Optimization of Measurements for Inverse Problem

A new method for obtaining the optimal experimental/measurement procedure for general estimation problems is proposed. This approach is based on the framework of the Kalman lter technique. The eigen values of a posteriori estimate error covariance matrix depend on measurement conditions, such as geometries of specimens, structure of experimental sets, locations of measurements and types of measurements. The optimal measurement condition is obtained by minimizing the maximum eigen value of a posteriori estimate error covariance matrix. Candidates of measurement condition are rstly put up, and combinational optimization method is carried out. Some examples are presented to demonstrate that the present method could be utilized e ectively for designing estimation system. INTRODUCTION Inverse Problems can be found in many topics of engineering. Generally speaking, solution of an inverse problem entails determining unknown causes based on observation of their e ects. Many researches have been done to overcome ill-conditioned problems (Trujillo,1997) (Engl,1996) (Hensel,1991). However, not many researches have been done on a guideline how to collect measurement data to relieve illcondition. For example, let's consider an inverse problem of the nondistructive void location detection(see Figure 1). Following questions would be arise. What kind of physical phenomena is the best to apply? (elasto-dynamics, elasto-statics, electricity, thermal transfer, etc.) What kind of physical quantity is the best to meaUltra sonic? Heat and Temp.? Force and Disp.? Electricity? Where is the best location?