Resumen de Static structural system identification using observability method
During the construction and operation stages of structures, various factors lead to irreversible degradation that could affect the normal use and the public safety of these structures. In recent years, it has been common to carry out condition assessment of structures using Structural System Identification (SSI) methods.
SSI is the application of parameter estimation in structural system. One key issue in SSI is to guarantee the observability of the parameters to be estimated. This was already addressed by the SSI by Observability Method (OM) using static tests. However, a systematic analysis of the effect of measurement and simulation errors for this method is lacking. A ramification of this analysis is the effective strategies to use redundant measurements to tackle measurement errors. Meanwhile, the linearization of unknowns in the SSI by OM might lead to the omission of observable unknowns.
This PhD thesis presents a unified SSI method under the framework of OM for 2D structures modelled by beam elements. The method is based on the information (external loads, measured deflections and rotations) obtained during static tests. This work gathers six methodological contributions conceived to (1) extract as much information as possible from measurements to ensure the observability of target parameters; (2) analyze the effect of measurement errors and simulation errors on the estimation results; (3) propose different strategies to use redundant measurements to improve the estimation accuracy; (4) place the sensors in an optimal configuration to obtain robust estimations for the target parameters.
Firstly, the procedure of the SSI by OM is presented and validated by error-free measurements in a beam-like structure. Then the effects of measurement errors and simulation errors on the accuracy of estimation result is analyzed for the minimum measurement sets that ensure the observability of all parameters. The studied factors include single measurement errors, random measurement errors, error levels and loading cases. The influence of the recursive process of SSI by OM is also discussed. To solve the problem of misjudging the minimum measurement sets caused by the linear assumption in the SSI by OM, the SSI by constrained OM is proposed. The nonlinear constraints are reintroduced by optimizations after the completion of the method when necessary. The method is validated by a simply supported beam and a high-rise frame.
Due to the unsatisfactory SSI results from the SSI by OM using minimum sets, three ways of using redundant measurements are proposed. The SSI by compatible OM reduces the incompatibility due to measurement errors by imposing the compatibility conditions in beam-like structures. In the second method, the theoretical advantage of using rotations in SSI is justified by a statistical analysis using the analytical expression of the target parameters and the inverse distribution theory. Then four strategies to use redundant rotations are proposed and compared. The model averaging method using only rotations is proposed. As the SSI by compatible OM and the model averaging method are subjected to the limit of structure type or measurement type, the SSI by Measurement Error-Minimizing OM (MEMOM) is proposed. In this method, the measurement error terms are separated from the coefficient matrix of the observability equations and the estimations are obtained by minimizing the square sum of the ratios between the error terms and the measurements. The performance of the method is investigated with respect to factors including loading cases, parameterization, measurement types and constraint types. The Optimal Sensor Placement problem for static SSI is addressed in this thesis and is formulated as maximizing the determinant of the Fisher Information Matrix (FIM) using genetic algorithm. Meanwhile, the identifiability of the structural parameters is evaluated according to the diagonal elements of the inversed FIM.
