ABSTRACT
Dynamic problems can be broadly categorized into the direct problem and the inverse problem. The inverse dynamic problem is one in which measurements are made on some of the state variables of the system to facilitate the solution on the unknown parameters (Trujillo and Busby, 1997). It is, essentially, the solution of an optimization problem. In the problem addressed by this book, a function representing the input is sought such that the discrepancy between the measured and calculated response is minimized. Various solution methods associated with the indirect force measurement have been proposed, e.g. dynamic programming (Busby and Trujillo, 1997; Law and Fang, 2001; Nordstrom, 2006; Law et al., 2007), regularization technique (Zhu and Law, 2002b; Nordberg and Gustafsson, 2006a; Zhu et al., 2006, and etc.). The moving load identification from measured responses is a typical inverse prob-
lem. Chapters 5 and 6 have shown that the moving forces can be identified in the time domain and the frequency and time domains. The regularization technique can enhance the accuracy of the solution in the inverse problem. In this chapter, two state space approaches are presented in Sections 7.2.1 and 7.3.1 with formulations of the equation of motion of the time-varying dynamic system. The time-varying system and moving loads are represented by Markov parameters. The first method described in Section 7.2.4 is a non-iterative recurrence algorithm for the moving force identification in time domain. Section 7.3.2 presents the secondmethod ofmoving load identification in state spacewith regularization. The different influencing factors, such as, the combination of strain and velocity measurements, the number of analytical modes included in the identification, the effect of load eccentricity and the choice of regularization parameters are studied in Sections 7.2.5 and 7.3.3. The effect of different regularization parameters on the identified loads is also studied and discussed. Experimental results from laboratory tests will be further used to support the above studies in Sections 7.2.6 and 7.3.4.
