## 6 Conclusions  
In this paper, an improved particle swarm optimization algorithm based on random weights (IPSOARW) was proposed to optimize the arrangement of modal measurement points on the deck of a steel tube truss girder bridge (STTGB). The calculated modal analysis results of the finite element model of the bridge deck were used as the training data, and the number and location of measurement points of the bridge deck were optimized using the IPSOARW. According to the experimental data, the proposed IPSOARW has faster convergence speed and better solution accuracy and can significantly improve the efficiency of the optimal arrangement of measurement points. This work will provide a new idea for optimizing the arrangement of modal measurement points of bridges and has certain reference significance. The specific conclusions are as follows:  
* The number of measurement points of the bridge deck based on the uniform distribution method was 50, while the number based on the IPSOARW was 28. By contrast, the number of points was reduced by 44%. The results show that the proposed IPSOARW can effectively improve the test efficiency of the STTGB and reduce the number of sensor arrangements, which will save a lot of test costs.
* In the modal frequencies obtained based on the uniform distribution method, the mode around 90 Hz was lost, while the IPSOARW did not lose the modes. The results show that the proposed IPSOARW can effectively identify the modes in the frequency-dense segment and has the advantage of not losing the modes easily.
* The average error between the frequency obtained by the uniform distribution method and the finite element analysis frequency of the bridge deck was 5.33%, while that based on the IPSOARW distribution method was 4.06%. The results show that the proposed IPSOARW is suitable for the optimal arrangement of measurement points of the STTGB deck and that the obtained modal parameters have high accuracy. The modal parameters identified based on this optimized arrangement method have high accuracy and can accurately reflect the actual dynamic characteristics of the bridge deck.
* The experimental examples used in this paper are idealized without considering the influence of environmental factors such as wind load and vehicle load. Therefore, these factors will be taken into account in our next work to further test the applicability and effectiveness of the proposed method.  
Conceptualization, J.Z. and K.W.; methodology, K.W.; software, Q.H.; validation, J.Z. and K.W.; formal analysis, K.W.; investigation, Q.H.; resources, J.Z.; data curation, K.W.; writing--original draft preparation, K.W.; writing--review and editing, J.Z. and D.W.; visualization, M.Y.; supervision, M.Y.; project administration, J.Z.; funding acquisition, J.Z. All authors have read and agreed to the published version of the manuscript.  
**Funding:** This research was funded by the Natural Science Foundation of Tianjin, grant number 16 JCXZDJC38600, and the Tianjin Enterprise Science and Technology Commissioner Project, grant number 20 YDTPJC00610.  
**Institutional Review Board Statement:** Not applicable.  
**Informed Consent Statement:** Not applicable.  
**Data Availability Statement:** Not applicable.  
**Conflicts of Interest:** The authors declare no conflict of interest.