ABSTRACT
Loads are traditionally measured statically with strain-based or other types of sensors. The technique of indirect load determination is of special interest when the applied loads cannot be measured directly, while the responses can be measured easily (Busby and Trujillo, 1987; Doyle, 1987b; Yen and Wu, 1995; Choi and Chang, 1996; Cao et al., 1998; Kammer, 1998; Moller, 1999; Rao et al., 1999; Liu et al., 2000). It is an ill-posed problem because the response is typically a continuous vector function in the spatial coordinates, and it is only defined at a few points of the structure. Therefore, solutions to the problem are frequently found to be unstable in the sense that small changes in the responses would result in large changes in the calculated load magnitudes. Existing methods, described in Chapter 1, are mainly for the identification of stationary (non-moving) loads. These methods can be classified into time domain method, frequency domain method, state space method, orthogonal function expansion method and neural network method. The Frequency and Time Domains Approach (FTDM) (Law et al., 1999) performs
Fourier transformation on the equations of motions, which are expressed in modal coordinates. The Fourier transforms of the responses and the forces are related in the frequency domain, and the time histories of the forces are found directly by the leastsquares method. Results obtained from this method are noise sensitive and they exhibit fluctuations at the beginning and 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. Later Law et al. (2001) introduces a regularization method in the ill-conditioned problem to provide bounds to the identified forces. The FTDM is introduced in this chapter and the results are compared with those by the Time Domain Method presented in Section 5.4.3.
