# Improved Acoustic Emission Tomography Algorithm Based on Lasso Regression
## 2 Conventional Algorithm of AE Tomography  
AE tomography is a non-destructive testing technology that identifies the AE source locations and the velocity distribution by using the arrival time of elastic waves. The source locations and the velocity distribution are evaluated simultaneously and affect each other while the evaluation. The AE source locations are calculated on the assumed elastic wave velocity distribution that is from the corresponding relay point to the receiver, and then, the velocity is reconstructed on the basis of the travel time between the AE sources and the receiver on the assumed elastic wave velocity distribution. The arrival time is obtained by the emission time and the first travel time. Then, AE source locations are revised based on the meshed cells to update the velocity. The homogeneous velocity of the material in each meshed cell determined as the initial velocity distribution is assumed to be the location of the AE source. After the emission time is determined, the tomography technique will be performed [8]. The flowchart of AE tomography is shown in Figure 1. It is noted that this process uses the straight-line ray path based on the homogeneity of the elastic wave velocity distribution. The travel time spanning from the nodal point to the receiver \(\Delta T_{ik}\) is determined by the following hypotheses:  
\[\Delta T_{ik}=\sum_{j=1}^{n}S_{j}l_{j}, \tag{1}\]  
where \(n\) is the number of the meshed elements, \(j\) is the number of elements, \(I\) represents the \(i\)th receiver, k depicts the kth nodal and relay point to be accessed, slowness is the reciprocal of elastic wave velocity represented as \(S_{j}\), and \(l_{j}\) is the ray-path length in cell \(j\). In the first stage, the source location and the emission time of AE events are calculated by using the arrival time according to the initial elastic wave velocity distribution and the receiver's position. In order to acquire the theoretical travel time, the second stage is to calculate the sum of the estimated emission time and the travel time from the estimated source location to the receiver [13]. Finally, the velocity distribution is reconstructed and updated by minimizing the difference between the theoretical and measured travel times. These two stages are performed iteratively, until the convergence criteria are satisfied and the source position and the elastic wave velocity are determined simultaneously. In the following subsections, the procedure of each stage is briefly introduced. The source location is estimated from the velocity distribution, the location of the receiver, and the arrival time of the AE in AE tomography [1]. The source location estimation starts with calculating the potential emission time. The idea of the computation of the potential emission time is shown in Figure 2. The potential emission time is calculated from the results of the ray trace between the receiver to each nodal and relay point as follows:  
\[P^{\prime}_{ik}=A_{i}-\Delta T_{ik}, \tag{2}\]  
where \(i\) represents the \(i\)th receiver, \(k\) depicts the \(k\)th nodal and relay point to be accessed, \(A_{i}\) is the observed arrival time at receiver \(i\), and \(P^{\prime}_{ik}\) is the potential emission time at point \(k\). The potential emission time denotes the time at which an AE event is expected to be emitted at the point \(k\) if the observed arrival time at the receiver \(i\) is \(A_{i}\) on the present elastic-wave velocity structure. This work is performed for each receiver associated with a single measurement event. For example, each node has \(n\) potential emission times for one event, when \(n\) receivers are installed. The potential emission time should be able to track the correct source location, when the elastic wave velocity distribution and ray path are accurate. However, it is usually selected based on the nodal and relay point with the minimum potential emission time variance due to the insufficient velocity distribution in this source location algorithm.