Research on Peak-detection Algorithm for High-precision Demodulation System of Fiber Bragg Grating

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1 , pp Research on Peak-detecton Algorthm for Hgh-precson Demodulaton System of Fber ragg Gratng Peng Wang 1, *, Xu Han 1, Smn Guan 1, Hong Zhao and Mngle Shao 1 1 College of Electrcal and Electronc Engneerng, Harbn Unversty of Scence and Technology, Harbn, , Chna Key Laboratory of Engneerng Delectrcs and Its Applcaton, Mnstry of Educaton of Chna, Harbn, , Chna wpkunpeng@163.com Abstract In order to mprove the detecton accuracy of wavelength, the flterng and curve fttng technologes were appled n the FG wavelength demodulaton system based on tunable F-P flter. These methods could realze the accurate peak-locaton of output sgnals of the photo detector. Accordng to the characterstcs of nose, the FIR low-pass flter was desgned to flter the obtaned lght power sgnals so as to provde the nput sgnals wth hgh SNR for the peak-detecton algorthms. y analyzng and comparng several typcal peak-searchng algorthms, the algorthm of Gauss formula nonlnear curve fttng (L-M) was chosen to ft the dgtzed lght power sgnals. The expermental results show that L-M fttng algorthm reduces the mean square error by 7.5% compared wth the Gauss fttng algorthm. For the Gauss sgnal n the wavelength demodulaton system desgned n the paper, the L-M algorthm has lower mean square error than other peak-searchng algorthms. Ths algorthm s sutable for FG wavelength demodulaton system based on tunable F-P flter. It can effcently rase the accuracy of wavelength demodulaton system. Keywords: fber ragg gratng, tunable Fabry-Perot flter, peak-detecton algorthm, Levenberg-Marquardt algorthm 1. Introducton Fber ragg gratng (FG) s a new type of optcal fber sensor [1]. It has many advantages, such as small volume, lght weght, hgh temperature resstance, corroson resstance, nsenstvty to electromagnetc nterference, easy to be embedded n ntellgent structure and composed of dstrbuted measurement network and so on [-3]. So t s wdely appled n structural health montorng, aerospace, petrochemcal and other felds [4-6]. The gratng perod and refractve ndex wll alter wth changes of external envronment. As a result, the central wavelength of FG wll drft. y detectng the shft n the ragg wavelength due to some physcal quanttes, ndrect measurement of these parameters can be completed [7-8]. The tunng-wavelength method and detectng-wavelength technology are two mportant aspects of research on FG. The former s sensng process of lght and the latter s demodulaton process of sgnals. The precson of FG sensors s manly determned by them. Among them, the detecton resoluton of demodulaton system and peak-searchng errors are mportant factors to determne precson [9]. In practcal applcaton, the accurate poston of center wavelength can be obtaned by dgtalzng optcal power sgnals and regresson analyss usng curve fttng technques. These methods can effectvely mprove the detecton accuracy [10-11]. Sgnal-to-nose rato (SNR) of the nput sgnal s the most ISSN: IJHIT Copyrght c 014 SERSC

2 mportant factor to affect errors of peak-searchng algorthms [1]. In ths paper, the wavelength demodulaton system based on tunable F-P flter was ntroduced. Frstly, the acqured lght power sgnals were processed by flters so as to provde nput sgnals wth hgh SNR for the peak-searchng algorthm. After analyzng and comparng several avalable peak-searchng algorthms, the algorthm of Gauss formula nonlnear curve fttng was chosen. It can effectvely control the errors and mprove the detecton precson of the demodulaton system.. Tunable F-P Flter Demodulaton System Demodulaton methods for FG sensng system manly nclude narrow-band laser scannng method, nterference method, flterng method, dsperson method, and tunable F-P flter method. In these methods, tunable F-P flter technology s more advantageous. It has advantages of hgh senstvty, wde tunng range, and sutable for mult-pont measurement. The wavelength demodulaton system based on tunable F-P flter s desgned as shown n Fgure 1. ASE Coupler FG S1 FG S FG Sn TFPF PD Amplfer A/D D/A Synchronous clock FPGA DDS Fgure 1. Wavelength Demodulaton System based on Tunable F-P Flter roadband lght source s connected wth the sensng gratng array by coupler. Each FG sensor s n seres wth other FG sensors on a sngle fber. They have dfferent center wavelengths and dfferent dynamc ranges. The lght emtted by broadband optcal source passes coupler, then ncdences FG sensors. The lght wave, whch meets the ragg equaton of some FG sensor, s reflected back nto the tunable F-P flter va the coupler. The tunable F-P flter s scannng perodcally under drvng by the trangular wave. Its scannng range covers the center wavelengths and maxmum dynamc ranges of all FG sensors. The optcal wave meetng peak transmsson condtons wll be transmtted out at dfferent tme. Then t s converted nto voltage sgnal by photoelectrc detector. Subsequently, the sgnal s transformed nto dgtal sgnal by A/D converson crcut after amplfcaton. The acquston crcuts of PD output, trangular wave sgnal generator and control unts are controlled by the sgnal processng unt. The drvng voltage of PZT and acquston crcuts of PD output can be synchronzed usng the synchronous clock. Then the wavelength nformaton fgured up n sgnal processng unt s uploaded to computer and done further processng. 338 Copyrght c 014 SERSC

3 3. Desgn of Flter Algorthm In order to mprove the locatng accuracy of peak value, nose must be removed from useful sgnals. Snce the nose n the FG demodulaton system was manly Gauss whte nose, the FIR low-pass flter was desgned to process collected sgnals. The samplng frequency was set to 4 MHz. The cut-off frequency of the deal low-pass flter was 5 KHz and the order s 3. Accordng to performance of the flter, the functon smulaton was done n MTALA. The center wavelength of the FG s nm. The result s demonstrated n Fgure. It can clearly be sawn that the sgnals become smoother due to flterng most of nose. 4. Peak-searchng Algorthm 4.1. Drect Peak-detecton Algorthm Fgure. Prmtve Sgnal and Fltered Sgnal The algorthm of drect peak-detecton s relatvely smple. It means to drectly calculate the maxmum peak poston of the collected data. In the case of low nose, t can drectly obtaned wavelength value correspondng to maxmum peak poston. Ths wavelength value s the center wavelength of the FG. ut t wll lead to large error that the nose s hgh, especally when the power around the peak pont strongly fluctuates n reflecton spectral. 4.. Gauss Curve Fttng Algorthm The algorthm of Gauss curve fttng s to process collected data by Gauss polynomal transform. After beng fttng accordng to general polynomal, the peak poston can be determned. The reflecton spectrum of FG may be descrbed by Gauss functon as formula (1). I( ) I exp[ 4 ln ( ) ] (1) 0 Where I s the ampltude of the refecton spectrum ntensty I, s ragg wavelength 0 of the FG, s 3d bandwdth of the refecton spectrum. Take logarthm on both sdes of formula (1) respectvely, and the formula () s got. ln 1 I( ) ( 4 ln ln I ) 8 ln 4 ln () 0 Copyrght c 014 SERSC 339

4 a P, a 0 ( 4 ln ln I ) 0 Where ( ) ln I ( ) 1 4 ln. And the formula (1) becomes formula (3).,, a 8 ln 1 a a a (3) 0 1 P ( ) Formula (3) s a typcal form of quadratc polynomal fttng. Assume there s n sample ponts (, I ), (=1, n). Accordng to the least squares method, the squared devatons sum S of formula (3) s descrbed as formula (4). S n 1 ( I P ( )) (4) When S s taken the mnmum, the numbers of a, a and a are obtaned. And then the 0 1 wavelength of the FG s descrbed as formula (5). a / a (5) Gauss Formula Nonlnear Curve Fttng Algorthm The algorthm of Gauss formula nonlnear curve fttng (Levenberg-Marquardt) s a knd of method for solvng nonlnear optmzaton. It s a typcal method for least - square optmal soluton. Actually, ths algorthm can be taken as a modfed Gauss Newton method. It combnes the steepest descent method (also called gradent method) wth Gauss Newton method. So t contans the global features of the steepest descent method and the local characterstcs of Gauss Newton method. And ts convergence rate s faster than the steepest descent method. In practcal applcaton, the L-M algorthm s better able to resst nfluence of nose. Even f the ntal values set devates from fnal solutons, t can accurately get the optmal soluton. The FG reflecton spectrum s Gauss shape and the model s descrbed as formula (6). Where x [ a, b, c ] T. Assume there s a M ( x, t) a exp[ t b ( ) ] (6) c x to satsfy formula (7). y M ( x, ) (7) t Where s the measurement error. The Error of f ( x ) and F ( x ) ( the quadratc sum of error) are respectvely descrbed as formula (8) and formula (9). m f (x) y M ( x, t ) (8) T F ( x ) ( f ( x )) f ( x ) f ( x ) f ( x ) (9) Copyrght c 014 SERSC

5 * The target s to fnd such a group of parameters as x, whch make F ( x ) have mnmum * value. It means F ( x ) F ( x ) and x x *, where s a very small postve number. The ntal parameters (a, b, c ) were respectvely set to 10.1, , The maxmum number of teratons s 00 and the dampng coeffcent s Implementaton of Flterng and Peak-searchng Algorthm on FPGA In order to ensure the system to relably run n real tme, FPGA has been chosen as the core part of the lower machne. The whole structure of sgnal processng unt s shown n Fgure 3. PD A/D Converter Clock Sgnal Data A/D Controller FIR Peak Clppng Photoswtch Controller FPGA Photoswtch Crystal Oscllator Clock Unt Data Fttng FIFO US PZT Resstance temperature detector Frequency Regulaton Ampltude Adjustment D/A Converter Temperature Measurement Clock Sgnal DDS D/A Controller Temperature Informaton Dgtal Phase Peak Searchng Temperature and Wavelength Mappng Wavelength Calculaton Curve Calculaton PC Fgure 3. Structure of Sgnal Processng Unt Snce FPGA has good characterstcs of hgh ntegraton and speed, t s consdered to have better real-tme performance to realze flterng and peak-searchng algorthm on FPGA than on PC. Frstly, the sgnal of the PD output was changed to dgtal sgnals by AD. And then the FIR low-pas flter was appled to flter the AD output sgnals so as to provde the nput sgnals wth hgh SNR for the peak-detecton algorthms. In order to reduce useless data and runnng tme, peaks-separatng and ampltude-cuttng-off was carred out to process data accordng to set threshold. The data above the threshold was processed by selected curve fttng algorthm. In ths way, t s more accurate to fnd the peak moment. In addton, FPGA can dvde the frequency of external crystal oscllator usng nner PLL to provde clocks for nner crcut unts. It can control AD to convert the output sgnals of PD nto dgtal sgnals. It can generate the trangular wave drvng sgnal of PZT and control sgnal output of DA. After beng processed by FPGA, the data are uploaded to upper computer by US to do further analyss, store and dsplay. 6. Expermental Result and Analyss ASE broadband lght source was used n experments. The scannng frequency of F-P cavty s 100 Hz. The temperature around the gratng array kept constant. The captured sgnals were fltered and ftted n order. For ten groups of expermental data, the Copyrght c 014 SERSC 341

6 locatons of peak voltage were detected respectvely by the drect peak-detecton algorthm, the Gauss curve fttng algorthm and L-M fttng algorthm. The dstrbuton of absolute errors s shown n Fgure 4. The mean square errors of three algorthms are lsted n Table 1. The expermental results demonstrate that the curve ftted by L-M algorthm s closer to fact among three algorthms, and the L-M algorthm has the lowest mean square error for locatng peak value. It can rase the precson of the demodulaton system, and s a practcal method. Fgure 4. Expermental Result Table 1. Mean Square Errors of Three Curve Fttng Algorthms Drect peak-detecton Gauss curve fttng L-M fttng algorthm algorthm algorthm pm 7.18 pm 6.64 pm 7. Concluson Accordng to the features of nose n FG wavelength demodulaton system, the low pass flter and curve fttng technque were appled to process sgnals. Frstly, the sgnals were processed by flters. Then curve fttng was carred out. Ths method can be more accurate on locaton of the peak. The expermental results show that L-M algorthm s more effectve than the algorthm of gauss fttng n solvng the least squares problem. For the desgn of wavelength demodulaton system desgned n ths paper, the L-M algorthm has mnmal mean square error among several avalable peaksearchng algorthms used to ft the sgnals, whose shapes are smlar to the Gauss sgnal. eng compared wth Gauss fttng algorthm, t reduces the mean square error by 7.5%. Theoretcal smulaton and expermental results demonstrate that ths algorthm s applcable to FG wavelength demodulaton system based on tunable F-P flter. It can effectvely mprove the demodulaton precson. 34 Copyrght c 014 SERSC

7 Acknowledgements Ths work was supported by Educatonal Commsson of Helongjang (151106). References [1] X.-C. Ma and Z.-A. Zhou, J. Journal of Optoelectroncs,Laser, vol. 7, no. 4, (003). [] G.-W. L, H.-F. Pe and J.-H. Yn, J. Measurement Journal of the Internatonal Measurement Confederaton, vol. 1, no. 49, (014). [3] J.-Z. L,.-C. Sun and Y.-L. Du, J. Optoelectroncs Letters, vol. 1, no. 10, (014). [4] H.-P. Wang, Y.-Q. Tan, Z.-J. Dong, J. Journal of Optoelectronc, Laser, vol. 11, no. 4, (013). [5] J. Jn, S. Ln and X.-Y. Ye, J. Optk, vol. 1, no. 15, (014). [6] J.-W. Fu, L.-Z. Xao and Y.-Z. Zhang, J. Optcal Technque, vol. 6, no. 3, (006). [7] Q. Lu, L.-J. Ca and Z.-Y. L, J. Journal of Optoelectroncs, Laser, vol. 7, no. 3, (01). [8] Y.-L. Yu, X.-W. Wang and H. Wang, J. Acta Photonca Snca, vol. 11, no. 41, (01). [9] J.-F. Jang, T.-G. Lu and K. Lu, J. Optcal Engneerng, vol. 3, no. 51, (01). [10] H.-H. Zhu, H.-K. Qn and M. Zhang, J. Chnese Journal of Lasers, vol. 6, no. 35, (008). [11] F.-G. Wu, Q.-S. Zhang and D.-S. Jang, J. Jounal of Wuhan Unversty of Technology, vol. 1, no. 9, (007). [1] F. Grzegorz and N. Pawel, R. J. McDonald, J. Optcal Engneerng, vol. 3, no. 46, (007). Copyrght c 014 SERSC 343

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