Cross‐Entropy of Power Spectral Density Function: A Modal Identification Framework

The power spectral density (PSD) function of measured structural response contains a significant amount of information, including the modal parameters (natural frequencies, damping ratios). Output‐only system identification or modal identification technique can be used for extracting such modal parameters from the measured response or its spectrum in the time or frequency domain, respectively. Akin to estimating the statistical parameters (mean, variance, etc.) from a probability density function (PDF), a parallel approach is introduced to extract modal parameters from the spectral description. This framework is based on a conceptual paradigm shift that views the PSD as a PDF. This perspective allows for the direct application of powerful statistical estimation techniques, like cross‐entropy (CE), to the modal identification problem. The proposed technique offers estimates of the mode shapes and concurrently extracts the natural frequency and damping ratio from the modal response decomposed by the mode shape. Furthermore, if the external load can be modeled in a PSD function format, the load model can be integrated into the proposed modal identification framework, allowing its parameters to be identified as well. The performance and efficacy of the proposed method are validated through numerical simulations and application to the measured response of a full‐scale building. Results show that the proposed CE‐based modal identification framework provides effective and reliable estimates of modal parameters for both classically and non‐classically damped systems, offering a powerful new approach to output‐only modal analysis.