## 1 Introduction
Partial cracks will undergo a change in stiffness [18], then will generate higher harmonics and have nonlinear characteristics [19; 20; 21; 22; 23]. Structural reliability and remaining life can be evaluated by analyzing nonlinear lamb wave signals [23; 24]. However, due to the dispersion effect, the lamb wave complicates the received signals, which is detrimental to signal analysis. It is hoped that an effective way to detect early damage from single-mode lamb waves can be found. The single-mode (S0) lamb wave has high energy and is easily excited [25; 26]. [PERSON] et al. and [PERSON] et al. have analyzed the effects of microcrack on nonlinear parameters by simulation when the S0 mode lamb wave is the fundamental wave [27; 21]. [PERSON] et al. also verified by experiments that the nonlinear Lamb wave of the low-frequency S0 mode can quantitatively identify the weak nonlinearity of the sheet materials [28]. However, there have been few studies to apply nonlinear S0 mode lamb waves to microcrack localization [8; 9; 14; 15; 16]. In this paper, the S0 mode lamb wave is used as the detection fundamental wave, and it is expected to reduce the difficulty of signal analysis and improve the positioning accuracy. In engineering applications, the microcrack needs to be located. Thereby, maintenance personnel can repair or carry out a further evaluation of the remaining life in time. At present, damage imaging algorithms mainly include the elliptical positioning method, the time inversion method, and the delay superposition algorithm [13; 29; 30; 31; 32]. These algorithms are needed to determine accurate wave velocity and modal information. However, lamb wave has multiple modes of different wave velocities at any excitation frequency because of the dispersion effect. The dispersion effect greatly interferes with the accuracy of these algorithms. At present, the positioning algorithms for sheet material rarely consider the influence of the dispersion effect and have not noticed the value of using a single mode to detect damage. In this paper, the single mode lamb wave is used as the detection fundamental wave, so the excitation signal is pure, the wave velocity information is clear, and the damage information is easier to extract. Moreover, most of these algorithms focus on macroscopic damage. The author believes that detecting and locating early microcracks is more meaningful. Especially when the material is in a harsh working environment, microcracks can cause function failure of structure. In this paper, it is expected that fewer sensors will be arranged on the surface of the sheet materials to scan closed microcracks. It is expected that fast and accurate positioning will be achieved by cooperating with the nonlinear single mode lamb wave. This paper presents a method for locating microcracks using a probability scan matrix. Through simulation and experiment, the positioning result is analyzed in detail when the microcrack is in different positions in the scanning area and the arrangement of the excitation and reception probes are different. Compared with the traditional study of macroscopic damage, this paper is more meaningful for the study of early damage. At the same time, this paper pays attention to the influence of the lamb wave dispersion effect on the signal analysis and positioning results, so the S0 single-mode lamb wave is used as the detection fundamental wave. The remainder of this paper is organized as follows. Section 2 explains the principle of a probabilistic scanning and positioning imaging matrix and how to obtain an S0 single mode lamb wave, and at the same time proposes ways to evaluate the positioning results. Section 3 compares the positioning results of microcracks by simulation when the microcrack is in different positions and the probe arrangement is different. In Section 4, the experiment is conducted to demonstrate its performance. The conclusions are presented in Section 5.