Application of Pattern Search and Genetic Algorithms to Optimize HDPE Pipe Joint Profiles and Strength in the Butt Fusion Welding Process
Abstract
:1. Introduction
2. Materials and Methods
3. Results and Discussion
3.1. Regression Analysis and ANOVA
3.2. Artificial Neural Network (ANN)
3.3. Genetic Algorithm Optimization
3.4. Pattern Search Optimization
4. Conclusions
- The heater plate temperature is most significant for the welding joint profile, while the welding pressure is most significant for the joint’s tensile strength.
- The results of the trained ANN model were more closely related to the experimental results than those of the regression analysis model based on ANOVA.
- Within certain limits, the combined increase in heater plate temperature and welding pressure leads to a significant increase in tensile strength and weld profiles for both upper and lower surfaces.
- For HDPE pipe joining, both pattern search and genetic algorithms can be considered suitable approaches for optimizing butt fusion welding parameters, with pattern search having a relative preference.
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
References
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Input Parameters | Unit | Code Level Value | ||
---|---|---|---|---|
−1 | 0 | 1 | ||
Welding Pressure | Bar | 0.2 | 0.6 | 1 |
Heater Temperature | °C | 160 | 200 | 240 |
Soaking Time | Minute | 2 | 6 | |
Cooling Time | Minute | 10 | 15 |
Run | P (bar) | T (°C) | ST (min) | CT (min) | Cap | Root | Tensile Stress (MPa) | ||
---|---|---|---|---|---|---|---|---|---|
Height (mm) | Width (mm) | Height (mm) | Width (mm) | ||||||
1 | 0.2 | 160 | 2 | 10 | 2.0 | 4.3 | 2.5 | 3.0 | 35.13 |
2 | 0.2 | 160 | 2 | 15 | 1.3 | 5.3 | 3.1 | 4.0 | 32.48 |
3 | 0.2 | 160 | 6 | 10 | 1.8 | 5.6 | 3.3 | 5.0 | 26.75 |
4 | 0.2 | 160 | 6 | 15 | 2.2 | 6.0 | 4.0 | 5.2 | 31.23 |
5 | 0.2 | 200 | 2 | 10 | 2.1 | 5.7 | 3.5 | 5.2 | 29.54 |
6 | 0.2 | 200 | 2 | 15 | 6.0 | 10.0 | 4.0 | 11.0 | 34.59 |
7 | 0.2 | 200 | 6 | 10 | 3.0 | 7.0 | 4.4 | 7.0 | 29.46 |
8 | 0.2 | 200 | 6 | 15 | 2.0 | 8.4 | 4.9 | 5.7 | 35.21 |
9 | 0.2 | 240 | 2 | 10 | 2.6 | 6.0 | 3.2 | 5.0 | 30.58 |
10 | 0.2 | 240 | 2 | 15 | 2.5 | 5.4 | 4.0 | 5.6 | 26.43 |
11 | 0.2 | 240 | 6 | 10 | 3.2 | 8.2 | 6.7 | 9.8 | 25.42 |
12 | 0.2 | 240 | 6 | 15 | 4.0 | 11.6 | 6.0 | 7.5 | 35.65 |
13 | 0.6 | 160 | 2 | 10 | 1.7 | 4.0 | 3.0 | 3.5 | 35.42 |
14 | 0.6 | 160 | 2 | 15 | 1.7 | 4.0 | 1.7 | 3.4 | 35.18 |
15 | 0.6 | 160 | 6 | 10 | 2.0 | 6.0 | 7.0 | 2.5 | 44.18 |
16 | 0.6 | 160 | 6 | 15 | 2.6 | 7.0 | 2.5 | 7.0 | 31.56 |
17 | 0.6 | 200 | 2 | 10 | 4.2 | 6.1 | 5.0 | 7.0 | 37.23 |
18 | 0.6 | 200 | 2 | 15 | 3.0 | 5.0 | 3.4 | 4.4 | 33.45 |
19 | 0.6 | 200 | 6 | 10 | 3.2 | 9.2 | 4.8 | 6.0 | 32.87 |
20 | 0.6 | 200 | 6 | 15 | 4.6 | 10.0 | 4.8 | 8.7 | 38.17 |
21 | 0.6 | 240 | 2 | 10 | 2.5 | 8.1 | 4.3 | 7.2 | 39.37 |
22 | 0.6 | 240 | 2 | 15 | 3.0 | 6.7 | 3.0 | 7.7 | 42.22 |
23 | 0.6 | 240 | 6 | 10 | 4.3 | 11.3 | 6.2 | 10.2 | 38.93 |
24 | 0.6 | 240 | 6 | 15 | 4.2 | 9.0 | 6.0 | 9.4 | 43.61 |
25 | 1 | 160 | 2 | 10 | 2.0 | 5.5 | 2.6 | 6.0 | 25.57 |
26 | 1 | 160 | 2 | 15 | 2.0 | 4.4 | 3.4 | 3.5 | 30.77 |
27 | 1 | 160 | 6 | 10 | 3.3 | 8.2 | 4.0 | 7.0 | 42.59 |
28 | 1 | 160 | 6 | 15 | 2.7 | 8.0 | 3.0 | 7.7 | 42.59 |
29 | 1 | 200 | 2 | 10 | 2.4 | 7.5 | 2.8 | 8.3 | 37.36 |
30 | 1 | 200 | 2 | 15 | 4.0 | 9.0 | 6.0 | 10.0 | 39.75 |
31 | 1 | 200 | 6 | 10 | 6.0 | 10.0 | 8.0 | 9.0 | 40.58 |
32 | 1 | 200 | 6 | 15 | 4.5 | 9.0 | 6.0 | 10.0 | 31.03 |
33 | 1 | 240 | 2 | 10 | 3.2 | 8.5 | 4.0 | 9.5 | 38.49 |
34 | 1 | 240 | 2 | 15 | 4.0 | 8.0 | 4.0 | 9.0 | 38.03 |
35 | 1 | 240 | 6 | 10 | 5.0 | 13.0 | 6.0 | 9.0 | 39.75 |
36 | 1 | 240 | 6 | 15 | 5.5 | 10.0 | 6.0 | 12.5 | 40.25 |
Terms | Regression Analysis Equation |
---|---|
Cap Height (Ch) | |
Cap Width (Cw) | |
Root Height (Rh) | |
Root Width (Rw) | |
Tensile Strength (TS) | |
: welding pressure, : heater temperature, : soaking time, : cooling time. |
Source | DF | Joint Cap Height | Joint Cap Width | ||
---|---|---|---|---|---|
F-Value | p-Value | F-Value | p-Value | ||
Regression | 12 | 4.61 | 0.001 | 3.58 | 0.004 |
P (bar) | 1 | 0.38 | 0.543 | 0.01 | 0.916 |
T (°C) | 1 | 6.91 | 0.015 | 2.25 | 0.147 |
ST (min) | 1 | 0.23 | 0.634 | 0.13 | 0.721 |
CT (min) | 1 | 0.00 | 0.969 | 0.04 | 0.844 |
P (bar) * P (bar) | 1 | 0.21 | 0.653 | 0.04 | 0.835 |
T (°C) * T (°C) | 1 | 8.46 | 0.008 | 2.88 | 0.103 |
P (bar) * T (°C) | 1 | 0.62 | 0.439 | 0.00 | 0.991 |
P (bar) * ST (min) | 1 | 5.49 | 0.028 | 0.05 | 0.818 |
P (bar) * CT (min) | 1 | 0.35 | 0.558 | 0.07 | 0.789 |
T (°C) * ST (min) | 1 | 1.17 | 0.291 | 1.68 | 0.207 |
T (°C) * CT (min) | 1 | 0.45 | 0.511 | 0.37 | 0.550 |
ST (min) * CT (min) | 1 | 0.71 | 0.408 | 1.82 | 0.190 |
Error | 23 | ||||
Total | 35 |
Source | DF | Joint Root Height | Joint Root Width | Tensile Strength | |||
---|---|---|---|---|---|---|---|
F-Value | p-Value | F-Value | p-Value | F-Value | p-Value | ||
Regression | 12 | 8.30 | 0.000 | 4.45 | 0.001 | 2.05 | 0.068 |
P (bar) | 1 | 0.09 | 0.767 | 0.97 | 0.336 | 0.86 | 0.363 |
T (°C) | 1 | 4.90 | 0.037 | 3.48 | 0.075 | 0.32 | 0.579 |
ST (min) | 1 | 0.05 | 0.830 | 0.10 | 0.752 | 0.06 | 0.815 |
CT (min) | 1 | 2.57 | 0.123 | 0.13 | 0.724 | 0.27 | 0.608 |
P (bar) * P (bar) | 1 | 1.31 | 0.263 | 2.21 | 0.151 | 4.90 | 0.037 |
T (°C) * T (°C) | 1 | 3.66 | 0.068 | 2.85 | 0.105 | 0.13 | 0.725 |
P (bar) * T (°C) | 1 | 0.49 | 0.490 | 0.56 | 0.462 | 1.54 | 0.227 |
P (bar) * ST (min) | 1 | 0.77 | 0.391 | 0.09 | 0.767 | 2.05 | 0.165 |
P (bar) * CT (min) | 1 | 5.71 | 0.025 | 0.00 | 0.991 | 0.86 | 0.363 |
T (°C) * ST (min) | 1 | 1.43 | 0.244 | 0.17 | 0.688 | 0.51 | 0.483 |
T (°C) * CT (min) | 1 | 0.86 | 0.364 | 0.11 | 0.740 | 0.77 | 0.390 |
ST (min) * CT (min) | 1 | 0.05 | 0.828 | 0.18 | 0.678 | 0.03 | 0.869 |
Error | 23 | ||||||
Total | 35 |
Outputs | Mean Values | P (bar) | T (°C) | ST (min) | CT (min) |
---|---|---|---|---|---|
Cap Height (mm) | 3.5 mm | 0.95 | 201 | 2.1 | 11.5 |
Cap Width (mm) | 8 mm | 0.93 | 202 | 3.4 | 14.5 |
Root Height (mm) | 4.5 mm | 0.87 | 224 | 2.48 | 14.1 |
Root Width (mm) | 7 mm | 0.54 | 218 | 2.33 | 14.2 |
Tensile Strength (MPa) | 35 MPa | 0.45 | 179 | 2.6 | 14.5 |
Parameters | Function |
---|---|
Poll Method | GPS positive basis 2 N |
Complete Poll | Off |
Polling Order | Consecutive |
Mesh Size | 1 |
Expansion Factor | 2 |
Contraction Factor | 0.5 |
Outputs | Mean Values | P (bar) | T (°C) | ST (min) | CT (min) |
---|---|---|---|---|---|
Cap Height (mm) | 3.5 mm | 0.933 | 204 | 2.24 | 10.5 |
Cap Width (mm) | 8 mm | 0.65 | 199 | 4.3 | 13.2 |
Root Height (mm) | 4.5 mm | 0.911 | 235 | 2.58 | 14.23 |
Root Width (mm) | 7 mm | 0.483 | 215 | 2.9 | 13.5 |
Tensile Strength (MPa) | 35 MPa | 0.45 | 167 | 2.74 | 14.6 |
Parameters | Method | Mean Values | P (bar) | T (°C) | ST (min) | CT (min) | Best Value |
---|---|---|---|---|---|---|---|
Cap Height (mm) | GA | 3.5 mm | 0.95 | 201 | 2.1 | 11.5 | 3.4859 mm |
PS | 0.933 | 204 | 2.24 | 10.5 | 3.4978 mm | ||
Cap Width (mm) | GA | 8 mm | 0.93 | 202 | 3.4 | 14.5 | 7.9831 mm |
PS | 0.906 | 210.7 | 3.02 | 13.95 | 8.0026 mm | ||
Root Height (mm) | GA | 4.5 mm | 0.87 | 224 | 2.48 | 14.1 | 4.4954 mm |
PS | 0.911 | 235 | 2.58 | 14.23 | 4.4989 mm | ||
Root Width (mm) | GA | 7 mm | 0.54 | 218 | 2.33 | 14.2 | 6.9822 mm |
PS | 0.483 | 215 | 2.9 | 13.5 | 6.9852 mm | ||
Tensile Strength (MPa) | GA | 35 MPa | 0.45 | 179 | 2.6 | 14.5 | 35.2044 MPa |
PS | 0.45 | 167 | 2.74 | 14.6 | 34.9975 MPa |
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Share and Cite
Mathkoor, M.S.; Jassim, R.J.; Al-Sabur, R. Application of Pattern Search and Genetic Algorithms to Optimize HDPE Pipe Joint Profiles and Strength in the Butt Fusion Welding Process. J. Manuf. Mater. Process. 2024, 8, 187. https://doi.org/10.3390/jmmp8050187
Mathkoor MS, Jassim RJ, Al-Sabur R. Application of Pattern Search and Genetic Algorithms to Optimize HDPE Pipe Joint Profiles and Strength in the Butt Fusion Welding Process. Journal of Manufacturing and Materials Processing. 2024; 8(5):187. https://doi.org/10.3390/jmmp8050187
Chicago/Turabian StyleMathkoor, Mahdi Saleh, Raad Jamal Jassim, and Raheem Al-Sabur. 2024. "Application of Pattern Search and Genetic Algorithms to Optimize HDPE Pipe Joint Profiles and Strength in the Butt Fusion Welding Process" Journal of Manufacturing and Materials Processing 8, no. 5: 187. https://doi.org/10.3390/jmmp8050187