This is evident from figure 6, where the search converged much quicker than in figure 2 whilst using the same objective function. Figure 7 also supports the initial explore to local exploitation concept because a number of models were initially pg as opposed to figure 3 but towards the end a firm favourite was converged on. The final model order in this simulation was m1, m6, m7, m2, m3, m8, m4 and then m5. Perhaps the AIC objective function is too critical of the model complexity as it seems to always select models according to it. 

## 5.1.3 Simulation Number 4

In simulation number 4 the PSO algorithm has the adaptive inertia weight but uses the SSE as the objective function. 

![0_image_0.png](0_image_0.png) 

![0_image_1.png](0_image_1.png)

The final model order in this simulation was m4, m1, m3, m6, m2, m7, m5 and then m8. Clearly the SSE objective function is not concerned with the complexity of the finite element model. The best model in this case is one of the most complex. It is not easy to directly compare the objective function magnitudes the algorithms converge to. 

This would have allowed for better analysis of why different models behave so differently under different objective functions. More conclusive decisions on the choice of objective function in this type of updating methodology can only be made with further experiments on different types of objective functions. 

## 6. Conclusions

A particle swarm based method of finite element model updating and selection is presented. The method updates finite element model parameters using a stochastic-population based optimization procedure. Each potentially correct model of a structure is treated as an adaptive particle in the finite element model updating problem space. This space is defined by the number of potentially updatable model parameters. A number of simulations, using different objective function, are performed on eight competing models of a particular structure. The particle swarm based optimization approach to finite element model updating offers the researcher an ability to simultaneously update and select the best model in a given group. This is desirable in the cases where multiple competing model updating models of one structure exist. This paper has also highlighted that the choice of objective function is crucial in obtaining a reasonable best model. 