Eigenvectors phase correction in inverse modal problem

Abstract

The solution of the inverse modal problem for the spatial parameters of mechanical and structural systems is heavily dependent on the quality of the modal parameters obtained from the experiments. While experimental and environmental noises will always exist during modal testing, the resulting modal parameters are expected to be corrupted with different levels of noise. A novel methodology is presented in this work to mitigate the errors in the eigenvectors when solving the inverse modal problem for the spatial parameters. The phases of the eigenvector component were utilized as design variables within an optimization problem that minimizes the difference between the calculated and experimental transfer functions. The equation of motion in terms of the modal and spatial parameters was used as a constraint in the optimization problem. Constraints that reserve the positive and semi-positive definiteness and the inter-connectivity of the spatial matrices were implemented using semi-definite programming. Numerical examples utilizing noisy eigenvectors with augmented Gaussian white noise of 1%, 5%, and 10% were used to demonstrate the efficacy of the proposed method. The results showed that the proposed method is superior when compared with a known method in the literature.