Operational modal analysis (OMA) is a widely recognized methodology initially developed for extracting modal parameters of large civil structures. Its mathematical formulation, however, has proven to be not only effective for such structures, but also a powerful asset for the health monitoring of operating equipment and its adjacent structures. Currently, the overall objective is to expand and enhance identification algorithms capable of fast, robust, and automatic identification of modal indicators and condition diagnosis by combining different techniques in the time-domain analysis of vibration signals from machines and structures under operation. Nevertheless, equipment with complex dynamics such as rotating machinery supported by flexible structures still presents several complications that make automatic extraction of modal parameters a rather challenging task. This study proposes an automatic identification algorithm for the extraction of structural modes of a rotating machine foundation structure system in various operating conditions, such as ramp-ups (accelerating shaft), which is a challenging transient excitation scenario. The algorithm combines OMA and hierarchical clustering with k-means to automatically identify stable modes. Additionally, structural modifications representing the presence of damage are addressed, and the sensitivity of the proposed technique is evaluated. The foundation structure modes are also determined with experimental modal analysis (EMA) of impact-excitation data to validate the results. The study demonstrates the reliability of the technique and offers an improvement on structural health monitoring methodologies.