## 4 Experiment
### Experiment in the Marine Environment  
To verify the effectiveness of the proposed method, the performance of the designed arrays in the marine environment was analyzed. Due to the long production cycle and  
Figure 21: The beampattern after position perturbation.  
Figure 20: Curve of the radiation impedance changing with the array element spacing.  
high investment of large-scale low-frequency sensor arrays, 40-element on-grid arrays were designed for the experiments. We extracted 40 elements from an 81-element uniform array to obtain the required arrays. The positions of the arrays designed using GA, PSO, WOA, and GEWOA are shown in Figure 22.  
All array elements are set on the grid points. The beampatterns of designed arrays are shown in Figure 23. The PSLLs and main lobe widths of the beampatterns are shown in Table 4. By analyzing the performance of the sparse-sensor array designed based on GEWOA in the marine environment and comparing with the performance of the arrays obtained by GA, PSO, and WOA, the effectiveness of the algorithm was verified. The experimental conditions were as follows: the experimental array was a uniform hydrophone array with a half wavelength of 0.4167 m as shown in Figure 24. The design frequency of the array was 1800 Hz, and the number of array elements was 81.  
The experimental data were from the 2020 South China Sea Experiment. The designed arrays were used to receive the transmit signal. The received data of 40-element on-grid arrays obtained by GA, PSO, WOA, and GEWOA were extracted from the 81-element uniform array. The relative azimuth angle between the sound source and the array was 15\({}^{\circ}\). The frequency of the transmitted signal was 1800 Hz. Its duration was 1 s, and the transmission period was 40 s.  
Figure 23: Beampatterns of the on-grid arrays (40-element) designed using GA, PSO, WOA, and GEWOA.  
Figure 22: The positions of arrays designed using GA, PSO, WOA, and GEWOA.  
The beampatterns were obtained by conventional beamforming processing of the direct wave signals. The PSLs of the beampatterns were analyzed to evaluate the array performance. The beampatterns obtained by the 40-element on-grid array designed using GA, PSO, WOA, and GEWOA are shown in Figure 25. The PSLs and main lobe widths of the beampatterns in marine environment are shown in Table 4. It can be seen that the PSLs of the beampatterns in the marine environment are degraded, due to the deviation of the array position from the designed ideal position.  
The main lobe widths vary relatively little. The PSLL of the array designed using GEWOA is \(-17.10\) dB in the marine environment. According to Table 4, it can be seen that compared to GA, the main lobe width expanded by nearly 0.06 degrees, which was only increased by 4.5% in the marine experiments. However, the PSLL decreased by 3.9 dB, which is a decrease of nearly 29.5%.  
Compared with WOA, the main lobe width expanded by 0.01 degree, which is an increase of only 0.7%, while the PSLL was reduced by 2.5 dB, which is a decrease of 17.1%. The PSLL of GEWOA was 3.9 dB lower than that of the traditional GA algorithm with a small change in the performance of the main lobe width. In comparison with PSLLs obtained using other arrays, the array designed using GEWOA had the lowest PSLL.  
Figure 24: Profile display of equipment in the marine environment.  
Figure 25: Beampatterns of the on-grid arrays (40-element) designed using four intelligence algorithms in the marine environment.