# Drilling Parameters Multi-Objective Optimization Method Based on PSO-Bi-LSTM
## 3 Results and Discussion
### The PSO-Bi-LSTM Model Drilling Parameters Optimization  
In the experiment, we used a dataset from a well in Xinjiang, China. The input and target parameters selected are shown in Table 3. The statistical information of this dataset is shown in Table 4. The ROP prediction model inputs weight on bit (WOB), rotary speed, flow rate, uniaxial compressive strength (UCS), and volume content of sandy particles (Vsand) and outputs ROP. The PSO-Bi-LSTM algorithm optimizes the three onsite controllable engineering parameters of weight on bit (WOB), rotation speed, and flow rate. The optimization space ranges of weight on bit (WOB), rotation speed, and flow rate are 25 KN to 230 KN, 11 r/min to 63 r/min, and 25 L/s to 39 L/s, respectively. The goal is to  
Figure 4: Flow chart of PSO-Bi-LSTM model building. achieve a dual objective optimization effect of maximum ROP and minimum MSE while maximizing drilling speed and drill bit footage. The Pareto optimal solution set is shown in Figure 5. It can be observed that as the ROP increases, the MSE slightly increases, and there is a parameter combination set that has a significant acceleration effect and almost does not affect the drill bit footage. The parallel representation of this optimal parameter combination set is shown in Figure 6. It can be seen that the preferred WOB is concentrated between 92.38 KN and 113 KN; the preferred flow rate is concentrated between 29 L/s and 30.35 L/s; the preferred rotational speed is concentrated between 25 r/min and 34 r/min. Within the optimal WOB range, WOB is taken to be 98 KN, 103 KN, and 108 KN, respectively. At this time, the distribution of rotational speed and the flow rate has an impact on ROP, as shown in Figure 7, and on MSE as shown in Figure 8. It can be seen that the highest ROP and lower MSE are both within the optimal range. We determined the optimized range of drilling parameter combinations through Figure 6 and drew two-dimensional cloud maps of all parameter combinations of rotational speed and flow rate based on randomly selected drilling pressures within this range, with respect to ROP and MSE. As shown in the two-dimensional cloud map, the optimized drilling parameter combination obtained within the range of drilling parameter combinations has the best performance among all parameter combinations. The validation results are consistent with the PSO experimental results, proving that the algorithm model has a good optimization \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & **WOB** & **Surface RPM** & **Flow Rate** & **UCS** & **Vsand** & **ROP** \\ \hline  & **(kN)** & **(r/min)** & **(L/s)** & **(MPa)** & & **(m/h)** \\ \hline Mean & 109.6 & 44.7 & 27.9 & 38.0 & 0.67 & 6.0 \\ Standard & 30.4 & 7.0 & 0.67 & 6.3 & 0.14 & 3.4 \\ Deviation & & & & & & \\ Min & 25.4 & 11.0 & 25.4 & 11.3 & 0.01 & 0.5 \\
25\% & 87.0 & 42.0 & 27.5 & 35.0 & 0.58 & 3.8 \\
50\% & 109.6 & 49.0 & 27.9 & 38.3 & 0.68 & 5.0 \\
75\% & 130.8 & 50.0 & 28.3 & 40.8 & 0.77 & 7.5 \\ Max & 231.5 & 63.0 & 38.6 & 70.0 & 1.0 & 30.0 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Data statistic results. Figure 5: The Pareto optimal solution set. Figure 8: _Cont_. Figure 7: Influence of the distribution of rotational speed and flow rate on ROP under different WOB: (a) WOB = 98 KN; (b) WOB = 103 KN; (c) WOB = 108 KN. The effect of the optimized parameter solution in practical application is shown in Figures 9 and 10. It can be seen that, after the optimized parameter solution is applied, the average ROP is increased from 6.05 m/h to 10.95 m/h and the ROP is increased by 81%. The average MSE is reduced from 464.05 MPa to 333.87 MPa, and the energy loss of the bit is reduced by 28%. The practical application effect is good, which can meet the requirements of practical field application and achieve the dual-objective optimization goal. Figure 8: Influence of the distribution of rotational speed and flow rate on MSE under different WOB: (a) WOB = 98 KN; (b) WOB = 103 KN; (c) WOB = 108 KN.