Function-weighted frequency response function sensitivity method for analytical model updating

Abstract

Since the frequency response function (FRF) sensitivity method was first proposed [26], it has since become a most powerful and practical method for analytical model updating. Nevertheless, the original formulation of the FRF sensitivity method does suffer the limitation that the initial analytical model to be updated should be reasonably close to the final updated model to be sought, due the assumed mathematical first order approximation implicit to most sensitivity based methods. Convergence to correct model is not guaranteed when large modelling errors exist and blind application often leads to optimal solutions which are truly sought. This paper seeks to examine all the important numerical characteristics of the original FRF sensitivity method including frequency data selection, numerical balance and convergence performance. To further improve the applicability of the method to cases of large modelling errors, a new novel function-weighted sensitivity method is developed. The new method has shown much superior performance on convergence even in the presence of large modelling errors. Extensive numerical case studies based on a mass-spring system and a GARTEUR structure have been conducted and very encouraging results have been achieved. Effect of measurement noise has been examined and the method works reasonably well in the presence of measurement uncertainties. The new method removes the restriction of modelling error magnitude being of second order in Euclidean norm as compared with that of system matrices, thereby making it a truly general method applicable to most practical model updating problems.