Transient Response Analysis for Temperature Modulated ...research.cs.tamu.edu/prism/lectures/talks/imcs02.pdf · Transient response analysis gObjective nCharacterize the transient

Multi-frequency Temperature Modulation for Metal-oxide Gas SensorsRicardo Gutierrez-OsunaTexas A&M University

1

Transient Response Analysis Transient Response Analysis for for

Temperature Modulated Temperature Modulated ChemoresistorsChemoresistors

R. Gutierrez-Osuna1,2, A. Gutierrez1,2 and N. Powar2

1Texas A&M University, College Station, TX2Wright State University, Dayton, OH


2

Outlineg Introduction

n Research objectivesn Temperature modulation approaches

g Transient Response Analysisn Time-domain analysisn Time-constant or spectral analysis

g Pattern Analysisn Feature extractionn Performance measures

g Resultsn Experimental setupn Sensitivity and selectivity enhancements

g Concluding remarks


3

Objectives of this workg Improve information content of COTS gas

sensors by means of n Instrumentation: temperature modulationn Computation: transient-response analysis

gEvaluate various types of transient analysis techniquesn Time-domain techniquesn Time-constant-domain techniques


4

Outline

Temperature modulation

Transient analysis

Pattern analysis

Experimental validation

Temperature oscillationTemperature transients

Time domainTime-constant domain

Feature extractionPerformance measures

Experimental setupResults


5

TEMPERATURE MODULATION


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Temperature modulationgBasic principle

n Selectivity of metal-oxide chemoresistors depends on operating temperature

n Capture the response of the sensor at multiple temperatures

from [Yamazoe and Miura, 1992]


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Temperature modulation approachesgTemperature oscillation

n Sensor heater is driven by a continuous function g e.g., sine wave, ramp

n Information is in the quasi-stationary or dynamic response

gTemperature transientn Sensor heater is driven by a

discontinuous functiong e.g., step function, pulse

n Information is in the transient response

time

VH

time

1/RS

time

VH

time

1/RS

time

VH

time

1/RS

time

VH

time

1/RS


8

Temperature modulation examples

100 200 300 400 500 600 700 8000

1

2

3

4

5x 10

-4 0.125Hz

A

B

D E

C

A AIRB ACETONEC AMMONIAD IPA E VINEGAR

100 200 300 400 500 600 700 8000

1

2

3

4

5x 10

-4 0.125Hz

A

B

D E

C

A AIRB ACETONEC AMMONIAD IPA E VINEGAR

Temperatureoscillation

Temperaturetransient

S#4, 1-2V

100 200 300 400

4

5

6

7

8

9

A

I

M

AI

AM

IM AIM

WS#4, 1-2V

100 200 300 400

4

5

6

7

8

9

A

I

M

AI

AM

IM AIM

W


9

TRANSIENTANALYSIS


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Transient response analysisgObjective

n Characterize the transient regime of a sensor tog Improve our understanding of the sensor’s behaviorg Extract information to discriminate target analytes

gHow can the transient be characterized?n Time domain

g Extract parameters directly from the time samples

n “Frequency” domaing Convert the transient into a distribution of time constants

( ) ττ τ deGtf t /

0)( −∞

∫=


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Time vs. spectral representations

100 200 300 400

2

4

6

8

S#2, 4-5V

100 200 300 400

2

4

6

8

S#4, 2-3V

100

101

-3

-2

-1

0

100 200 300 400

2

4

6

8

S#1, 2-3V

100

101

-6

-4

-2

0

-0.5

100

101

0

0.5

4

5

6

7

8

9

S#4, 1-2V

100

101

-4

-3

-2

-1

0

100 200 300 400


12

Time vs. spectral representations

4

5

6

7

8

9

S#4, 1-2V

100

101

-4

-3

-2

-1

0

100 200 300 400

4

5

6

7

8

9

4

5

6

7

8

9

S#4, 1-2V

100

101

-4

-3

-2

-1

0

100

101

-4

-3

-2

-1

0

100 200 300 400100 200 300 400


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The Pade-Z Transformg Pade-Z is a system-identification technique that finds

a discrete multi-exponential model of the form

g Pade-Z in a nutshelln Compute the Z-transform of the sampled transient (at z0)n Fit a Pade approximant to the Z-transformn Compute the partial fraction expansion n Convert poles/residues into time-constants/amplitudesn Select a subset of the time-constants/amplitudes

∑=

−=M

m

tm

meGtf1

/)( τ


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Multi-Exponential Transient Spectroscopy g METS is a signal-processing technique that yields a

distribution or spectrum of time constants n A differentiation of the sensor transient in logarithmic-time scale

n METS is the convolution product of the true distribution with anasymmetric kernel

( )∫∞ −

==01 )(

)(ln)( ττ

ττ deGttf

tddtMETS

t

)ln())exp(exp()( tywithyyyh =−=


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Ridge Regression Curve Fittingg RRCF is statistical regression technique modified to

produce a spectral representation of the transientn Based on the minimum mean-square error solution

g Problemsn The system of equations is non-linear in the time constantsn M is unknown, meta-search is computationally intensiven Solution is ill-posed due to co-linearity

g Solutionsn Pre-specify a fixed number of time constants

n Stabilize the solution with a regularization term

−= ∑ ∑

−

= =

−21

0 1

/

,,minarg},,{

N

k

M

m

kTmk

GMmm

m

mm

eGfGM τ

ττ

{ }LLLL ,9,,2,1,9.0,,2.0,1.0,09.0,,02.0,01.0=τ


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Validation on synthetic datagSynthetic transient with

three decaysn τ1=0.1sec, τ2=1s, τ3=10sn G1=-10, G2=+10, G3=-10n DC offset G0=10n Gaussian noise N(µ=0,σ=0.1)

0 5 10 15 20 25 30

0

1

2

3

4

5

6

7

8

9

Training dataPade-Z modelResidual error

Time (s)

Tran

sien

t sig

nal

10-1 100 101

-3

-2

-1

0

1

2

3

MET

S 1

Time constant (s)10-2 10-1 100 101 102

-3

-2

-1

0

1

2

3

4

5

6

Time constant (s)

Ampl

itude

s

DC Offset


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FEATURE EXTRACTION


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Feature extractiongFeatures can be extracted from the sensor

transient through window time slicing (WTS)n WTS can also be used in spectral representations

g Interpretation as filter banks

0 10 20 30 40 50 60time (s)

0

0.2

0.4

0.6

0.8

1

Sens

or re

spon

se

100 101Time constants (s)

0

0.2

0.4

0.6

0.8

1

Spec

trum


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Pade-Z feature extractiong Can the model parameters

{Gm,τm} be used as features?

n Partial fraction expansion is an ill-conditioned problem

n Small variations in the transient samples can lead to solutions with different number of exponentials

g Conventional pattern-analysis techniques will expect a fixed dimensionality M for all examples

0 1 2 3 4 5 6

-6

-4

-2

0

2

4

6

8

10

A

A

A

I

I

I

MA

A

A

I

I

I

MA

A

A

I

I

I

MA

A

A

I

I

I

M

Log (time constant)

Am

plitu

de

0 1 2 3 4 5 6

-6

-4

-2

0

2

4

6

8

10

A

A

A

I

I

I

MA

A

A

I

I

I

MA

A

A

I

I

I

MA

A

A

I

I

I

M

Log (time constant)

Am

plitu

de


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Pade-Z feature extractiong Solution

n Consider the Taylor-series expansion of ex:

n Re-grouping terms in the multi-exponential model:

n Yields any desired (and fixed) number of features, regardless ofthe number of exponentials M returned by Pade-Z

∑∞

=

=++++=0

32

!!3!21

n

nx

nxxxxe L

( )∑ ∑∑∞

= ==

− −==

0 11

/

!...

n

M

mnm

mnM

m

tm

GnteG m

ττ

∑ ∑ ∑ ∑= = = =

M

m

M

m

M

m

M

m m

m

m

m

m

mm

GGGG1 1 1 1

22 ,,,, Lτττ


21

EXPERIMENTAL VALIDATION


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Experimental setupgSensor array

n Four TGS Figaro sensors (2600, 2620, 2611, 2610)gOdor delivery

n Static headspace analysisgAnalyte database

n Acetone (A), Isopropyl alcohol (I) and Ammonia (M)gPerformance measures

n Sensitivity and selectivitygTemperature profile

n Staircase temperature modulation (STM)


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Staircase temperature modulation

0 1000 2000 30000

5

10TGS 2600

0 1000 2000 30000

5

10TGS 2620

0 1000 2000 30000

5

10TGS 2611

0 1000 2000 30000

5

10TGS 2610

AcetoneIPA

AmmoniaHeater


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Feature setsg Transient dataset

n Four sensorsn Six transients per sensorn Four features per transient

g Five feature setsn WTS: 48 dimensionsn Pade-Z: 48 dimensionsn METS: 48 dimensionsn RRCF: 48 dimensionsn DC: 12 dimensions

g Two datasetsn Sensitivity on serial dilutionsn Selectivity on binary/ternary mixtures


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Sensitivity: performance measureg Rationale

n Evaluate misclassification cost as a function of analyte concentration

g Classification based on the nearest neighbor rule

n Misclassification costg Penalize misclassifying

analyte X as analyte Yg Penalize misclassifying

concentration i as concentration j

100 101 102 103 104 105

0

10

20

30

40

50

60

70

80

90

100

Analyte Concentration

Cla

ssifi

catio

n ra

te (%

)

Feature set 2

Feature set 1

100 101 102 103 104 105

0

10

20

30

40

50

60

70

80

90

100

Analyte Concentration

Cla

ssifi

catio

n ra

te (%

)

Feature set 2

Feature set 1

( ) ( ) ( )

( ) ( )

≠=

=−=

+=

YX1YX0

YX,dandjiji,dwhere

ji,dβ1YX,d

α1YXCost ji


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Sensitivity: resultsgSerial dilutions of

individual analytesn Base concentration (v/v)

g A:10-4%, I:10-1%, M:1.0%n These are near the DC-

isothermal detection threshold

n Dilutionsg 5 levels with a 1/10 dilution

factorg Distilled water is treated as

a 6th dilution leveln Data collection

g 17 samples per dayg 4 days 1 2 3 4 5

55

60

65

70

75

80

85

90SENSITIVITY

Concentration level

Cla

ssifi

catio

n ra

te

SSTMWTS

PADE-ZMETSRRCF (a)


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Selectivity: performance measureg Rationale

n A good feature set will partition feature space into linearly separable odor-specific regions

n For each analyte A, compute a linear discriminant function

g Examplesn gA(AB)=1n gA(BC)=0

n Discriminant functions are found with the Ho-Kashyap procedureg Guaranteed solution in the linearly separable caseg Guaranteed convergence otherwise

-2 -1.5 -1 -0.5 0 0.5-1

-0.5

0

0.5

1

AAAA AAAA A

A

B BB

BBBB

BBB

CCCCCCC

C CC

ABABABABABAB ABAB AB

AB

ACACACACACACACAC

ACAC

BCBCBCBCBCBCBCBCBC

BCABC

ABC

ABCABCABCABCABCABCABC

ABCBC

BC

ABC

gB(x)gA(x)

gC(x)

Feature 1

Feat

ure

2

-2 -1.5 -1 -0.5 0 0.5-1

-0.5

0

0.5

1

AAAA AAAA A

A

B BB

BBBB

BBB

CCCCCCC

C CC

ABABABABABAB ABAB AB

AB

ACACACACACACACAC

ACAC

BCBCBCBCBCBCBCBCBC

BCABC

ABC

ABCABCABCABCABCABCABC

ABCBC

BC

ABC

gB(x)gA(x)

gC(x)

Feature 1

Feat

ure

2

( ) ⊃

=otherwise0

Axif1xgA


28

Selectivity: resultsgBinary/ternary

mixtures of analytesn Base concentration (v/v)

g A:0.3%, I:1.0%, M:33%n Equivalent analyte

intensity on isothermal sensor response

n Dilutionsg 3 levels with a 1/3 dilution

factor

n Data collectiong 24 samples per dayg 3 days

1 3 5 7 9 11 13 15 17 1955

60

65

70

75

80

85

90

95

100

Principal components

Cla

ssifi

catio

n ra

te

SSTMWTS

PADE-ZMETSRRCF

SELECTIVITY


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CONCLUDING REMARKS


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ConclusionsgTransient analysis

n Time-domain vs. spectral characterizationn Ridge Regression Curve Fitting

gPattern analysisn Feature extractionn Performance measures

gExperimental resultsn Thermal transients provide improved sensitivity and

selectivityn Thermal transients are faster; no need to reach S-Sn Time-domain characterization provides a more

compact code


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Directions for future workgData-driven placement of WTS kernels

n Kernels should be placed to maximize class separability

g Improvements to Pade-Z characterizationn Regularization of partial fraction expansion n Development of classifiers for multi-modal densities

gExperimental improvementsn Optimizing the duration of thermal transientsn Comparison of ON/OFF and OFF/ON transientsn Evaluation with micro hot-plates


32

QUESTIONS …


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THANK YOU

Documents

Transient Response Analysis for Temperature Modulated ...research.cs.tamu.edu/prism/lectures/talks/imcs02.pdf · Transient response analysis gObjective nCharacterize the transient