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