Recurrence Quantification Analysis for Extracting Features in Complex Systems

Satish T.S. BukkapatnamOklahoma State Universityhttp://www.okstate.edu/ceat/iembsatish@okstate.edu

INFORMS 2004

2

AgendaIntroduction

Sensor-based Modeling

Problem Motivation and Background

Research Methodology

Implementation and Results

Summary, Benefits and Future Directions

3

IntroductionSensor-based approaches provide an automated and cost-effective way to

Assure quality in manufactured productsquality specifications have shrunk by 3 orders since 1940’s

Manage nation’s engineering and information assets,maintenance currently costs exceed $1Trillion per year

Signal AnalysisRepresentation

De -noisingFeature Extraction

Process ModelingState vector

Structure selectionModeling fitting

Quality Monitoring

Process Control

Process Kn.

Signal

Process Knowledge

-

Process ModelingState

Structure selectionModeling fitting

Process ControlComplex Nonlinear

Processes

Process CharacterizationSignal based

Physics based

Quantifiers

Features

State Estimates

4

On-line Quality and Integrity MonitoringReal-world systems including various manufacturing machines and processes are complex

Nonlinear stochastic dynamicsnonstationarity, bursts and intermittencies in sensor data

Models and Representations capturing this complexity are imperative for effective monitoring and control

0 0.5 1 1.5 2 2.5 3 3.5 4

x 10-3

-1.5

-1

-0.5

0

0.5

1

1.5x 10

4

Acoustic Emissionfrom High-precision Machining

Vibration Time-Series fromGrinding Processesat Honeywell

Aggregate Network Packet TrafficTime-series

Optical profilometerdata of wire-saw cut silicon wafer surface from Siemens

5

Sensor-based Modeling ResearchAugments the statistical and qualitative reasoning foundations of conventional monitoring technologies with nonlinear dynamic systems theoryCaptures this complex process dynamics from sensor signals in the form of

Customized multi-scale representations and Formal nonlinear stochastic differential/difference equation (n-SDE) models

Statistics Qualitative Reasoning

Nonlinear Dynamic SystemsApplications

Traditional and Emerging Manufacturing Machines and ProcessesProcess stability, Degradation, Product surface monitoring

Structural health monitoring, Network traffic monitoring, Dynamics characterization

7

Agenda

Introduction

Problem Motivation & BackgroundChallenges to Quality and Integrity Monitoring

Attractor based Approaches

Research Methodology

Results and Discussion

Summary

8

Sensor-data CharacteristicsNonstationary

Strong bursts

Continuous band of frequencies

Classical time-series models and signal representations not adequate

9

Long Range Dependencies

10

State Portraits

Structurally StableTopologically Invariant

11

Time Delay Plots

Ceramic tool, 100 Cr-Mo 6 Steel, Sampling rate: 40 MHz

AE Signals Lag = 4Accelerometer signals Lag = 2

12

Literature on Attractor-Based Models and Features

Prediction Error and diffeomorphism (Todd et al. 2001; Nichols et al. 00, 03; Pecora and Carrol 02)Wavelet Features

Coefficients (e.g., Kamarthi et al., 1999; Kamarthi and Pittner 03)Energy (e.g., Suh et al. 1999; Kamarthi and Pittner 02)Entropy (e.g., Bukkapatnam et al. 1999)

Scaling LawsHolder Exponents (Wang et al. 2001)Fractal dimensions (e.g., Craig et al. 2000; Bukkapatnam et al.,1994, 2000)

Recurrence AnalysisRecurrence plots (Eckmann et al. 1987)Pseudo-probability space (Bukkapatnam et al. 1999)RQA (Kurths 2002; Zbilut and Webber Jr. 1992)

Gap: Locally optimal transformation that allows perfect reconstruction

13

Agenda

Introduction

Problem Motivation & Background

Research MethodologyRecurrence Quantification

Ensemble Extraction

Results and Discussion

Summary

14

Properties of Signals y(t)Emanates from an (chaotic) attractor ALet x(t) = f(x(0), t) a.s, be process trajectory

y(t) is a measurement of x(t) with x(0) ∈ A

Theorem: If ζ(t) ∈ A are reconstructed from lags of y(t), a diffeomorphism exists between A and observable subspace of A

15

Pseudoprobability space

Invariant measure µ on A exists; ∀t

Theorem (Poincare recurrence theorem):

Fact: Poincare section Λ of an attractor A is invariant with respect to the Poincare map ρ

Create a probability space (Λ, B, µ) with Λ as one-sided Poincare section containing ζref

Λ∈∀∀Λ⊂⇒∈Λ→ ζζρρ k, ,)}({ ,: k BAA

)),(()( tf Λ=Λ⊂Λ∀ µµA,

16

Poincare section

17

Artificial ensemblesLocal evolutions from neighborhood of yref are independent realizations

18

Local eigenfunctions αl(t)

Extracted from artificial ensembles

19

Customized Multiscale RepresentationUses Lifting Scheme (2nd generation wavelets)

20

Two-stage representation

0 200 400 600 800 1000 1200−20

−15

−10

−5

0

5

10

15

20Signal contaminated with 10% additive noise

Time unit

Mag

nitu

de

0 200 400 600 800 1000 1200−25

−20

−15

−10

−5

0

5

10

15

20

25Signal contaminated with 10% additive noise after Haar filtering

Time unit

Mag

nitu

de

0 50 100 150 200 250 300−250

−200

−150

−100

−50

0

50

100

150

200

250−N the level approximation of 01% additive noise contaminated signal

Coefficient number

Coe

ffici

ent m

agni

tude

0 100 200 300 400 500 600−4

−3

−2

−1

0

1

2

3

4Higher level coefficients of 10% additive noise contaminated signal

Coefficient number

Coe

ffici

ent m

agni

tude

HaarPrefilter

0 50 100 150 200 250 300−15

−10

−5

0

5

10

15−N the level details of 01% additive noise contaminated signal

Coefficient number

Coe

ffici

ent m

agni

tude

21

Entropy values

Scaling function EntropyCoiflet 1Daubechies 4Daubechies 20Cosine packetSuboptimal (SWPR)

4.795.324.533.840.05

2-stage 0.04

22

Further Improvement

Different strands have different local evolution patterns

23

Research ApproachStrandlets: Piecewise eigen representation

Recurrence Plot RQA

Local PCA

Characteristic Signal Strand for Lifting

Signal with Bursts

24

Recurrence PlotsDepicts the neighborhood structureCaptures time indices at which trajectories return to a neighborhood

25

Trajectory SplicingSegment trajectories based on similarity in the recurrence patterns

26

Piecewise Ensembles

27

Piecewise Eigenfunctions

Capture the basic shape of the trajectory

28

Noise Reduction Result50-80% reduction in noise

Green line: Noisy trajectoryBlue line: Nominal trajectoryRed line: Recurrence-based De-noised trajectory

29

Results Under 30% Noise Contamination

Can blindly track the process (attractor)Knowledge of the noise-free trajectory is not necessary

30

Contributions

Theoretical contributionsNew approach to represent signals from nonlinear systemsOperationalization of recurrence concept

Contributions to practiceNew methods to reduce noise from signals when the process dynamics is unknownFeatures sensitive to local variations

31

Extensions Planned

Strandlet extraction from lifting piecewise eigenfunctionsImprovements in pattern matching methods to select strands

32

ApplicationsQuality monitoring in manufacturing machines and processes

Process TypeTraditional Manufacturing ProcessesEmerging Manufacturing Processes

AnomalyMacroscopic stability analysis using vibration sensor dataMicroscopic stability analysis using Acoustic EmissionMacroscopic quality product variability analysis

Integrity monitoring and coordination of infrastructure and lifeline systems

Structural SystemsLarge structural sensor networksSmart material and structural systems

Large-Scale NetworksCommunication networksTransportation and supply networks

33

Summary and Acknowledgments

Enhance current quality monitoring and improvement practice through a rigorous use of information from electro-vibro-photo-acoustic sensors

Use process physics and sensor data to optimize/adjust settingsFounded on Dynamic Systems, Statistics and Qualitative Reasoning foundations

Sponsors of this research thus far:National Science Foundation (NSF)Office of Naval Research (ONR)HoneywellHewlett PackardNational InstrumentsFordCaltrans

34

Network Traffic and Intrusion Monitoring

Aggregate data packet counts exhibit significant burst characteristicsn-SDE models proposed for network traffic dynamics

1)1/()()1(0/)1(

{ 22

22

11

11

1 <<−−−++<<−−++

=+n

mmnn

nmm

nnn xdddxx

dxddxxx

εεεε

35

Investigate the physical principles underlying the generation of AE waveforms in precision (meso-scale) machining

M a c h in in g m o d e l

D is lo c a t io n m o d e l

P r o p a g a t io n m o d e l

ε&

M ic ro - v a r ia b l e sρ (x ) ,b ,v

M a c ro - v a r ia b l e s

P ro c e s s p a ra m e te r sV , f ,d

U n it A E w a v e fo r m c h a ra c te r is t ic s E e m

S o u rc e d e n s i t yp (ρ Α (x ,t ) )

A E (A g g r e g a te d ) a t a s e n s o r lo c a tio n

Sour

ce d

istr

ibut

ion

mod

el

A E u n it s o u r c e m o d e l•D is lo c a t io n a n n ih i la t io n•M ic ro c ra c k g ro w th•S h e a r lo c a liz a t io n

M a c h in in g m o d e l

D is lo c a t io n m o d e l

P r o p a g a t io n m o d e l

ε&

M ic ro - v a r ia b l e sρ (x ) ,b ,v

M a c ro - v a r ia b l e s

P ro c e s s p a ra m e te r sV , f ,d

U n it A E w a v e fo r m c h a ra c te r is t ic s E e m

S o u rc e d e n s i t yp (ρ Α (x ,t ) )

A E (A g g r e g a te d ) a t a s e n s o r lo c a tio n

Sour

ce d

istr

ibut

ion

mod

el

A E u n it s o u r c e m o d e l•D is lo c a t io n a n n ih i la t io n•M ic ro c ra c k g ro w th•S h e a r lo c a liz a t io n

Workpiecesurface

Slip line

b

b

Slip line

Schematic of microscopic deformation mechanisms in shear

zone.

Work-piece under cutting

Chip

Receiving transducer

Cutter

Secondary deformation zone Primary

deformation zone

AE propagation path

Tertiary Zone

Model Coefficients

Step 1: Signal

Analysis

Mec

hani

stic

wav

efor

m p

rinc

iple

s

Step 2: Model

Development

Nonlinear stochastic dynam

ics & W

avelets

De-noised signals

Step 3: Feature extraction &

anomaly detection

0 0 . 5 1 1 . 5 2 2 . 5 3 3 . 5 4

x 1 0- 3

- 1 . 5

- 1

- 0 . 5

0

0 . 5

1

1 . 5x 1 0

4

T i m e ( S e c o n d s )

Dis

pla

ce

me

nt

0 0 . 5 1 1 . 5 2 2 . 5 3 3 . 5 4

x 1 0- 3

- 4 0 0 0

- 3 0 0 0

- 2 0 0 0

- 1 0 0 0

0

1 0 0 0

2 0 0 0

3 0 0 0

4 0 0 0

T i m e ( S e c o n d s )

Di

sp

la

ce

me

nt

Comparison of Burst CountsR1 S1 Burst Count Threshold

0.5 × Maximum

0.7 × Maximum

345333

3942

Acoustic Emission Microdynamics

Publications:Chang and Bukkapatnam, Machining Sciences and Technology, 2004.

36

Stability and Chatter in Machining of Plate Structures

Simulation and Experimental studyConsider coupled dynamics of tool and workpieceImpact at the beginning and end of cut and tool wear

Milling, Drilling and Turning Configurations

Table

Spindle

Tool

Workpiece

Amplifier

Accelerometer

X

Yx 0x

0y

y

O

φ

Ad

Workpiece

Tool

Publications: Bukkapatnam et al., ASME Transactions JMSE, 1999Bukkapatnam et al., Physical Review, 1995 Bukkapatnam et al., CIRP Mfg. Systems, 1999Bukkapatnam and Fofana, FAIM 2000 Bukkapatnam et al., ASME Transactions JDMC, 2000

0

0.5

1

1.5

22.5

33.5

4

4.5

0 1 2 3 4 5 6 7 8

width of cut, w (in 10^-3 m)

num

ber o

f tee

th, N

Stable N=2Stable to Finite Amplitude N=2

Unstable N=2Stable N=4

Stable to Finite Amplitude N=4Unstable N=4

0

0.2

0.4

0.6

0.8

1

1.2

35 40 45 50

Length of tool, l (in 10^-3 m)

Wid

th o

f cut

, w (i

n 10

^-3

m)

Stable

Unstable

37

CC Quality Monitoring

To detect anomalies in extrusion-based processes

Process Modeling

Quantitative Characterization

Qualitative Characterization

Lumped System Model Synthesis

Model-based Monitoring

Signal Analysis

Feature Extraction

and Anomaly Detection

Signals

Process physics

On-line SignalS

)()1( 21 tFxyxkxcx xxx =++++ αα&&& (1a)

)()1( 21 tFyyxkycy yyy =++++ ββ&&& (1b)

/fb bF Ve Dµ=

2 /MVMV rF Dπ= Τ

( )y V B fb MVF t F F F F= = + +)VbhVb(VF reeB ξγρ −= −1 2

)(0 Ttyyhh −−+=

)2

(4 2

2y

D

b

DV rfe

e &+=ωπ

γ

Filament

DriveWheels

ExtrudedMaterial

HeatingElements

Nozzle

NozzleBarrel

Platform

Velocity profile during extrusion

Side view

Front view

Side

tro

wel

Top trowel

Velocity profile after extrusion

z

x

z

y

Velocity profile during extrusion

Side view

Front view

Side

tro

wel

Top trowel

Velocity profile after extrusion

z

x

z

y

Fy(t)

mFx(t)

kcc

k

x

x. y y

.

Modeling

Results

Publications:Kwon, Bukkapatnam, Khoshnevis, Saito, Rapid Prototyping, 2002Bukkapatnam and Clark, ASME Transactions 2003 (under review)

38

NDE & Health MonitoringApplications to health monitoring and NDE

Incipient damage detection in connected structuresEffective features for damage/anomaly detection, e.g., Wavelet distortion energy, fractal quantifiersShown to be better than conventional modal analysis

Sensor-based Modeling

Dat

a A

cqui

sitio

n Computational Models and Relations from Literature

Characterization (Qualitative and Quantitative)

Signal Analysis Formal Modeling

Feature Extraction

Damage Detection and Location

Distortion Energy & basis functions Model Coefficients

Model Structures Quantifiers

Dat

a

Con

ditio

ned

sign

als

Instrumented Complex Structure

Publications:Bukkapatnam et al., SHM Journal, 2004

0”

2/16”

3/16”

39

Flank wear estimation

•••°°

Signalrepresentation

Signalseparation

Featureextraction

Flank wear measurements

Signalrepresentation

Signalseparation

Featureextraction

Fractalestimator

Offlinetraining

Onlineestimation

AE signalestimator

Over 90% accuracy in estimating flank wear in turning process(MSE < 0.0012 in)