# Fast Measurements with MOX Sensors: A Least-Squares Approach to Blind Deconvolution

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. A Simple Nonlinear Model of MOX Sensors

## 3. A Linearization Technique from Logarithmic Transformation

## 4. Supervised Identification/Deconvolution in the Log-Domain

## 5. Blind Deconvolution Using Two Sensors

## 6. Extensions

#### 6.1. More Than Two Sensors

#### 6.2. Different Time Constants for Rise and Decay

## 7. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Appendix A

_{2}) or ethanol diluted in synthetic air is delivered to the sensors. The two outer valves are used to send the flow that is not being delivered to the sensors (i.e., the one corresponding to the inner valve, which is currently closed) to the exhaust in order to avoid overpressure in the system. The ethanol gas cylinder contained 100 ppm of ethanol diluted in synthetic air with 21 ± 1% O

_{2}, which was further diluted with synthetic air to reach concentrations below 100 ppm. Three mass flow controllers (MFCs), which had full-scale flow rates of 1000 mL/min, were used to control the rate of dilution of the ethanol gas stream and to fix the flow rate of the final gas stream delivered to the sensors at 1 L/min to match the input flow rate of the pump inside the miniPID.

**Figure A1.**Test bench used in the step experiments. The electrovalves are two-way: normally open (NO) or normally closed (NC). See text in Appendix A for details.

## References

- Li, X.; Jin, L.; Kan, H. Air pollution: A global problem needs local fixes. Nature
**2019**, 570, 437–439. [Google Scholar] [CrossRef] [PubMed] - Apte, J.S.; Messier, K.P.; Gani, S.; Brauer, M.; Kirchstetter, T.W.; Lunden, M.M.; Marshall, J.D.; Portier, C.J.; Vermeulen, R.C.; Hamburg, S.P. High-Resolution Air Pollution Mapping with Google Street View Cars: Exploiting Big Data. Environ. Sci. Technol.
**2017**, 51, 6999–7008. [Google Scholar] [CrossRef] [PubMed] - Anjomshoaa, A.; Duarte, F.; Rennings, D.; Matarazzo, T.J.; De Souza, P.; Ratti, C. City Scanner: Building and Scheduling a Mobile Sensing Platform for Smart City Services. IEEE Internet Things J.
**2018**, 5, 4567–4579. [Google Scholar] [CrossRef] - Monroy, J.G.; Gonzalez-Jimenez, J.; Blanco, J.L. Overcoming the Slow Recovery of MOX Gas Sensors through a System Modeling Approach. Sensors
**2012**, 12, 13664–13680. [Google Scholar] [CrossRef] [PubMed][Green Version] - Szyszka, P.; Stierle, J.S.; Biergans, S.; Galizia, C.G. The Speed of Smell: Odor-Object Segregation within Milliseconds. PLoS ONE
**2012**, 7, e36096. [Google Scholar] [CrossRef] [PubMed] - Martinez, D.; Arhidi, L.; Demondion, E.; Masson, J.-B.; Lucas, P. Using Insect Electroantennogram Sensors on Autonomous Robots for Olfactory Searches. J. Vis. Exp.
**2014**, 90, e51704. [Google Scholar] [CrossRef] [PubMed] - Burgués, J.; Hernández, V.; Lilienthal, A.J.; Marco, S. Smelling Nano Aerial Vehicle for Gas Source Localization and Mapping. Sensors
**2019**, 19, 478. [Google Scholar] [CrossRef] [PubMed] - Gonzalez-Jimenez, J.; Monroy, J.G.; Blanco, J.L. The Multi-Chamber Electronic Nose—An Improved Olfaction Sensor for Mobile Robotics. Sensors
**2011**, 11, 6145–6164. [Google Scholar] [CrossRef] [PubMed] - Di Lello, E.; Trincavelli, M.; Bruyninckx, H.; De Laet, T. Augmented Switching Linear Dynamical System Model for Gas Concentration Estimation with MOX Sensors in an Open Sampling System. Sensors
**2014**, 14, 12533–12559. [Google Scholar] [CrossRef] [PubMed][Green Version] - Clifford, P.K.; Tuma, D.T. Characteristics of semiconductor gas sensors I. Steady state gas response. Sens. Actuators
**1982**, 3, 233–254. [Google Scholar] [CrossRef] - Hung, P.; McLoone, S.; Irwin, G.; Kee, R.; Brown, C. In Situ Two-Thermocouple Sensor Characterisation using Cross-Relation Blind Deconvolution with Signal Conditioning for Improved Robustness. In Informatics in Control, Automation and Robotics. Lecture Notes in Electrical Engineering; Filipe, J., Cetto, J.A., Ferrier, J.L., Eds.; Springer: Berlin/Heidelberg, Germany, 2009; Volume 24. [Google Scholar]
- Li, Y.; Zhang, Z.; Hao, X. Blind system identification of two-thermocouple sensor based on cross-relation method. Rev. Sci. Instrum.
**2018**, 89, 034901. [Google Scholar] [CrossRef] [PubMed] - Martinez, D.; Rochel, O.; Hugues, E. A biomimetic robot for tracking specific odors in turbulent plumes. Auton. Robot.
**2006**, 20, 185–195. [Google Scholar] [CrossRef] - Burgués, J.; Valdez, L.F.; Marco, S. High-bandwidth e-nose for rapid tracking of turbulent plumes. In Proceedings of the 2019 IEEE International Symposium on Olfaction and Electronic Nose (ISOEN), Fukuoka, Japan, 26–29 May 2019. [Google Scholar]
- Gutierrez-Osuna, R.; Nagle, H.; Schiffman, S.S. Transient response analysis of an electronic nose using multi-exponential models. Sens. Actuators B Chem.
**1999**, 61, 170–182. [Google Scholar] [CrossRef] - Martinez, D. On the right scent. Nature
**2007**, 445, 371–372. [Google Scholar] [CrossRef] [PubMed]

**Figure 1.**Deconvolution of metal oxide (MOX) gas sensors sensors. The deconvolution operation consists of reconstructing the fast-varying concentration u(t) encountered in turbulent plumes by inverting the low-pass filtering effect of MOX sensors.

**Figure 2.**

**A**The step response of MOX sensors. The sensor conductance $G$ is measured over time in response to ethanol steps at different concentrations. See Appendix A for details of the experimental setup.

**B**Transient response analysis. Top) The conductance change $\Delta G$ over time in response to a step-like stimulus. The transient is well-fitted by a sum of two exponential functions that represent the adsorption process of the chemical compound onto the sensing element. Here, the time constant corresponds to the time at which the MOX reaches (1 − 1/e) × 100% ≈ 63.2% of the steady state value. Bottom) The time constant (10.4 ± 0.46 and 6.1 ± 0.47 for the 2 × TGS2602, 1.7 ± 0.19 for the TGS2610 in sec.) depends on the sensor type but is relatively independent on input intensity (ethanol concentration).

**C**Steady state response analysis. The steady-state conductance is well-described by a power law function.

**Figure 3.**

**A**The LN model of MOX sensors described by a cascade of a linear filter (Equation (2)) and a static power-law nonlinearity (Equation (3)).

**B**Comparisons with experimental data. Simulation of the LN model (dashed black curve with $a$ = 0.9999, $\alpha $ = 0.0157, $r$ = 0.7256) and comparison with real data (plain black curve) in response to a step-like stimulation of ethanol (blue curve) at different concentrations.

**Figure 4.**Numerical evaluation of the lower bound (Equation (5)) for different values of $a$. The line in the graphs corresponds to equality (Equation (6)). For a given value of $a$, the variables x and u are sampled randomly in the unit interval, each point corresponding to a particular realization.

**Figure 5.**Deconvolution in the log-domain based on the sensor model Equations (2) and (3). The deconvolution operation consists of taking the logarithm of the MOX signal, processing this log signal with a linear filter (Equation (9)), and recovering the output via an exponential function.

**Figure 6.**Supervised identification/deconvolution with a simulated MOX sensor.

**A**Least-squares identification using Equations (13) and (14) (n = 30 trials). For each trial, the model parameters $\tau ,r,\alpha $ are randomly generated within (0,10 s), (0,1) and (0,10), respectively.

**B**Deconvolution of the MOX output in the worst-case scenario: $\tau =10s,r=1,\alpha =10$ (maximum estimation bias in A).

**Figure 7.**Generation of ethanol plumes in an open environment. The test bench uses a pressurized air outlet (6.3 mm radius, 20 L/min) and a vessel (5 cm radius) filled with 200 mL of ethanol (gas source). The sensing board, which consists of MOX sensors and a fast PID, was placed at 15 cm and 105 cm from the gas source.

**Figure 8.**Supervised deconvolution experiments with a real MOX sensor.

**A**Deconvolved MOX at 105 cm from the gas source (ethanol).

**B**Deconvolved MOX at 15 cm from the gas source (ethanol).

**C**Same as in B but with acetone as the gas source.

**Figure 9.**Blind deconvolution with two MOX sensors. The deconvolved outputs ${u}_{1}^{\prime}$ and ${u}_{2}^{\prime}$ should be similar as both sensors are excited by the same input $u$. The original input can be reconstructed as $\left({e}^{{u}_{1}^{\prime}}+{e}^{{u}_{2}^{\prime}}\right)/2$.

**Figure 10.**Blind identification of the time constants ${\tau}_{1}$ and ${\tau}_{2}$ for two simulated MOX sensors. Experiments with simulated MOX sensors (same conditions as in Figure 6). The blind identification method leads to a valid, but biased, estimate: $\widehat{{\tau}_{1}}=1.1{\tau}_{1}$ and $\widehat{{\tau}_{2}}=1.1{\tau}_{2}$.

**Figure 11.**Blind deconvolution, experiments with two real MOX sensors. In blue, the signals ${y}_{1}$ and ${y}_{2}$ of the two MOX sensors within an ethanol plume (recording at 15 cm from the releasing source). In red, the signal (${u}_{1}$ + ${u}_{2}$)/2 obtained from the deconvolution of the two MOX sensors. In black, the signal $u$ recorded by the PID at the same location as the MOX sensors. Note that $u$ was not used for the deconvolution (blind) and is shown here for comparison only. Moreover, for comparison, the signals are normalized between 0 and 1 as the blind procedure can only provide $u$ up to a scaling factor.

© 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Martinez, D.; Burgués, J.; Marco, S.
Fast Measurements with MOX Sensors: A Least-Squares Approach to Blind Deconvolution. *Sensors* **2019**, *19*, 4029.
https://doi.org/10.3390/s19184029

**AMA Style**

Martinez D, Burgués J, Marco S.
Fast Measurements with MOX Sensors: A Least-Squares Approach to Blind Deconvolution. *Sensors*. 2019; 19(18):4029.
https://doi.org/10.3390/s19184029

**Chicago/Turabian Style**

Martinez, Dominique, Javier Burgués, and Santiago Marco.
2019. "Fast Measurements with MOX Sensors: A Least-Squares Approach to Blind Deconvolution" *Sensors* 19, no. 18: 4029.
https://doi.org/10.3390/s19184029