## 5 Conclusions  
In this article, a hybrid model updating method by integration of GMPSO and Kriging meta-model has been proposed. Compared to ordinary polynomial meta-models, the stochastic process in Kriging meta-model increases the accuracy, and meanwhile, it first uses the LHS technique to improve the quality of input datasets. Compared to direct GMPSO method, the only FE analysis calls are used in forming the Kriging meta-model. By combining advantages of both GMPSO and Kriging meta-model, the proposed hybrid method can prohibitively reduce the computation time without losing accuracy. Thus, this method is suitable for model updating of engineering applications with large-scale, multi-dimensional parameter structures involving implicit performance functions. After the validation study of this hybrid method and its application to a self-anchored suspension bridge with extra-width located in China, several conclusions can be drawn from this article as follows:  
* Through the application of the hybrid method to a damaged simply supported beam, it was evident that the updating process of hybrid method, compared to direct GMPSO, can be performed more efficiently without losing accuracy. This demonstrates that the proposed hybrid method is applicable to model updating of engineering applications.
* Based on the mode frequency results of ambient vibration test of Hunan Road Bridge, it was clear seen that the differences between the initial FE model and experiment were large enough, some of which are up to 38%, but the vibration modes show high agreements with a lowest MAC value of 0.849. Moreover, due to the extra-width, the torsion mode emerged earlier than ordinary bridges, which enhanced the importance of yielding a precise FE model for further performance evaluation.
* Ten sensitive parameters--module of main girder, main tower and main cable, density of main girder, moment of inertia of vertical bending, transverse bending and torsion, moment of inertia of main tower, area of section of main girder, and secondary dead load--were selected after sensitivity analysis as updated parameters of Hunan Road Bridge. After model updating using hybrid method, both of the mode frequencies and shapes showed a relatively high agreement  
Figure 7: Comparisons of each vibration mode and images of each vibration mode form test: (**a**) Mode No. 1; (**b**) Mode No. 2; (**c**) Mode No. 3; (**d**) Mode No. 4; (**e**) Mode No. 5.  
with the results of the experiment. The differences of mode frequencies drop sharply and are all below 6%. Meanwhile, all the MACs increase over 0.87, which indicates the vibration mode has a higher agreement. The successful model updating of this bridge fills in the blank of model updating of a complex self-anchored suspension bridge. In addition, the updating process makes it possible for other model updating issues of complex bridge structures.  
The authors are gratefully thankful to National Natural Science Foundation of China (No. 51278104), Doctoral Program Foundation of Institutions of Higher Education of China (No. 20133204120015), Natural Science Foundation of the Jiangsu Higher Education Institutions of China (No. 12 KJB560003), a Project Funded by the Priority Academic Program Development of Jiangsu Higher Education Institutions (PAPD) (No. CE02-1-35) and the sponsored by China Scholarship Council (CSC) to National University of Singapore. The authors are also grateful to [PERSON] of National University of Singapore for his comments, suggestions, and guidance in writing of some parts of this article. [PERSON] did the mathematical modeling, performed the simulations, and contributed to the experiment and writing. [PERSON], [PERSON], and [PERSON] contributed to the revisions and discussion of the contents. The authors declare no conflict of interest.