Abstract
Surrogate models have been proven to be reliable and effective methods for the application of engineering problems. This article presents a comparative study of three common surrogate models Polynomial Response Surface (PRS), Radial Basis Function (RBF) neural network, and Kriging model in terms of optimization. For the optimization of plane 10-bar truss structure and 25 bar space truss, the effectiveness of the surrogate model algorithm is verified by different surrogate models. Finally for a typical complex truss structure such as lattice boom of crawler crane, the Optimal Latin Hypercube Design (OLHD) is used to sample the optimized sample points for fitting and interpolation of three surrogate models and analyzing their errors, in order to get better surrogate effect, PRS is combined with RBF Neural Network, and secondly, the global optimization algorithm (Multi-Island Genetic Algorithm, MIGA) and gradient algorithm (Modified Method of Feasible Directions, MMFD) are used to optimize the fitted four surrogate models. Through the comparison of the optimization results, the optimization of PRS-RBF combined surrogate model using MIGA-MMFD algorithm instead of finite element model optimization has good stability and reliability. The total mass of the optimized model has been reduced by 24.47%. The number of optimization iterations is within 250 generations. The new method proposed in this paper can greatly promote the reduction of the period of analysis and optimization of engineering structures.
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Abbreviations
- APSO:
-
Adaptive Particle Swarm Optimization
- d t :
-
An appropriate step size
- DOE:
-
Design of Experiment
- EPSO:
-
Evolutionary Particle Swarm Optimization
- G h3 :
-
Anti-overturning performance parameters of crawler crane
- HPSO:
-
Harmonious Particle Swarm Optimization
- HPSSO:
-
Hybrid Particle Swarm Optimization and Swallow Swarm Optimization
- LHD:
-
Latin Hypercube Design
- M 0 :
-
The overturning moment
- MAPE:
-
Maximum Absolute Percentage Error
- MIGA:
-
Multi-Island Genetic Algorithm
- MMFD:
-
Modified Method of Feasible Directions
- M s :
-
The stabilizing moment
- MSPSO:
-
Multiple Swarm Particle Swarm Optimization
- n :
-
The number of design variables
- OLHD:
-
Optimal Latin Hypercube Design
- PRS:
-
Polynomial Response Surface
- PSO:
-
Particle Swarm Optimization
- R 2 :
-
R-squared Error
- R :
-
A symmetric correlation matrix
- RBF:
-
Radial Basis Function
- RMSE:
-
Root Mean Square Error
- R(x i, x j):
-
The correlation kernel function
- S k :
-
Feasible direction
- x i :
-
The i-th component of m-dimensional independent variable x
- Y :
-
Esponse value of the model
- Y max :
-
The maximum displacement of the head of the crawler crane boom
- [Y]:
-
The maximum displacement specified in the specification
- y i :
-
The true value at the validation point
- β 0, β i and β ij :
-
Each coefficient, It can be expressed as β vector
- ε :
-
The error at the unknown point
- σ max :
-
The maximum stress
- [σ]:
-
The maximum permissible stress
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Acknowledgments
This work was supported by the Shanxi provincial Key Research and Development Project, China [201903D121067], the Fund for Shanxi ‘1331 Project’ Key Subjects Construction (1331KSC). Project supported by the National Natural Science Foundation of China (Grant No. 51478290).
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Yang, C., Yang, J. & Qin, Y. Research on Comparative of Multi-Surrogate Models to Optimize Complex Truss Structures. KSCE J Civ Eng 28, 2268–2278 (2024). https://doi.org/10.1007/s12205-024-0196-3
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DOI: https://doi.org/10.1007/s12205-024-0196-3