ABSTRACT
The main objective of this chapter is to provide the necessary mathematical background needed in the use of three powerful techniques for solving inverse parameter estimation problems. The following techniques are considered here: Technique I—Levenberg-Marquardt method; Technique II—conjugate gradient method and Technique III—conjugate gradient method with adjoint problem for parameter estimation. It is assumed in this chapter that no prior information is available regarding the values of the unknown parameters before the solution of the inverse problem. If this information is available, either from previous experience or from literature data, it can be taken into account for the solution of the parameter estimation problem, as presented in Chapter 3. This chapter describes the basic steps and presents the solution algorithms for the Levenberg-Marquardt method and for the conjugate gradient method by using a whole time-domain approach. The physical and mathematical significances of sensitivity coefficients are discussed and three different methods for their computation are described. The design of optimum experiments and the estimation of uncertainties related to the estimated parameters are also addressed in this chapter.
