Cable Tension of Long-Span Steel Box Tied Arch Bridges Based on Radial Basis Function-Support Vector Machine Optimized by Quantum-Behaved Particle Swarm Optimization
Abstract
:1. Introduction
2. Derivation of Theoretical Formulae for Flexible Hanger
- (1)
- Articulated at both ends
- (2)
- Articulated at one end and fixed at the other
- (3)
- Fixed at both extremities
3. QPSO-RBF-SVM Model
3.1. RBF-SVM Modeling
3.2. QPSO Algorithm
3.3. Model Construction Steps
4. Modeling and Prediction Results
4.1. Project Overview
4.2. Data Collection
4.3. Data Processing and Model Building
4.4. Prediction Results of Cable Force
5. Comparative Analysis
5.1. Comparison with Formula
5.2. Comparison with Other Machine Learning Algorithms
6. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
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Spreader Bar Number | Length L (m) | Linear Density (kg/m) | Elastic Modulus E (kN/mm2) | Theoretical Cable (kN) |
---|---|---|---|---|
D1 | 7.149 | 42.20 | 195 | 1196 |
D2 | 10.100 | 42.20 | 195 | 1276 |
D3 | 12.385 | 42.20 | 195 | 1288 |
D4 | 14.014 | 42.20 | 195 | 1287 |
D5 | 14.990 | 42.20 | 195 | 1285 |
D6 | 15.312 | 42.20 | 195 | 1285 |
D7 | 14.981 | 42.20 | 195 | 1285 |
D8 | 13.994 | 42.20 | 195 | 1287 |
D9 | 12.348 | 42.20 | 195 | 1288 |
D10 | 10.046 | 42.20 | 195 | 1276 |
D11 | 7.102 | 42.20 | 195 | 1195 |
Data Number | Actual Measured Value (kN) | Projected Value (kN) | Relative Error |
---|---|---|---|
1 | 1261.89 | 1268.57 | 0.53% |
2 | 1275.78 | 1274.01 | −0.14% |
3 | 1348.07 | 1341.01 | −0.52% |
4 | 1303.29 | 1300.34 | −0.23% |
5 | 1347.37 | 1339.11 | −0.61% |
6 | 1342.61 | 1333.67 | −0.67% |
7 | 1170.76 | 1169.54 | −0.10% |
8 | 1412.81 | 1403.64 | −0.65% |
9 | 1228.15 | 1257.88 | 2.42% |
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Shi, H.; Shi, M.; Xu, W. Cable Tension of Long-Span Steel Box Tied Arch Bridges Based on Radial Basis Function-Support Vector Machine Optimized by Quantum-Behaved Particle Swarm Optimization. Appl. Sci. 2024, 14, 7163. https://doi.org/10.3390/app14167163
Shi H, Shi M, Xu W. Cable Tension of Long-Span Steel Box Tied Arch Bridges Based on Radial Basis Function-Support Vector Machine Optimized by Quantum-Behaved Particle Swarm Optimization. Applied Sciences. 2024; 14(16):7163. https://doi.org/10.3390/app14167163
Chicago/Turabian StyleShi, Hongcai, Menglin Shi, and Weisheng Xu. 2024. "Cable Tension of Long-Span Steel Box Tied Arch Bridges Based on Radial Basis Function-Support Vector Machine Optimized by Quantum-Behaved Particle Swarm Optimization" Applied Sciences 14, no. 16: 7163. https://doi.org/10.3390/app14167163