Spectral optimization-based modal identification: A novel operational modal analysis technique

Abstract

In this work, we introduce a novel method, namely Spectral Optimization-based Modal Identification (SOMI) for estimating the modal parameters of structures. SOMI is developed to estimate highly accurate modal damping ratios and mode shapes using the Frequency Domain Decomposition (FDD) principles. The FDD method (and most of the present modal identification techniques), encounters some problems such as modal complexity, lack of accuracy in the case of large damping ratios, and noticeable error in mode shape estimation. In the FDD formulation, the Singular Value Decomposition (SVD) estimation is precise only for lightly damped structures for obtaining the mode shapes and the Power Spectral Density (PSD) function of the modal coordinates. Moreover, the complexity of the mode shapes obtained from the FDD method is significantly biased and should not be used for physical interpretations. The main idea behind the proposed SOMI method is the elimination of the SVD estimation and obtaining the PSD function of the modal coordinates and the mode shapes with the least approximations. Moreover, the modal damping ratio is directly estimated in the frequency domain without any transformation into time domain using two equations derived in this paper. SOMI method uses optimization to make the PSD function of the modal coordinates follow the theoretical equations and estimates highly accurate mode shapes. In this work, the derivations are given for the displacement, velocity, and acceleration signals. The detailed formulation of the proposed method is presented, it is validated with some examples, and its competitive accuracy is compared with the FDD method. The accuracy and robustness of SOMI in noisy conditions are also assessed, with results indicating its effectiveness in handling noise and maintaining accuracy.