Transient Response Analysis
for
Temperature Modulated
Chemoresistors
R. Gutierrez-Osuna1,2, A. Gutierrez1,2 and N. Powar2
1Texas
A&M University, College Station, TX
2Wright State University, Dayton, OH
Multi-frequency Temperature Modulation for Metal-oxide Gas Sensors
Ricardo Gutierrez-Osuna
Texas A&M University
1
Outline
g
Introduction
n
n
g
Transient Response Analysis
n
n
g
n
Feature extraction
Performance measures
Results
n
n
g
Time-domain analysis
Time-constant or spectral analysis
Pattern Analysis
n
g
Research objectives
Temperature modulation approaches
Experimental setup
Sensitivity and selectivity enhancements
Concluding remarks
Multi-frequency Temperature Modulation for Metal-oxide Gas Sensors
Ricardo Gutierrez-Osuna
Texas A&M University
2
Objectives of this work
g
Improve information content of COTS gas
sensors by means of
Instrumentation: temperature modulation
n Computation: transient-response analysis
n
g
Evaluate various types of transient analysis
techniques
Time-domain techniques
n Time-constant-domain techniques
n
Multi-frequency Temperature Modulation for Metal-oxide Gas Sensors
Ricardo Gutierrez-Osuna
Texas A&M University
3
Outline
Temperature modulation
Temperature oscillation
Temperature transients
Transient analysis
Time domain
Time-constant domain
Pattern analysis
Feature extraction
Performance measures
Experimental validation
Experimental setup
Results
Multi-frequency Temperature Modulation for Metal-oxide Gas Sensors
Ricardo Gutierrez-Osuna
Texas A&M University
4
TEMPERATURE
MODULATION
Multi-frequency Temperature Modulation for Metal-oxide Gas Sensors
Ricardo Gutierrez-Osuna
Texas A&M University
5
Temperature modulation
g
Basic principle
Selectivity of metal-oxide chemoresistors depends on
operating temperature
n Capture the response of the sensor at multiple
temperatures
n
from [Yamazoe and Miura, 1992]
Multi-frequency Temperature Modulation for Metal-oxide Gas Sensors
Ricardo Gutierrez-Osuna
Texas A&M University
6
Temperature modulation approaches
g
Temperature oscillation
n
Sensor heater is driven by a
continuous function
g
n
g
VH
e.g., sine wave, ramp
Information is in the quasistationary or dynamic response
time
1/RS
time
Temperature transient
n
Sensor heater is driven by a
discontinuous function
g
n
e.g., step function, pulse
Information is in the transient
response
VH
time
1/RS
time
Multi-frequency Temperature Modulation for Metal-oxide Gas Sensors
Ricardo Gutierrez-Osuna
Texas A&M University
7
Temperature modulation examples
Temperature
oscillation
-4
0.125Hz
x 10
5
4
D
E
B
3
2
C
S#4, 1-2V
W
A
B
C
D
E
AIR
ACETONE
AMMONIA
IPA
VINEGAR
9
A
M
AM
8
7
6
5
1
0
Temperature
transient
A
AI
4
100 200 300 400 500 600 700 800
Multi-frequency Temperature Modulation for Metal-oxide Gas Sensors
Ricardo Gutierrez-Osuna
Texas A&M University
AIM
IM
I
100
200
300
400
8
TRANSIENT
ANALYSIS
Multi-frequency Temperature Modulation for Metal-oxide Gas Sensors
Ricardo Gutierrez-Osuna
Texas A&M University
9
Transient response analysis
g
Objective
n
Characterize the transient regime of a sensor to
g
g
g
Improve our understanding of the sensor’s behavior
Extract information to discriminate target analytes
How can the transient be characterized?
n
Time domain
g
n
Extract parameters directly from the time samples
“Frequency” domain
g
Convert the transient into a distribution of time constants
∞
f (t ) = ∫ G (τ ) e −t /τ dτ
0
Multi-frequency Temperature Modulation for Metal-oxide Gas Sensors
Ricardo Gutierrez-Osuna
Texas A&M University
10
Time vs. spectral representations
S#4, 2-3V
S#4, 1-2V
0
0
9
8
8
-1
7
-2
6
-3
4
6
-1
-2
-3
5
-4
2
4
100
200
300
400
10
0
10
100
1
200
300
S#1, 2-3V
8
400
10
0
10
1
S#2, 4-5V
0
8
-2
6
0.5
0
6
-4
4
4
-0.5
-6
2
2
100
200
300
400
10
0
10
1
100
Multi-frequency Temperature Modulation for Metal-oxide Gas Sensors
Ricardo Gutierrez-Osuna
Texas A&M University
200
300
400
10
0
10
11
1
Time vs. spectral representations
S#4, 1-2V
0
9
8
-1
7
-2
6
-3
5
-4
4
100
200
300
400
Multi-frequency Temperature Modulation for Metal-oxide Gas Sensors
Ricardo Gutierrez-Osuna
Texas A&M University
10
0
10
1
12
The Pade-Z Transform
g
Pade-Z is a system-identification technique that finds
a discrete multi-exponential model of the form
M
f (t ) = ∑ G m e − t / τ m
m =1
g
Pade-Z in a nutshell
n
n
n
n
n
Compute the Z-transform of the sampled transient (at z0)
Fit a Pade approximant to the Z-transform
Compute the partial fraction expansion
Convert poles/residues into time-constants/amplitudes
Select a subset of the time-constants/amplitudes
Multi-frequency Temperature Modulation for Metal-oxide Gas Sensors
Ricardo Gutierrez-Osuna
Texas A&M University
13
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
t
−
∞ t
d
METS1 (t ) =
f (t ) = ∫ G (τ )e τ dτ
0 τ
d (ln t )
n
METS is the convolution product of the true distribution with an
asymmetric kernel
h( y ) = exp( y − exp( y )) with y = ln(t )
Multi-frequency Temperature Modulation for Metal-oxide Gas Sensors
Ricardo Gutierrez-Osuna
Texas A&M University
14
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
2
M
 N −1 

− kT / τ m 
{M , Gm ,τ m } = arg min ∑  f k − ∑ Gm e
 
M ,Gm ,τ m  k = 0 
m =1
 

g Problems
n
n
n
g
The system of equations is non-linear in the time constants
M is unknown, meta-search is computationally intensive
Solution is ill-posed due to co-linearity
Solutions
n
Pre-specify a fixed number of time constants
τ = {0.01, 0.02, L,0.09, 0.1, 0.2, L,0.9, 1, 2, L,9,L}
n
Stabilize the solution with a regularization term
Multi-frequency Temperature Modulation for Metal-oxide Gas Sensors
Ricardo Gutierrez-Osuna
Texas A&M University
15
Validation on synthetic data
Synthetic transient with
three decays
n
τ1=0.1sec, τ2=1s, τ3=10s
8
7
G1=-10, G2=+10, G3=-10
n DC offset G =10
0
n Gaussian noise N(µ=0,σ=0.1)
n
Transient signal
g
9
6
5
4
3
Training data
Pade-Z model
Residual error
2
1
0
0
5
10
15
20
25
30
Time (s)
6
3
DC Offset
5
4
2
3
Amplitudes
METS1
1
0
2
1
0
-1
-1
-2
-2
-3
-3
10
-1
0
10
Time constant (s)
10
1
10
Multi-frequency Temperature Modulation for Metal-oxide Gas Sensors
Ricardo Gutierrez-Osuna
Texas A&M University
-2
10
-1
0
1
10
10
Time constant (s)
10
2
16
FEATURE
EXTRACTION
Multi-frequency Temperature Modulation for Metal-oxide Gas Sensors
Ricardo Gutierrez-Osuna
Texas A&M University
17
Feature extraction
g
Features can be extracted from the sensor
transient through window time slicing (WTS)
n
WTS can also be used in spectral representations
Interpretation as filter banks
1
1
0.8
0.8
Spectrum
Sensor response
g
0.6
0.4
0.4
0.2
0.2
0
0.6
0
10
20
30
time (s)
40
50
60
0
Multi-frequency Temperature Modulation for Metal-oxide Gas Sensors
Ricardo Gutierrez-Osuna
Texas A&M University
100
101
Time constants (s)
18
Pade-Z feature extraction
A
Can the model parameters
{Gm,τm} be used as
features?
n
Partial fraction expansion is
an ill-conditioned problem
10
AA
8
4
2
0
III
g
Small variations in the
transient samples can lead to
solutions with different
number of exponentials
I III
A
A
A
-2
M
MM
M
III
-4
n
A
6
Amplitude
g
AAA
-6
0
1
2
A
3
4
Log (time constant)
5
6
Conventional pattern-analysis techniques will expect
a fixed dimensionality M for all examples
Multi-frequency Temperature Modulation for Metal-oxide Gas Sensors
Ricardo Gutierrez-Osuna
Texas A&M University
19
Pade-Z feature extraction
g
Solution
n
Consider the Taylor-series expansion of ex:
∞
x 2 x3
xn
e = 1+ x + + +L = ∑
2! 3!
n = 0 n!
x
n
Re-grouping terms in the multi-exponential model:
∞
(− t )n
n =0
n!
M
−t /τ m
G
e
= ... = ∑
∑ m
m =1
n
M
Gm
∑τ
m =1
n
m
Yields any desired (and fixed) number of features, regardless of
the number of exponentials M returned by Pade-Z
M
∑ Gm ,
 m =1

, ∑ 2 , ∑ 2 ,L
∑
m =1 τ m
m =1 τ m
m =1 τ m

M
Gm
M
Gm
Multi-frequency Temperature Modulation for Metal-oxide Gas Sensors
Ricardo Gutierrez-Osuna
Texas A&M University
M
Gm
20
EXPERIMENTAL
VALIDATION
Multi-frequency Temperature Modulation for Metal-oxide Gas Sensors
Ricardo Gutierrez-Osuna
Texas A&M University
21
Experimental setup
g
Sensor array
n
g
Odor delivery
n
g
Acetone (A), Isopropyl alcohol (I) and Ammonia (M)
Performance measures
n
g
Static headspace analysis
Analyte database
n
g
Four TGS Figaro sensors (2600, 2620, 2611, 2610)
Sensitivity and selectivity
Temperature profile
n
Staircase temperature modulation (STM)
Multi-frequency Temperature Modulation for Metal-oxide Gas Sensors
Ricardo Gutierrez-Osuna
Texas A&M University
22
Staircase temperature modulation
TGS 2600
10
TGS 2620
10
5
Acetone
IPA
Ammonia
Heater
5
0
0
0
1000
2000
3000
TGS 2611
10
0
1000
3000
TGS 2610
10
5
2000
5
0
0
0
1000
2000
3000
0
1000
Multi-frequency Temperature Modulation for Metal-oxide Gas Sensors
Ricardo Gutierrez-Osuna
Texas A&M University
2000
3000
23
Feature sets
g
Transient dataset
n
n
n
g
Five feature sets
n
n
n
n
n
g
Four sensors
Six transients per sensor
Four features per transient
WTS: 48 dimensions
Pade-Z: 48 dimensions
METS: 48 dimensions
RRCF: 48 dimensions
DC: 12 dimensions
Two datasets
n
n
Sensitivity on serial dilutions
Selectivity on binary/ternary mixtures
Multi-frequency Temperature Modulation for Metal-oxide Gas Sensors
Ricardo Gutierrez-Osuna
Texas A&M University
24
Sensitivity: performance measure
Rationale
n
Evaluate misclassification cost
as a function of analyte
concentration
g
n
90
Classification based on the
nearest neighbor rule
Misclassification cost
g
g
Penalize misclassifying
analyte X as analyte Y
Penalize misclassifying
concentration i as
concentration j
Feature set 1
80
Classification rate (%)
g
100
70
60
50
Feature set 2
40
30
20
10
0
0
10
1
10
2
3
10
10
Analyte Concentration
4
5
10
10
1
1
Cost (Xi Yj ) = d(X, Y ) + d(i, j)
α
β
0 X = Y
where d(i, j) = i − j and d(X, Y ) = 
1 X ≠ Y
Multi-frequency Temperature Modulation for Metal-oxide Gas Sensors
Ricardo Gutierrez-Osuna
Texas A&M University
25
Sensitivity: results
Serial dilutions of
individual analytes
n
Base concentration (v/v)
g
g
n
These are near the DCisothermal detection
threshold
Dilutions
g
5 levels with a 1/10 dilution
factor
Distilled water is treated as
a 6th dilution level
Data collection
g
g
85
A:10-4%, I:10-1%, M:1.0%
n
n
SENSITIVITY
90
17 samples per day
4 days
80
Classification rate
g
75
70
65
SSTM
WTS
PADE-Z
METS
RRCF
60
55
1
Multi-frequency Temperature Modulation for Metal-oxide Gas Sensors
Ricardo Gutierrez-Osuna
Texas A&M University
2
(a)
3
4
Concentration level
5
26
Selectivity: performance measure
Rationale
n
n
A good feature set will partition
feature space into linearly
separable odor-specific
regions
For each analyte A, compute a
linear discriminant function
if x ⊃ A
1
g A (x ) = 
0 otherwise
g
Examples
n
n
n
CCC
C
CC
CCC
C
1
gA(x)
gB(x)
0.5
Feature 2
g
0
AC
AC AC
ACAC
AC
AC
AC
AC
A
A
AA
AAA
A
AA
-0.5
gA(AB)=1
gA(BC)=0
gC(x)
AB AB
AB
AB
AB AB
ABAB
AB AB
-1
-2
ABC
ABC
ABC
ABC
ABC
ABC
ABC ABC
ABC
ABCABC
-1.5
-1
-0.5
Feature 1
BCBC
BC BC
BC
BC
BC
BCBC
BC
BC
BC
BB
BB
B
B BB
B
0
0.5
Discriminant functions are found with the Ho-Kashyap procedure
g
g
Guaranteed solution in the linearly separable case
Guaranteed convergence otherwise
Multi-frequency Temperature Modulation for Metal-oxide Gas Sensors
Ricardo Gutierrez-Osuna
Texas A&M University
27
Selectivity: results
Binary/ternary
mixtures of analytes
n
n
Equivalent analyte
intensity on isothermal
sensor response
Dilutions
g
3 levels with a 1/3 dilution
factor
Data collection
g
g
90
A:0.3%, I:1.0%, M:33%
n
n
95
Base concentration (v/v)
g
24 samples per day
3 days
SELECTIVITY
100
85
Classification rate
g
80
75
70
65
SSTM
WTS
PADE-Z
METS
RRCF
60
55
1
Multi-frequency Temperature Modulation for Metal-oxide Gas Sensors
Ricardo Gutierrez-Osuna
Texas A&M University
3
5
7
9
11 13 15
Principal components
17
19
28
CONCLUDING
REMARKS
Multi-frequency Temperature Modulation for Metal-oxide Gas Sensors
Ricardo Gutierrez-Osuna
Texas A&M University
29
Conclusions
g
Transient analysis
Time-domain vs. spectral characterization
n Ridge Regression Curve Fitting
n
g
Pattern analysis
Feature extraction
n Performance measures
n
g
Experimental results
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
n
Multi-frequency Temperature Modulation for Metal-oxide Gas Sensors
Ricardo Gutierrez-Osuna
Texas A&M University
30
Directions for future work
g
Data-driven placement of WTS kernels
n
g
Kernels should be placed to maximize class
separability
Improvements to Pade-Z characterization
Regularization of partial fraction expansion
n Development of classifiers for multi-modal densities
n
g
Experimental improvements
Optimizing the duration of thermal transients
n Comparison of ON/OFF and OFF/ON transients
n Evaluation with micro hot-plates
n
Multi-frequency Temperature Modulation for Metal-oxide Gas Sensors
Ricardo Gutierrez-Osuna
Texas A&M University
31
QUESTIONS …
Multi-frequency Temperature Modulation for Metal-oxide Gas Sensors
Ricardo Gutierrez-Osuna
Texas A&M University
32
THANK YOU
Multi-frequency Temperature Modulation for Metal-oxide Gas Sensors
Ricardo Gutierrez-Osuna
Texas A&M University
33