High-Accuracy and Fast Calculation Framework for Berthing Collision Force of Docks Based on Surrogate Models
Abstract
:1. Introduction
2. Construction of the CBCF Framework Based on Surrogate Models
2.1. Construction of Collision Surrogate Model
- 1
- Col-Kriging
- 2
- Col-PCE
- 3
- Col-PCK
- 4
- Col-SVR
2.2. Evaluation and Optimization of Surrogate Models
2.3. CBCF Framework Process
3. Framework Application
3.1. Project Introduction
3.2. The Establishment of the Finite Element Model
3.2.1. Material Parameter Setting
3.2.2. Model Validity Verification
Berthing Collision Force Verification
Berthing Collision Energy Verification
Self-Vibration Frequency Verification
3.3. The Acquisition of the “Input-Output” Dataset
3.4. Comparative Analysis of Surrogate Models
- (1)
- The four surrogate models for exhibited a significant reduction in error as increased. For , both the Col-PCK and Col-SVR models demonstrated a substantial decrease in errors with increasing , while, for , the errors of these two models remained relatively stable. Similarly, Col-PCE followed a similar trend around . On the other hand, the error of Col-Kriging displayed considerable fluctuations.
- (2)
- In terms of the metric, as increased, all four surrogate models demonstrated a reduction in error, albeit at varying rates. Comparatively speaking, both the Col-Kriging and Col-PCK models manifested a more rapid decrease in the metric with increasing .
- (3)
- The Col-PCK model consistently exhibited a high prediction accuracy across different values. Even for , the evaluation error remained within the range of 10−2 to 10−3. When , both the evaluation indexes of the Col-PCK model reached an acceptable level (at the 10−3 level). However, one of the evaluation indexes for Col-Kriging, Col-PCE, and Col-SVR failed to meet the standard, with an error exceeding 10−2.
3.5. Framework Verification through Physical Model Testing
3.6. Sensitivity Analysis
3.7. Comparison with Existing Methodologies
4. Conclusions
- The surrogate model based on the “Input-Output” dataset demonstrates effective substitution for the finite element model, enabling the rapid prediction of the berthing collision force. Notably, among these models, the Col-PCK model exhibits superior performance in predicting the berthing collision force.
- The sensitivity analysis conducted using the CBCF framework proposed in this study reveals that berthing speed is the most influential factor, followed by ship tonnage. This suggests that a greater emphasis should be placed on controlling berthing speed during ship berthing processes.
- The PCK-CBCF model demonstrates significant advantages over existing berthing collision force prediction methods in terms of reducing sample requirements, enhancing prediction accuracy, and improving computational efficiency when applied to a case study of a wharf in the Jiangsu province. This finding underscores the extensive potential of the proposed framework for future applications and its role in promoting safe wharf operations.
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
References
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Ship Tonnage (ton) | Overall Length × Beam × Draft (m) | Container Capacity (TEU) |
---|---|---|
2500 | 78.2 × 15.6 × 3.5 | 180 |
5000 | 98 × 18.0 × 6.5 | 350 |
8000 | 121 × 19.2 × 7.0 | 351~710 |
12,000 | 151 × 23.6 × 9.3 | 711~1040 |
20,000 | 183 × 27.6 × 10.5 | 1041~1900 |
Part | Material | Characteristic | Parameters |
---|---|---|---|
Upper structures | C40 | Density (kg/m3) | 2300 |
Elastic modulus (MPa) | 3.25 × 104 | ||
Poisson’s ratio | 0.2 | ||
PHC tubular piles | C80 | Density (kg/m3) | 2500 |
Elastic modulus (MPa) | 3.8 × 104 | ||
Poisson’s ratio | 0.2 | ||
Ship model | Steel | Density (kg/m3) | 7800 |
Elastic modulus (MPa) | 2.06 × 105 | ||
Poisson’s ratio | 0.3 | ||
Fender | Rubber | Density (kg/m3) | 1800 |
Poisson’s ratio | 0.4997 | ||
Elastic modulus (MPa) | 4 | ||
533,333 | |||
133,333 |
Order | FEM/Hz | Measurement/Hz | Error/% |
---|---|---|---|
1 | 0.675 | 0.681 | 0.87 |
2 | 1.451 | 1.428 | 1.67 |
3 | 1.701 | 1.671 | 1.78 |
Category | Parameters | Symbol | Number | Range | Units |
---|---|---|---|---|---|
Input parameters | Ship tonnage | (2000, 20,000) | |||
Berthing speed | (0.1, 0.8) | ||||
Elastic modulus of rubber fender | (3, 8) | ||||
Berthing angle | (0, 15) | ° | |||
Output parameters | Berthing collision force | - |
Ship Tonnage (t) | Berthing Speed (m/s) | Peak Collision Force (kN) | PCK-CBCF (kN) | Error (%) | |
---|---|---|---|---|---|
Fully loaded | 6000 | 0.1 | 664.72 | 633 | 1.7 |
6000 | 0.2 | 1185.08 | 1267 | 6.9 | |
Unloaded | 2600 | 0.1 | 389.14 | 410 | 5.4 |
2600 | 0.2 | 795.65 | 820 | 3.1 |
Berthing Condition | FEM | PCK-CBCF | RBFNN-CBCF | BPNN-CBCF |
---|---|---|---|---|
(2500, 0.3, 3.0, 0) | 1265 | 1295 | 1358 | 1351 |
(5500, 0.25, 3.5, 5) | 1998 | 2033 | 2135 | 2071 |
(9800, 0.2, 4.0, 0) | 2456 | 2511 | 2611 | 2697 |
(11,000, 0.18, 4.2, 8) | 2341 | 2355 | 2120 | 2514 |
(13,400, 0.12, 4.5, 10) | 1723 | 1758 | 1601 | 1864 |
MAPE | - | 1.81% | 7.41% | 7.17% |
Time (ms) | - | 1280 | 4570 | 4110 |
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Zeng, H.; Zhu, R.; Wang, Q.; Zou, J. High-Accuracy and Fast Calculation Framework for Berthing Collision Force of Docks Based on Surrogate Models. J. Mar. Sci. Eng. 2024, 12, 898. https://doi.org/10.3390/jmse12060898
Zeng H, Zhu R, Wang Q, Zou J. High-Accuracy and Fast Calculation Framework for Berthing Collision Force of Docks Based on Surrogate Models. Journal of Marine Science and Engineering. 2024; 12(6):898. https://doi.org/10.3390/jmse12060898
Chicago/Turabian StyleZeng, Haikun, Ruihu Zhu, Qiming Wang, and Junjie Zou. 2024. "High-Accuracy and Fast Calculation Framework for Berthing Collision Force of Docks Based on Surrogate Models" Journal of Marine Science and Engineering 12, no. 6: 898. https://doi.org/10.3390/jmse12060898
APA StyleZeng, H., Zhu, R., Wang, Q., & Zou, J. (2024). High-Accuracy and Fast Calculation Framework for Berthing Collision Force of Docks Based on Surrogate Models. Journal of Marine Science and Engineering, 12(6), 898. https://doi.org/10.3390/jmse12060898