超声导波频散与多模态问题及其形态解卷积方法研究
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摘要
超声导波无损检测技术由于其传播距离远、检测范围大等优良性能，被广泛应用于航空航天、油气管道、压力容器等领域的检测。由于沿波导的长距离传播，超声导波除了有一般体波的特点外，还具有频散和多模态特性，该特性极大地限制了超声导波的检测效果，增大了特征识别的困难。因此频散的抑制和模态的选择一直是国际上超声导波无损检测领域的研究热点。开展针对超声导波频散和多模态特性的研究具有重要的理论和现实意义。
本文通过分析超声导波频散和多模态特性的特点，提出从导波信号处理角度出发，采用形态分量分析的信号处理技术，深入研究导波信号的建模、稀疏分解、形态分解以及解卷积等问题，并通过仿真及实验信号对方法的有效性进行了验证，为解决频散和多模态的影响以及为复杂导波信号的分析提供关键技术。
论文首先对形态分量分析相关理论进行了探讨和研究，从信号的稀疏性及稀疏表示入手，对稀疏分解相关算法进行了分析；分析了增强信号稀疏性的范数正则化方法和压缩传感方法，为超声信号解卷积以及导波信号形态分解提供预备知识。
基于弹性波的控制方程和超声导波传播特性，论文对波动问题在频域内进行了分析和公式推导，利用频域内频散和非频散波的传播方程以及频散波重构方程，提出了频散补偿和频散移除方法，从而更进一步了解了频散产生的机理并为频散信号建模提供基础。在此基础上，提出了包含频散参数的导波信号建模方法，利用3阶多项式对频散曲线进行拟合，多项式系数作为频散参数来刻画频散特性，为形成包含频散参数的原子库做准备。论文对不同结构中模态的分类进行了归纳，研究了互易关系和模态正交化以及简正模态展开理论，根据模态正交性为利用形态分量方法进行模态分解提供了理论支持。
论文通过对超声信号稀疏性和解卷积过程中由于稀疏性不强所造成问题的分析，利用范数正则化方法和压缩传感方法，分别设计了基于l_0范数约束的最小熵解卷积方法和基于压缩传感重构的稀疏解卷积方法。l_0范数方法通过对稀疏先验条件的增强将解卷积问题转换为范数规范的优化问题，进而获得时域上更稀疏的结果。压缩传感重构方法获得稀疏子波，在解卷积过程中同样增强了稀疏性，由于稀疏性的增强也加快了算法收敛速度。提出用l_0范数逼近函数代替直接使用该范数，解决由于l_0范数不连续产生的问题。仿真及实验结果显示两种方法对于相邻或重叠的回波信号有很好的分离效果，对于信噪比不高的情况同样适用。
为分析导波信号中不同模态信息，论文在研究导波信号频散、模态正交性的基础上，提出利用形态分量分析处理导波信号的方法。构建了包含Gabor原子、Chirp原子、小波原子和离散余弦原子在内的原子库。对Gabor原子增加利用3阶多项式进行频散刻画的频散参数，对Chirp原子提出用Chirp斜率进行模态识别，通过对参数的分类可以形成不同的模态库。
论文采用所提出的原子库进行导波信号的匹配追踪分解和形态分量分解，与匹配追踪方法相比，形态分量方法能有效的对模态进行分离，同时还提出了利用离散余弦库对信号中的噪声信号进行形态方法分离。多原子库的形态分量分析方法通过仿真和实验信号验证了其有效性，获得了相应的形态解卷积结果。该方法继承了稀疏分解的优点，能够利用不同形态的字典有效地处理导波信号中多模态问题。进一步扩展模态原子库以及对其特征的精确描述，将有能力对导波信号中更复杂的多模态信息进行处理，从而降低复杂导波信号分析的困难。
最后论文对超声导波系统协同仿真方法进行了研究。分析了导波仿真的有限元方法和半解析有限元方法。
Ultrasonic guided waves were widely used in aeronautics, pipeline, vessels and soon because of its long distance propagation and large range detection property. Due tothe long distance propagation along waveguides, the guided waves were not onlypossess the feature of ultrasonic bulk waves, but also dispersion and multi-modescharacters, which limited detection effect of guided waves and increased the difficultyof feature recognition. Hence, dispersion suppression and multi-modes selection hasbeen a research hotspot in international non-destructive testing field. It has greattheoretical and realistic sense to research the dispersion and multi-modes for ultrasonicguided waves.
In this dissertation, the characters of dispersion and multi-modes were analyzedcarefully, and a signal processing point of view was considered. The modeling, sparsedecomposition, morphology decomposition and deconvolution of guided waves signalswere proposed by the use of morphology component analysis techniques. The validationof these methods were realized through simulations and experiments. Dispersion andmulti-modes phenomenon which increasing complexity of guided waves signals couldbe effectively eliminated though research results.
Firstly this dissertation studied the theory of morphology component analysismethod, and the sparsity and sparse representation have been explored emphatically.Based on the properties of norm regularization and compressive sensing method, a newsparsity enhancement method was perhaps useful. Such research can provide theessential preliminary knowledge for ultrasonic signals deconvolution and morphologydecomposition.
Based on its governing equations of elastic waves and the futures of guided wavespropagation, the wave motion problem was researched in frequency domain and studiedby theoretical deduct. By the use of dispersed or not dispersed wave propagationequations and reconstruction equations, a compensate method and a cancellationmethod of dispersion were proposed, which can further study the mechanism ofdispersion and provide useful information for modeling of dispersed signal. According to above analysis, this dissertation established a modeling method for guided waves thatincluded the parameters of dispersion. A3order polynomial was used to fit thedispersion curves and the coefficients of the polynomial were used to describe thedispersion characters, which prepared for dictionary construction with dispersionvariable. This dissertation also summarized the catalog of modes and made theoreticalguarantees for modes decomposition through the research of orthogonality of modesand normal modes expansion method.
Because of the sparsity of signal was not guaranteed during deconvolution process,this dissertation used norm regularization method and compressive sensing method topresent two different deconvolution algorithm:l0norm regularized minimum entropydeconvolution algorithm and compressive sensing reconstructed sparse deconvolutionalgorithm. According tol0norm method, the deconvolution problem was transformedinto a norm regularized optimization problem with further regularization of sparsityprior condition to obtain more sparser results in time domain. In the process of echowavelet reconstruction, compressive sensing method can also enhance the sparsity. Inorder to solve the problem caused by discontinue ofl0norm, this dissertationpresented a smooth function to approximatel0norm. The simulation and experimentresults showed good performance in separating nearby or overlapped echoes and therobust to noisy.
In order to separate the different modes in guided waves signals, this dissertationresearched characters of dispersion and orthogonality of modes, and then established adecomposition method based on morphology components analysis technique. Themorphology dictionary was constructed by different sub dictionaries, included Gaboratoms, Chirp atoms, wavelet atoms and discrete cosine atoms. The improvement of thesub dictionaries could be realized by add dispersion parameters which obtain from thecoefficient of3order polynomialh to Gabor sub dictionary and add Chirp slopeparameters to Chirp dictionary. The improvements were more suitable for guided wavesignals. The catalog of above parameters also can form different modes dictionaries.
The dictionaries proposed in this dissertation could be used to realize match pursuitdecomposition and morphology decomposition and the morphology method couldachieve more efficient results compared to match pursuit method. Furthermore, theseparation of noisy by means of morphology method with discrete cosine atoms was presented and the rustles were satisfactory. The decomposition and decomvolutionresults were validated by simulation and experiment signals. The procedure inheritedthe advantages of sparse decompose method and could use different morphologydictionaries to decompose guided wave multi mode signals effectively. The expansionof mode dictionaries will achieve accurate description for mode features, and couldobtain capabilities to process complex multi modes signals, which reduced thecomplexity significantly in guided waves signals analysis.
Finally, collaborated simulation method was researched for ultrasonic guidedwaves system. Finite element method and semi-analytical finite element method wereanalysed.
本文通过分析超声导波频散和多模态特性的特点，提出从导波信号处理角度出发，采用形态分量分析的信号处理技术，深入研究导波信号的建模、稀疏分解、形态分解以及解卷积等问题，并通过仿真及实验信号对方法的有效性进行了验证，为解决频散和多模态的影响以及为复杂导波信号的分析提供关键技术。
论文首先对形态分量分析相关理论进行了探讨和研究，从信号的稀疏性及稀疏表示入手，对稀疏分解相关算法进行了分析；分析了增强信号稀疏性的范数正则化方法和压缩传感方法，为超声信号解卷积以及导波信号形态分解提供预备知识。
基于弹性波的控制方程和超声导波传播特性，论文对波动问题在频域内进行了分析和公式推导，利用频域内频散和非频散波的传播方程以及频散波重构方程，提出了频散补偿和频散移除方法，从而更进一步了解了频散产生的机理并为频散信号建模提供基础。在此基础上，提出了包含频散参数的导波信号建模方法，利用3阶多项式对频散曲线进行拟合，多项式系数作为频散参数来刻画频散特性，为形成包含频散参数的原子库做准备。论文对不同结构中模态的分类进行了归纳，研究了互易关系和模态正交化以及简正模态展开理论，根据模态正交性为利用形态分量方法进行模态分解提供了理论支持。
论文通过对超声信号稀疏性和解卷积过程中由于稀疏性不强所造成问题的分析，利用范数正则化方法和压缩传感方法，分别设计了基于l_0范数约束的最小熵解卷积方法和基于压缩传感重构的稀疏解卷积方法。l_0范数方法通过对稀疏先验条件的增强将解卷积问题转换为范数规范的优化问题，进而获得时域上更稀疏的结果。压缩传感重构方法获得稀疏子波，在解卷积过程中同样增强了稀疏性，由于稀疏性的增强也加快了算法收敛速度。提出用l_0范数逼近函数代替直接使用该范数，解决由于l_0范数不连续产生的问题。仿真及实验结果显示两种方法对于相邻或重叠的回波信号有很好的分离效果，对于信噪比不高的情况同样适用。
为分析导波信号中不同模态信息，论文在研究导波信号频散、模态正交性的基础上，提出利用形态分量分析处理导波信号的方法。构建了包含Gabor原子、Chirp原子、小波原子和离散余弦原子在内的原子库。对Gabor原子增加利用3阶多项式进行频散刻画的频散参数，对Chirp原子提出用Chirp斜率进行模态识别，通过对参数的分类可以形成不同的模态库。
论文采用所提出的原子库进行导波信号的匹配追踪分解和形态分量分解，与匹配追踪方法相比，形态分量方法能有效的对模态进行分离，同时还提出了利用离散余弦库对信号中的噪声信号进行形态方法分离。多原子库的形态分量分析方法通过仿真和实验信号验证了其有效性，获得了相应的形态解卷积结果。该方法继承了稀疏分解的优点，能够利用不同形态的字典有效地处理导波信号中多模态问题。进一步扩展模态原子库以及对其特征的精确描述，将有能力对导波信号中更复杂的多模态信息进行处理，从而降低复杂导波信号分析的困难。
最后论文对超声导波系统协同仿真方法进行了研究。分析了导波仿真的有限元方法和半解析有限元方法。
Ultrasonic guided waves were widely used in aeronautics, pipeline, vessels and soon because of its long distance propagation and large range detection property. Due tothe long distance propagation along waveguides, the guided waves were not onlypossess the feature of ultrasonic bulk waves, but also dispersion and multi-modescharacters, which limited detection effect of guided waves and increased the difficultyof feature recognition. Hence, dispersion suppression and multi-modes selection hasbeen a research hotspot in international non-destructive testing field. It has greattheoretical and realistic sense to research the dispersion and multi-modes for ultrasonicguided waves.
In this dissertation, the characters of dispersion and multi-modes were analyzedcarefully, and a signal processing point of view was considered. The modeling, sparsedecomposition, morphology decomposition and deconvolution of guided waves signalswere proposed by the use of morphology component analysis techniques. The validationof these methods were realized through simulations and experiments. Dispersion andmulti-modes phenomenon which increasing complexity of guided waves signals couldbe effectively eliminated though research results.
Firstly this dissertation studied the theory of morphology component analysismethod, and the sparsity and sparse representation have been explored emphatically.Based on the properties of norm regularization and compressive sensing method, a newsparsity enhancement method was perhaps useful. Such research can provide theessential preliminary knowledge for ultrasonic signals deconvolution and morphologydecomposition.
Based on its governing equations of elastic waves and the futures of guided wavespropagation, the wave motion problem was researched in frequency domain and studiedby theoretical deduct. By the use of dispersed or not dispersed wave propagationequations and reconstruction equations, a compensate method and a cancellationmethod of dispersion were proposed, which can further study the mechanism ofdispersion and provide useful information for modeling of dispersed signal. According to above analysis, this dissertation established a modeling method for guided waves thatincluded the parameters of dispersion. A3order polynomial was used to fit thedispersion curves and the coefficients of the polynomial were used to describe thedispersion characters, which prepared for dictionary construction with dispersionvariable. This dissertation also summarized the catalog of modes and made theoreticalguarantees for modes decomposition through the research of orthogonality of modesand normal modes expansion method.
Because of the sparsity of signal was not guaranteed during deconvolution process,this dissertation used norm regularization method and compressive sensing method topresent two different deconvolution algorithm:l0norm regularized minimum entropydeconvolution algorithm and compressive sensing reconstructed sparse deconvolutionalgorithm. According tol0norm method, the deconvolution problem was transformedinto a norm regularized optimization problem with further regularization of sparsityprior condition to obtain more sparser results in time domain. In the process of echowavelet reconstruction, compressive sensing method can also enhance the sparsity. Inorder to solve the problem caused by discontinue ofl0norm, this dissertationpresented a smooth function to approximatel0norm. The simulation and experimentresults showed good performance in separating nearby or overlapped echoes and therobust to noisy.
In order to separate the different modes in guided waves signals, this dissertationresearched characters of dispersion and orthogonality of modes, and then established adecomposition method based on morphology components analysis technique. Themorphology dictionary was constructed by different sub dictionaries, included Gaboratoms, Chirp atoms, wavelet atoms and discrete cosine atoms. The improvement of thesub dictionaries could be realized by add dispersion parameters which obtain from thecoefficient of3order polynomialh to Gabor sub dictionary and add Chirp slopeparameters to Chirp dictionary. The improvements were more suitable for guided wavesignals. The catalog of above parameters also can form different modes dictionaries.
The dictionaries proposed in this dissertation could be used to realize match pursuitdecomposition and morphology decomposition and the morphology method couldachieve more efficient results compared to match pursuit method. Furthermore, theseparation of noisy by means of morphology method with discrete cosine atoms was presented and the rustles were satisfactory. The decomposition and decomvolutionresults were validated by simulation and experiment signals. The procedure inheritedthe advantages of sparse decompose method and could use different morphologydictionaries to decompose guided wave multi mode signals effectively. The expansionof mode dictionaries will achieve accurate description for mode features, and couldobtain capabilities to process complex multi modes signals, which reduced thecomplexity significantly in guided waves signals analysis.
Finally, collaborated simulation method was researched for ultrasonic guidedwaves system. Finite element method and semi-analytical finite element method wereanalysed.
引文
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