Static structural system identification for beam-like structures using compatibility conditions

Abstract

SummaryDue to the inevitable noise existing in the measured responses, structural system identification is often a challenging task in terms of the accuracy of the estimations. Structural system identification by the observability method, which is characterized by the analysis of null spaces, is a powerful tool to determine the observability of structural parameters. However, it did not cope well with measurement errors so far. In this paper, for the first time, functional relations among displacements, denoted by the term compatibility conditions, in beam-like structures are derived by the observability method. Then, compatibility conditions are imposed in an optimization procedure to minimize the discrepancy between the measured response and the compatible one. The compatible response obtained by the optimization is used to obtain the final estimations of the parameters. In a simply supported bridge example, the proposed method is thoroughly evaluated regarding the number of measurements, error levels, and load cases. In an example of a continuous bridge, different load cases are used to estimate the bending stiffnesses of different zones. The accuracy and the efficacy of the proposed method are verified by the numerical results.

Structural system identification by measurement error‐minimizing observability method

“…The coefficient matrix of the observability equations (Equation ) takes in the measurements together with the errors, which is a perturbation to the accurate matrix. Previous study shows that the least square solution of observability equations is greatly biased even with redundant sets . This section proposes a MEMOM.…”

“…In Section , the performance of the MEMOM and the SSI by OM is compared when essential sets are used. In Section , regarding the same structure, the performance of MEMOM and SSI by compatible OM is compared when redundant sets are used. The considered factors include error levels, number of measurements, and load cases.…”

“… Here, the measurements, , are simulated by adding proportional errors to the theoretical values, δ , that are obtained by direct analysis. E level is the error level in measurement, and ξ is a random number following normal distribution with mean of zero and standard deviation of 0.5, same as in Lei et al…”

“…Hence, redundant sets (essential sets plus redundant measurements) are used to reduce estimation errors. In beam‐like structures, the compatibility conditions (the geometrical relations that the displacements should satisfy) can be obtained symbolically via SSI by compatible OM . These conditions can be used to improve estimation accuracy.…”

“…In Section , the performance of the proposed method is validated in a beam‐like structure. The estimations obtained from essential sets and redundant sets are compared with those obtained by the numerical OM and the compatible OM, respectively. In addition, a table summarizing the characteristics of these methods is provided at the end of this section.…”