In the engineering practice, merging statistical analysis into structural evaluation and assessment is a tendency in the future. As a combination of mathematical and statistical techniques, response surface(RS) methodology has been successfully applied to design optimization, response prediction and model validation. With the aid of RS methodology,these two serial papers present a finite element(FE) model updating and validation method for bridge structures based on structural health monitoring. The key issues to implement such a model updating are discussed in this paper, such as design of experiment,parameter screening, construction of high-order polynomial response surface model,optimization methods and precision inspection of RS model. The proposed procedure is illustrated by a prestressed concrete continuous rigid-frame bridge monitored under operational conditions. The results from the updated FE model have been compared with those obtained from online health monitoring system. The real application to a full-size bridge has demonstrated that the FE model updating process is efficient and convenient.The updated FE model can relatively reflect the actual condition of Xiabaishi Bridge in the design space of parameters and can be further applied to FE model validation and damage identification.
Because of uncertainties involved in modeling, construction, and measurement systems,the assessment of the FE model validation must be conducted based on stochastic measurements to provide designers with confidence for further applications. In this study,based on the updated model using response surface methodology, a practical model validation methodology via uncertainty propagation is presented. Several criteria of testing/analysis correlation are introduced, and the sources of model and testing uncertainties are also discussed. After that, Monte Carlo stochastic finite element(FE) method is employed to perform the uncertainty quantification and propagation. The proposed methodology is illustrated with the examination of the validity of a large-span prestressed concrete continuous rigid frame bridge monitored under operational conditions. It can be concluded that the calculated frequencies and vibration modes of the updated FE model of Xiabaishi Bridge are consistent with the measured ones. The relative errors of each frequency are all less than 3.7%. Meanwhile, the overlap ratio indexes of each frequency are all more than75%; The MAC values of each calculated vibration frequency are all more than 90%. The model of Xiabaishi Bridge is valid in the whole operation space including experimental design space, and its confidence level is upper than 95%. The validated FE model of Xiabaishi Bridge can reflect the current condition of Xiabaishi Bridge, and also can be used as basis of bridge health monitoring, damage identification and safety assessment.
