Multi−Objective Collaborative Optimization Design of Key Structural Parameters for Coal Breaking and Punching Nozzle
Abstract
:1. Introduction
2. Numerical Simulation and Analysis
2.1. Structure and Key Parameters of the Nozzle
2.2. Numerical Simulation and Boundary Condition
2.3. Model Meshing and Independence Verification
3. Multi-Objective Collaborative Optimization Design and Analysis
3.1. Collaborative Optimization Scheme Design
3.1.1. Multi−Objective Orthogonal Test Matrix
3.1.2. Analysis of Multi−Objective Orthogonal Test Matrix
3.2. Multi-Objective Collaborative Optimization
3.2.1. Network Training
3.2.2. Training Network Analysis and Verification
3.2.3. Optimal Parameter Determination
4. Coal Breaking and Punching Experiment
4.1. Experiment Scheme
4.2. Preparation of Briquette
4.3. Experiment Analysis
5. Conclusions
- (1)
- The multi−objective weight analysis method is used to optimize the parameters of the high−pressure water jet coal breaking and punching nozzle. It is concluded that the primary and secondary order affecting the maximum velocity in X-axis and effective extension distance in Y-axis of the water jet is as follows: divergence angle, contraction angle and length-to-diameter ratio. For the multi-index model, the weight analysis method can efficiently and accurately analyze the influence of parameters on multiple indexes.
- (2)
- The multi−objective collaborative optimization of the nozzle is carried out by using the collaborative optimization scheme of the BP neural network and GA. It is concluded that the optimal combination of its structure is as follows: the contraction angle is , the length-to-diameter ratio is , and the divergence angle is . Compared with the nozzle before optimization, the punching depth is increased by 72.71% and the punching diameter is increased by 106.72%. The combination of BP neural network and GA not only improves the global search efficiency, but also avoids falling into the local optimal solution.
- (3)
- The water jet punching experiment shows that the punching depth and punching diameter affect each other. When multiple objectives are considered synergistically, the performance of the water jet is significantly improved compared with considering each optimization objective separately, which not only provides a new idea for the optimization of the nozzle structure, but also can be used in other multi−objective and multi-parameter models.
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
References
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Area | Number of Grid | Maximum Velocity of X-axis (m/s) | Deviation (%) |
---|---|---|---|
Nozzle | 643,765 | 199.241 | 0.212 |
1,257,283 | 199.865 | 0 | |
2,345,759 | 199.395 | 0.115 | |
Externalflowfield | 4,165,783 | 199.383 | 0.241 |
4,987,351 | 199.865 | 0 | |
5,634,524 | 200.068 | 0.102 |
Structure Parameter | Numerical Value |
---|---|
Contraction angle (°) | 30 |
Length-to-diameter ratio | 2 |
Divergence angle (°) | 0 |
Parameter | Initial Value | Range of the Value |
---|---|---|
A () | 30° | 30–70° |
B () | 2 | 2–3 |
C () | 0° | 0–15° |
Factors | A | B | C | Maximum Velocityin X-axis (m/s) | Effective Extension Distance in Y-axis (mm) |
---|---|---|---|---|---|
Test Number | 1(°) | 2 | 3(°) | ||
1 | 30 | 2 | 0 | 199.865 | 1.212 |
2 | 30 | 2 | 10 | 199.868 | 1.323 |
3 | 30 | 2 | 15 | 198.397 | 1.463 |
4 | 30 | 2.5 | 0 | 200.393 | 1.303 |
5 | 30 | 2.5 | 10 | 199.424 | 1.503 |
6 | 30 | 2.5 | 15 | 198.118 | 1.563 |
7 | 30 | 3 | 0 | 199.879 | 1.221 |
8 | 30 | 3 | 10 | 200.024 | 1.402 |
9 | 30 | 3 | 15 | 198.35 | 1.532 |
10 | 50 | 2 | 0 | 200.484 | 1.242 |
11 | 50 | 2 | 10 | 199.181 | 1.341 |
12 | 50 | 2 | 15 | 197.16 | 1.502 |
13 | 50 | 2.5 | 0 | 199.382 | 1.283 |
14 | 50 | 2.5 | 10 | 198.277 | 1.522 |
15 | 50 | 2.5 | 15 | 198.476 | 1.582 |
16 | 50 | 3 | 0 | 199.426 | 1.281 |
17 | 50 | 3 | 10 | 198.39 | 1.401 |
18 | 50 | 3 | 15 | 195.748 | 1.441 |
19 | 70 | 2 | 0 | 198.331 | 1.183 |
20 | 70 | 2 | 10 | 195.775 | 1.361 |
21 | 70 | 2 | 15 | 188.234 | 1.421 |
22 | 70 | 2.5 | 0 | 198.936 | 1.191 |
23 | 70 | 2.5 | 10 | 195.603 | 1.381 |
24 | 70 | 2.5 | 15 | 193.189 | 1.602 |
25 | 70 | 3 | 0 | 199.225 | 1.101 |
26 | 70 | 3 | 10 | 195.284 | 1.321 |
27 | 70 | 3 | 15 | 191.606 | 1.522 |
Hierarchical Structure | Model |
---|---|
Target layer | The two indexes |
Factor layer | A, B, C |
Horizontal layer | A1–A3, B1–B3, C1–C3 |
Weight Matrix | Numerical Value | Weight Matrix | Numerical Value | Weight Matrix | Numerical Value |
---|---|---|---|---|---|
WA1 | 0.093052 | WB1 | 0.062866 | WC1 | 0.165514 |
WA2 | 0.093238 | WB2 | 0.065545 | WC2 | 0.17845 |
WA3 | 0.090959 | WB3 | 0.063391 | WC3 | 0.186986 |
Category | Result | ||
---|---|---|---|
Sensitivity of each factor | A | B | C |
0.2772 | 0.1918 | 0.5310 | |
Primary and secondary order of factors | C > A > B | ||
Optimal combination | A2B2C3 |
Serial Number of the Function | Training Function | Training Times | Serial Number of the Function | Training Function | Training Times |
---|---|---|---|---|---|
1 | Traingda | 115 times to reach the target | 5 | Traincgf | 22 times to reach the target |
2 | Trainbfg | 29 times to reach the target | 6 | Trainscg | 26 times to reach the target |
3 | Trainoss | 20 times to reach the target | 7 | Trainrp | 76 times to reach the target |
4 | Traincgb | 17 times to reach the target | 8 | Trainlm | 19 times to reach the target |
Evaluation Index | Category | Test 1 | Test 2 | Test 3 | Test 4 | Test 5 |
---|---|---|---|---|---|---|
Target 1 | Actual value (m/s) | 199.865 | 199.424 | 200.484 | 198.476 | 195.775 |
Predicted value (m/s) | 197.541 | 201.56 | 200.484 | 198.476 | 197.003 | |
Relative error (m/s) | 1.16 | 1.07 | 0 | 0 | 0.63 | |
Target 2 | Actual value (m/s) | 1.212 | 1.503 | 1.242 | 1.582 | 1.361 |
Predicted value (m/s) | 1.231 | 1.503 | 1.256 | 1.57 | 1.389 | |
Relative error (%) | 1.57 | 0 | 1.13 | 0.76 | 2.05 |
Category | Optimization Parameter | Category | Optimization Parameter | ||||||
Contraction Angle θ (°) | Length-to-Diameter Ratio l/d | Divergence Angle γ (°) | Contraction Angle θ (°) | Length-to-Diameter Ratio l/d | Divergence Angle γ (°) | ||||
Initial value | 30 | 2 | 0 | Optimal value of orthogonal test | 50 | 2.5 | 15 | ||
Collaborative optimization value | 42.512 | 2.5608 | 12.431 | Collaborative optimization value | 42.512 | 2.5608 | 12.431 | ||
Change rate | 41.71% | 28.04% | ∞ | Change rate | 14.98% | 2.43% | −17.13% | ||
Category | Optimization Target | Category | Optimization Target | ||||||
Target 1 (m/s) | Target 2 (mm) | Target 1 (m/s) | Target 2 (mm) | ||||||
Initial value | 199.865 | 1.212 | Optimal value of orthogonal test | 198.476 | 1.582 | ||||
Collaborative optimization value | 203.77 | 1.632 | Collaborative optimization value | 203.77 | 1.632 | ||||
Optimization rate | 1.95% | 34.65% | Optimization rate | 2.67% | 3.16% |
Specimen Number | 1 | 2 | 3 | 4 | 5 |
---|---|---|---|---|---|
Compressive strength/MPa | 14.9 | 15.1 | 15.0 | 15.0 | 14.8 |
Absolute errorof compressive strength | 0.67% | 0.67% | 0 | 0 | 1.33% |
Nozzle Model | Experiment Number | Arithmetic Mean | Standard Deviation | Improve Rate | ||
---|---|---|---|---|---|---|
1 | 2 | 3 | ||||
1 | 43.3 mm | 44.5 mm | 44.3 mm | 44.03 mm | 0.5249 | 72.71% |
2 | 57.4 mm | 57.0 mm | 57.7 mm | 57.36 mm | 0.2867 | 31.88% |
3 | 75.2 mm | 76.4 mm | 75.6 mm | 75.73 mm | 0.4989 | optimal value |
Nozzle Model | Experiment Number | Arithmetic Mean | Standard Deviation | Improve Rate | ||
---|---|---|---|---|---|---|
1 | 2 | 3 | ||||
1 | 6.5 mm | 6.4 mm | 6.3 mm | 6.40 mm | 0.0816 | 106.72% |
2 | 10.4 mm | 10.7 mm | 10.6 mm | 10.56 mm | 0.1249 | 25.28% |
3 | 13.2 mm | 13.4 mm | 13.1 mm | 13.23 mm | 0.1248 | optimal value |
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Chen, L.; Cheng, M.; Cai, Y.; Guo, L.; Gao, D. Multi−Objective Collaborative Optimization Design of Key Structural Parameters for Coal Breaking and Punching Nozzle. Processes 2022, 10, 1036. https://doi.org/10.3390/pr10051036
Chen L, Cheng M, Cai Y, Guo L, Gao D. Multi−Objective Collaborative Optimization Design of Key Structural Parameters for Coal Breaking and Punching Nozzle. Processes. 2022; 10(5):1036. https://doi.org/10.3390/pr10051036
Chicago/Turabian StyleChen, Lihuan, Muzheng Cheng, Yi Cai, Liwen Guo, and Dianrong Gao. 2022. "Multi−Objective Collaborative Optimization Design of Key Structural Parameters for Coal Breaking and Punching Nozzle" Processes 10, no. 5: 1036. https://doi.org/10.3390/pr10051036