## 3 Results and Discussions
### Optimization Procedure Based on ANN with Genetic Algorithm (GA)  
Figure 13 illustrates the Pareto front solutions derived from genetic algorithm (GA) optimization, revealing inherent trade-off relationships among the optimal solution sets. As evidenced in Figure 13, the mutually constrained variables demonstrate that increases in the peak wall shear stress and water consumption correlate with a reduction in the cleaning area.  
Figure 12: Comparison of predicted data with CFD numerical simulation data.  
A subsequent analysis of the optimized solutions quantifies the discretization intervals for each design variable, as categorized in Figure 14. A parametric analysis revealed distinct optimal solution ratios across critical operational ranges [52]. The nozzle outlet widths range of 5.5-6.0 mm yielded the highest optimal solution ratio (98.5%), while configurations within 4.0-5.5 mm exhibited a markedly lower ratio (1.5%). For V-shaped grooving angles between 20.0\({}^{\circ}\) and 27.5\({}^{\circ}\), the optimal solution ratio peaked at 37.5%, surpassing the 25% threshold observed in other angular intervals. Jet target distances of 17.5-20.0 mm achieved a 65% optimal solution ratio, whereas jet incidence angles of 5-10\({}^{\circ}\) demonstrated superior performance with 90% optimal solutions. Notably, incidence pressures within 0.35-0.4 MPa and a gas void fraction of 7.5-11.2% attained optimal solution ratios of 49.5% and 99.5%, respectively. Under these constrained boundaries, the objective functions--the peak wall shear stress (951.08 Pa), action area (70.14 mm\({}^{2}\)), and water consumption (20.80 L/min)--simultaneously reached their optima. The derived parameter combination included the following: d = 5.83 mm, \(\alpha\) = 38.36\({}^{\circ}\), s = 17.55 mm, \(\theta\) = 8.68\({}^{\circ}\), p = 0.29 MPa, and r = 8.91%.  
Figure 14: Number of intervals for each variable.  
Figure 13: Pareto optimal solution sets.  
A comparative analysis between the optimized model and the baseline configuration was conducted [53] for three response metrics--the peak wall shear stress, action area, and water consumption--as illustrated in Figure 15. The optimized model demonstrated a reduction of 1.34% in the peak wall shear stress and 16.82% in water consumption relative to the baseline, whereas the cleaning area increased by 7.6%. This mutually dependent variation among the three metrics aligns with the trends observed in Figure 13. The optimization framework thus effectively enhances the jet-cleaning performance by simultaneously improving critical operational parameters.  
The above optimization framework can quickly predict and optimize the jet-cleaning performance of the fan-type nozzle, and the cleaning performance after optimization has been improved to a certain extent, but due to the limitation of space, only the case of a single nozzle has been considered. In the subsequent process of improving and upgrading the jet-type self-cleaning screen filters, the optimization framework proposed in this paper can be applied to consider the structural optimization of multiple nozzles to broaden the application scope of this optimization framework.