基于互相关-LM法的布里渊峰值拟合算法
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摘要
基于互相关法和Levenberg-Marquardt(LM)算法,提出了互相关-LM算法以拟合布里渊频谱的中心频率。此方法发挥互相关法无需给定初值且对噪声不敏感的优点,将其用来寻找迭代初值,得到精度较低结果作为初值输入LM算法中进行迭代,最终得出布里渊散射频谱的精确信息。同时提出了新的双峰布里渊谱的拟合方法和出现双峰时的布里渊峰值选择原则。此算法有效提高了拟合精度和拟合效率,使得单峰拟合误差在1 MHz以内,双峰拟合误差在2 MHz以内,拟合度达0.9988。为了检验其实用性,将其应用于变压器绕组变形检测。对改造过的外表面敷设光纤的绕组施加两处应变,互相关-LM算法能精确提取中心频率,解耦出应变信息,平行测试误差在3MHz以内,拟合度可达0.9964,均方根误差约0.005,并能实现应变的精确定位,充分证明了此方法的优越性和实用性。
Based on the correlation method and the Levenberg-Marquardt(LM)algorithm,this study proposes a correlation-LM algorithm for fitting the central frequency of the Brillouin spectrum.The proposed algorithm exploits the correlation method because it does not require an initial value and is insensitive to noise.Therefore,the correlation method is used to determine the iterative initial value.Inputting the initial value into the LM algorithm for iteration yields less-accurate results.Accurate information of the Brillouin scattering spectrum is finally obtained.Thus,overcoming the problem of iteration using the LM method is necessary as it has the disadvantage of being extremely sensitive to the initial value.Therefore,this study also proposes a new bimodal Brillouin spectrum fitting method and the Brillouin peak selection principle with double peaks.This algorithm can effectively improve the fitting accuracy and the fitting efficiency,making the single-peak fitting error within 1 MHz,the double-peak fitting error within 2 MHz,and the fitting degree to be 0.9988.To test the practicability of the algorithm,it is used to detect the transformer winding deformation.Two strains are applied to the modified winding.The correlation-LM algorithm could extract the central frequency accurately and decouple the strain information.The parallel test error is within 3 MHz,the fitting degree reaches 0.9964,and the strain is accurately located,thereby proving the superiority and practicality of this method.
Based on the correlation method and the Levenberg-Marquardt(LM)algorithm,this study proposes a correlation-LM algorithm for fitting the central frequency of the Brillouin spectrum.The proposed algorithm exploits the correlation method because it does not require an initial value and is insensitive to noise.Therefore,the correlation method is used to determine the iterative initial value.Inputting the initial value into the LM algorithm for iteration yields less-accurate results.Accurate information of the Brillouin scattering spectrum is finally obtained.Thus,overcoming the problem of iteration using the LM method is necessary as it has the disadvantage of being extremely sensitive to the initial value.Therefore,this study also proposes a new bimodal Brillouin spectrum fitting method and the Brillouin peak selection principle with double peaks.This algorithm can effectively improve the fitting accuracy and the fitting efficiency,making the single-peak fitting error within 1 MHz,the double-peak fitting error within 2 MHz,and the fitting degree to be 0.9988.To test the practicability of the algorithm,it is used to detect the transformer winding deformation.Two strains are applied to the modified winding.The correlation-LM algorithm could extract the central frequency accurately and decouple the strain information.The parallel test error is within 3 MHz,the fitting degree reaches 0.9964,and the strain is accurately located,thereby proving the superiority and practicality of this method.
引文
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[16]Xiao S H,New fitting method for Brillouin-based scattering spectrum of fibre-optic distributed sensing systems[J].Optical Technique,2009,35(6):897-900,904.肖尚辉,李立.一种新的光纤布里渊传感散射谱拟合方法[J].光学技术,2009,35(6):897-900,904.
[16]Xiao S H,Li L.New fitting method for Brillouinbased scattering spectrum of fibre-optic distributed sensing systems[J].Optical Technique,2009,35(6):897-900,904.肖尚辉,李立.一种新的光纤布里渊传感散射谱拟合方法[J].光学技术,2009,35(6):897-900,904.
[17]Ida T,Ando M,Toraya H.Extended pseudo-voigt function for approximating the voigt profile[J].Journal of Applied Crystallography,2000,33(6):1311-1316.
[18]Jia W.The multi-peak spectrum feature extraction technology research of BOTDR distributed optical sensing systems[D].Qinhuangdao:Yanshan University,2015:18-31.贾伟.BOTDR分布式光纤传感系统多峰谱特征提取技术研究[D].秦皇岛:燕山大学,2015:18-31.
[19]Zhang Y J,Jin P J,Fu X Het al.Feature extraction of multi-peak Brillouin scattering spectrum based on SFLA-LSSVM algorithm[J].Chinese Journal of Lasers,2018,45(1):0106004.张燕君,金培俊,付兴虎,等.基于SFLA-LSSVM算法的多峰Brillouin散射谱的特征提取[J].中国激光,2018,45(1):0106004.
[20]Liu Y P,Tian Y,Jiang S,et al.Effect of optical fiber sheath on thermal ageing characteristics of transformer oil[J].Insulating Materials,2017,50(12):54-59.刘云鹏,田源,姜烁,等.光纤护套材料对变压器油热老化特性影响研究[J].绝缘材料,2017,50(12):54-59.
[2]LüJ G,Wei C T.Fitting algorithm for BOTDABrillouin back scattered-light spectrum data[J].Optical Technique,2015,41(4):380-384.吕健刚,韦春桃.基于BOTDA布里渊背向散射光谱数据的拟合算法[J].光学技术,2015,41(4):380-384.
[3]Li D.The key signal processing technology of BOTDR distributed sensing systems[D].Qinhuangdao:Yanshan University,2013:25-30.李达.BOTDR分布式光纤传感信号处理关键技术研究[D].秦皇岛:燕山大学,2013:25-30.
[4]Yu C J.Research on high accuracy extraction of BOTDR distributed sensor signal[D].Qinhuangdao:Yanshan University,2015:25-42.宇春娟.BOTDR分布式光纤传感信号高精度提取研究[D].秦皇岛:燕山大学,2015:25-42.
[5]Zhang Y J,Liu W Z,Fu X H,et al.The high precision analysis research of multichannel BOTDRscattering spectral information based on the TTDFand CNS algorithm[J].Spectroscopy and Spectral Analysis,2015,35(7):1802-1807.张燕君,刘文哲,付兴虎,等.基于TTDF和CNS算法的多路BOTDR散射谱信息高精度分析研究[J].光谱学与光谱分析,2015,35(7):1802-1807.
[6]Zhang Y J,Liu W Z,Fu X H,et al.A Brillouin scattering spectrum feature extraction based on flies optimization algorithm with adaptive mutation and generalized regression neural network[J].Spectroscopy and Spectral Analysis,2015,35(10):2916-2923.张燕君,刘文哲,付兴虎,等.基于自适应变异果蝇优化算法和广义回归神经网络的布里渊散射谱特征提取[J].光谱学与光谱分析,2015,35(10):2916-2923.
[7]Horiguchi T,Shimizu K,Kurashima T,et al.Development of a distributed sensing technique using Brillouin scattering[J].Journal of Lightwave Technology,1995,13(7):1296-1302.
[8]Zheng HR,Fang Z J,Wang Z Y,et al.Brillouin frequency shift of fiber distributed sensors extracted from noisy signals by quadratic fitting[J].Sensors,2018,18(2):409.
[9]Liang H,Zhang X P,Li X H,et al.Design and implementation of data fitting algorithm for Brillouin back scattered-light spectrum data[J].Acta Photonica Sinica,2009,38(4):875-879.梁浩,张旭苹,李新华,等.布里渊背向散射光谱数据拟合算法设计与实现[J].光子学报,2009,38(4):875-879.
[10]Wang F,Zhan W W,Lu Y G,et al.Determining the change of Brillouin frequency shift by using the similarity matching method[J].Journal of Lightwave Technology,2015,33(19):4101-4108.
[11]Farahani M A,Castillo-Guerra E,Colpitts B G.Accurate estimation of Brillouin frequency shift in Brillouin optical time domain analysis sensors using cross correlation[J].Optics Letters,2011,36(21):4275-4277.
[12]Farahani M A,Castillo-Guerra E,Colpitts B G.Adetailed evaluation of the correlation-based method used for estimation of the Brillouin frequency shift in BOTDA sensors[J].IEEE Sensors Journal,2013,13(12):4589-4598.
[13]Shang Q F,Hu Y T,Liu W.Feature extraction of Brillouin scattering spectrum based on crosscorrelation convolution and high-order centroid calculation[J].Chinese Journal of Lasers,2017,44(11):1106011.尚秋峰,胡雨婷,刘薇.基于互相关卷积与高阶矩质心计算的布里渊散射谱特征提取[J].中国激光,2017,44(11):1106011.
[14]Agrawal G P.Nonlinear fiber optics[M].Heidelberg:Springer,2000:195-211.
[15]Xiao S H,Li L.Analytical model of Brillouin scattering spectrum measurements in fibre-optic distributed sensing systems[J].Journal of Southwest Jiaotong University,2009,44(6):946-950.肖尚辉,李立.光纤分布式布里渊传感散射谱数据分析模型[J].西南交通大学学报,2009,44(6):946-950.
[16]Xiao S H,New fitting method for Brillouin-based scattering spectrum of fibre-optic distributed sensing systems[J].Optical Technique,2009,35(6):897-900,904.肖尚辉,李立.一种新的光纤布里渊传感散射谱拟合方法[J].光学技术,2009,35(6):897-900,904.
[16]Xiao S H,Li L.New fitting method for Brillouinbased scattering spectrum of fibre-optic distributed sensing systems[J].Optical Technique,2009,35(6):897-900,904.肖尚辉,李立.一种新的光纤布里渊传感散射谱拟合方法[J].光学技术,2009,35(6):897-900,904.
[17]Ida T,Ando M,Toraya H.Extended pseudo-voigt function for approximating the voigt profile[J].Journal of Applied Crystallography,2000,33(6):1311-1316.
[18]Jia W.The multi-peak spectrum feature extraction technology research of BOTDR distributed optical sensing systems[D].Qinhuangdao:Yanshan University,2015:18-31.贾伟.BOTDR分布式光纤传感系统多峰谱特征提取技术研究[D].秦皇岛:燕山大学,2015:18-31.
[19]Zhang Y J,Jin P J,Fu X Het al.Feature extraction of multi-peak Brillouin scattering spectrum based on SFLA-LSSVM algorithm[J].Chinese Journal of Lasers,2018,45(1):0106004.张燕君,金培俊,付兴虎,等.基于SFLA-LSSVM算法的多峰Brillouin散射谱的特征提取[J].中国激光,2018,45(1):0106004.
[20]Liu Y P,Tian Y,Jiang S,et al.Effect of optical fiber sheath on thermal ageing characteristics of transformer oil[J].Insulating Materials,2017,50(12):54-59.刘云鹏,田源,姜烁,等.光纤护套材料对变压器油热老化特性影响研究[J].绝缘材料,2017,50(12):54-59.