The Inverse Finite Element Method: Sensitivity to Measurement Setup
In the inverse finite element method (iFEM), given a finite element model of a structure and imperfect displacement measurements, the external loads acting on the structure can be assessed. The basic idea behind iFEM is the optimization of a quadratic cost function of the difference between the measured and estimated values, with a high cost corresponding to a high precision of the measurements. In the present research it is firstly shown how the iFEM theory was broadened to accommodate for strain measurements through the construction of cost matrices to express the cost associated with the estimation of the response. The main focus of the research falls however on the influence that the measurement set-up has on the quality of the iFEM estimates. Only a limited number of measurements may be available, therefore it is essential to plan the measurement set-up carefully to obtain the highest quality of estimates. The number of measurements and the precision required to obtain a realistic result from an iFEM analysis is also a factor which plays a role and varies for different types of measurements. A numerical method for systematic sensitivity study of the measurements set-up without involving the actual measurement data, is presented. Two examples consisting of structures with both displacement measurements and strain measurements being taken, are presented. It illustrates how the sensitivity study method can be used to plan a more effective measurement set-up.