On the use of regularisation techniques for finite element model updating

The first Dart of this paper is a review of existing regularisation techniq ues with emphasis on the updating of finite element models for structural d ynamics. Tikhonov regularisation, truncated singular value decomposition, t otal least-squares method and maximum entropy method are examined in some d etail for their applicability to a set of noise-polluted linear equations a rising from the use of measured vibration test data. Several comparative st udies were conducted for three simulated examples: a 10-DOF mass-spring sys tem, a 3D frame and a plate structure. A frequency response function based updating technique, that yields an over-determined set of equations by sele cting data from a number of frequency points, was used throughout the numer ical investigation. For most methods, the correct choice of the controlling regularisation parameter, such as the SVD truncation level, was found to b e of primary importance for improving the quality of the solution. Possible parameter selection strategies were identified and discussed in some detai l. The total least-squares method was observed to be particularly useful fo r dealing with noise and its accuracy was seen to increase with the increas ing number of measurements. Using an L-curve technique, the determination o f an optimum regularisation parameter was relatively straightforward for th e maximum entropy method. However, the method was also found to be computat ionally very expensive. For all three cases considered, the improvement in the solution accuracy did not appear to warrant the additional computationa l effort required.