Keywords: evolutionary computation, particle swarm optimization, inverse problems, damage detection, structural optimization, dynamic responses, finite element method.

In this study, a novel auto-configured micro-particle swarm optimization algorithm (ACm-PSO) for structural health monitoring is proposed. The effects of three neighborhood topologies (fully connected, local best and wheel) are studied in order to assess their impact in the ACm-PSO convergence rate. The approach presented uses a quite small population and a restart process, both concepts, borrowed from the genetic algorithms [1]. In addition, a new concept is introduced, the idea of an elitist leader to guide the search. Finally, the novel strategy (presented by Begambre and Laier [2] for the control of the particle swarm optimization (PSO) parameters based on the Nelder-Mead algorithm (the PSOS algorithm) is used.

To define the ACm-PSO heuristic and taking into consideration the PSOS proposed by Begambre and Laier [2], has revealed guaranteed convergence properties. We used the procedure described in [2] with the modifications described below. First, a very small number of particles were used in the PSO subroutine (four particles). Second, for all swarms generated by the simplex, the best result was stored and, in the next contraction (reflexion, expansion or shrinkage), the information of the best particle is used (this particle is called the Elitist Leader). The restart process is accomplished when the simplex performs a vertex movement.

The ACm-PSO was tested in four high dimensional benchmark functions [3] and is validated in a structural damage detection problem. The numerical results indicate that the ACm-PSO is computationally efficient and needs fewer function evaluations to find the global optimum (of the tested functions) than the classical guaranteed convergence PSO (GPPSO [4]). A comparison between the performances of the ACm-PSO and the classical GCPSO, in the damage detection example, is presented.

The ACm-PSO algorithm for structural health monitoring allows the proper identification of damaged elements in the beam studied when the minimum degradation in stiffness of the element is 15%. The identification gives very good results with simulated vibration noisy polluted data and only four modes. This fact makes the ACm-PSO (with fully connected topology) a good candidate for real-world damage identification problems. In order to achieve this goal, further investigation must be done to assess the ACm-PSO`s behaviour in very high dimensional problems.

1

K. Krishnakumar, "Micro-genetic algorithm for stationary and non-stationary Function optimization", ion "SPIE proceedings: intelligent control and adaptive systems", 289-96, 1989.

2

O. Begambre, J.E. Laier, "A hybrid Particle swarm optimization simplex algorithm for structural damage detection", Advances in Engineering Software, 40(9), 883-891, 2009. doi:10.1016/j.advengsoft.2009.01.004

3

A. Georgieva, I. Jordanov, "Global optimization based on novel heuristics, low-discrepancy sequences and genetic algorithms", European Journal of Operational Research, 196, 413-422, 2009. doi:10.1016/j.ejor.2008.03.019

4

E.S. Pier, F. Van den Bergh, A.P. Engelbrecht, "Using neighbourhoods with the guaranteed convergence PSO", in "Proc. IEEE Swarm Intelligence Sym.", Indianapolis, IN, 235-242, 2003.

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