Power spectral density estimation for wireless fluctuation enhanced gas sensor nodes

Transcription

1 Submtted to Fluctuaton and Nose Letters Power spectral densty estmaton or wreless luctuaton enhanced gas sensor nodes R. MINGESZ, G. VADAI, and Z. GINGL Department o Techncal Inormatcs Unversty o Szeged, Árpád tér., Szeged, H-670, Hungary mngesz@n.u-szeged.hu Fluctuaton enhanced sensng (FES) s a promsng method to mprove the selectvty and senstvty o semconductor and nanotechnology gas sensors. Most measurement setups nclude hgh cost sgnal condtonng and data acquston unts as well as ntensve data processng. However, there are attempts to reduce the cost and energy consumpton o the hardware and to nd ecent processng methods or low cost wreless solutons. In our paper we propose hghly ecent sgnal processng methods to analyze the power spectral densty o luctuatons. These support the development o ultra-low-power ntellgent luctuaton enhanced wreless sensor nodes whle several urther applcatons are also possble. Keywords: luctuaton enhanced sensng; wreless sensor network; spectral estmaton. Introducton Fluctuaton enhanced sensng (FES) has become an actve research area n the eld o gas sensors snce ts ntroducton a ew years ago [1]. Typcally, measurng the DC value o sensor resstance s used to determne the gas concentraton. In ths case, each sensor s calbrated and prepared or a certan type o gas, thereore several sensors are used n parallel to detect and measure gas mxtures. The FES prncple uses the tme-dependent luctuatons o the sensors resstance as an normaton source. Measurng these luctuatons caused by adsorpton-desorpton and duson nose

2 PSD estmaton or wreless luctuaton enhanced gas sensor nodes provdes enhanced selectvty and senstvty, thereore t could be used to measure derent gases or mxtures even wth a sngle sensor. There are several examples o successul applcatons, ncludng gas mxture detecton, harmul gas and bacteral odor sensng usng Taguch sensors [-4], ncreasng selectvty o nanotechnology gas sensors [5-9] and detectng scents usng semconductor sensors [10]. A typcal measurement setup requres hgh cost sgnal condtonng and data acquston unts. Data processng s usually done olne by usng hgh perormance personal computers that perorm complex calculatons ncludng spectral analyss, removal o external ntererences and pattern recognton [5-7]. Durng the last ew years, suggestons have been made to replace these complex systems by small, wreless data acquston modules [11-13]. In addton, derent methods wth low processng needs have been smultaneously proposed [14, 15]. In the case o the bnary ngerprnt method [14], the power spectrum o the nose s dvded nto derent regons. The sgnal power present n these regons s used to determne the components o a gas mxture. Derent, band-pass and low-pass lter based unts were desgned to support ths analyss method [16, 17]. Recently, we have developed a complete, standalone ntellgent FES sensor node [13] based on the prncple o measurng the varance o the nose at the outputs o eght rst order low-pass lters wth logarthmcally dstrbuted corner requences. These lters are used to estmate the power o the nose n derent requency regons [14]. In our current paper we propose two derent power spectral densty reconstructon methods usng the same system and analyze ther perormance n detal. We also compare the perormance o the proposed methods wth Fourer-transormaton based ones. Our measurement and analyss system contans the entre analogue and dgtal sgnal processng requred or ecent unversal spectral estmaton n wreless sensng and sensor networks. Consequently, t has applcatons n several nterdscplnary elds other than FES as well.

3 R. Mngesz, G. Vada and Z. Gngl System Fg. 1. Block dagram o the low power FES devce Fg. 1 contans the block dagram o the ntellgent sensor node. The processng unt s a low-power hgh-perormance mxed sgnal mcrocontroller (C8051F410). The unt s desgned to process the nose o semconductors (Taguch) or nanotechnology based sensors. The exctaton o the sensor s provded by a current generator wth selectable current levels. A 1 Hz hgh-pass lter s used to remove the DC component o the sensor output, and an amplcaton o 1000 s appled to ensure proper sgnal levels. Ths sgnal s ed nto a bank o rst order passve RC low-pass lters. We estmated the power spectra o the nose by measurng only the average output power level o each lter. We used eght lters wth the ollowng logarthmcally dstrbuted nomnal corner requences: 10 Hz, 7 Hz, 7 Hz, 193 Hz, 518 Hz, 1389 Hz, 378 Hz and Hz. The outputs o the lters are selected usng a bult-n analogue multplexer o the mcrocontroller and then dgtzed by a precson 1-bt analogue-to-dgtal converter. An aggregate samplng requency o 8 khz was used, resultng a 1 khz eectve samplng requency or each lter. Note that whle ths requency does not satsy the samplng theorem, we need to measure the output power level o the output only, whch can be measured even by undersamplng, snce the sgnal and the samplng tme nstants are uncorrelated. The output varance o each lter can be sent to a host computer va USB or wreless lnk or urther processng. However, our am was to nd ecent sgnal processng algorthms or recognzng gas concentraton and gas mxtures drectly by the sensor node tsel. The power consumpton o the system, the eect o the precson o the lters and the eect o measurement length are evaluated n our prevous publcaton [13].

4 PSD estmaton or wreless luctuaton enhanced gas sensor nodes Methods Our proposed data processng method s based on the prncple o approxmatng the resstance luctuaton s power spectral densty (PSD) usng the measured power o the adjacent requency bands at the outputs o the low-pass lter bank. We have examned the senstvty and selectvty o the sensor node and evaluated the PSD reconstructon methods theoretcally and by numercal smulatons as well. Estmaton o each lter s output power We estmated the output power (varance) o each lter or sgnals wth derent power spectral denstes. In order to calculate the varance, one can use the ollowng equaton: max h 1 X ( ) d, (1) h where X() s the PSD o the sgnal s output nose, σ s the varance o th lter s output, and max s the bandwdth o the system. Snce we wanted our method to work or arbtrary spectral dependence, we used numercal ntegraton to calculate the result. The parameters o the ntegraton are: Δ = 0.1 Hz, max = 1 MHz. We also used numercally smulated measurements n order to approxmate the output varance o the lter. By perormng multple measurements, we could also approxmate the standard devaton (SD) o each measured varance. In order to be able to work wth arbtrary spectral denstes, we used Fourer-transormaton based methods to generate an arbtrary sgnal as well as to mplement low-pass and hgh-pass lters. Each sgnal was generated usng a samplng requency o 100 khz, the duraton was 10 s [13]. The output o each lter was resampled at 1 khz to smulate the operaton o the sensor node. Each varance value was calculated usng samples.

5 R. Mngesz, G. Vada and Z. Gngl PSD reconstructon methods The drect method or spectrum reconstructon assumes deal low-pass and hgh-pass lters, thus power present n the th requency band s equal to σ - σ -1. Based on ths assumpton the reconstructed PSD ampltude s gven by: ys 1 1 1, otherwse y s1 1 1 h, () where s the cut-o requency o the th lter and h s the cut-o requency o the hgh-pass lter. The x coordnates o the spectrum are gven by the geometrc mean o the begnnng and the end o selected band: * * 1 1, otherwse 1 1 h, (3) Whle mplementng ths method s really smple, t does not take the transer uncton o the appled lters nto account. For ths reason, we used an alternatve method, the 1/ normalzed method. Assumng, that we have a 1/ nose at the output o the sensor, we can calculate the expected varances at the output o each lter accordng to the ollowng ormula: max h 1 1 V Hz N d, (4) 0 max 1 1 h Note that ths nose s generated by 1/ lterng o a whte nose wth varance o 1 V and bandwdth o max. As n the case o drect method, we can also calculate the power o the th requency band: σ N - σ N-1. Snce the PSD o the measured nose wll der rom the reerence nose, the measured power n ths band wll be derent rom ths value. The rato between the power levels wll be approxmately equal to the rato between the two PSD-s n ths band. Accordng to the prevous assumpton, we gve the PSD approxmaton by the ollowng ormula: y p N 1 N 1 1 V Hz * max 1, otherwse y p N 1 V Hz, (5) * max

6 PSD estmaton or wreless luctuaton enhanced gas sensor nodes where the requences * are calculated n the same way as gven n Eq. (3). The eght values o σ N can be calculated and stored n a look-up table n the mcrocontroller. As a result, the second method does not requre sgncantly more resources than the rst one. In Fg. we compare the perormance o the two methods n case o 1/ nose. We can observe, as expected, that the weghted method gves exactly the 1/ spectrum. Note that the drect method also gves a good approxmaton o the spectrum. By multplyng the PSD values wth the requency we can enlarge the devaton rom the deal 1/ spectrum. In the case o the rst requency band o the drect method, the devaton s sgncant. Thus, we can conclude that the results o the smulatons are n accordance wth the theoretcal results. Fg.. Comparng the result o the presented methods n the case o 1/ nose. On the rght sde the PSD s multpled by the requency to enlarge the devatons. Note that the theoretcal values o the reconstructed PSD are nterpreted only n eght ponts, we connected them only to ncrease the readablty o the gure. On Fg. 3 we examne the perormance o the two methods n case o 1/ α noses. Whle the normalzed method does not gve the exact PSD values, t stll perorms much better than the drect method. For ths reason, n the ollowng sectons o the paper we wll only use the normalzed method.

7 R. Mngesz, G. Vada and Z. Gngl Fg. 3. Comparng the perormance o the two methods n the case o 1/ 1. (let) and 1/ 0.8 (rght). The vertcal scale s logarthmc. Evaluaton o the requred number o lters In order to test the resoluton o the spectral reconstructon method we added a plateau (or peak) to 1/ nose PSD as dened by Eq. (6) and llustrated on Fg. 4. The maxmum devaton rom the 1/ nose occurs at c, the center requency o the plateau (316 Hz), the wdth o the peak s Δ (158 Hz) and the ampltude s two tmes hgher than the ampltude o 1/ nose at the center requency (A = 1). S( ) 1V Hz 1 Aexp max c, (6) Fg. 4. The PSD o the nose used to test the resoluton o the spectral reconstructon method. On the let sde o Fg. 5 we can observe the result o the reconstructon usng eght lters. We can see that the peak n the reconstructon s sgncantly wder than the orgnal one due to the moderate roll-o o the

8 PSD estmaton or wreless luctuaton enhanced gas sensor nodes low pass lters. In the case o sxteen lters, the wdth does not decrease, however, we get the wde peak wth much hgher resoluton. The slow decay o rst order lters (0 db/decade) s the major lmtng actor o the resoluton o the method. To ncrease the resoluton one may use hgher order lters, deconvoluton based methods or even more complex algorthms [18]. However, these methods would sgncantly ncrease the complexty and power consumpton o the sensor node. Fg. 5. The reconstructon o a plateau (peak) n the PSD. Both the PSD and the reconstructon s multpled by to ncrease the readablty o the gure. On the let 8 lters were used, whle on the rght 16 lters. Results and dscusson In the next secton we analyze the perormance o the proposed 1/ normalzed PSD reconstructon method. We perorm test usng 1/ α noses wth derent exponents, test the eect o derent peak heghts and wdths and we also test our method by smulatng sgnals wth PSD dentcal o derent publshed measurement results. Reconstructng artcal noses wth derent PSD-s On the let sde o Fg. 6 we demonstrate the perormance o the normalzed method n the case o derent 1/ α noses. The exponents o the noses were 0.8, 0.9, 1.0, 1.1, and 1. respectvely. The error bars were calculated based on 0 smulatons each, showng the standard devaton o the varance. In the case o the rst band, the error s hgher than n the case o hgher

9 R. Mngesz, G. Vada and Z. Gngl requency bands, but stll very low. Ths low error value can gve us the opportunty to reduce the length o the measurement and to save power. Fg. 6. On the let the reconstructon o derent 1/ α noses s llustrated. On the rght the result o the PCA analyss or the same noses s shown. In our prevous work [5-7] we have used PCA based pattern recognton methods n order to dstngush between derent knds o gases. In the reerred works the PCA was calculated rom the averaged spectrums, each o them consstng o around 000 ponts. Our reconstructon method provdes only 8 ponts as an nput or the PCA analyss. However, as seen on the rght sde o Fg. 6, these 8 ponts gve enough normaton to dstngush between derent nose exponents whle the processng tme s reduced radcally. In addton, we have examned the eect o ampltude o the peak. The parameters A or the peaks were 0.5, 0.0, 0.5, 1.0, and.0 respectvely. As can be seen n Fg. 7 the derent PSD-s can be clearly dstngushed rom each other both by spectral recognton, and by PCA analyss. Fg. 7. The spectral reconstructon n the case o derent PSD peak ampltudes.

10 PSD estmaton or wreless luctuaton enhanced gas sensor nodes Moreover, we have tested the reconstructon algorthm or peaks wth derent wdths. Δ values o 15 Hz, 30 Hz, 70 Hz, 157 Hz and 300 Hz were used. As t s dsplayed on Fg. 8, wde peaks wth hgh power can be rather accurately recognzed. In the case o narrow peaks, the requency bands close to them der rom the reerence values; ths derence s slghtly hgher than the SD o the varance. However the PCA pont groups n the case o narrow peaks overlap (Fg. 9). As a result, we conclude that PCA analyss n ts current orm may not be the best classcaton method or the current applcaton. At the same tme, the ponts o the reconstructed PSD are sutable as an nput data or more elaborated pattern recognton methods lke support vector machne [15, 19, 0]. Fg. 8. The eect o the bandwdth o the peaks. Fg. 9. The PCA analyss o the eect o the bandwdth o the peaks. Reconstructon examples o measured spectra In order to test our algorthm, we have generated noses based on the PSD o nose dependng on bacteral odors [14 Fg. 6]. As llustrated n Fg. 10 the reconstructon can detect the presence o bactera and dstngush between

11 R. Mngesz, G. Vada and Z. Gngl derent bacterum types. The groups o dots can also be dstngushed n the calculated PCA plots. Fg. 10. Reconstructon o PSD n the case o bactera odor sensng on the let, and the results o the PCA algorthm on the rght. In the second analyss we generated the test nose wth smlar PSD that had been prevously observed n a carbon nanotube gas sensors n 50 ppm CO and 50 ppm N O envronments. Our goal was to contrast the perormance o the gas detecton compared to the PCA based method descrbed n [5]. For each measurement pont we calculated the PSD o the nose by averagng 100 spectra consstng o 4096 samples per spectrum. The samplng requency was 10 khz and we used the spectrum components over 100 Hz or the PCA analyss. The result o the analyss or the smulated sgnals s shown on the let sde o Fg. 11. Our method uses the same measurement length (40.96 s) whle the samplng requency was 1 khz per lter. As t can be seen on the rght sde o Fg. 11, our method perorms as well as the orgnal one. Note that whle the value o PCA components cannot be drectly compared to each other snce they used nput data wth derent orders o magntude, the sgnal-to-nose rato can be compared based on the results.

12 PSD estmaton or wreless luctuaton enhanced gas sensor nodes Fg. 11. Comparng the perormance o pattern reco gnton method ntroduced n [5] (let sde) wth our PSD reconstructon method (rght sde) n the case o smulated noses correspondng to a carbon nanotube sensor n 50 ppm CO and 50 ppm N O envronments. Concluson In the present paper we nvestgated two spectral reconstructon methods that use output sgnals o an analogue low-pass lter bank. The reconstructon methods were desgned to be used wth our recently presented low power wreless sensor node and optmzed to estmate PSDs smlar to the PSD o 1/ noses. We tested the perormance o the methods usng derent spectral denstes and ound that although the resoluton s rather lmted even slghtly derent spectral denstes can be dstngushed. Ths eature supports low power FES measurements n small devces. Moreover, the output data o the PSD reconstructon can be used as an nput or derent pattern recognton algorthms. We compared the perormance to prevously used pattern recognton methods, and we ound that the same precson requres at least 50 tmes less operatons and 0 tmes less memory sze. Snce our algorthm can be mplemented by usng only 16 or 3 bt nteger arthmetc, combned wth the low memory needs, t can be embedded nto ultra-low-power mcrocontrollers, whle the FFT based method exceeds the possbltes o the hardware. The 1/ normalzed method s ne-tuned or processng 1/ lke noses, but by modyng Eq. (4) and (5) t can be appled or other sgnal types as well. The possble applcatons nclude gas mxture detecton, bacteral odor and scent sensng by very low power ntellgent sensor nodes. Note that

13 R. Mngesz, G. Vada and Z. Gngl relablty testng, vbraton montorng or other tasks requrng spectral analyss done by power ecent compact devces mght also be supported. Acknowledgements Ths research was supported by the European Unon and the State o Hungary, co-nanced by the European Socal Fund n the ramework o TÁMOP-4..4.A/-11/ Natonal Excellence Program. Reerences [1] L. B. Ksh, R. Vajta, and C. G. Granqvst, Extractng normaton rom the nose spectra o chemcal sensors: Electronc nose and tongue by one sensor, Sens. Actuators B, Chem. 71 (000) [] L. B. Ksh, Y. L, J. L. Sols, W. H. Marlow, R. Vajta, C. G. Granqvst, V. Lantto, J. M. Smulko and G. Schmera, Detectng Harmul Gases Usng Fluctuaton-Enhanced Sensng Wth Taguch Sensors, IEEE Sensors J. 5 (005) [3] M. M. Kotarsk and J. M. Smulko, Hazardous gases detecton by luctuaton-enhanced gas sensng, Fluct. Nose Lett. 9 (010) [4] L. B. Ksh, H. C. Chang, M. D. Kng, C. Kwan, J. O. Jensen, G. Schmera, J. Smulko, Z. Gngl and C. G. Granqvst, Fluctuaton-Enhanced Sensng or Bologcal Agent Detecton and Identcaton, IEEE Trans. Nanotechnol. 10 (011) [5] D. Molnár, P. Heszler, R. Mngesz, Z. Gngl, Á. Kukovecz, Z. Kónya, H. Haspel, M. Mohl, A. Sáp, I. Krcs, K. Kordás, J. Mäkln, N. Halonen, G. Tóth, H. Molanen, S. Roth, R. Vajta, P.M. Ajayan, Y. Poullon and A. Rubo, Increasng Chemcal Selectvty O Carbon Nanotube-Based Sensors By Fluctuaton-Enhanced Sensng, Fluct. Nose Lett. 9 (010) [6] Á. Kukovecz, D. Molnár, K. Kordás, Z. Gngl, H. Molanen, R. Mngesz, Z. Kónya, J. Mäkln, N. Halonen, G. Tóth, H. Haspel, P. Heszler, M. Mohl, A. Sáp, S. Roth, R. Vajta, P. M. Ajayan, Y. Poullon, A. Rubo and I. Krcs, Carbon nanotube based sensors and luctuaton enhanced sensng, Phys. Status Sold C 7 (010) [7] H. Haspel, R. Ionescu, P. Heszler, Á. Kukovecz, Z. Kónya, Z. Gngl, J. Makln, T. Mustonen, K. Kordás, R. Vajta and P. M. Ajayan, Fluctuaton enhanced gas sensng on unctonalzed carbon nanotube thn lms,phys. Status Sold B 45 (008) [8] M. M. Kotarsk and J. M. Smulko, Nose measurement set-ups or luctuatons-enhanced gas sensng, Metrol. Meas. Syst. 16 (009)

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