Methods For Concrete Nondestructive Testing Based On Forward Modeling And Inversion Of Maxwell's Equations

Concrete is one of most widely used material which is applied in architectural en-gineering. Its structure safety has been the focus of attention. In view of particularityof concrete structure, it is necessary to carry out nondestructive testing before repair-ing, strengthening or reconstructing the concrete. Then we can obtain the informationof defect about location, size and property. So concrete nondestructive testing has veryimportant significance.GPR nondestructive testing has the advantages of high resolution, fast detect speedand convenient operation, so it wins the good graces of engineering geophysics. Thistechnique has become an important means for concrete nondestructive testing at present.However, when the work of GPR data explanation is compared to radar theory, seismicexploration and fast developed hardware technology, it is found that this work is far awayfrom systematic and mature stage. Now this work mainly is artificial analysis and estima-tion after data precondition, it has not become mechanized processing mode. It is difficultto estimate some of defect signals because of attenuation of electromagnetic wave withhigh frequency. So it often occurs erroneous estimation due to difference of person'sexperience, it results in low accuracy and efficiency of this method. This circumstanceseriously restrict development of GPR technique in aspects of concrete nondestructivetesting, it is badly in need of more visual and automatic estimated system. Concretenondestructive testing belongs to small size testing problem compared with resource ex-ploration. Its Characteristics are small size of object, high accuracy and resolution, badhomogeneity. For complicated testing problem, radar CT tomography based on ray the-ory and waveform inversion based on Born and Rytov weak scattering approximation areall inability. So it must start from coefficient estimation(permittivity or conductivity),develops full waveform numerical inversion method.In this paper, the theoretical foundation and testing means are based on electromag-netic wave propagation theory and GPR respectively. We build TM model which is accordwith concrete structure and observation system and investigate concrete nondestructivetesting from forward modeling and inversion aspects.At present, people don't clearly understand propagation law of electromagnetic wave in concrete and its defect, especially lack quantitative analysis for different re?ection in-tensity of defect. This results in enormous difference for GPR profile explanation. Thispaper uses the finite difference in time domain for simulating electromagnetic wave prop-agation law. It not only analyze re?ection characterize of electromagnetic wave on con-crete's defect but also provide forword results for inversion iteration algorithm. In orderto simulate propagation law of electromagnetic wave in concrete more accurately andavoid the change of frequency and accumulated error, numerical dispersion is consideredat the same time. At the boundary, we employ Mur absorbing boundary condition insteadof Dirichlet or Newman boundary condition that are usually used for theory analysis, itcan weaken electromagnetic wave re?ection intensity. In Numerical examples, accordingto cavity, water and reinforcement that always appears in concrete, we analyze re?ectioncharacteristics of different medium. Through the comparison of three mediums in sameor different depth, we can decrease error of analysis for GPR profile.Concrete GPR profile only present location of defect formally, the size and propertyneed further analysis by expert. In order to make the explanation of GPR data more ac-curate and visual, this paper implements the estimation to concrete defect by inversionof permittivity in view of coefficient estimation. There is certain investigation about thisthought in the field of seismic exploration, but the similar application is not appeared inconcrete nondestructive testing. The main reason lies in highly ill-posed and tremendouschange of solution with little disturbance of observe data when this coefficient estimationmethod is abstracted to inverse problems of Maxwell's equations. In addition this inverseproblem is highly nonlinear, existence of local minimum makes classical method invalidthat couldn't accurately estimate the structure of concrete. According to this two diffi-culties, this paper designed homotopy optimization method which has the regularizaitoneffect. It can not only overcome the ill-posedness but also implement wide convergenceby selecting different homotopy coefficient for changing convexity. In order to improvealgorithm convergency and avoid phenomenon of non-convergence such as bifurcation,cyclotron and so on, we disturb solution and increase ensemble. In Numerical examples,comparing the true model, radar profile and inversion, results showed that it couldn'taccurately estimate the structure of concrete only by GPR profile. However, inversionresults could estimate the location, size and property of defect more accurately.According to multi-local extremum problem in concrete inversion imaging, we in- troduce wavelet multiscale method into inverse problem of Maxwell's equations. We de-signed wavelet multiscale method combined with Tikhonov regularizaiotn. Inverse prob-lem is decomposed onto different scale by wavelet decomposition. The inverse problempresents convexity on large scale, we solve sub-inverse problem on every scale from largeto small, thus large range convergence is implemented. Considering how to select reg-ularization parameter, because it is impossible to obtain data error ??, we employ GCVmethod to select regularization parameter. The simulated example started from singlecavity model, verified the convergence and stability of wavelet multiscale algorithm. Ac-cording to all kinds of structure of concrete, we complemented inversion of permittivityfrom simplicity to complexity, and verified that this method could accurately estimate thestructure of concrete combined with practical data.In a word, this paper starts from concrete nondestructive testing, investigates electro-magnetic wave re?ection characterize in different defect. We sign homotopy method andwavelet multiscale method which is wide convergence, resolve ill-posedness and localminimum problem appeared in coefficient estimation method. The explanation of the twomethods are more quantitative and visual, overcame the shortcoming of traditional expla-nation method. The two method not only test the location but also accurately determinethe size and property of defect.