A Data-Driven System Identification Method for Random Eigenvalue Problem Using Synchrosqueezed Energy and Phase Portrait Analysis

The primary purpose of this research is to evaluate the uncertainty associated with modal parameter estimation for an inverse dynamic problem in which the structural parameters are random. The random nature of the structure’s parameters will be reflected in the modal features of the respected system. However, this may result in additive/subtractive errors in modal parameter identification, affecting the identification technique’s efficiency. With this in mind, the present study aims to develop an automated modal identification algorithm for a random eigenvalue problem. This is achieved by a recently developed advanced version of the wavelet transform (i.e., synchrosqueezing), which offers better resolution. Using this technique, the measured responses are transformed into a time-frequency plane, which is further processed by unsupervised learning using K-means clustering for quantification of the modal parameters. This automated identification is repeated for an ensemble of measurements to quantify the random eigenvalues in a statistical sense. The proposed methodology is first tested using simulated time histories of a two degree-of-freedom (dof) system. It is followed by an experimental validation using a beam whose mass matrix is random. The numerical results presented in this work clearly demonstrate the performance (i.e., in terms of efficiency and accuracy) of the proposed output-only automated data-driven identification scheme for random eigenvalue problems.