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Transient Response Analysis Transient Response Analysis for for Temperature Modulated Temperature Modulated Chemoresistors Chemoresistors

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

1Texas A&M University, College Station, TX 2Wright State University, Dayton, OH

Outline

g Introduction

n Research objectives n Temperature modulation approaches

g Transient Response Analysis

n Time-domain analysis n Time-constant or spectral analysis

g Pattern Analysis

n Feature extraction n Performance measures

g Results

n Experimental setup n Sensitivity and selectivity enhancements

g Concluding remarks

Objectives of this work

gImprove information content of COTS gas

sensors by means of

n Instrumentation: temperature modulation n Computation: transient-response analysis

gEvaluate various types of transient analysis

techniques

n Time-domain techniques n Time-constant-domain techniques

Outline

Temperature modulation Transient analysis Pattern analysis Experimental validation

Temperature oscillation Temperature transients Time domain Time-constant domain Feature extraction Performance measures Experimental setup Results

TEMPERATURE TEMPERATURE MODULATION MODULATION

Temperature modulation

gBasic principle

n Selectivity of metal-oxide chemoresistors depends on

• perating temperature

n Capture the response of the sensor at multiple

temperatures

from [Yamazoe and Miura, 1992]

Temperature modulation approaches

gTemperature 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 transient

n Sensor heater is driven by a

discontinuous function

g 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

Temperature modulation examples

100 200 300 400 500 600 700 800 1 2 3 4 5 x 10

• 4

0.125Hz A B D E C A AIR B ACETONE C AMMONIA D IPA E VINEGAR 100 200 300 400 500 600 700 800 1 2 3 4 5 x 10

• 4

0.125Hz A B D E C A AIR B ACETONE C AMMONIA D IPA E VINEGAR

Temperature

• scillation

Temperature transient

S#4, 1-2V 100 200 300 400 4 5 6 7 8 9 A I M AI AM IM AIM W S#4, 1-2V 100 200 300 400 4 5 6 7 8 9 A I M AI AM IM AIM W

TRANSIENT TRANSIENT ANALYSIS ANALYSIS

Transient response analysis

gObjective

n Characterize the transient regime of a sensor to

g Improve our understanding of the sensor’s behavior g 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” domain

g Convert the transient into a distribution of time constants

( )

τ τ

τ d

e G t f

t /

) (

− ∞

∫

=

Time vs. spectral representations

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• 1

Time vs. spectral representations

4 5 6 7 8 9 S#4, 1-2V 10 10

1

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• 1

100 200 300 400 4 5 6 7 8 9 4 5 6 7 8 9 S#4, 1-2V 10 10

1

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• 1

10 10

1

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• 1

100 200 300 400 100 200 300 400

The Pade-Z Transform

g Pade-Z is a system-identification technique that finds

a discrete multi-exponential model of the form

g Pade-Z in a nutshell

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

∑

= −

=

M m t m

m

e G t f

1 /

) (

τ

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 an

asymmetric kernel

( )

∫

∞ −

= =

1

) ( ) (ln ) ( τ τ τ

τ d

e G t t f t d d t METS

t

) ln( )) exp( exp( ) ( t y with y y y h = − =

Ridge Regression Curve Fitting

g RRCF is statistical regression technique modified to

produce a spectral representation of the transient

n Based on the minimum mean-square error solution

g Problems

n The system of equations is non-linear in the time constants n M is unknown, meta-search is computationally intensive n Solution is ill-posed due to co-linearity

g Solutions

n Pre-specify a fixed number of time constants n Stabilize the solution with a regularization term

              − =

∑ ∑

− = = − 2 1 1 / , ,

min arg } , , {

N k M m kT m k G M m m

m m m

e G f G M

τ τ

τ

{ }

L L L L , 9 , , 2 , 1 , 9 . , , 2 . , 1 . , 09 . , , 02 . , 01 . = τ

Validation on synthetic data

gSynthetic transient with

three decays

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

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• 1

FEATURE FEATURE EXTRACTION EXTRACTION

Feature extraction

gFeatures 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 10 20 30 40 50 60 time (s) 0.2 0.4 0.6 0.8 1 Sensor response 100 101 Time constants (s) 0.2 0.4 0.6 0.8 1 Spectrum

Pade-Z feature extraction

g 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

1 2 3 4 5 6

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2 4 6 8 10

A A A I I I M A A A I I I M A A A I I I M A A A I I I M

Log (time constant) Amplitude 1 2 3 4 5 6

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2 4 6 8 10

A A A I I I M A A A I I I M A A A I I I M A A A I I I M

Log (time constant) Amplitude

Pade-Z feature extraction

g 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 of

the number of exponentials M returned by Pade-Z

∑

∞ =

= + + + + =

3 2

! ! 3 ! 2 1

n n x

n x x x x e L

( )

∑ ∑ ∑

∞ = = = −

− = =

1 1 /

! ...

n M m n m m n M m t m

G n t e G

m

τ

τ

     ∑

∑ ∑ ∑

= = = = M m M m M m M m m m m m m m m

G G G G

1 1 1 1 2 2

, , , , L τ τ τ

EXPERIMENTAL EXPERIMENTAL VALIDATION VALIDATION

Experimental setup

gSensor array

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

gOdor delivery

n Static headspace analysis

gAnalyte database

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

gPerformance measures

n Sensitivity and selectivity

gTemperature profile

n Staircase temperature modulation (STM)

Staircase temperature modulation

1000 2000 3000 5 10 TGS 2600 1000 2000 3000 5 10 TGS 2620 1000 2000 3000 5 10 TGS 2611 1000 2000 3000 5 10 TGS 2610 Acetone IPA Ammonia Heater

Feature sets

g Transient dataset

n Four sensors n Six transients per sensor n Four features per transient

g Five feature sets

n WTS: 48 dimensions n Pade-Z: 48 dimensions n METS: 48 dimensions n RRCF: 48 dimensions n DC: 12 dimensions

g Two datasets

n Sensitivity on serial dilutions n Selectivity on binary/ternary mixtures

Sensitivity: performance measure

g Rationale

n Evaluate misclassification cost

as a function of analyte concentration

nearest neighbor rule

n Misclassification cost

analyte X as analyte Y

concentration i as concentration j

( )

( ) ( ) ( ) ( )

   ≠ = = − = + = Y X 1 Y X Y X, d and j i j i, d where j i, d β 1 Y X, d α 1 Y X Cost

j i

Sensitivity: results

gSerial dilutions of

individual analytes

n Base concentration (v/v)

g A:10-4%, I:10-1%, M:1.0%

isothermal detection threshold

n Dilutions

g 5 levels with a 1/10 dilution

factor

g Distilled water is treated as

a 6th dilution level

n Data collection

g 17 samples per day g 4 days

1 2 3 4 5 55 60 65 70 75 80 85 90

SENSITIVITY

Concentration level Classification rate SSTM WTS PADE-Z METS RRCF

(a)

Selectivity: performance measure

g 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

n Discriminant functions are found with the Ho-Kashyap procedure

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A A A A AA A A A A B B B B B B B B B B C C C CC C C C C C ABAB AB AB AB AB AB AB AB AB ACAC AC AC AC AC AC AC AC AC BC BC BC BC BC BC BCBC BC BC ABC ABC ABC ABC ABC ABC ABC ABC ABC ABC BC BC ABC gB(x) gA(x) gC(x)

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• 0.5

A A A A AA A A A A B B B B B B B B B B C C C CC C C C C C ABAB AB AB AB AB AB AB AB AB ACAC AC AC AC AC AC AC AC AC BC BC BC BC BC BC BCBC BC BC ABC ABC ABC ABC ABC ABC ABC ABC ABC ABC BC BC ABC gB(x) gA(x) gC(x)

( )

   ⊃ =

• therwise

A x if 1 x gA

Selectivity: results

gBinary/ternary

mixtures of analytes

n Base concentration (v/v)

g A:0.3%, I:1.0%, M:33%

intensity on isothermal sensor response

n Dilutions

g 3 levels with a 1/3 dilution

factor

n Data collection

g 24 samples per day g 3 days

1 3 5 7 9 11 13 15 17 19 55 60 65 70 75 80 85 90 95 100 Principal components Classification rate SSTM WTS PADE-Z METS RRCF

SELECTIVITY

CONCLUDING CONCLUDING REMARKS REMARKS

Conclusions

gTransient analysis

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

gPattern analysis

n Feature extraction n Performance measures

gExperimental results

n Thermal transients provide improved sensitivity and

selectivity

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

compact code

Directions for future work

gData-driven placement of WTS kernels

n Kernels should be placed to maximize class

separability

gImprovements to Pade-Z characterization

n Regularization of partial fraction expansion n Development of classifiers for multi-modal densities

gExperimental improvements

n Optimizing the duration of thermal transients n Comparison of ON/OFF and OFF/ON transients n Evaluation with micro hot-plates

QUESTIONS … QUESTIONS …

THANK YOU THANK YOU