ABSTRACT
The dynamic behavior of a continuous beam and an orthotropic plate under moving loads has been analyzed in Chapter 2. This chapter is on the development of the moving force identification method in time domain on these structures without knowledge of the load characteristics. Law et al. (1997) modeled the moving loads on a simply supported Euler beam as step functions in a small time interval. Based on system identification theory and modal superposition, the moving forces are identified by using the least-squares method in time domain. Chan, Yu and Law (2000) compared this method with other moving load identification methods using laboratory results and they found that this method has the best performances except for the computation time. However, the identified results are noise sensitive and exhibit fluctuations at the beginning and the end of the time histories. These moments correspond to the switching of free vibration state of the structure to the forced vibration state, and vice versa, and the solutions are ill-conditioned. Law et al. (2001) introduced the regularization technique in the ill-posed problem to provide bounds to the identified forces. The results obtained are greatly improved over those without regularization with acceptable errors from using different combinations of measured responses. Another time domain method (Zhu and Law, 2002b) was developed to give exact
solution to the forces with improved formulation over existing methods for a more efficient computation. Least-Squares solution technique is applied to the Time Domain Method, while Tikhonov regularization procedure is applied to the Exact Solution Technique Method (EST) to provide bounds to the solution in time domain. The latter method also features an improved formulation with the large matrices in TDM breaking up into smaller matrices in the solution, leading to enhanced computation efficiency. The continuous beammodel and the orthotropic plate model are used in the identification. Numerical examples are used to demonstrate the feasibility and accuracy of the method, and factors affecting the errors in the identification are discussed. Laboratory results are also reported to verify the effectiveness and validity of the proposed method. Finally a comparison on the computation accuracy of the FTDM, TDM and EST method is presented in Section 6.3.3.
