APPLICATION OF ON-LINE

MULTIVARIATE TIME-SERIES

SEGMENTATION FOR

PROCESS MONITORING AND

CONTROLLászló Dobos, János Abonyi

University of Pannonia, Hungary

Department of Process Engineering

What time-series means?

A time series is a collection of observations

made sequentially in time.

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The goal is: extract valuable knowledge from

the collected data sets.

Introduction (1/3) T-S segmentation (4) Methodology (5) Case study (1) Summary (1)

Time-series analysis: methods

Database C

2

1

4

3

5

7

6

9

8

10

Query Q

(template)

Classification

Clustering

Query by Content

10

s = 0.5

c = 0.3

Rule Discovery

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Introduction (2/3) T-S segmentation (4) Methodology (5) Case study (1) Summary (1)

Time series analysis – Why?Similarity

An accurate similarity measure is a must for every

successful times series data mining application but how

people recognize similarity?

*The picture can be found in Mr. E. J. Keogh’ excellent tutorial, A Tutorial on Indexing and Mining Time Series

Data, 2002

We know if we ‘look at it’

Emotions, feelings

We concentrate on the

whole picture and pair the

most extreme features

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Introduction (3/3) T-S segmentation (4) Methodology (5) Case study (1) Summary (1)

Time series segmentation? On-line?

What is time-series segmentation?

Extract internally homogeneous segments

from a given time series to:

locate stable periods of time

identify change point

On-line?

Segmenting the time series when the

measurements are collected

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Introduction (3) T-S segmentation (1/4) Methodology (5) Case study (1) Summary (1)

What does homogeneity mean?

Homogeneity – adjacent measurement points with

similar properties in process variables

Homogeneous? – Formalized: cost function

2

2,5

3

3,5

4

4,5

5

5,5

6

6,5

0 2 4 6 8 10 12

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How to segment streaming data?

Sliding window segmentation technique

A segment is grown until it exceeds some

error bound. The process repeats with the

next data point not included in the newly

created segment.

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Introduction (3) T-S segmentation (3/4) Methodology (5) Case study (1) Summary (1)

Sliding window segmentation

technique

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Introduction (3) T-S segmentation (4/4) Methodology (5) Case study (1) Summary (1)

In crosshair: process dynamics

Changes in process dynamics can be

the main information

PCA-based methods are widely applied

for multivariate process monitoring

Dynamic PCA can handle process

dynamics

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Introduction (3) T-S segmentation (4) Methodology (1/5) Case study (1) Summary (1)

The key:

Dynamic Principal Component Analysis

Applying PCA on „dynamised” data:

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

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

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

nmtunmtymumymumy

ntuntytutytuty

ntuntytutytuty

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aiyk i b juk jj 0

m

i 0

n

xk

xk1

xm

Introduction (3) T-S segmentation (4) Methodology (2/5) Case study (1) Summary (1)

Recursive covariance matrix

variable forgetting factor

On-line PCA based solution

Every measurement needs a covariance

matrix – recursive computation

Neglect the effect of unnecessary

measurements: forgetting factor

Pk 1

jk

Pk1 Pk1xkxk

TPk1

jk xkTPk1xk

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P 1

N 1(xk x)(xk x)

T

k1

N

Introduction (3) T-S segmentation (4) Methodology (3/5) Case study (1) Summary (1)

Cost function: PCA similarity factor

Data reduction technique

The similarity between the

hyperplanes defined by

Krzanowski:

Compares the whole processes

Segmentation

p

UUUUtr

pYXs

pX

T

pYpY

T

pX

p

i

p

j

jinnPCA

nnnn)(

cos1

),(

,,,,

1 1

,

2

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Introduction (3) T-S segmentation (4) Methodology (4/5) Case study (1) Summary (1)

The segmentation algorithm

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1. Collect the new values of measurement

2. Determine the forgetting factor

3. Compute the latest covariance matrix

4. Determine the merge cost – Krzanowsky

distance

5. If merge cost < previous determined error

Merge the point

Else start new segment

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Case study – LTV test system

Consider a second order

system

Segment it

based on DPCA

K1, τ1 change at t=200 sec

K2 changes at t= 666 sec

τ2 changes at t= 800 sec

K1, τ1 change here

K1

1 s1K2

2 s1

K2 changes hereτ2 changes here

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PCA based segmentation

No segregated segments!

Introduction (3) T-S segmentation (4) Methodology (5) Case study (1/1) Summary (1)

Summary

Multivariate time-series segmentation

DPCA based

Efficient way to segregate homogeneous

operation regimes on-line

Ability to support:

Control purposes

Process monitoring

Alarm management

Fault detection

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Introduction (3) T-S segmentation (4) Methodology (5) Case study (1) Summary (1/1)

THANK YOU FOR YOUR

ATTENTION!László Dobos, János Abonyi

University of Pannonia, Hungary

Department of Process Engineering