Multi-Objective Optimization Study of Annular Fluid Flow Structure in Cordless Core Drilling Tools
Abstract
:1. Introduction
2. Structural Design and Principles of Hydraulic Lifting Cordless Coring Drilling Tool
3. Numerical Simulation and Calculation of Fluid Flow in Spearhead and Spool Annulus of Cordless Core Drilling Tools
3.1. Numerical Simulation Model of Spearhead and Spool Flow
3.2. Orthogonal Test Design
3.3. Numerical Prediction Model of Spool Annular Flow Field Based on BP Neural Network
4. Optimization of Structural Dimensions of an Annular Hollow Fluid Flow Runner Based on Improved NSGA-II Algorithm
4.1. Principles of the Improved NSGA-II Algorithm
- (1)
- For each individual p, its objective function value is compared with other individuals in the population;
- (2)
- The set of individuals Sp is determined, dominated by individual p, and the number of dominated individuals np;
- (3)
- Dominance relationships are used to stratify the population, which is not dominated by any individual belonging to the first frontier.
Algorithm 1: Fast Non-Dominated Sorting |
Input: Population P |
Output: Sorted fronts F and Pareto ranks R |
1: Initialize empty lists F and R |
2: for each individual p in P do |
2.1: Initialize empty list Sp and set np = 0 |
2.2: for each individual q in P do |
2.2.1: if p dominates q then |
2.2.1.1: Add q to Sp |
2.2.2: else if q dominates p then |
2.2.2.1: Increment np by 1 |
2.3: if np == 0 then |
2.3.1: Set rank of p to 1 |
2.3.2: Add p to the first front F1 |
3: Set i = 1 |
4: while Fi is not empty do |
4.1: Initialize empty list Q |
4.2: for each individual p in Fi do |
4.2.1: for each individual q in Sp do |
4.2.1.1: Decrement nq by 1 |
4.2.1.2: if nq == 0 then |
4.2.1.2.1: Set rank of q to i + 1 |
4.2.1.2.2: Add q to Q |
4.3: Increment i by 1 |
4.4: Add Q to F |
5: Return F and R |
Algorithm 2: Crowding Distance Calculation |
Input: Front F |
Output: Crowding distances D |
1: Initialize D with zeros for all individuals in F |
2: for each objective function m do |
2.1: Sort the individuals in F based on objective m |
2.2: Set the crowding distance of boundary points to infinity |
2.3: for i = 2 to |F| − 1 do |
2.3.1: Calculate the distance using the m-th objective: |
D[i] += (f_m[i + 1] − f_m[i − 1])/(f_m_max − f_m_min) |
3: for each decision variable j do |
3.1: Sort the individuals in F based on decision variable j |
3.2: for i = 2 to |F| − 1 do |
3.2.1: Calculate the distance using the j-th decision variable: |
D[i] += (x_j[i + 1] − x_j[i − 1])/(x_j_max − x_j_min) |
4: Return D |
Algorithm 3: Genetic Operators |
Input: parent1, parent2, p_c, p_m, eta_c, eta_m, lower_bound, upper_bound |
Output: child1, child2 |
1: Initialize child1 and child2 with parent1 and parent2 |
2: // Simulated Binary Crossover (SBX) |
3: if random(0, 1) < p_c then |
4: for i = 1 to number_of_variables do |
5: if abs(parent1[i] − parent2[i]) > EPS then |
6: y1 = min(parent1[i], parent2[i]) |
7: y2 = max(parent1[i], parent2[i]) |
8: rand = random(0, 1) |
9: beta = 1.0 + (2.0 * (y1 − lower_bound[i])/(y2 − y1)) |
10: alpha = 2.0 − (1.0/((1.0 + beta)^(eta_c + 1.0))) |
11: if rand <= (1.0/alpha) then |
12: beta_q = (rand * alpha)^(1.0/(eta_c + 1.0)) |
13: else |
14: beta_q = (1.0/(2.0 − rand * alpha))^(1.0/(eta_c + 1.0)) |
15: end if |
16: child1[i] = 0.5 * ((y1 + y2) − beta_q * (y2 − y1)) |
17: child2[i] = 0.5 * ((y1 + y2) + beta_q * (y2 − y1)) |
18: // Ensure children are within bounds |
19: child1[i] = min(max(child1[i], lower_bound[i]), upper_bound[i]) |
20: child2[i] = min(max(child2[i], lower_bound[i]), upper_bound[i]) |
21: end if |
22: end for |
23: end if |
24: // Polynomial Mutation |
25: for i = 1 to number_of_variables do |
26: if random(0, 1) < p_m then |
27: delta = if random(0, 1) < 0.5 then (2.0 * random(0, 1))^(1.0/(eta_m + 1.0)) − 1.0 |
28: else 1.0 − (2.0 * (1.0 − random(0, 1)))^(1.0/(eta_m + 1.0)) |
29: child1[i] += delta * (upper_bound[i] − lower_bound[i]) |
30: child2[i] += delta * (upper_bound[i] − lower_bound[i]) |
31: // Ensure children are within bounds |
32: child1[i] = min(max(child1[i], lower_bound[i]), upper_bound[i]) |
33: child2[i] = min(max(child2[i], lower_bound[i]), upper_bound[i]) |
34: end if |
35: end for |
36: return child1, child2 |
4.2. Multi-Objective Optimization of Annular-Air Liquid Flow Structure
4.3. Numerical Simulation Verification of the Optimised Annular Fluid Flow Structure
5. Field Trial Study Conclusion
6. Conclusions and Discussion
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
Appendix A
Serial Number | Number of Water Inlets (pcs) | Inlet Diameter (mm) | Number of Water Outlets (pcs) | Outlet Diameter (mm) | Distance between the Centres of the Two Circles of the Outlet (mm) | Ratio of Fluid Back Pressure to Spring Force Pressure | Drilling Fluid Flow Rate (m/s) |
---|---|---|---|---|---|---|---|
1 | 3.00 | 18.50 | 3.00 | 18.00 | 10.00 | 1.461 | 2.14 |
2 | 4.00 | 19.50 | 3.00 | 16.50 | 16.00 | 1.463 | 2.215 |
3 | 3.00 | 19.50 | 3.00 | 17.00 | 14.00 | 1.463 | 2.205 |
4 | 3.00 | 16.50 | 3.00 | 20.00 | 12.00 | 1.459 | 1.96 |
5 | 3.00 | 19.50 | 2.00 | 20.00 | 10.00 | 1.461 | 2.59 |
6 | 3.00 | 16.00 | 2.00 | 17.50 | 14.00 | 1.449 | 2.775 |
7 | 3.00 | 20.00 | 2.00 | 20.00 | 14.00 | 1.465 | 2.48 |
8 | 3.00 | 18.00 | 3.00 | 17.50 | 14.00 | 1.461 | 2.19 |
9 | 4.00 | 16.50 | 2.00 | 18.00 | 10.00 | 1.46 | 3.155 |
10 | 4.00 | 20.00 | 2.00 | 19.00 | 12.00 | 1.455 | 2.91 |
11 | 3.00 | 17.00 | 2.00 | 16.50 | 10.00 | 1.4386 | 3.295 |
12 | 3.00 | 17.50 | 2.00 | 16.50 | 10.00 | 1.451 | 3.075 |
13 | 3.00 | 19.00 | 3.00 | 16.50 | 12.00 | 1.463 | 2.21 |
14 | 3.00 | 20.00 | 2.00 | 18.50 | 10.00 | 1.4589 | 2.685 |
15 | 3.00 | 20.00 | 2.00 | 18.00 | 12.00 | 1.461 | 2.77 |
16 | 3.00 | 16.50 | 2.00 | 17.00 | 16.00 | 1.455 | 2.66 |
17 | 3.00 | 18.50 | 2.00 | 19.50 | 14.00 | 1.457 | 2.12 |
18 | 4.00 | 18.00 | 3.00 | 18.00 | 18.00 | 1.467 | 1.45 |
19 | 3.00 | 18.00 | 3.00 | 18.50 | 10.00 | 1.459 | 2.185 |
20 | 3.00 | 16.00 | 3.00 | 19.00 | 18.00 | 1.455 | 1.209 |
21 | 3.00 | 19.00 | 2.00 | 19.50 | 14.00 | 1.4589 | 2.27 |
22 | 3.00 | 19.00 | 2.00 | 19.00 | 10.00 | 1.457 | 2.76 |
23 | 3.00 | 17.00 | 2.00 | 18.50 | 12.00 | 1.451 | 2.64 |
24 | 4.00 | 18.50 | 2.00 | 19.00 | 16.00 | 1.463 | 2.695 |
25 | 3.00 | 18.00 | 2.00 | 16.00 | 16.00 | 1.453 | 3.005 |
26 | 4.00 | 18.50 | 2.00 | 16.00 | 14.00 | 1.45 | 2.89 |
27 | 4.00 | 17.50 | 2.00 | 20.00 | 10.00 | 1.464 | 3.175 |
28 | 3.00 | 19.50 | 2.00 | 17.50 | 10.00 | 1.4589 | 3.351 |
29 | 3.00 | 19.50 | 3.00 | 16.00 | 12.00 | 1.459 | 2.95 |
30 | 3.00 | 17.00 | 3.00 | 20.00 | 16.00 | 1.459 | 1.48 |
31 | 3.00 | 18.50 | 2.00 | 20.00 | 12.00 | 1.4589 | 2.81 |
32 | 3.00 | 16.00 | 2.00 | 16.50 | 20.00 | 1.449 | 3.14 |
33 | 3.00 | 16.00 | 2.00 | 16.00 | 10.00 | 1.4376 | 3.16 |
34 | 3.00 | 17.50 | 3.00 | 17.50 | 16.00 | 1.461 | 1.52 |
35 | 4.00 | 16.50 | 2.00 | 16.50 | 12.00 | 1.459 | 2.905 |
36 | 4.00 | 16.00 | 2.00 | 18.50 | 16.00 | 1.461 | 2.41 |
37 | 3.00 | 16.50 | 3.00 | 19.00 | 10.00 | 1.457 | 1.725 |
38 | 3.00 | 20.00 | 2.00 | 19.50 | 16.00 | 1.4628 | 2.025 |
39 | 3.00 | 16.00 | 2.00 | 18.00 | 12.00 | 1.4473 | 2.77 |
40 | 4.00 | 16.00 | 2.00 | 17.00 | 12.00 | 1.459 | 2.93 |
41 | 4.00 | 19.00 | 2.00 | 18.50 | 14.00 | 1.469 | 2.89 |
42 | 4.00 | 16.00 | 3.00 | 20.00 | 14.00 | 1.463 | 1.47 |
43 | 3.00 | 17.00 | 3.00 | 19.50 | 12.00 | 1.457 | 1.72 |
44 | 4.00 | 17.00 | 2.00 | 16.00 | 18.00 | 1.456 | 3.125 |
45 | 3.00 | 16.50 | 2.00 | 18.50 | 14.00 | 1.4512 | 2.43 |
46 | 3.00 | 20.00 | 3.00 | 17.00 | 18.00 | 1.461 | 1.96 |
47 | 4.00 | 17.00 | 3.00 | 19.00 | 14.00 | 1.461 | 1.69 |
48 | 4.00 | 18.00 | 2.00 | 16.50 | 14.00 | 1.463 | 2.652 |
49 | 4.00 | 19.50 | 2.00 | 18.00 | 14.00 | 1.465 | 2.93 |
50 | 3.00 | 17.00 | 2.00 | 18.00 | 20.00 | 1.449 | 2.5915 |
51 | 3.00 | 17.50 | 3.00 | 18.00 | 14.00 | 1.455 | 1.94 |
52 | 3.00 | 19.00 | 3.00 | 16.00 | 20.00 | 1.461 | 1.452 |
53 | 4.00 | 17.50 | 2.00 | 17.00 | 20.00 | 1.465 | 2.685 |
54 | 3.00 | 18.00 | 2.00 | 19.00 | 12.00 | 1.4589 | 2.605 |
55 | 4.00 | 19.00 | 2.00 | 20.00 | 18.00 | 1.465 | 2.64 |
56 | 4.00 | 19.00 | 3.00 | 17.00 | 10.00 | 1.465 | 2.28 |
57 | 3.00 | 19.00 | 2.00 | 18.00 | 16.00 | 1.4589 | 2.85 |
58 | 3.00 | 17.50 | 2.00 | 19.50 | 18.00 | 1.461 | 2.37 |
59 | 3.00 | 18.50 | 2.00 | 16.50 | 18.00 | 1.4608 | 2.86 |
60 | 4.00 | 18.50 | 3.00 | 17.50 | 12.00 | 1.465 | 1.95 |
61 | 3.00 | 20.00 | 3.00 | 16.50 | 14.00 | 1.459 | 1.9 |
62 | 3.00 | 18.00 | 2.00 | 17.00 | 12.00 | 1.457 | 2.85 |
63 | 4.00 | 20.00 | 3.00 | 16.00 | 10.00 | 1.461 | 2.57 |
64 | 4.00 | 17.50 | 3.00 | 18.50 | 12.00 | 1.465 | 1.96 |
65 | 3.00 | 17.00 | 2.00 | 17.00 | 14.00 | 1.4551 | 2.705 |
66 | 3.00 | 16.50 | 2.00 | 16.00 | 14.00 | 1.4531 | 3.115 |
67 | 3.00 | 16.50 | 2.00 | 17.50 | 18.00 | 1.4589 | 2.625 |
68 | 3.00 | 18.50 | 2.00 | 17.00 | 10.00 | 1.4589 | 3.135 |
69 | 3.00 | 17.50 | 2.00 | 19.00 | 14.00 | 1.4551 | 2.625 |
70 | 4.00 | 17.00 | 2.00 | 17.50 | 10.00 | 1.465 | 2.885 |
71 | 3.00 | 18.00 | 2.00 | 20.00 | 20.00 | 1.4551 | 1.6735 |
72 | 3.00 | 16.00 | 3.00 | 19.50 | 10.00 | 1.451 | 2.18 |
73 | 3.00 | 19.50 | 2.00 | 19.00 | 20.00 | 1.4628 | 2.15 |
74 | 3.00 | 19.00 | 2.00 | 17.50 | 12.00 | 1.4551 | 3.15 |
75 | 4.00 | 19.50 | 2.00 | 19.50 | 12.00 | 1.467 | 2.91 |
76 | 4.00 | 18.00 | 2.00 | 19.50 | 10.00 | 1.461 | 2.66 |
77 | 3.00 | 19.50 | 2.00 | 18.50 | 18.00 | 1.4608 | 2.3995 |
78 | 3.00 | 18.50 | 3.00 | 18.50 | 20.00 | 1.4599 | 1.425 |
79 | 4.00 | 20.00 | 2.00 | 17.50 | 20.00 | 1.4599 | 2.65 |
80 | 4.00 | 16.50 | 3.00 | 19.50 | 20.00 | 1.465 | 1.241 |
81 | 3.00 | 17.50 | 2.00 | 16.00 | 12.00 | 1.4512 | 3.315 |
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1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | |
---|---|---|---|---|---|---|---|---|---|
A | 3 | 4 | |||||||
B | 16 | 16.5 | 17 | 17.5 | 18 | 18.5 | 19 | 19.5 | 20 |
C | 2 | 3 | |||||||
D | 16 | 16.5 | 17 | 17.5 | 18 | 18.5 | 19 | 19.5 | 20 |
E | 10 | 12 | 14 | 16 | 18 | 20 |
Test Function | Indicator | Improved NSGA-II | Normal NSGA-II |
---|---|---|---|
ZDT3 | mean (IGD) | 3.13 × 10−3 | 5.84 × 10−3 |
std (IGD) | 1.79 × 10−4 | 1.07 × 10−3 |
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Zhu, Z.; Huang, F.; Zhao, Y.; Li, C.; Wei, H.; Liu, G.; Shao, Y.; Jia, M. Multi-Objective Optimization Study of Annular Fluid Flow Structure in Cordless Core Drilling Tools. Appl. Sci. 2024, 14, 7200. https://doi.org/10.3390/app14167200
Zhu Z, Huang F, Zhao Y, Li C, Wei H, Liu G, Shao Y, Jia M. Multi-Objective Optimization Study of Annular Fluid Flow Structure in Cordless Core Drilling Tools. Applied Sciences. 2024; 14(16):7200. https://doi.org/10.3390/app14167200
Chicago/Turabian StyleZhu, Zhitong, Fan Huang, Yan Zhao, Changping Li, Hairui Wei, Guang Liu, Yutao Shao, and Minghao Jia. 2024. "Multi-Objective Optimization Study of Annular Fluid Flow Structure in Cordless Core Drilling Tools" Applied Sciences 14, no. 16: 7200. https://doi.org/10.3390/app14167200