# An Algorithm of Acoustic Emission Location for Complex Composite Structure
###### Abstract  
Acoustic emission (AE) is widely used in engineering and rock mechanics. The algorithm of AE location based on homogeneous medium or single velocity structure is confronted with lower accuracy when it is applied to the actual working conditions that are prevailing complicated and heterogeneous. In this paper, an AE location algorithm based on complex composite structure (CCS) is proposed via carrying out the following studies: (1) A new travel time calculation scheme suitable for CCS with step-like velocity change is proposed based on an optimized shortest path algorithm. By doing this, a reasonable ray path that is only deflected at the interface is obtained to improve the travel time accuracy. The time complexity of the new algorithm is \(O(n\log_{2}n)\). (2) The availability of the new algorithm is verified via a theoretical analysis under a one-dimensional velocity structure as well as an AE experiment using a complex structure under artificial excitation. (3) The AE location during the failure of a simulated CCS in the laboratory indicates that the new algorithm can effectively calculate the travel time and ray path of the sample. complex composite structure; three-dimensional velocity model; acoustic emission location; the shortest path method; ray tracing +
Footnote †: journal: Applied Sciences  
The main difficulty of seismic location under 3D velocity model is how to obtain the path and travel time of seismic rays. The studies of seismic tomography have greatly improved the techniques of seismic ray tracing and travel time calculation. As a result, a variety of algorithms have been proposed, such as trial shooting, bending, finite difference, and the shortest path method, etc. [31; 32; 33; 34; 35]. Among these algorithms, the shortest path method and the finite differential method have been widely used since they are easy to conduct 3D modeling and the subsequent seismic location calculation. The shortest path method is based on Fermat's principle. It determines the path and travel time of seismic rays by finding the path of the shortest time. The algorithm is stable and avoids the calculations of the normal direction, incidence angle, or refraction angle at the interface. Moreover, the problems of non-convergence or convergence to the local minimum point are also avoided by using the method. Thus, it has obvious advantages compared with other travel time calculation methods. Accordingly, various algorithms based on the shortest path method have been applied to the calculation of seismic ray and travel time [32; 33; 15; 34]. For example, [PERSON]'s algorithm [32] has a great impact, although the error of calculation will be large when this algorithm is applied to the velocity structures with step-like change. It was suggested to subdivide the grid to reduce the calculation error [32], but this will also increase the amount of calculation. Complex structures composed of blocks with different wave velocities are common in 3D velocity structures. Such a complex structure is referred to as a complex composite structure (CCS) in this paper. A CCS is characterized by homogeneous wave velocity inside a block but step-like change in wave velocity at block boundaries. Accordingly, the seismic ray is straight inside a block and only deflects at block boundaries. In addition, the path of the seismic ray at block boundaries is non-differentiable. In this paper, a new algorithm of AE location for the CCS is proposed, which is still based on the 3D grid model and the shortest path algorithm. Furthermore, the grid node division, computing efficiency, and path correction are improved in the new algorithm to ensure that the ray path is straight inside a block and deflects only at block boundaries. Secondly, the travel time from all nodes of a five-layer 1D velocity structure to a designated position is calculated by using our algorithm and compared with the theoretical travel time. By doing this, the travel time error and influencing factors are confirmed.