ISOMAP CVA 1,2 1

1

E-mail 790665113@qq.com

2. 730050

E-mail xqzhao@lut.cn

CVA

ISOMAP CVA

ISOMAP

CVA SPE TE

TE

Fault Detection CVA Algorithm of Chemical Process Based on

ISOMAP

ZHAO Xiaoqiang1,2, ZHANG Xiaoxiao1

1. College of Electrical and Information Engineering, Lanzhou University of Technology, Lanzhou 730050, China

E-mail:790665113@qq.com

2. Key Laboratory of Gansu Advanced Control for Industrial Processes, Lanzhou 730050, China

E-mail: xqzhao@lut.cn

Abstract: Strong auto-correlation and cross-correlation in chemical processes data can be dealt well by canonical variate

analysis (CVA) algorithm, but this algorithm can’t solve nonlinear problem of chemical process data. So a fault diagnosis CVA

algorithm of chemical process based on isometric feature mapping (ISOMAP) is proposed in this paper. At first, this algorithm

uses ISOMAP algorithm of manifold learning to achieve realize nonlinear dimensionality reduction for initial data and

maintain internal geometry structure of data. Then CVA is used to the extracted low dimensional data to obtain process state

space description and SPE statistics. Fault detection simulation results of TE process show that the proposed algorithm is more

effective to detect faults of chemical process than CVA algorithm.

Key Words: Fault detection, ISOMAP, CVA, TE Process

1 [1]

Proceedings of the 33rd Chinese Control ConferenceJuly 28-30, 2014, Nanjing, China

3147

[2]

[3] PCA

[4] PLS

PCA[5] ICA PCA

ICA

[6]DPCA

CVA

CVA

[7] CVATE

PCA PLS [8]CVA-ICA CSM

[9]

ISOMAP

CVA

2 ISOMAP

ISOMAP[10] Tenenbaum

MDS

X

ix jx , 1,2, ,i j nn,

( , )E i jd x x k

jx ix ( , )E i jd x x

ix k ix

jx ( , )E i jd x x

MD M

( , )M i jd x x ix jx

( , )G i jd x x = = ( , )M G G i jD D d x x

Dijkstra [11] Floyd [12]

d 1 2 dddd

( ) / 2G GD HS H

2=G ij ijG GS S D =ijH H

1 /ij n i j 1ij 0ij d

1 2, , dv v vdvd d

n pX pd F n dY

1 2 1 1 2 2 2 2, , , , , ,TTn d

nY y y y v v vTT

ny T v v vvy 2 21 1 2 2 2 21 1 2 21 1 2 22 21 2 221 1 2 22 21 21 1 2 2v2 2v vv 221 1 2 21 21 1 21 1 2 22 21 21 1 2

mnewx R

F Y TC Y Y newx

X k 1 2, ,L L Lkx x xLkxL 2

newx X ( 1,2, )ix i n)

1 1

2 2

, min{ ( , ) ( , ),( , ) ( , ), , ( , ) ( , )}

G new i E new k G k i

E new k G k i E new kk G kk i

d x x d x x d x xd x x d x x d x x d x xE new, (, ((((((, (((

2

1 2[ ( , ), ( , ), , ( , )]Tnew G new G new G new kD d x x d x x d x xG new, (((, (

3 newx F dnewy R

3148

1 2 2

1 1

1 1 ( , ) ( , )2

n n

new j G i j G new ij i

y C y d x x d x xn

3

3 ISOMAP CVA

ISOMAP CVAISOMAP

CVA [13]

SPE Step 1 m nY R m

nk k

pY k k fY

ISOMAP

1pY 1fY

Step 2 1pY 1fY

ppY ffY , pfY

SVD CVA

1/2 1/2 Tff fp pp U V

U n nU

n n n V n nV

Step 3

n

n

Akaike [14]

Kullback-Leibler

Step 4 k ( )x k

1/2 1/2( ) ( )Tn n pp px k V y k 5

k+1 k+N-1

1ˆ ( 1)( ) ( ) ( )

ˆ ( )T TA x k

E x k E x k x ky kC

( 1) ( ) ( )( ) ( ) ( )

x k Ax k Be ky k Cx k e k

7

Step 5 i SPE 2

1

ˆ( )m

i ij ijj

SPE y y

8 SPE

Step 6

ISOMAP j

i SPE2 2ˆ( )ij ij ij ijSPE e y y

4

4.1

TE(Tennessee Eastman - )[15] Eastman

Downs and Vogel TE

TE 5

TE 4112 21

3 min48 h 960

9608 h TE

3149

FIC

A1

FIC

D2

FIC

E3

FIC

C4

F1

6

TIC

LIC

TIC

PIC

TIC

13

FIC

8

JICPI

FIC

XS

9

TI

LIC

FIC

LICTIC XF

10

FIC

FCFCFCC

H

PI 5

7

1112

1 TE

4.2

960ISOMAP CVA CVA

95% 3

2- 5 1A 5

SPE

2 CVA 1 SPE 3 ISOMAP CVA 1 SPE

4 CVA 5 SPE 5 ISOMAP CVA 5 SPE

3150

170 230 270 1

2 200170

230 270 31 SPE 1

230 270CVA

180 230 270 310 5

54 CVA 180 230 270

310 SPE330

ISOMAP CVA CVA

5

ISOMAP CVA ISOMAPCVA

SPECVA

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