Identification of Hydrodynamic Coefficients of the SUBOFF Submarine Using the Bayesian Ridge Regression Model
Abstract
:1. Introduction
2. Mathematical Model
2.1. Submarine Motion Equation
2.2. Bayesian Ridge Regression Model
3. Model and CFD Methods
3.1. Model
3.2. CFD Methods
3.3. Spatial Motion Simulation
3.3.1. Grid
3.3.2. Body Force Propeller Model
3.3.3. Spatial Motion Result
3.4. Simulated Restraint Model Test
3.4.1. Oblique Towing Tests on the Vertical Plane
3.4.2. Pure Heaving
3.4.3. Pure Pitch
4. Results and Discussion
4.1. Results of Hydrodynamic Coefficient Identification
4.2. Spatial Motion Prediction and Analysis
5. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
References
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Parameter | Symbol | Unit | Value |
---|---|---|---|
Total length | L | m | 2.178 |
Diameter | D | m | 0.254 |
Sail length | LS | m | 0.184 |
Sail height | LD | m | 0.112 |
Mass of model | ms | kg | 88.02 |
Center of mass | (xg, yg, zg) | m | (1.005, 0.0, −0.003) |
Center of buoyancy | (xb, yb, zb) | m | (1.005, 0.0, 0.001) |
Moment of inertia | (Ixx, Iyy, Izz) | kg·m2 | (0.88, 25.43, 25.43) |
Method | Grid Level | Cells (Millions) | Drag Force (N) | Relative Error (%) |
---|---|---|---|---|
Experiment | - | - | 283.8 | - |
CFD | Coarse | 2.96 | 299.87 | 5.66% |
Medium | 7.25 | 291.76 | 2.81% | |
Fine | 16.78 | 290.57 | 2.39% |
Parameter | Symbol | Value |
---|---|---|
Blades | - | 5 |
Diameter | DP | 0.15 |
Hub-to-diameter ratio | d/DP | 0.2 |
Disk aspect ratio | Ae/A0 | 0.725 |
Force Direction | R2 | Force Direction | R2 |
---|---|---|---|
X | 0.985 | K | 0.989 |
Y | 0.997 | M | 0.973 |
Z | 0.987 | N | 0.964 |
Coefficients | Bayesian × 10−4 | Coefficients | Bayesian × 10−4 | Coefficients | Bayesian × 10−4 |
---|---|---|---|---|---|
X | −8.31 | Z | −8.39 | M | −17.2 |
Xuu | −11.0 | Zvr | −453.8 | Mq | −34.35 |
Xvv | 171.6 | Zq | −71.47 | Mw | 98.99 |
Y | −141.68 | Zw | −144.05 | Mvr | −5.2 |
Y | −5.11 | K | −0.52 | Mδs | −36.66 |
Y | 4.47 | K | −0.03 | N | 2.92 |
Yr | 57.05 | Kp | −4.8 | N | −7.31 |
Yp | −29.7 | Kr | 2.6 | N | −0.086 |
Yv|r| | 4.5 | Kwr | 11.3 | Nr | −46.31 |
Yv | 280.76 | Kv | −6.46 | Nv | −145.05 |
Yv|v| | −1160.1 | Kδr | −0.1 | N|v|r | −20.8 |
Yδr | 71.43 | Z|w| | −20.0 | Nδr | −26.83 |
Yvw | −3025.7 | Zδs | −49.21 | ||
Z | −115.55 | M | −2.85 |
Coefficients | CFD × 10−4 | Bayesian × 10−4 | Errors Compared to CFD Method % |
---|---|---|---|
Zw | −131.85 | −144.05 | 9.25 |
Mw | 95.34 | 98.99 | 3.82 |
Zq | −71.32 | −79.43 | 11.37 |
Mq | −35.59 | −34.35 | −3.49 |
Z | −110.19 | −115.55 | 4.87 |
M | −5.02 | −2.85 | −43.26 |
Z | −7.68 | −8.39 | 9.30 |
M | −7.88 | −7.39 | −6.21 |
Zδs | - | −49.21 | - |
Mδs | - | −36.66 | - |
Yv | 261.14 | 280.76 | 7.51 |
Nv | −142.96 | −145.05 | 1.46 |
Kv | - | −6.46 | - |
Yr | 57.35 | 57.05 | −0.53 |
Nr | −50.20 | −46.31 | −7.75 |
Y | −139.94 | −141.68 | 1.24 |
N | 2.57 | 2.92 | 13.76 |
Y | 4.32 | 4.47 | 3.47 |
N | −7.96 | −7.31 | −8.11 |
Yδr | - | 71.43 | - |
Nδr | - | −26.83 | - |
Kδr | - | −0.10 | - |
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Xiang, G.; Ou, Y.; Chen, J.; Wang, W.; Wu, H. Identification of Hydrodynamic Coefficients of the SUBOFF Submarine Using the Bayesian Ridge Regression Model. Appl. Sci. 2023, 13, 12342. https://doi.org/10.3390/app132212342
Xiang G, Ou Y, Chen J, Wang W, Wu H. Identification of Hydrodynamic Coefficients of the SUBOFF Submarine Using the Bayesian Ridge Regression Model. Applied Sciences. 2023; 13(22):12342. https://doi.org/10.3390/app132212342
Chicago/Turabian StyleXiang, Guo, Yongpeng Ou, Junjie Chen, Wei Wang, and Hao Wu. 2023. "Identification of Hydrodynamic Coefficients of the SUBOFF Submarine Using the Bayesian Ridge Regression Model" Applied Sciences 13, no. 22: 12342. https://doi.org/10.3390/app132212342
APA StyleXiang, G., Ou, Y., Chen, J., Wang, W., & Wu, H. (2023). Identification of Hydrodynamic Coefficients of the SUBOFF Submarine Using the Bayesian Ridge Regression Model. Applied Sciences, 13(22), 12342. https://doi.org/10.3390/app132212342