# Impact Features Extracting Method for a Reciprocating Compressor Based on the ABC-SGMD Model
## 2 Theoretical Algorithms
### ABC-Optimized SGMD  
The Artificial Bee Colony algorithm (ABC) is a heuristic optimization algorithm inspired by the foraging behavior of bees [23]. It is a swarm intelligence-based algorithm that simulates the search behavior of bees to find the optimal solution. The basic idea is to view the problem to be optimized as the process of bees searching for food. In the algorithm, bees are divided into three roles: employed bees, onlooker bees, and scout bees. Each bee represents a solution (parameter combination) and finds a better solution through search and information exchange.  
In optimization algorithms, the colony size refers to the total number of employed bees and observer bees, which affects the search capability. The max cycles determines the total running time or maximum iterations of the algorithm, and the search range influences the area of the solution space explored: if it is too small, the global optimum might be  
Figure 1: SGMD flowchart.  
missed, while, if it is too large, the convergence speed might be reduced. The search step size is the extent of solution updates in each iteration; if it is too small, convergence will be slow; otherwise, the optimal solution might be missed. The specific implementation steps of Symplectic Geometry Mode Decomposition (SGMD) optimized by ABC are as follows:  
1. Initialization: A group of initial solutions (bees) is randomly generated, with each bee representing a parameter combination of SGMD. Simultaneously, each bee is assigned a fitness value to assess its impact on the system's reconstruction.
2. SGMD and Reconstruction: According to the parameter combination represented by the current bee, perform SGMD and reconstruction to obtain the reconstruction result of the system.
3. Fitness Evaluation: Calculate the corresponding fitness value based on the reconstruction result of SGMD. The fitness value can be evaluated based on the difference between the reconstruction result and the original data, the frequency range of the mode, and other indicators to measure the quality of the reconstruction effect.
4. Employed Bee Stage: Each bee improves the parameters through a local search based on the current parameter combination. The bee will choose a neighborhood solution for the search and calculate the fitness value after the search. If the solution obtained by the search is better, the bee's parameter combination will be updated to the new solution.
5. Onlooker Bee Stage: Each bee will observe the parameter combinations of other bees and choose the parameter combination with the best fitness value as a reference.
6. Scout Bee Stage: If a bee has not found a better solution than the current parameter combination after a certain number of searches, it is regarded as a scout bee, and its parameter combination is randomly regenerated.
7. Follower Bee Stage: Each bee will follow the parameter combination with the best fitness value observed before and conduct further searches. If a better parameter combination is found, update the current solution.
8. Selection Bee Stage: According to the fitness value of each bee, select the parameter combination with the best fitness value as the global optimal solution.
9. Termination Judgment: Determine whether to terminate the algorithm according to the preset termination conditions (such as reaching the maximum number of iterations or reaching the target fitness). If the termination condition is not reached, return to step 4 to continue optimization.  
By utilizing the ABC algorithm, the SGMD can efficiently navigate the parameter space, finding the optimal or near-optimal parameters that enhance the performance of the decomposition process, even in the presence of noise or other complexities in the data. This results in more accurate and robust signal decomposition, which is crucial for the subsequent simulation and experimental analysis.