoring method for large-scale multiunit

continuous processes. Although the efﬁciency is both theo-

retically analyzed and experimentally tested, the monitoring

scheme is designed for continuous processes and assumes

that the co rrelations among the process keep co nstant within

the duration of an operation cycle. Evidently, this assumption

is easily v iolated in batch processes since the correlation

relations may change time to time. In addition, the GAR-CCA-

based fault detection generates an overall monitoring statistic,

without further considering the type of a detected fault.

The main contributions of this brief are summarized as

follows.

1) A time-slice CCA-based local fault detection scheme

for monitoring key operation units of a batch process

is proposed. In a batch process, the correlation rela-

tions among the entire process may change time to

time or phase to phase. Therefore, the three-way batch

process data are unfolded into time-slice data and the

CCA modeling is performed at each time instant to

explore the relation between the local unit and the

See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.

This article has been accepted for inclusion in a future issue of this journal. Content is final as presented, with the exception of pagination.

2 IEEE TRANSACTIONS ON CONTROL SYSTEMS TECHNOLOGY

entire pro cess at the time instant. Then, the time-slice

CCA-based monitoring considers both the local vari-

ables within the key operation units and the information

provided by related variables from the other units.

2) The CCA-based fault detection residual is further

decomposed, and corresponding monitoring statistics

are designed to discriminate both the process status,

normal or faulty, and the type of a detected fault,

relevant or irrelevant to the other units.

3) Application examples on a numerical example and an

industrial injection molding process are provided. The

efﬁciency of the proposed time-slice CCA-based key

operation unit monitoring scheme for batch processes

is veriﬁed.

The reminder of this brief is organized as follows.

In Section II, the basics of CCA and multivariate statistical

fault detection is brieﬂy reviewed. The key unit monitoring

problem for batch processes is formulated. In Section III,

the proposed time-slice CCA-based key operation unit mon-

itoring scheme for batch processes is detailed and some

characteristics are discussed. Then, the proposed monitoring

scheme is applied on a numerical example and an industrial

injection molding process in Section IV. Last, conclusions are

drawn in Section V.

II. P

RELIMINARIES AND PROBLEM FORMULATION

A. Multivariate Statistical Fault Detection

Multivariate statistical fault detection aims to ﬁnd if there

exists a fault in a process within the multivariate statistical

framework of hypothesis testing. Assume a measurement

∈

with m measured variables is expressed as [1]

= x

+ f (1)

where x

∼ N(0, 

) denotes the process data from normal

status, 

is the covariance matrix, f denotes a fault

in which th e fault direction is determined by ,andthe

fault magnitude is determined by f . For fault detection,

the Hotelling T

statistic is generally constructed as [1]

= x



−1

≤ T

(2)

where T

is the threshold of the T

statistic. The probability

prob{T

> T

| f = 0} is known as false alarm rate (FAR),

whereas the probability prob{T

≤ T

| f = 0} is known as

nondetection rate (NDR) [16]. T

statistic has been theoreti-

cally proved to provide the m inimal NDR for a given FAR [1].

After some derivations, the NDR is expressed as [16], [21]

NDR(T

, f ) = F



; m,ν



(3)

where F

; m,ν) is the cumulative distribution function

of the noncentral chi-squared distribution with degree of

freedom m and noncentral parameter v = (f )



−1

(f ).

B. CCA-Based Fault Detection

CCA explores the correlation between two sets of random

variables. Given u ∈

and y ∈

with





∼ N



E(u)

E( y)









(E(·) denotes the expectation and 

(·)

denotes the covariance),

CCA ﬁnds canonical correlation vectors J and L which max-

imize the correlation between J

u and L

y, i.e., [19], [21]

( J, L) = arg max

( J ,L)

( J

u)(L

= arg max

( J ,L)



( J



1/2



1/2

. (4)

The solution to this optimization problem can be obtained

through singular value decomposing on a matrix K

as [19], [21]

K = 

−1/2



−1/2

= R V

(5)

where

 =



diag(σ

,...,σ

) 0



∈

p×q

is a rectangular matrix and l = rank(

). The canonical

correlation vectors are derived as

J =[J

··· J

]=

−1/2

R ∈

p×p

(6)

L =[L

··· L

]=

−1/2

V ∈

q×q

. (7)

Then, a fault detection residual is generated as [21]

r = J

u −  L

y. (8)

The statistical properties of the residual are [21]

E(r) = J

E(u) −  L

E( y) = 0 (9)



= I

− 

. (10)

Based on the residual, the T

monitoring statistic can be

constructed as

= r



−1

r ≤ χ

). (11)

A fault is detected once the T

exceeds the conﬁdence

limit χ

),whereα denotes the level of signiﬁcance.

C. Problem Formulation and Motivation

For a batch process, assume that m (generally use J in

batch processes) process variables are measured at k =

1, 2,...,K time instants throughout an operation cycle. Then

after I batches, a three-way matrix X(I × J × K ) is obtained.

For process monitoring, the three-way data should be unfolded

into two-way data [7], [22]. Here we unfold it along the

time dimension, and K time-slice data matrices are obtained

as illustrated in Fig. 1. Since uneven length batches can

be synchronized through various methods [23], [24], this

brief assumes that the batches are synchronized, and variable

relations remain th e same at the same time instant of different

batches.

A batch process generally consists of several operation

units. For instance, an injection molding process consists of

the clamping unit, the injection unit, the power unit, and the

control unit, etc., In a batch process, there are some operation

units that are fault sensitive and these key operation units

should be monitored emphatically.

Assume that a key unit in a batch process contains p(< J )

measured variables which can be denoted as u(k) at the time

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