Establishment of a Pressure Variation Model for the State Estimation of an Underwater Vehicle
Abstract
:1. Introduction
2. Methodology and Results
2.1. Test Model
2.2. Pressure Variation Model (PVM)
2.2.1. Velocity Estimation
2.2.2. State Estimation
2.3. Flow Simulation
2.3.1. Governing Equation and Boundary Condition
2.3.2. Simulation Set-Up
2.4. Numerical Results
3. Conclusions
- The dynamic pressure characteristics were analyzed by numerical simulations for straight, turning, and gliding motions under speed, angular velocity, and angle of attack conditions.
- The coefficients for the PVM were derived by performing regression analysis on the dynamic pressure obtained from numerical simulations, considering the coefficient of determination and the MAE for evaluation.
- The state estimation algorithm was presented by combining the regression equations of the pressure sensors array to form an inverse matrix. Furthermore, it was validated for single and multiple motions, confirming the targeted prediction accuracy within 15%.
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
Abbreviations
PVM | pressure variation model |
UUVs | unmanned underwater vehicles |
LLSs | lateral line systems |
ALLSs | artificial lateral line systems |
ALL | artificial lateral line |
AUV | autonomous underwater vehicle |
R, L, T, B | pressure sensor position: right (starboard), left (port), top, bottom |
PVs | pressure variations |
MAE | mean absolute error |
CFD | computational fluid dynamics |
EFD | experimental fluid dynamics |
RANS | Reynolds-averaged Navier–Stokes |
SIMPLE | semi-implicit method for pressure-linked equation |
SST | shear stress transport |
ITTC | International Towing Tank Conference |
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Length overall [m] | 1.345 |
Max. diameter [m] | 0.191 |
Design speed [knots] | 3.0 |
Motion | Motion Variable | Note |
---|---|---|
Straight | U = 1.0~4.0 [knots] *Interval 0.5 knots | α = 0, β = 0, r = 0, q = 0 |
Turning | U = 2.0~4.0 [knots] *Interval 1.0 knots r = 0~30 [deg/s] *Interval 5 deg/s | α = 0, β = 0, r ≠ 0, q = 0 |
Gliding | U = 1.0~4.0 [knots] *Interval 0.5 knots α = 0~−30 [deg] *Interval 5 deg | α ≠ 0, β = 0, r = 0, q = 0 |
Motion | Sensor | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 |
---|---|---|---|---|---|---|---|---|---|---|---|---|
Straight (C1, C6) | R2 | 1.00 | 0.99 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 0.99 | 0.99 | 0.99 |
MAE | 0.24 | 0.24 | 0.28 | 0.27 | 0.25 | 0.23 | 0.21 | 0.38 | 0.42 | 0.42 | 0.42 | |
Turning (C2, C3) | R2 | 0.93 | 0.94 | 0.95 | 0.90 | 0.74 | 0.70 | 0.84 | 0.94 | 0.94 | 0.94 | 0.94 |
MAE | 6.62 | 2.34 | 0.27 | 0.33 | 0.32 | 0.30 | 0.26 | 0.24 | 0.37 | 0.39 | 11.48 | |
Gliding (C4, C5) | R2 | 0.12 | 0.92 | 0.97 | 0.97 | 0.96 | 0.96 | 0.97 | 0.97 | 0.97 | 0.97 | 0.97 |
MAE | 24.87 | 17.28 | 5.25 | 3.18 | 3.30 | 3.22 | 3.30 | 4.36 | 5.60 | 6.26 | 6.67 |
Motion | Sensor | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 |
---|---|---|---|---|---|---|---|---|---|---|---|---|
Gliding (D1, D4) | R2 | 0.93 | 0.99 | 1.00 | 0.99 | 0.97 | 0.96 | 0.94 | 0.97 | 0.98 | 0.97 | 0.97 |
MAE | 29.42 | 16.00 | 6.05 | 12.05 | 18.91 | 24.77 | 35.44 | 22.39 | 18.21 | 21.29 | 26.42 | |
Turning (D2, D3) | R2 | 0.98 | 0.99 | 0.99 | 0.99 | 0.98 | 0.94 | 0.52 | 0.64 | 0.20 | 0.84 | 0.94 |
MAE | 10.03 | 14.62 | 2.37 | 11.14 | 22.04 | 49.06 | 947.1 | 1097 | 1567 | 795.9 | 710.5 |
Sensor | C1 | C2 | C3 | C4 | C5 | C6 | D1 | D2 | D3 | D4 |
---|---|---|---|---|---|---|---|---|---|---|
1 | −305.1 | −396.1 | −206.1 | −3803.3 | 1976.2 | −174.5 | −1533.5 | −2328.1 | 1947.2 | 145.28 |
2 | −64.5 | −364.6 | −2336.0 | −52.7 | −543.6 | −177.0 | −1350.0 | 97.21 | 829.76 | 46.93 |
3 | −288.4 | −328.4 | −1701.4 | −510.0 | −34.3 | −179.5 | −1098.3 | 264.52 | 480.09 | −10.02 |
4 | −433.6 | −295.8 | −1311.6 | −307.3 | 31.0 | −180.4 | −858.9 | 5.64 | 358.47 | −18.15 |
5 | −515.2 | −257.3 | −1119.0 | −209.4 | 36.3 | −180.5 | −656.3 | −79.53 | 248.60 | −21.85 |
6 | −535.6 | −232.4 | −1075.2 | −209.8 | 42.2 | −180.1 | −488.2 | −52.10 | 128.54 | −21.81 |
7 | −488.6 | −230.2 | −1192.8 | −252.3 | 42.4 | −179.7 | −365.5 | 11.14 | 26.08 | −22.23 |
8 | −323.7 | −228.5 | −1522.9 | −254.4 | −6.0 | −183.5 | −325.8 | −36.75 | 29.30 | −13.58 |
9 | −212.7 | −236.8 | −1743.7 | −261.3 | −25.1 | −181.9 | −297.3 | −31.41 | 11.47 | 58.43 |
10 | −158.8 | −244.4 | −1843.9 | −252.2 | −23.4 | −181.0 | −265.1 | −23.95 | −18.61 | 104.23 |
11 | −126.1 | −248.1 | −1900.1 | −20.1 | −229.9 | −180.4 | −240.3 | −24.64 | −41.54 | 144.74 |
U | 1.0 | 1.5 | 2.0 | 2.5 | 3.0 | 3.5 | 4.0 |
---|---|---|---|---|---|---|---|
Predicted (knots) | 0.991 | 1.498 | 2.002 | 2.504 | 3.004 | 3.498 | 3.999 |
Relative Err. (%) | −0.944 | −0.109 | 0.098 | 0.163 | 0.118 | −0.048 | −0.016 |
U | 2.0 | 3.0 | 4.0 | |||
---|---|---|---|---|---|---|
r | Predicted (Knots) | Relative Err. (%) | Predicted (Knots) | Relative Err. (%) | Predicted (Knots) | Relative Err. (%) |
0 | 2.004 | 0.176 | 3.005 | 0.179 | 3.999 | 0.035 |
5 | 2.001 | 0.049 | 3.007 | 0.223 | 3.997 | 0.087 |
10 | 2.012 | 0.606 | 3.015 | 0.499 | 4.017 | 0.417 |
15 | 2.001 | 0.046 | 3.022 | 0.737 | 4.010 | 0.262 |
20 | 2.001 | 0.034 | 3.000 | −0.006 | 4.015 | 0.377 |
25 | 2.016 | 0.297 | 2.994 | −0.200 | 3.984 | −0.400 |
30 | 2.045 | 2.241 | 2.995 | −0.170 | 3.978 | −0.544 |
U | 1.0 | 2.0 | 3.0 | 4.0 | ||||
---|---|---|---|---|---|---|---|---|
α | Predicted (Knots) | Relative Err. (%) | Predicted (Knots) | Relative Err. (%) | Predicted (Knots) | Relative Err. (%) | Predicted (Knots) | Relative Err. (%) |
0 | 0.995 | −0.484 | 2.001 | 0.057 | 3.002 | 0.079 | 4.000 | −0.008 |
−5 | 1.022 | 2.235 | 2.026 | 1.278 | 3.018 | 0.604 | 4.012 | 0.293 |
−10 | 1.041 | 4.099 | 2.012 | 0.605 | 2.984 | −0.537 | 3.952 | −1.201 |
−15 | 1.058 | 5.775 | 1.998 | −0.112 | 2.966 | −1.145 | 3.911 | −2.215 |
−20 | 1.065 | 6.492 | 2.003 | 0.132 | 2.933 | −2.225 | 3.868 | −3.305 |
−25 | 1.008 | 0.761 | 1.977 | −1.142 | 2.905 | −3.173 | 3.835 | −4.137 |
−30 | 0.997 | −0.315 | 2.089 | 4.450 | 3.129 | 4.299 | 4.179 | 4.472 |
U | 1.0 | 1.5 | 2.0 | 2.5 | 3.0 | 3.5 | 4.0 |
---|---|---|---|---|---|---|---|
Predicted | 1.33 | 0.58 | 0.32 | 0.20 | 0.14 | 0.11 | 0.08 |
Predicted | 1.18 | 0.51 | 0.29 | 0.18 | 0.13 | 0.09 | 0.07 |
U | 2.0 | 3.0 | 4.0 | |||
---|---|---|---|---|---|---|
r | Predicted | Predicted | Predicted | Predicted | Predicted | Predicted |
0 | 0.32 | 0.29 | 0.14 | 0.13 | 0.08 | 0.07 |
5 | 0.38 | 0.39 | 0.19 | 0.31 | 0.12 | 0.23 |
10 | 0.32 | 0.15 | 0.17 | −0.31 | 0.14 | 0.14 |
15 | 0.33 | 0.21 | 0.16 | 0.02 | 0.14 | 0.01 |
20 | 0.33 | 0.18 | 0.14 | 0.04 | 0.10 | −0.03 |
25 | 0.33 | 0.21 | 0.14 | 0.00 | 0.07 | −0.04 |
30 | 0.31 | 0.37 | 0.14 | −0.07 | 0.07 | −0.12 |
U | 1.0 | 2.0 | 3.0 | 4.0 | ||||
---|---|---|---|---|---|---|---|---|
Predicted | Relative Err. (%) | Predicted | Relative Err. (%) | Predicted | Relative Err. (%) | Predicted | Relative Err. (%) | |
0 | 1.32 | - | 0.32 | - | 0.14 | - | 0.08 | - |
−5 | −3.75 | −25.07 | −4.84 | −3.23 | −5.09 | 1.86 | −5.19 | 3.78 |
−10 | −8.36 | −16.43 | −9.91 | −0.93 | −10.31 | 3.12 | −10.50 | 5.04 |
−15 | −12.57 | −16.22 | −14.99 | −0.04 | −15.46 | 3.08 | −15.82 | 5.48 |
−20 | −16.90 | −15.48 | −19.80 | −0.99 | −20.82 | 4.11 | −21.27 | 6.34 |
−25 | −24.10 | −3.61 | −25.74 | 2.95 | −26.81 | 7.23 | −27.27 | 9.07 |
−30 | −30.18 | 0.60 | −27.66 | −7.81 | −27.58 | −8.08 | −27.28 | −9.08 |
U | 1.0 | 2.0 | 3.0 | 4.0 | ||||
Predicted | ||||||||
0 | 1.17 | 0.29 | 0.13 | 0.07 | ||||
−5 | 1.12 | 0.28 | 0.13 | 0.07 | ||||
−10 | 1.08 | 0.29 | 0.13 | 0.07 | ||||
−15 | 1.00 | 0.29 | 0.13 | 0.08 | ||||
−20 | 1.06 | 0.29 | 0.13 | 0.08 | ||||
−25 | 1.13 | 0.30 | 0.14 | 0.08 | ||||
−30 | 1.16 | 0.27 | 0.12 | 0.07 |
Motion | Motion Variable | Note |
---|---|---|
Turning w/drift | U = 3.0 [knots] β = 10, 20 [deg] r = 10, 20, 30 [deg/s] | α = 0, β ≠ 0, r ≠ 0, q = 0 |
Gliding w/drift | U = 1.5, 3.0 [knots] α = −10, −20 [deg] β = 10, 20 [deg] | α ≠ 0, β ≠ 0, r = 0, q = 0 |
Spiral | U = 3.0 [knots] α = −10, −20, −30 [deg] r = 10, 20, 30 [deg/s] | α ≠ 0, β = 0, r ≠ 0, q = 0 |
r | 10 | 20 | 30 | ||||||
---|---|---|---|---|---|---|---|---|---|
β | 0 | 10 | 20 | 0 | 10 | 20 | 0 | 10 | 20 |
Predicted (knots) | 3.004 | 2.960 | 2.681 | 2.994 | 3.059 | 2.934 | 2.996 | 3.182 | 3.116 |
Relative Err. (%) | 0.119 | 1.354 | 10.64 | 0.196 | 1.947 | 2.204 | 0.134 | 6.071 | 3.865 |
U | 1.5 | 3.0 | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|
α | −10 | −20 | −10 | −20 | ||||||||
β | 0 | 10 | 20 | 0 | 10 | 20 | 0 | 10 | 20 | 0 | 10 | 20 |
Predicted (knots) | 1.525 | 1.527 | 1.483 | 1.534 | 1.546 | 1.475 | 2.984 | 3.004 | 2.921 | 2.933 | 2.987 | 2.910 |
Relative Err. (%) | 1.655 | 1.765 | 1.109 | 2.227 | 3.040 | 1.693 | 0.545 | 0.110 | 2.631 | 2.233 | 0.426 | 3.010 |
α | −10 | −20 | −30 | ||||||
---|---|---|---|---|---|---|---|---|---|
r | 10 | 20 | 30 | 10 | 20 | 30 | 10 | 20 | 30 |
Predicted (knots) | 3.115 | 3.019 | 3.084 | 2.625 | 3.082 | 3.129 | 2.982 | 2.982 | 3.352 |
Relative Err. (%) | 3.810 | 0.619 | 2.799 | 12.52 | 2.733 | 4.297 | 0.623 | 0.612 | 11.73 |
r | 10 | 20 | 30 | |||
---|---|---|---|---|---|---|
β | ||||||
0 | 0.17 | 0.14 | 0.14 | |||
10 | 0.15 | 0.15 | 0.13 | |||
20 | 0.19 | 0.16 | 0.14 | |||
r | 10 | 20 | 30 | |||
β | Predicted | Relative Err. (%) | Predicted | Relative Err. (%) | Predicted | Relative Err. (%) |
0 | −0.32 | - | 0.03 | - | −0.06 | - |
10 | 10.83 | 8.29 | 10.21 | 2.07 | 10.34 | 3.44 |
20 | 24.79 | 23.93 | 20.70 | 3.50 | 19.41 | −2.94 |
−10 | ||||||||
U | 1.5 | 3.0 | ||||||
Predicted | Relative Err. (%) | Predicted | Relative Err. (%) | Predicted | Relative Err. (%) | Predicted | Relative Err. (%) | |
0 | −9.45 | −5.48 | 0.49 | - | −10.31 | 3.12 | 0.13 | - |
10 | −8.83 | −11.72 | 10.17 | 1.66 | −9.88 | −1.18 | 10.16 | 1.64 |
20 | −9.97 | −0.31 | 22.04 | 10.19 | −10.70 | 7.01 | 22.06 | 10.30 |
−20 | ||||||||
U | 1.5 | 3.0 | ||||||
Predicted | Relative Err. (%) | Predicted | Relative Err. (%) | Predicted | Relative Err. (%) | Predicted | Relative Err. (%) | |
0 | −18.85 | −5.73 | 0.49 | - | −20.82 | 4.11 | 0.13 | - |
10 | −19.45 | −2.73 | 9.63 | −3.69 | −21.07 | 5.33 | 9.86 | −1.44 |
20 | −21.16 | 5.82 | 20.90 | 4.51 | −21.22 | 6.09 | 20.59 | 2.97 |
−10 | −20 | −30 | ||||
---|---|---|---|---|---|---|
r | Predicted | Relative Err. (%) | Predicted | Relative Err. (%) | Predicted | Relative Err. (%) |
10 | −10.03 | 0.29 | −28.71 | 43.57 | −33.94 | 13.12 |
20 | −9.96 | −0.38 | −20.89 | 4.45 | −33.87 | 12.92 |
30 | −9.89 | −1.14 | −20.55 | 2.77 | −26.94 | −10.20 |
U | −10 | −20 | −30 | |||
r | Predicted | |||||
10 | 0.29 | −0.57 | −0.03 | |||
20 | 0.42 | 0.22 | 0.08 | |||
30 | 0.69 | 0.43 | 0.91 |
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Kim, J.-H.; Mai, T.L.; Cho, A.; Heo, N.; Yoon, H.K.; Park, J.-Y.; Byun, S.-H. Establishment of a Pressure Variation Model for the State Estimation of an Underwater Vehicle. Appl. Sci. 2024, 14, 970. https://doi.org/10.3390/app14030970
Kim J-H, Mai TL, Cho A, Heo N, Yoon HK, Park J-Y, Byun S-H. Establishment of a Pressure Variation Model for the State Estimation of an Underwater Vehicle. Applied Sciences. 2024; 14(3):970. https://doi.org/10.3390/app14030970
Chicago/Turabian StyleKim, Ji-Hye, Thi Loan Mai, Aeri Cho, Namug Heo, Hyeon Kyu Yoon, Jin-Yeong Park, and Sung-Hoon Byun. 2024. "Establishment of a Pressure Variation Model for the State Estimation of an Underwater Vehicle" Applied Sciences 14, no. 3: 970. https://doi.org/10.3390/app14030970
APA StyleKim, J.-H., Mai, T. L., Cho, A., Heo, N., Yoon, H. K., Park, J.-Y., & Byun, S.-H. (2024). Establishment of a Pressure Variation Model for the State Estimation of an Underwater Vehicle. Applied Sciences, 14(3), 970. https://doi.org/10.3390/app14030970