Combination of Various Weighting Functions to Improve Modal Curve Fitting for Actual Mechanical Systems

Abstract

Modal curve fitting methods on frequency domain are based on the least square method to estimate the modal parameters from frequency response functions (FRFs in brief) of test structures. In order to minimize the least square errors between experimental and estimated FRFs, several kinds of weighting functions were proposed and widely applied in practical use. However, using the same weighting function in modal curve fitting for a set FRFs of test structure often makes the results of the FRFs of some measurement points be fitted with good accuracy but other ones be not. In this paper, the authors propose the combination use of various kinds of weighting functions in least square process of modal curve fitting methods to deal with the measurement data of actual and complex mechanical systems. This method automatically selects and applies the most appropriate weighting function to the FRF of each measurement point by comparing the minimum total relative mean square error (RMSE). The case study shows that the proposed idea allows the modal curve fitting method puts better curve fitting results out so that more accurate mathematical model will be obtained.