ABSTRACT
Inverse problems can be found in many areas of engineering mechanics (Tanaka and Bui, 1992; Bui, 1994; Zabaras et al., 1993; Friswell and Mottershead, 1996; Trujillo and Busby, 1997; Tanaka and Dulikravich, 1998; Friswell et al., 1999; Tanaka and Dulikravich, 2000). A successful solution of the inverse problems covers damage detection (Ge and Soong, 1998), model updating (Fregolent et al., 1996; Ahmadian et al., 1998), load identification (Lee and Park, 1995), image or signal reconstruction (Mammone, 1992) and inverse heat conduction problems (Trujillo and Busby, 1997). Generally, the inverse problem is concerned with the determination of the input and the characteristics of a system given certain information on its output. Mathematically, such problems are ill-posed and have to be overcome through the development of new computational schemes, regularization techniques, objective functions and experimental procedures. This chapter gives a brief description of the basic knowledge of ill-conditionedmatri-
ces. Discussions on the Singular Value Decomposition (SVD) and the discrete Picard condition give insight into the discrete ill-posed problem. Section 2.4 gives three optimization algorithms for the solution of the inverse problem. Section 2.5 describes some of the techniques to obtain a regularized solution. Finally, criteria for convergence of the solution are discussed in Section 2.7. Information in this chapter forms the basis for understanding the solution process
of system identification in the following chapters, apart from Chapter three that deals with damage models of a structure.
