用分数阶微分实现时频重叠多模式兰姆波的模式分离  

Mode separation for multimode Lamb waves overlapped in time and frequency domains by using fractional differential

作　　者：陈晓[1,2] 倪龙[1] CHEN Xiao;NI Long(School of Electronic and Information Engineering,Nanjing University of Information Science and Technology Nanjing 210044;Collaborative,Innovation Center of Atmospheric,Environment and Equipment Technology,Nanjing University of Information Science and Technology Nanjing 210044)

机构地区：[1]南京信息工程大学电子与信息工程学院,南京210044 [2]南京信息工程大学大气环境与装备技术协同创新中心,南京210044

出　　处：《声学学报》2020年第2期205-214,共10页Acta Acustica

基　　金：江苏省自然科学基金项目(BK20161536);江苏省“333高层次人才培养工程”项目;江苏高校优势学科建设工程项目资助。

摘　　要：为了分离时频重叠多模式超声兰姆波,提出了一种用分数阶微分理论实现多模式兰姆波模式分离的方法。以时频重叠的S1和A1模式混合信号为例,用赛利斯分布作为幅值谱的模型,首先对信号做频散补偿,由补偿后信号幅值谱分数阶微分推导了幅值谱特征参数的计算式并根据信号模型重建幅值谱,然后结合兰姆波的频散特性推导出对应的相位谱,并通过幅值谱和相位谱重构各模式的信号,实现模式分离。对1 mm钢板中仿真时频重叠的S1和A1模式信号分离结果显示分离出信号的幅值和带宽相对误差小于6%,中心频率相对误差小于0.25%。实验结果也证实了方法的可行性。因此当混合信号幅值谱不完全交叠时,本方法可以实现多模式兰姆波信号的分离,有助于多模式兰姆波频散信号的分析和识别。To separate multimode Lamb waves overlapped in time and frequency domains,a multimode Lamb wave signal separation method by using fractional differential is proposed.The Tsallis function is used as the model of the amplitude spectrum.The amplitude spectra of Lamb wave signals are divided into fractional order differential.The characteristic parameters of each mode are extracted by using the polynomials between the maximum amplitude and the derivative order as well as those between the peak frequency and the derivative order.The corresponding phase spectrum is derived from the dispersion characteristics.The signal of each mode is constructed through the amplitude spectrum and phase spectrum.The test results of simulated Si and A1 modes in a 1 mm-thick steel plate show that the relative errors of amplitude and bandwidth of both modes are less than 6%,and that the relative errors of central frequency of both modes are less than 0.25%.Therefore,this method could be used to separate the time-frequency overlapped multimode Lamb wave signals when the amplitude spectra of the mixed signal are not completely overlapped.It is helpful for the analysis and recognition of multimode Lamb wave signal.

关 键 词：分数阶微分 特征参数 频散特性 兰姆波 模式分离 时频重叠 幅值谱 混合信号 相位谱 频散补偿 

分 类 号：TN911.7[电子电信—通信与信息系统]