Transient Response Analysis Transient Response Analysis for for Temperature Modulated Temperature Modulated Chemoresistors Chemoresistors R. Gutierrez-Osuna 1,2 , A. Gutierrez 1,2 and N. Powar 2 1 Texas A&M University, College Station, TX 2 Wright State University, Dayton, OH 1 Multi-frequency Temperature Modulation for Metal-oxide Gas Sensors Ricardo Gutierrez-Osuna Texas A&M University
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 2 Multi-frequency Temperature Modulation for Metal-oxide Gas Sensors Ricardo Gutierrez-Osuna Texas A&M University
Objectives of this work g Improve information content of COTS gas sensors by means of n Instrumentation: temperature modulation n Computation: transient-response analysis g Evaluate various types of transient analysis techniques n Time-domain techniques n Time-constant-domain techniques 3 Multi-frequency Temperature Modulation for Metal-oxide Gas Sensors Ricardo Gutierrez-Osuna Texas A&M University
Outline Temperature oscillation Temperature modulation Temperature transients Time domain Transient analysis Time-constant domain Feature extraction Pattern analysis Performance measures Experimental setup Experimental validation Results 4 Multi-frequency Temperature Modulation for Metal-oxide Gas Sensors Ricardo Gutierrez-Osuna Texas A&M University
TEMPERATURE TEMPERATURE MODULATION MODULATION 5 Multi-frequency Temperature Modulation for Metal-oxide Gas Sensors Ricardo Gutierrez-Osuna Texas A&M University
Temperature modulation g Basic 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] 6 Multi-frequency Temperature Modulation for Metal-oxide Gas Sensors Ricardo Gutierrez-Osuna Texas A&M University
Temperature modulation approaches g Temperature oscillation V H V H n Sensor heater is driven by a continuous function g e.g., sine wave, ramp time time 1/R S 1/R S n Information is in the quasi- stationary or dynamic response time time g Temperature transient V H V H n Sensor heater is driven by a discontinuous function g e.g., step function, pulse time time 1/R S 1/R S n Information is in the transient response time time 7 Multi-frequency Temperature Modulation for Metal-oxide Gas Sensors Ricardo Gutierrez-Osuna Texas A&M University
Temperature modulation examples Temperature Temperature oscillation transient -4 -4 0.125Hz 0.125Hz S#4, 1-2V S#4, 1-2V x 10 x 10 W W 5 5 M M E E A A AIR AIR D D 9 9 AM AM B B ACETONE ACETONE 4 4 8 8 B B C C AMMONIA AMMONIA 3 3 D D IPA IPA 7 7 A A E E VINEGAR VINEGAR 2 2 6 6 C C AI AI AIM AIM 5 5 IM IM 1 1 A A 4 4 I I 0 0 100 100 200 200 300 300 400 400 500 500 600 600 700 700 800 800 100 100 200 200 300 300 400 400 8 Multi-frequency Temperature Modulation for Metal-oxide Gas Sensors Ricardo Gutierrez-Osuna Texas A&M University
TRANSIENT TRANSIENT ANALYSIS ANALYSIS 9 Multi-frequency Temperature Modulation for Metal-oxide Gas Sensors Ricardo Gutierrez-Osuna Texas A&M University
Transient response analysis g Objective 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 g How 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 d ∫ − = τ τ t / f ( t ) G e 0 10 Multi-frequency Temperature Modulation for Metal-oxide Gas Sensors Ricardo Gutierrez-Osuna Texas A&M University
Time vs. spectral representations S#4, 2-3V S#4, 1-2V 0 0 9 8 -1 -1 8 6 7 -2 -2 6 -3 4 -3 5 -4 2 4 100 200 300 400 0 1 100 200 300 400 0 1 10 10 10 10 S#1, 2-3V S#2, 4-5V 0 8 0.5 8 -2 6 0 6 -4 4 4 -0.5 -6 2 2 0 1 100 200 300 400 0 1 100 200 300 400 10 10 10 10 11 Multi-frequency Temperature Modulation for Metal-oxide Gas Sensors Ricardo Gutierrez-Osuna Texas A&M University
Time vs. spectral representations S#4, 1-2V S#4, 1-2V 0 0 0 9 9 9 -1 -1 -1 8 8 8 7 7 7 -2 -2 -2 6 6 6 -3 -3 -3 5 5 5 -4 -4 -4 4 4 4 100 100 100 200 200 200 300 300 300 400 400 400 0 0 0 1 1 1 10 10 10 10 10 10 12 Multi-frequency Temperature Modulation for Metal-oxide Gas Sensors Ricardo Gutierrez-Osuna Texas A&M University
The Pade-Z Transform g Pade-Z is a system-identification technique that finds a discrete multi-exponential model of the form M ∑ − τ = t / f ( t ) G e m m = m 1 g Pade-Z in a nutshell n Compute the Z-transform of the sampled transient (at z 0 ) 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 13 Multi-frequency Temperature Modulation for Metal-oxide Gas Sensors Ricardo Gutierrez-Osuna Texas A&M University
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 d t ∞ − ( ) τ d ∫ = = τ τ METS ( t ) f ( t ) G e 1 τ d (ln t ) 0 n METS is the convolution product of the true distribution with an asymmetric kernel = − = h ( y ) exp( y exp( y )) with y ln( t ) 14 Multi-frequency Temperature Modulation for Metal-oxide Gas Sensors Ricardo Gutierrez-Osuna Texas A&M University
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 − N 1 M ∑ ∑ − τ τ = − kT / { M , G , } arg min f G e m m m k m τ M , G , = = k 0 m 1 m m 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 { } τ = 0 . 01 , 0 . 02 , , 0 . 09 , 0 . 1 , 0 . 2 , , 0 . 9 , 1 , 2 , , 9 , L L L L n Stabilize the solution with a regularization term 15 Multi-frequency Temperature Modulation for Metal-oxide Gas Sensors Ricardo Gutierrez-Osuna Texas A&M University
Validation on synthetic data g Synthetic transient with 9 8 three decays 7 6 Transient signal n τ 1 =0.1sec , τ 2 =1s , τ 3 =10s 5 n G 1 =-10 , G 2 =+10 , G 3 =-10 4 3 Training data n DC offset G 0 =10 Pade-Z model 2 Residual error 1 n Gaussian noise N( µ =0, σ =0.1) 0 0 5 10 15 20 25 30 Time (s) 6 DC Offset 3 5 4 2 3 1 Amplitudes 2 METS 1 0 1 0 -1 -1 -2 -2 -3 -3 -2 -1 0 1 2 -1 0 1 10 10 10 10 10 10 10 10 Time constant (s) Time constant (s) 16 Multi-frequency Temperature Modulation for Metal-oxide Gas Sensors Ricardo Gutierrez-Osuna Texas A&M University
FEATURE FEATURE EXTRACTION EXTRACTION 17 Multi-frequency Temperature Modulation for Metal-oxide Gas Sensors Ricardo Gutierrez-Osuna Texas A&M University
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 g Interpretation as filter banks 1 1 0.8 0.8 Sensor response Spectrum 0.6 0.6 0.4 0.4 0.2 0.2 0 0 0 10 20 30 40 50 60 10 0 10 1 time (s) Time constants (s) 18 Multi-frequency Temperature Modulation for Metal-oxide Gas Sensors Ricardo Gutierrez-Osuna Texas A&M University
Pade-Z f eature extraction A A g Can the model parameters 10 10 { G m , τ m } be used as A A A A 8 8 A A features? 6 6 I I 4 4 I I Amplitude Amplitude I I I I A A A A A A A A 2 2 M M M M M M M M I I I I I I n Partial fraction expansion is I I 0 0 an ill-conditioned problem -2 -2 I I I I I I I I -4 -4 A A A A A A n Small variations in the -6 -6 A A transient samples can lead to 0 0 1 1 2 2 3 3 4 4 5 5 6 6 Log (time constant) Log (time constant) solutions with different number of exponentials g Conventional pattern-analysis techniques will expect a fixed dimensionality M for all examples 19 Multi-frequency Temperature Modulation for Metal-oxide Gas Sensors Ricardo Gutierrez-Osuna Texas A&M University
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