An Algorithm of Acoustic Emission Location for Complex Composite Structure
Abstract
:1. Introduction
2. Algorithms
2.1. Location Algorithm
2.2. Dijkstra’s Algorithm
- (1)
- A travel time array and a ray source array are defined for each detector. The size of each array is equal to the total number of nodes. The elements in each array and the nodes are in one-to-one correspondence. Each element of the travel time array stores the travel time from the node, where the detector is located, to the corresponding node of the element. Consider that a ray emits from Node A to Node B, and the element of the ray source array corresponding to Node B is used to store the identifier number of Node A. Furthermore, a candidate queue, which is initially empty, is defined to store the identifier numbers of candidate nodes.
- (2)
- Define P as a source node where the detector locates. The element in the travel time array corresponding to Node P is set to zero. Define Q as the current secondary source node. The initial value of the element in the travel time array corresponding to Node Q is equal to TP-Q which is the travel time from Node P to Node Q.
- (3)
- Calculate the travel time from Node P to all the adjacent nodes of Node Q. Let be the ith adjacent node of Node Q, be the travel time from Node P to Node , and be the travel time from Node Q to , then we can obtain = TP-Q + . If is less than the value that has been previously stored in the travel time array, the previously stored value is replaced by . Accordingly, the path source array is also modified, and the identifier numbers of are added to the candidate queue if they are not in the queue.
- (4)
- The calculation ends when the candidate queue is empty. Otherwise, let Q to be the node with the minimum travel time in the candidate queue, then Node Q should be removed from the candidate queue since the path and travel time of Node Q has been determined. Then, go back to the step (3) and continue to calculate.
2.3. Optimization of Dijkstra’s Algorithm
- (1)
- The use of heap sort. It is very popular to add heap sort to Dijkstra’s algorithm [41]. In the original Dijkstra’s algorithm, the candidate queue is in a disordered state, the time complexity for seeking the node of minimum travel time from the candidate queue is , where is the total number of nodes in the candidate queue. If heap sort is used to manage the candidate queue, the time consumption for seeking the node of minimum travel time from the candidate queue includes k times of inserting or adjusting nodes into the heap, and one time of heap reconstruction after removing the minimum value. Specifically, k, which depends on the adjacency radius, is the number of nodes that need to be inserted or adjusted in the candidate queue. Thus, the time complexity is to insert or adjust nodes, and is to rebuild the heap after removing the minimum value. On average, is a big number, but is relatively small, then is much less than . Therefore, we add heap sort into the original Dijkstra’s algorithm to improve the calculation efficiency for seeking nodes of minimum travel time from the candidate queue.
- (2)
- The use of parallel computing. This can largely improve the utilization of multi-cored CPU. Specifically, the nodes in the sample space are assigned to different threads, and a sub-heap is established for each thread. The travel time calculation of adjacent nodes as well as the addition and adjustment of the nodes in candidate queues are implemented by parallel computing. However, the removal of the nodes of minimum travel time from the candidate queue still uses the serial processing.
2.4. Construction of 3D Structure Model
2.5. Correction of Travel Time Error for Straight Path Inside a Block
2.6. Efficiency Test of Travel Time Calculation
3. The Algorithm Testing
3.1. Theoretical Verification
3.2. Experimental Verification
4. Application: An Experiment on a Simulated CCS with a Hole
5. Discussion
5.1. Algorithm Optimization
5.2. Limitations of the Algorithm
- (1)
- Only the first arrival wave can be used to obtain the path and travel time by using our algorithm. The first arrival wave may be P wave, head wave, or diffraction wave.
- (2)
- Our algorithm is only suitable for models with step-like change in wave velocity, such as layered model or block model, but not for models with gradual change in wave velocity.
- (3)
- Our algorithm stipulates that two nodes in the same block are adjacent nodes if the spacing in all directions of , and between the two nodes is less than or equal to the adjacency radius, and that the waves can directly propagate between the adjacent nodes. As a result, an interlayer of the third material between two nodes, which is thinner than the adjacency radius, will be omitted during the calculation so as to guarantee calculation speed. To solve this problem, the material, which contains the thin interlayer, should be cut into two blocks along the two boundaries of the thin interlayer during 3D model meshing.
5.3. Comparison with Moser’s Algorithm
6. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
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Adjacency Radius (Cell Number) | Maximum Relative Error |
---|---|
4 | 1.46% |
5 | 1.15% |
6 | 0.74% |
7 | 0.50% |
8 | 0.40% |
9 | 0.34% |
10 | 0.27% |
Total Nodes n | Time Consumption t (s) | Memory Usage (MB) |
---|---|---|
1,000,000 | 6 | 94 |
8,000,000 | 65 | 385 |
27,000,000 | 292 | 1169 |
64,000,000 | 786 | 2647 |
125,000,000 | 1745 | 5126 |
216,000,000 | 3139 | 8826 |
343,000,000 | 5231 | 13,863 |
512,000,000 | 7377 | 20,699 |
Grid Spacing (mm) | Adjacency Radius (Cell Number) | Path Correction | The Maximum Relative Errors |
---|---|---|---|
2 | 5 | No | 1.43% |
2 | 5 | Yes | 1.28% |
1 | 5 | No | 1.16% |
1 | 5 | Yes | 0.64% |
0.5 | 5 | No | 1.16% |
0.5 | 5 | Yes | 0.61% |
0.5 | 7 | No | 0.50% |
0.5 | 7 | Yes | 0.33% |
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Liu, P.; Guo, Y.; Zhuo, Y.; Qi, W.; Feng, J.; Chen, H.; Chen, S. An Algorithm of Acoustic Emission Location for Complex Composite Structure. Appl. Sci. 2022, 12, 12323. https://doi.org/10.3390/app122312323
Liu P, Guo Y, Zhuo Y, Qi W, Feng J, Chen H, Chen S. An Algorithm of Acoustic Emission Location for Complex Composite Structure. Applied Sciences. 2022; 12(23):12323. https://doi.org/10.3390/app122312323
Chicago/Turabian StyleLiu, Peixun, Yanshuang Guo, Yanqun Zhuo, Wenbo Qi, Jiahui Feng, Hao Chen, and Shunyun Chen. 2022. "An Algorithm of Acoustic Emission Location for Complex Composite Structure" Applied Sciences 12, no. 23: 12323. https://doi.org/10.3390/app122312323
APA StyleLiu, P., Guo, Y., Zhuo, Y., Qi, W., Feng, J., Chen, H., & Chen, S. (2022). An Algorithm of Acoustic Emission Location for Complex Composite Structure. Applied Sciences, 12(23), 12323. https://doi.org/10.3390/app122312323