# An Investigation of Particle Swarm Optimization Topologies in Structural Damage Detection
## 5 Conclusions  
The main factors that affect the performance of the PSO algorithm include parameter strategies, topology structure, and boundary conditions. Researchers have designed many different schemes for each of these factors. This article investigates the effects of eight PSO topologies in SDD, and some guidelines are given. For the eight PSO topologies, their success rates and mean iterations for three types of damages on the cantilever beam are presented and discussed in this paper. From the point of view of success rate, it can be concluded that the Local, Von Neumann, Four Clusters, and Multi-Ring topologies perform the best, followed by the Clan Global and Clan Local topologies, and the Global and Wheel topologies are the last. Subsequently, the comparison of the mean iterations among the four best topologies in success rate is performed. The Four Clusters topology provides the smallest mean iterations. In summary, it is verified that the most commonly used Global topology is less effective in SDD; the Four Clusters topology has the best overall performances and it should be choosen for this application.  
Future work will conduct the influences of the boundary conditions and configuration parameter strategies on the performance of the PSO algorithm in SDD. In addition, although this study only simulated the SDD of a cantilever beam to investigate PSO topologies, the deformation and force characteristics of other types of beams are consistent with the studied cantilever beam. Therefore, it is reasonable to believe that the findings of this study can be generally applied to SDD problems of other beam structures. Nevertheless, for non-beam structures, such as plates and columns, similar investigation procedures are required, and the conclusion may be different.  
Conceptualization, X-L.L.; methodology, X-L.L.; software, X-L.L. and J.O. validation, X-L.L., R.S. and J.O.; formal analysis, X-L.L., R.S. and J.O.; investigation, X-L.L.; resources, R.S.; data curation, X-L.L., R.S. and J.O.; writing--original draft preparation, X-L.L.; writing--review and editing, R.S. and J.O.; visualization, X-L.L.; supervision, R.S. and J.O.; project administration, R.S.; funding acquisition, R.S. All authors have read and agreed to the published version of the manuscript.  
This research was funded by China Scholarship Council program with the grant number 201801810100.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Damage Type** & **Local** & **Von Neuman** & **Four Cluster** & **Multi-Ring** \\ \hline I & 4 & 2 & **1** & 3 \\ II & 4 & 2 & **1** & 3 \\ III & 4 & 2 & **1** & 3 \\ Overall & 4 & 2 & **1** & 3 \\ \hline \hline \end{tabular}
\end{table}
Table 6: The average rank of mean iterations for the four best performing topologies.  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Damage Type** & **Global** & **Local** & **Von Neuman** & **Wheel** & **Four Cluster** & **Clan Global** & **Clan Local** & **Multi-Ring** \\ \hline I & 7.3333 & 3 & 2.6667 & 7.6667 & 3.6667 & 4.6667 & **2.3333** \\ II & 7 & **1.8333** & 2.5 & 8 & 3.5 & 5.1667 & 5.8333 & 2.1667 \\ III & 6.6667 & **1.6667** & 2.6667 & 7.8333 & 3.3333 & 6.1667 & 5.3333 & 2.3333 \\ Overall & 7 & **2.1667** & 2.6111 & 7.8333 & 3.5 & 5.3333 & 5.2778 & 2.2778 \\ \hline \hline \end{tabular}
\end{table}
Table 5: Average rank of success rate for each damage type among PSO topologies.  
**Conflicts of Interest:** The authors declare no conflict of interest. The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript, or in the decision to publish the results.