Author Contributions
Conceptualization, X.L. and H.L.; methodology, M.L.; software, M.L.; validation, M.L. and J.X.; formal analysis, M.L.; investigation, M.L.; resources, X.L., S.Y. and H.L.; data curation, M.L., X.L. and H.L.; writing–original draft preparation, M.L.; writing–review and editing, M.L., J.X., S.Y. and X.L.; visualization, M.L.; supervision, X.L. and H.L.; project administration, X.L. and H.L.; funding acquisition, X.L.
Figure 1.
The working process of the deep-sea self-sustaining profile buoy (DSPB).
Figure 1.
The working process of the deep-sea self-sustaining profile buoy (DSPB).
Figure 2.
The energy consumption of each working stage.
Figure 2.
The energy consumption of each working stage.
Figure 3.
The force analysis of the deep-sea self-sustaining profile buoy (DSPB) in the ascent stage. is the DSPB’s buoyancy in ascent stage. is the DSPB’s resistance in ascent stage. G is the DSPB’s gravity.
Figure 3.
The force analysis of the deep-sea self-sustaining profile buoy (DSPB) in the ascent stage. is the DSPB’s buoyancy in ascent stage. is the DSPB’s resistance in ascent stage. G is the DSPB’s gravity.
Figure 4.
The fitting result of the density data at depth 0 m to 1500 m and 1500 m to 4000 m.
Figure 4.
The fitting result of the density data at depth 0 m to 1500 m and 1500 m to 4000 m.
Figure 5.
The fitting result of the density data in the southern hemisphere. Panel (a) shows the seawater’s density data in summer and (b) shows the seawater’s density data in winter.
Figure 5.
The fitting result of the density data in the southern hemisphere. Panel (a) shows the seawater’s density data in summer and (b) shows the seawater’s density data in winter.
Figure 6.
The fitting result of the density data in the equator area. Panel (a) shows the seawater’s density data in summer and (b) shows the seawater’s density data in winter.
Figure 6.
The fitting result of the density data in the equator area. Panel (a) shows the seawater’s density data in summer and (b) shows the seawater’s density data in winter.
Figure 7.
The fitting result of the density data in the nouthern hemisphere. Panel (a) shows the seawater’s density data in summer and (b) shows the seawater’s density data in winter.
Figure 7.
The fitting result of the density data in the nouthern hemisphere. Panel (a) shows the seawater’s density data in summer and (b) shows the seawater’s density data in winter.
Figure 8.
The fitting effect of the temperature at depth 0 m to 2000 m.
Figure 8.
The fitting effect of the temperature at depth 0 m to 2000 m.
Figure 9.
The fitting result of the temperature data in the southern hemisphere. Panel (a) shows the seawater’s temperature data in summer and (b) shows the seawater’s temperature data in winter.
Figure 9.
The fitting result of the temperature data in the southern hemisphere. Panel (a) shows the seawater’s temperature data in summer and (b) shows the seawater’s temperature data in winter.
Figure 10.
The fitting result of the temperature data in the equator area. Panel (a) shows the seawater’s temperature data in summer and (b) shows the seawater’s temperature data in winter.
Figure 10.
The fitting result of the temperature data in the equator area. Panel (a) shows the seawater’s temperature data in summer and (b) shows the seawater’s temperature data in winter.
Figure 11.
The fitting result of the temperature data in the nouthern hemisphere. Panel (a) shows the seawater’s temperature data in summer and (b) shows the seawater’s temperature data in winter.
Figure 11.
The fitting result of the temperature data in the nouthern hemisphere. Panel (a) shows the seawater’s temperature data in summer and (b) shows the seawater’s temperature data in winter.
Figure 12.
The fitting effect of the oil draining speed and motor’s operating current.
Figure 12.
The fitting effect of the oil draining speed and motor’s operating current.
Figure 13.
The one-time oil draining control mode.
Figure 13.
The one-time oil draining control mode.
Figure 14.
Parameters of the DSPB’s ascent stage of the one-time oil draining method.
Figure 14.
Parameters of the DSPB’s ascent stage of the one-time oil draining method.
Figure 15.
The process of the stage quantitative oil draining control mode.
Figure 15.
The process of the stage quantitative oil draining control mode.
Figure 16.
The optimization process of the non-dominated sorted genetic algorithm-II (NSGA-II) method.
Figure 16.
The optimization process of the non-dominated sorted genetic algorithm-II (NSGA-II) method.
Figure 17.
The optimal result of NSGA-II method with different ODR.
Figure 17.
The optimal result of NSGA-II method with different ODR.
Figure 18.
The optimal result of different optimal parameters. Panel (a) shows the optimal result of different populations and (b) shows the optimal result of different generations.
Figure 18.
The optimal result of different optimal parameters. Panel (a) shows the optimal result of different populations and (b) shows the optimal result of different generations.
Figure 19.
The optimal result of different ODR in the southern hemisphere. Panel (a) shows the optimal result in summer where the total energy consumption reduced by 13.5% and (b) shows the optimal result in winter where the total energy consumption reduced by 12.0%.
Figure 19.
The optimal result of different ODR in the southern hemisphere. Panel (a) shows the optimal result in summer where the total energy consumption reduced by 13.5% and (b) shows the optimal result in winter where the total energy consumption reduced by 12.0%.
Figure 20.
The optimal result of different ODR in the equator area. Panel (a) shows the optimal result in summer where the total energy consumption reduced by 11.9% and (b) shows the optimal result in winter where the total energy consumption reduced by 11.8%.
Figure 20.
The optimal result of different ODR in the equator area. Panel (a) shows the optimal result in summer where the total energy consumption reduced by 11.9% and (b) shows the optimal result in winter where the total energy consumption reduced by 11.8%.
Figure 21.
The optimal result of different ODR in the nouthern hemisphere. Panel (a) shows the optimal result in summer where the total energy consumption reduced by 12.6% and (b) shows the optimal result in winter where the total energy consumption reduced by 10.9%.
Figure 21.
The optimal result of different ODR in the nouthern hemisphere. Panel (a) shows the optimal result in summer where the total energy consumption reduced by 12.6% and (b) shows the optimal result in winter where the total energy consumption reduced by 10.9%.
Figure 22.
The optimal result of traversal method (ODR = 50 mL).
Figure 22.
The optimal result of traversal method (ODR = 50 mL).
Figure 23.
Optimal results of multi-objective optimization model. Panel (a) shows the Pareto optimization results and (b) shows the variety of the hypervolume value.
Figure 23.
Optimal results of multi-objective optimization model. Panel (a) shows the Pareto optimization results and (b) shows the variety of the hypervolume value.
Figure 24.
Parameters of the DSPB’s ascent stage optimized by the NSGA-II method.
Figure 24.
Parameters of the DSPB’s ascent stage optimized by the NSGA-II method.
Table 1.
The running states of devices and sensors of the deep-sea self-sustaining profile buoy (DSPB) in the whole working stage.
Table 1.
The running states of devices and sensors of the deep-sea self-sustaining profile buoy (DSPB) in the whole working stage.
Devices and Seneors | First Descent | Hovering | Second Descent | Ascent | Surface Communication |
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CTD sensor | ● | ● | ● | ● | ● |
Steering engine | ◖ | ◖ | ◖ | ○ | ○ |
Oil pump motor | ○ | ◖ | ○ | ◖ | ○ |
GPS module | ○ | ○ | ○ | ○ | ● |
Comet module | ○ | ○ | ○ | ○ | ● |
Embedded control system | ● | ☉ | ● | ● | ● |
Table 2.
The coefficient values for polynomial fitting of .
Table 2.
The coefficient values for polynomial fitting of .
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Table 3.
The coefficient values for polynomial fitting of .
Table 3.
The coefficient values for polynomial fitting of .
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Table 4.
The coefficient values for polynomial fitting of .
Table 4.
The coefficient values for polynomial fitting of .
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Table 5.
The coefficient values for polynomial fitting of .
Table 5.
The coefficient values for polynomial fitting of .
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Table 6.
The coefficient values for polynomial fitting of .
Table 6.
The coefficient values for polynomial fitting of .
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Table 7.
The coefficient values for polynomial fitting of .
Table 7.
The coefficient values for polynomial fitting of .
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Table 8.
The coefficient values for polynomial fitting of .
Table 8.
The coefficient values for polynomial fitting of .
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Table 9.
Parameters of proposed non-dominated sorted genetic algorithm-II (NSGA-II) method.
Table 9.
Parameters of proposed non-dominated sorted genetic algorithm-II (NSGA-II) method.
Size of population | 50 |
Chromosome structure | Real number coding |
Selection scheme | Binary tournament selection |
Reproduction | Simulated binary crossover and Polynomial mutation |
Produced distribution index | 20 |
Selected distribution index | 20 |
Maximum generation | 200 |
Table 10.
Optimization time of different optimal parameters.
Table 10.
Optimization time of different optimal parameters.
Parameters of NSGA-II | Optimization Time (s) |
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population = 50, generation = 100 | 3487.088273 |
population = 25, generation = 200 | 3609.206185 |
population = 50, generation = 200 | 7315.951831 |
population = 75, generation = 200 | 10,455.033943 |
population = 50, generation = 300 | 10,513.551947 |
population = 100, generation = 200 | 13,965.117581 |
Table 11.
The optimization effect of the NSGA-II method after 10 repetitions.
Table 11.
The optimization effect of the NSGA-II method after 10 repetitions.
Execution Times | Optimal (J) | Optimal ( m/s) | Optimal ( mL) | Optimization Time(s) |
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1 | 53,731.76245 | 0.09 | [180,50,50,60,70, | 7227.545857 |
| | | 70,90,20,10] | |
2 | 53,720.31747 | 0.09 | [170,30,40,40,60, | 7191.563176 |
| | | 50,50,70,90] | |
3 | 53,731.76245 | 0.09 | [180,50,50,60,70, | 7404.939277 |
| | | 70,90,20,20] | |
4 | 53,716.03741 | 0.09 | [170,30,40,30,40, | 7047.592007 |
| | | 50,60,70,90,20] | |
5 | 53,727.2845 | 0.09 | [180,40,10,50,60, | 7015.543344 |
| | | 60,60,60,80] | |
6 | 53,718.10196 | 0.09 | [170,30,20,40,40, | 7163.158171 |
| | | 60,60,70,80,30] | |
7 | 53,722.04461 | 0.09 | [160,40,40,40,30, | 7404.939277 |
| | | 40,60,70,90,30] | |
8 | 53,716.84258 | 0.09 | [160,30,30,40,50, | 7047.592007 |
| | | 50,60,70,80,30] | |
9 | 53,717.98512 | 0.09 | [160,30,30,40,50, | 7015.543344 |
| | | 60,60,70,80,20] | |
10 | 53,720.96775 | 0.09 | [180,40,40,40,50, | 7163.158171 |
| | | 60,70,80,40] | |
Table 12.
Parameters of proposed NSGA–II algorithm for multi-objective optimization.
Table 12.
Parameters of proposed NSGA–II algorithm for multi-objective optimization.
Size of Population | 50 |
Chromosome Structure | Real number coding |
Selection Scheme | Binary tournament selection |
Reproduction | Simulated binary crossover and Polynomial mutation |
Produced Distribution Index | 20 |
Selected Distribution Index | 20 |
Maximum Generation | 600 |
Table 13.
The optimization effect of the NSGA-II method compared with pre-optimization.
Table 13.
The optimization effect of the NSGA-II method compared with pre-optimization.
| Before Optimization | After Optimization | Optimal Ratio |
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(mL) | [600] | [160,30,30,40,50,50,60,70,80,30] | – |
(m/s) | – | 0.9 | – |
t (s) | 28,704 | 40,699 | – |
(J) | 15,007.51 | 21,278.95 | – |
(J) | 45,325.47 | 32,198.96 | 28.9% |
(J) | 60,332.98 | 53,716.84 | 11.0% |