SLIDE 1
ICASSP 2013 | MAYOUE Aurélien | 2
- OVERVIEW
- Context
- Prototype
- RECURSIVE LEAST SQUARES ALGORITHM
- Theorical basis & Principle
- One dimensional signal case
- Regularization
- Multisensor adaptation
- EXPERIMENTS
- Description
- Results
RECURSIVE LEAST SQUARES ALGORITHM DEDICATED TO EARLY RECOGNITION OF - - PowerPoint PPT Presentation
RECURSIVE LEAST SQUARES ALGORITHM DEDICATED TO EARLY RECOGNITION OF - - PowerPoint PPT Presentation
RECURSIVE LEAST SQUARES ALGORITHM DEDICATED TO EARLY RECOGNITION OF EXPLOSIVE COMPOUNDS THANKS TO MULTI- TECHNOLOGY SENSORS Aurlien MAYOUE, Aurlie MARTIN, Guillaume LEBRUN and Anthony LARUE ICASSP 2013, VANCOUVER OUTLINE OVERVIEW
SLIDE 2
SLIDE 3
ICASSP 2013 | MAYOUE Aurélien | 3
CONTEXT
EGDN TNT DNT NM
interferents
e-nose gas sensor + algorithm compounds detection identification quantification Recursive Least Squares decision detection signal
- analyte
- sensitive material
- technology
EGDN DNT TNT NM interferents
GAS SENSOR ALGORITHM
SLIDE 4
ICASSP 2013 | MAYOUE Aurélien | 4
PROTOTYPE
inhaler QCM SAW OPTO
Prototype based on a gas sensor array:
technology active layers Fluorescence (OPTO) 1 Quartz Crystal Microbalance (QCM) 2 Surface Acoustic Wave (SAW) 2
SLIDE 5
ICASSP 2013 | MAYOUE Aurélien | 5
THEORICAL BASIS
( )
β α δ β α
τ δ τ
+ + − =
−
t e Q t f
t
. 1 . Q. , , ,
,
Langmuir model:
- parameters depending on the absorption affinity between the unknown gas and the sensor:
- τ time constant
- δ sensitivity
- parameters depending on experimental conditions:
- Q concentration of the compound
- α slope of the sensor linear drift
- β sensor offset
first order response linear drift
= +
used to build models estimated by RLS algorithm
SLIDE 6
ICASSP 2013 | MAYOUE Aurélien | 6
PRINCIPLE
are set using training examples to build models
) , (
) ( ) ( c c
δ τ
interferents NM EGDN DNT TNT
are estimated in such a way each model best fits the real data
) , , (
) ( ) ( ) ( c c c
Q β α
DNT TNT NM EGDN interferents
MODELS RECURSIVE LEAST SQARES DECISION ACQUISITION
eDNT eTNT eEGDN eNM einterferents PDNT PTNT PEGDN PNM Pinterferents
SLIDE 7
ICASSP 2013 | MAYOUE Aurélien | 7
RLS: ONE DIMENSIONAL SIGNAL CASE
Ε + = θ H Z Ε + = Q 1 t ) e
- (1
t
- β
α δ
τ
Μ Μ
- Z acquisition vector
- H model matrix
- θ vector of parameters
- E error
Pseudo-inverse solution:
Z H H H
T T 1
) ( ˆ
−
= θ
Least Squares: Recursive Least Squares:
Ε + =
+ + + 1 1 1 k k k k k k
h H z Z ε θ
1 1 1 + + +
Ε + = ⇔
k k k
H Z θ
Solution:
) ˆ ( ˆ ˆ
1 1 1 1 1 k k k T k k k k
h z h P θ θ θ
+ + + + +
− + =
1 1 1 1 1
1
+ + + + +
+ − =
k k T k k k T k k k k
h P h P h h P P P
with
= ˆ θ Id P =
SLIDE 8
ICASSP 2013 | MAYOUE Aurélien | 8
RLS: REGULARIZATION
Q, α and β can freely evolve: the sensor drift and the exponential part cannot be discriminated correctly
Real Data Estimated Data
- Hyp. TNT
- Hyp. EGDN
- Hyp. EtOH
- Hyp. DCM
- Hyp. MEK
Reguralization:
( )
2 2
min arg ˆ θ θ θ
θ
Γ + − = Z H
Γ Γ Γ = Γ
β α Q
with ГQ, Гα and Гβ are used to set each parameter inertial.
Real Data Estimated Data
- Hyp. TNT
- Hyp. EGDN
- Hyp. EtOH
- Hyp. DCM
- Hyp. MEK
Solution:
) ˆ ( ˆ ˆ
1 1 1 1 1 k k k T k k k k
h z h P θ θ θ
+ + + + +
− + =
1 1 1 1 1
1
+ + + + +
+ − =
k k T k k k T k k k k
h P h P h h P P P
with
= ˆ θ
1
) (
−
Γ Γ =
T
P
SLIDE 9
ICASSP 2013 | MAYOUE Aurélien | 9
RLS: MULTISENSOR CASE
Z
SLIDE 10
ICASSP 2013 | MAYOUE Aurélien | 10
RLS: MULTISENSOR CASE
Z
SLIDE 11
ICASSP 2013 | MAYOUE Aurélien | 11
RLS: MULTISENSOR CASE
Z
- work in real time
- process samples from sensors
with different sampling frequencies
- discriminate compounds with
different kinetics and/or amplitude ratio from the multi-sensor
SLIDE 12
ICASSP 2013 | MAYOUE Aurélien | 12
EXPERIMENTS: DESCRIPTION
Compounds: Protocol:
EtOH DCM MEK TNT EGDN
Training set: only h100 acquisitions Test set: h100, h50 and h10 acquisitions
- lab condition
- vapour generation cell
- different concentrations
SLIDE 13
ICASSP 2013 | MAYOUE Aurélien | 13
EXPERIMENTS: RESULTS
Quantification: 1) Identification rate:
Theoritical values Estimated values
Explosives TNT EGDN Concentration h100 h50 h10 h100 h50 h10 Identification rate 3/3 3/3 3/3 3/3 3/3 3/3 Identification time (s) 47 43 47 31 32 32 Interferents EtOH DCM MEK Concentration h100 h50 h10 h100 h100 Identification rate 3/3 3/3 2/3 2/3 3/3 Identification time (s) 35 32 31 31 34 2) Identification rate: Explosives TNT EGDN Concentration h100 h50 h10 h100 h50 h10 QCM+SAW 0/3 0/3 0/3 3/3 3/3 3/3 OPTO+SAW 3/3 3/3 3/3 3/3 2/3 0/3 OPTO+QCM 3/3 3/3 3/3 3/3 2/3 1/3 Interferents EtOH DCM MEK Concentration h100 h50 h10 h100 h100 QCM+SAW 3/3 3/3 2/3 2/3 3/3 OPTO+SAW 2/3 3/3 2/3 2/3 1/3 OPTO+QCM 1/3 1/3 2/3 2/3 0/3
- identification rate: 94%
- identification time < 60s
- robustness to variations of
concentration
- performances are deteriorated
when a technology is missing
SLIDE 14
Recursive Least Squares Algorithm Dedicated to Early Recognition of Explosive Compounds thanks to Multi-technology Sensors ICASSP 2013 Aurelien.mayoue @cea.fr CEA LIST 91191 Gif-sur-Yvette Cedex, France