Improved Wavelet Lifting Algorithm And Its Application In Refined Analysis Of GPR Signals

The ground penetrating radar(GPR)method can effectively detect and infer the distribution of the internal medium of the measured object,and has been widely used in engineering quality detection and disaster assessment.However,there are currently still many deficiencies in the data processing of GPR,the accurate interpretation and refined recognition of image information.This paper took the detection of common cavity defect behind the tunnel lining structure as the research object,based on the improved lifting scheme wavelet construction algorithm and the newly constructed lifting scheme wavelet basis function,combining the GPR method with the lifting scheme wavelet method,the problems of strong amplitude interference signal suppression,reflection signal migration imaging of defect target and quantitative analysis of GPR signals in geological radar detection were deeply discussed and studied.The main research works are as follows:(1)On the basis of traditional wavelet analysis principle and biorthogonal wavelet construction algorithm,aiming at the problems of uncertainty and blindness in the selection of wavelet basis for the analysis of GPR signals,the method of constructing a biorthogonal wavelet basis function that matches the waveform of GPR signals and has excellent properties was carried out.The concepts of wavelet lifting scheme and the principles of algorithm implementation were expounded and the general process of wavelet basis construction algorithm based on lifting scheme was analyzed and discussed.An improved lifting scheme wavelet construction algorithm and its basic implementation flow were proposed by demonstrating and deducing the characteristics of filter coefficients in the lifting method and the relationship between filter banks.Based on the perfect reconstruction filter equation,the realization process of the construction of biorthogonal wavelet basis with good matching with GPR signals and high vanishing moment was put out,and by using the principle of compactly supported wavelet regularity index,the regularity of the newly constructed wavelet basis was checked and compared.(2)In the light of the interference shielding effect caused by the strong reflection of reinforcement in GPR image and the difficulty of separating the strong reflection interference from the weak effective signal by the conventional one-dimensional wavelet decomposition,a strong reflection interference removal method for GPR signals based on two-dimensional image wavelet transform and wavelet energy spectrum entropy theory was proposed(TDWE method)according to the characteristics that two-dimensional wavelet transform can decompose the image signals into a series of sub-bands with different directions and local changes in space,and that wavelet entropy can reflect the energy distribution of the signal.The symmetry of each wavelet basis function,the similarity with the waveform of GPR signals,and the reconstruction error of GPR signals after decomposition were analyzed and compared,from the perspective of wavelet function properties and signal energy entropy calculation,the optimal wavelet basis function suitable for GPR image processing was selected.Based on the optimal wavelet basis,the TDWE method was used to perform strong reflection suppression and image resolution enhancement on the reinforcement-cavity forward image and the actual measurement results of the reinforcement-cavity detection test.(3)In the light of the problems that the migration speed in the migration processing of the defective target in GPR image is difficult to be determined and the refined imaging of the diffraction signal cannot be realized,a GPR signals migration algorithm based on two-dimensional undecimated wavelet transform and F-K algorithm was proposed(UWFK migration method)by using the characteristics that the undecimated wavelet has no loss of phase information and the F-K algorithm has fast migration speed and good stability.Based on the introduction of the principle of traditional F-K migration algorithm and the theory of two-dimensional undecimated wavelet transform,the general process of the UWFK migration method was described.By performing migration processing on the weak diffraction signal and calculating the image information entropy value,the optimal speed value required for the migration processing was analyzed.According to the optimal migration speed obtained by comparison,the UWFK migration method was used to analyze the GPR cavity forward image and the measured GPR images of cavities of different shape respectively.(4)To realize the refined identification and accurate localization of concealed cavity defect boundary,the wavelet modulus maximum method and wavelet time-energy density method were used to accurately extract and identify singular points of the GPR detection signals.A GPR multi-frequency pulse analog signal was constructed,and the feasibility of the two identification methods in the singularity detection of the GPR signals was verified.Based on the new wavelet basis of Tshg3.5 and the existing general wavelet function in the MALAB wavelet library,the wavelet modulus maximum method and wavelet time-energy density method were used to extract the feature point information of the GPR forward simulation signal of cavity and the data of longitudinal and transverse survey lines for cavity detection and for the quantitative analysis of cavity size,and the optimal wavelet basis and the better recognition method used for the quantitative analysis of the GPR signals of RIS type were compared and chosen,finally,the 3D imaging of the cavity was analyzed.The research work done in this paper was based on the front of the subject,focusing on the hot issues in the image processing and signal analysis of GPR at this stage.The construction and algorithm realization of wavelet basis for GPR signals analysis,the suppression of strong reflection interference signal in GPR image,the migration imaging of reflection signal of defective target and the quantitative recognition of GPR signals were studied comprehensively and deeply,which had high theoretical significance and practical value,and laid a theoretical and technical foundation for the health diagnosis and quality safety evaluation of the tunnel lining structure.