Modal parameter identification of radial gate vibrations under discharge excitation based on an improved potential-based hierarchical agglomerative clustering algorithm

The vibration of radial gates under partial-opening flood-discharge conditions is directly linked to the operational safety of hydraulic structures, making reliable modal parameter identification under discharge-induced excitation essential for risk assessment and control. This study aims to develop a robust, noise-resilient, and largely automated operational modal analysis (OMA) workflow tailored to complex flow-induced environments. To this end, we propose an improved potential-based hierarchical agglomerative (IPHA) clustering method integrated into a covariance-driven stochastic subspace identification (COV-SSI) framework. The methodological objective is to suppress spurious poles arising from background turbulence and excessive model orders, while reliably recovering natural frequencies, damping ratios, and representative mode shapes from field measurements without relying on fragile, user-defined thresholds. Methodologically, the workflow proceeds in three stages. First, dense stabilization diagrams are generated over a broad range of model orders using COV-SSI, ensuring that physical modes are represented even when the true order is unknown or deliberately overestimated. Second, IPHA clusters candidate poles in a joint feature space that combines frequency consistency and mode-shape similarity (via MAC-type measures), thereby consolidating pseudo-stable axes and scattered numerical artifacts into compact, physically meaningful clusters. This clustering eliminates ad hoc distance cutoffs and minimizes manual intervention, improving identification repeatability. Third, the pipeline is validated progressively: (i) a six-degree-of-freedom (6-DOF) shear model with proportional damping is used to verify accuracy and noise robustness; (ii) a multi-DOF finite-element (FE) model of the gate supporting arms is employed to examine the feasibility of replacing ideal white-noise excitation with realistic flow-induced fluctuating loads; and (iii) two fluid–structure interaction (FSI) models—an added-mass formulation and a direct-coupling formulation—are developed to interpret prototype vibration measurements of a partially opened gate. The results show that, on the 6-DOF benchmark, the IPHA-based COV-SSI consistently suppresses spurious poles caused by strong measurement noise and excessive system orders, yielding stable estimates of frequencies and damping ratios across repeated runs. In the FE study, when the structure is subjected to fluctuating hydrodynamic pressure representative of discharge conditions (rather than ideal white noise), the identified modal parameters closely match FE reference values in the low- to mid-frequency band most relevant to safety assessment. This confirms that the turbulence-induced pressure acting on the gate panels can be approximated as band-limited white noise and provides sufficient broadband energy to excite global structural modes without artificial excitation devices. In the prototype application, the two FSI approaches exhibit distinct characteristics. The added-mass method requires iterative calibration of a reduction factor ξ to reconcile simulations with measurements, and ξ varies with opening and flow conditions, which limits its applicability across operating states. By contrast, the direct-coupling model captures the bidirectional gate–water interaction at the wetted interface and reproduces measured dynamics without ad hoc adjustments, providing a more reliable physical interpretation of the identified modes. Quantitatively, comparison between the identified modal parameters and simulation results indicates that, aside from a few higher-order modes with localized participation or limited sensor observability, frequency identification errors are generally within 10%. Mode-shape agreement is satisfactory for the dominant global modes, supporting the consistency between the operationally identified “wet” modes and their numerically predicted counterparts. Taken together, these findings verify the accuracy and robustness of the proposed IPHA-based COV-SSI method under realistic discharge conditions and demonstrate its capability to deliver stable, interpretable results from noise-contaminated field data. In conclusion, the study contributes (i) an automated, parameter-efficient clustering strategy that enhances the reliability of COV-SSI stabilization diagrams; (ii) evidence that flow-induced fluctuating pressure can serve as a substitute for white-noise excitation within the target frequency band, enabling practical in-situ OMA; and (iii) guidance that direct fluid–structure coupling is preferable when accurate representation of gate–water interaction is required, whereas added-mass models should be applied with caution due to their dependence on empirically calibrated reduction factors. The proposed workflow provides a theoretical and technical foundation for reliable modal identification of radial gates under discharge excitation, supporting safety assessment, vibration mitigation design, and risk-informed operation of hydraulic structures.