Study On Morphological Deconvolution Method For Dispersive And Multi-modes Phenomena In Ultrasonic Guided Waves

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.