Document Type : Article
Authors
1
Department of Civil Engineering, University of Tehran, Tehran, Iran
2
Department of Civil Engineering, Sharif University of Technology, Tehran, Iran
Abstract
This paper investigates the accuracy and convergence rate of different metaheuristic algorithms in determining the stiffness of structural elements using structural modal parameters and defining a suitable objective function. To achieve this purpose, three different structures, including a three-story one-dimensional frame, a six-story one-dimensional frame and a two-dimensional truss, were investigated. The metaheuristic algorithms, employed in this study, were Genetic Algorithm, Particle Swarm Optimization, and Teaching–learning-based Optimization. The objective function utilized in this study consists of two terms; the first part involves the squared difference between the first frequency of the structure obtained from the responses of the investigated structure and the first frequency obtained from the hypothetical stiffness matrix in each generation of algorithms. The second part measures the norm of the difference between the first mode shape of the structure obtained from the responses of the investigated structure and the first mode shape obtained from the hypothetical stiffness matrix in each generation of algorithms. By minimizing the objective function, the Genetic Algorithm, Particle Swarm Optimization, and Teaching–learning-based Optimization determined the element stiffness of the three-story, six-story and truss structures, thus demonstrating the high efficiency of metaheuristic algorithms in resolving unknown parameters of structures. The average run time for the Genetic Algorithm was 3.38 seconds, 4.47 seconds, and 15.73 seconds for the three respective problems. For Particle Swarm Optimization, the times were 3.76 seconds, 6.47 seconds, and 16.76 seconds. The Teaching–learning-based Optimization achieved times of 1.92 seconds, 4.51 seconds, and 12.76 seconds. The Teaching–learning-based Optimization exhibited the highest convergence rate and the lowest error compared to the Genetic Algorithm and Particle Swarm Optimization. For example, in the two-dimensional truss, the values of the objective function in the last iteration of the Genetic Algorithm, Particle Swarm Optimization, and Teaching–learning-based Optimization were 0.012, 6×10-4 and 4×10-4, respectively. The Particle Swarm Optimization demonstrated an acceptable convergence rate and error compared to the Genetic algorithm. The Genetic Algorithm, however, displayed a significant error rate in determining the stiffness of structural elements compared to the other two algorithms.
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