Inverse Analysis

Techniques and applications of inverse and identification problems are presented in this chapter. A general-purpose formulation of the inverse problem, based on system identification techniques and least-squares fitting of parameterized models to experimental data, is presented in detail, since this is the most general approach available today. Nevertheless, one must underline here that no general method is available for the solution of all problems of practical interest. The reasons for this, as it will be discussed in more detail later in several parts of this text, is that inverse problems lead to difficult optimization problems (ill-posed) whose solution is not always straightforward with current numerical optimization techniques. Therefore, one should consider semiempirical methods and experimental testing techniques as well. All these methods are, usually, of restricted applicability and are related to one specific application. The compensation for this is that a large amount of experience is incorporated in these methods, so that their results are, within the limits of their applicability, superior to the ones provided by the general-purpose, optimization-based method. To be fair one should add here that empirical methods are restricted to the identification of a significant change in the system's response and, in some cases, try to estimate the extent of the existing damage. Alternatively, the general error minimization technique is, in principle, able both to detect the existence of a defect and estimate its nature and extent.Here the error-minimization-based approach to inverse analysis is called model calibration technique, while all other methods are collectively characterized as diagnostic identification. The second section of this chapter is devoted to a brief description of both methods together with their areas of applicability. The solution of inverse problems is based on classical optimization techniques and more recent data processing techniques like the ones studied in the area of soft computing. Therefore, the third section is devoted to a brief presentation of the relevant techniques. Various applications from material and structural identification are presented in more detail in the last section of this chapter.