# Improved Acoustic Emission Tomography Algorithm Based on Lasso Regression
## 5 Experiment  
After numerical simulations, the lower velocity area described as defect can be accurately identified, and the effectiveness and ability of Lasso regression used in AE tomography for velocity distribution were verified. The following experiments were designed to validate the proposed method in practical works, whose results were compared with the results of the SIRT in the AE tomography technology. The specimen was an aluminum plate, and its size was 1 m \(\times\) 1 m \(\times\) 0.005 m. A slit of 0.5 m \(\times\) 0.04 m was made in the lower right area in the specimen as an artificial defect. The specimen was modeled as a two-dimensional plate, since the thickness of the specimen was small in comparison with its size. At the same time, the source of acoustic wave emission and the sensors were placed on the same side of the specimen. The velocity of elastic wave propagation in the specimen was 5500 m/s. There were nine sensors arranged around the specimen at the interval of 0.4 m with one located in the center of the specimen, as shown in Figure 14. In each sensor, the threshold to start recording, the preamp amplifies, and the frequency range of the bandpass filter were set to 50 dB, 60 dB, and 1 kHz to 1 MHz, respectively. Therefore, the accuracy of the arrival time had six decimal places. Seventy-two source locations are shown as white points with an interval of 0.1 m and an even distribution in the model as illustrated in Figure 14b. Figure 14: Overview of the specimen: (**a**) photograph of the specimen; (**b**) schematic diagram of the specimen. Figure 13: Identified results of case 3: (**a**) LASSO algorithm; (**b**) SIRT algorithm. The inspection steps for AE tomography with LASSO are as follows: (1) The method is the application of the elastic wave generated by breaking a pencil lead at the individual source locations, as shown in Figure 15a. A 2H pencil lead with a length of 3 mm was broken on the surface of the 72 setting positions to emit the events [23], and nine sensors received the elastic wave separately, which were then transmitted to the acquisition system to obtain the detected measured AE wave after being amplified by a preamplifier. The noise and signal parts of the AE events wave were clearly distinguished in this case. (2) The arrival times were selected at the end of the noise part of each measurement path, shown in Figure 15b. It is worth noting that the relay point part divided each meshed cell edge into seven parts, meaning that 60 relay points were in each mesh. The model was meshed by squares with a length of about 0.13 m, meaning that there were 36 (6\(\times\)6) cells in total. (3) To reconstruct the elastic velocity distribution, the travel time between source locations and sensors was collected from the corresponding time history, since the amplitudes of the signal and noise components varied considerably. (4) The internal velocity distribution of the model was described as the difference slowness vector \(\Delta\)s in Equation (10), and the slowness distribution was updated by using \(\Delta\)s.  
The reconstructions of the velocity distribution by the SIRT and LASSO algorithms were conducted to verify the proposed algorithm with different numbers of events. The numbers of events of 9, 18, 27, 36, 45, 54, 63, and 72 were selected, and related occupations of the entire event and measurement paths are shown in Figure 16.  
The red circle is the event selected on the model, and the selection was as uniform as possible to ensure for making the reconstructed velocity distributions were relatively accurate. In the reconstructed results, the red part is the damaged area with a velocity lower than 3000 m/s, and the higher velocity (5500 m/s) part is a healthy condition detected as the blue area for both algorithms.