## 2 Theory
### Impact Signal Arrival Time Algorithm  
In addition to the influence of the energy factor, the degree of coupling between the sensor and the panel, the distance difference between the impact source to the sensors, the frequency response of the sensors, and the electromagnetic noise interference will also cause the same impact source signal received by different sensors to respond quietly differently in the time domain and frequency domain, which increases the difficulty of locating, especially for impact points close to one sensor. In order to ensure that the S0 mode Lamb waves used for locating are all in the same frequency band and in phase, the threshold selection should be adaptively determined according to the signal characteristics. In this paper, an energy compensation threshold method is proposed to obtain the arrival time of the S0 mode Lamb wave. The principle is as follows:  
Assuming that the number of sensors used in the experiment is \(n\) and the impact signal is \(S_{0}\), the expression of the signal received by the \(i\)-th sensor \(S(i)\) is expressed as:  
\[S(i)=G_{r}(i)G_{s}(i)S_{0}, \tag{5}\]  
where \(G_{r}(i)\) represents the transfer function of the propagation path to the signal during the impact signal to the \(i\)-th sensor, \(G_{s}(i)\) is the transfer function of the sensor of the \(i\)-th to the signal. Filter. According to the energy factor curve, the appropriate frequency band is selected, and the signal received by the sensor is band-pass filtered by the infinite impulse response (IIR) digital filter to ensure that the signal is the Lamb wave in the same frequency band and the interference is removed. The filtered signal expression is expressed as:  
\[S_{f}(i)=S(i)G_{f}, \tag{6}\]  
where \(G_{f}\) is the transfer function of the filter. The threshold benchmark is determined based on noise. In the noise segment of the filtered signal, a noise signal of 0.33 ms duration is taken every 1 ms, and a total of 10 segments are taken. The absolute value of the envelope extreme value of each segment of the noise signal is arranged in descending order, and the partial points of the sequence header are removed to prevent burst type electromagnetic interference. The average value of the amplitude of the sequence 1/7-3/7 segment is the benchmark for this segment noise. The average of the 10-segment noise benchmarks is calculated as the threshold benchmark for this channel. The equation can be expressed as:  
\[\overline{T}_{c}(i)=\sum_{i=1}^{10}\overline{T_{p}}(j)/10, \tag{7}\]  
\[\overline{T_{p}}(j)=\sum_{k=m/7}^{3m/7}N_{j}(k)/(2m/7), \tag{8}\]  
where \(\overline{T}_{c}(i)\) is the threshold benchmark of the \(i\)-th channel, \(\overline{T_{p}}(j)\) is the benchmark of the \(j\)-th segment noise, \(N_{j}\) is the descending order of the absolute value of the extremum of the noise signal envelope, \(k\) is the serial number of the point used to calculate the noise benchmark, \(m\) is the number of points of \(N_{j}\). Determine the threshold amplification factor. By using the average value of the 11-20 points in the descending order of the absolute value of the signal as the energy benchmark, the proportional relationship of the energy benchmark of each channel can be obtained. The threshold amplification factor of the channel with the smallest energy benchmark is set to 25, and the threshold amplification factors of the remaining channels are calculated based on the energy benchmark ratio relationship. The equation can be expressed as:  
\[T(i)=K(i)\overline{T_{c}}(i), \tag{9}\]  
Equation (14) is a hyperbolic implicit function equation for the polar coordinates of \(\rho_{x}\) and \(\theta_{x}\). According to the magnitude of \(t_{i}\) and \(t_{j}\), the branch of the hyperbola can be determined. After calculating the signals received by each of the two sensors, a hyperbola can be drawn. Due to the error, the three hyperbolas intersect at three points, and the triangle center of gravity composed of three points is used as the impact locating point.