J. Cent. South Univ. (2019) 26: 3057−3065 DOI: https://doi.org/10.1007/s11771-019-4236-y OMHT method for weak signal processing of GPR and its application in identification of concrete micro-crack LING Tong-hua(凌同华)1, ZHANG Liang(张亮)1, 2, HUANG Fu(黄阜)1, GU Dan-ping(谷淡平)1, YU Bin(余彬)1, ZHANG Sheng(张胜)3 1. School of Civil Engineering, Changsha University of Science and Technology, Changsha 410114, China; 2. Hunan Province Engineering Laboratory of Bridge Structure, Changsha University of Science and Technology, Changsha 410114, China; 3. College of Civil Engineering, Hunan City University, Yiyang 413000, China © Central South University Press and Springer-Verlag GmbH Germany, part of Springer Nature 2019 Abstract: In the light of the problem of weak reflection signals shielded by strong reflections from the concrete surface, the detection and the recognition of hidden micro-cracks in the shield tunnel lining were studied using the orthogonal matching pursuit and the Hilbert transform(OMHT method). First, according to the matching pursuit algorithm and the strong reflection-forming mechanism, and based on the sparse representation theory, a sparse dictionary, adapted to the characteristics of the strong reflection signal, was selected, and a matching decomposition of each signal was performed so that the weak target signal submerged in the strong reflection was displayed more strongly. Second, the Hilbert transform was used to extract multiple parameters, such as the instantaneous amplitude, the instantaneous frequency, and the instantaneous phase, from the processed signal, and the ground penetrating radar (GPR) image was comprehensively analyzed and determined from multiple angles. The results show that the OMHT method can accurately weaken the effect of the strong impedance interface and effectively enhance the weak reflected signal energy of hidden micro-crack in the shield tunnel segment. The resolution of the processed GPR image is greatly improved, and the reflected signal of the hidden micro-crack is easily visible, which proves the validity and accuracy of the analysis method. Key words: orthogonal matching pursuit; Hilbert transform; shield tunnel; lining structure; hidden micro-crack Cite this article as: LING Tong-hua, ZHANG Liang, HUANG Fu, GU Dan-ping, YU Bin, ZHANG Sheng. OMHT method for weak signal processing of GPR and its application in identification of concrete micro-crack [J]. Journal of Central South University, 2019, 26(11): 3057−3065. DOI: https://doi.org/10.1007/s11771-019-4236-y. part of the shield tunnel support system, the quality 1 Introduction of the lining segment is directly related to the overall quality and safety of the tunnel. However, Because of the advantages of low impact on because of factors such as design, construction the surrounding environment, a wide range of technology, and cyclic load, segments of shield adaptability, safety and rapid construction, shield tunnels commonly exhibit defects, e.g., varying tunnel construction is increasingly favored in the degrees of cracks and water leakage. Particularly, infrastructures of various countries. As an important when hidden cracks appear in the lining structure, Foundation item: Projects(51678071, 51608183) supported by the National Natural Science Foundation of China; Projects(CX2018B530, CX2018B531) supported by the Postgraduate Research and Innovation-funded Project of Hunan Province, China; Projects(16BCX13, 16BCX09) supported by Changsha University of Science and Technology, China Received date: 2018-07-24; Accepted date: 2019-07-04 Corresponding author: ZHANG Liang, Doctoral Candidate; Tel: +86-18974934275; E-mail: [email protected]; ORCID: 0000- 0002-7119-9315 3058 J. Cent. South Univ. (2019) 26: 3057−3065 they are more serious and difficult to address Most signals in nature (such as GPR signals) are because they are concealed, imperceptible and thus usually not sparse; therefore, they must be sparsely undetectable. The timely detection of concealed represented. Sparse representation means using a quality defects in lining structures is of great linear combination of notably few elements in a significance for maintaining the safety of tunnel dictionary to represent a signal. For example, signal engineering. x can be represented by the superposition of S basic Scholars have conducted much meaningful signal atoms φs as follows: work in the detection and identification of typical S harmful geologic bodies. The research on the xDass (1) s1 quality defects of shield tunnel lining mainly focuses on the detection of the void and where a=[α1, α2, …, αs] is the sparse representation grouting-backfilling [1−6], and there is little coefficient of x in dictionary D=[φ1, φ2, …, φs]. In reference to the detection and recognition of the discrete-time and finite-length signal processing, a lining cracks, particularly the hidden micro-cracks dictionary is a matrix with dimensions N×S with (width=0.5 mm). In the field of underground atomic φs as a column vector. When the number of engineering, the main research objects of cracking columns in the dictionary is greater than the number are rock and rock-like materials [7, 8]. Since the of rows (i.e., S>N), the dictionary is an micro-crack size is too small, the reflection signal is overcomplete dictionary. too weak, and the high- frequency electromagnetic 2.1.2 Basic principle of matching pursuit algorithm wave of the GPR is easily attenuated and dispersed The matching pursuit algorithm adaptively during the propagation process, it is notably decomposes the signal by decomposing the signal difficult to identify and locate the hidden cracks in in an overcomplete time-frequency atomic library the shield tunnel lining. (dictionary D); hence, the signal can be expressed In this work, a signal analysis method that as a linear combination of the matched time- combines the orthogonal matching pursuit with the frequency atoms [12]. A dictionary is a collection of Hilbert transform (OMHT method) is proposed and a series of time-frequency atoms; the commonly applied to identify micro-cracks in concrete used atomic library categories are Gabor atoms, structures. In the OMHT method, the original GPR chirplet atoms, and Ricker wavelet atoms. The image of the concrete with hidden water-filled specific mathematical principle of the classic micro-crack is processed to remove the strong reflection interference, which causes the weak matching pursuit algorithm is then expressed as follows [13−15]: signal submerged in the strong reflection to emerge. The processed energy-enhanced image is handled aDaxˆ=argmin 2 s.t. a (2) 2 0 by the Hilbert transform. Then, from the obtained where aˆ is the sparse representation coefficient of three-parameter diagrams of instantaneous the original signal; x is the GPR signal; δ is the amplitude, instantaneous phase and instantaneous sparse constraint coefficient in the matching pursuit frequency, the abnormal reflection signals of the algorithm; D is the sparse dictionary. hidden water micro-crack in the middle of the image can be clearly observed, which verifies the The matching pursuit algorithm reduces the effectiveness of the method in the identification of computational complexity using greedy techniques. hidden micro-cracks. It is an iterative algorithm that adopts the inner product as the correlation metric and selects the 2 Theories and algorithms atom most related to the residual signal in each iteration from the dictionary. Performing this action 2.1 Sparse representation theory and matching at each iteration increases the optimization of the pursuit algorithm approximation of signal x. The specific steps of the 2.1.1 Sparse representation of signals algorithm are as follows: A signal that can be expressed as x=[x1, x2, …, 1) Initialization: Set the initial residual signal T 0 xN] , if there are only n (n<<N) sample points with equal to the original signal, i.e., R=xx, and the nonzero values, is considered a sparse signal [9−11]. initial iteration number to i=0; J. Cent. South Univ. (2019) 26: 3057−3065 3059 2) Inner product coefficient calculation: [16, 17]. Calculate the coefficient of the inner product of the Let the input signal be g(t), and the output 1 residual signal R x and all atoms in the dictionary, signal be expressed as g()t after the filtering of i i.e., Rx,; Hilbert frequency response of H(w). The Hilbert 3) Inner product maximization: Maximize the transform formula is as follows: inner product i arg max and record the 1 gt() gt () (5) t atomic subscript γi and the inner product coefficient αγ ; The GPR signals are represented as follows: i 4) Residual signal updating: Update the 1 residual signal using R=Ri+1xxi α φ ; ut() gt () igt () gt () igt () (6) γγii t 5) Rule for stopping the iterations: If the Formula (6) is the complex signal residual signal energy is less than the given representation of the real GPR signal g(t). i+1 2 threshold ξstop, i.e., R x stop , then stop The following feature parameter estimations iterating. Otherwise, let i=i+1 and return to Step 2. are defined from Formula (6) as follows: After N iterations, the signal x can be sparsely a) Instantaneous amplitude estimation: N 1 N decomposed as xxα φ R.When N 2 2 γγii A()tgtgt () () (7) i0 approaches infinity, RN x exponentially converges The instantaneous amplitude A(t) has a positive correlation with the square root of the total as limRN x 0 in the finite-dimensional signal N energy of the reflected signal at a given moment; space. The signal is then represented as follows: the variation of the correlation magnitude is related to the signal propagation distance, the dielectric x αφ (3) γγii constant difference, etc. i0 b) Instantaneous phase estimation: One of the keys to successfully removing the g()t strong reflection interference using the orthogonal (t ) arctan (8) g()t matching pursuit is the selection of the sparse dictionary D.