In the classical Stochastic Subspace Identification (SSI) method, mode selection is primarily based on frequency stability, damping stability, and mode shape similarity using the Modal Assurance Criterion (MAC). However, these criteria are often insufficient for reliable modal identification in high-noise environments. This study
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In the classical Stochastic Subspace Identification (SSI) method, mode selection is primarily based on frequency stability, damping stability, and mode shape similarity using the Modal Assurance Criterion (MAC). However, these criteria are often insufficient for reliable modal identification in high-noise environments. This study advances beyond the classical approach by introducing a multi-criteria optimization framework for mode evaluation. In addition to the conventional frequency and damping assessments utilized in the classical SSI method, the proposed approach incorporates a range of supplementary structural metrics. These include Density, Cosine Similarity Difference (CSD), Damping Stability (DS), Spatial Roughness (SR), Mode Shape Complexity (MSC), Signal Energy Coherence (SEC), and Normalized Modal Difference (NMD). These metrics are computed within specifically optimized windows on the stabilization diagram. By integrating spatial, phase, and energy-based characteristics of mode shapes alongside traditional metrics such as the MAC, the method enables a more comprehensive and robust mode selection process that surpasses the limitations of relying solely on frequency and damping stability. Compared to the classical SSI, the optimized window approach provides a significant advantage by enabling the reliable selection of consistent modes by considering the continuity and multi-criteria coherence of modes across window transitions. As a result, the elimination of noise modes and the reliable separation of structural modes are established on a more systematic basis. To achieve this, a two-stage optimization strategy is implemented: the first stage determines the optimal frequency window width and minimum mode count threshold, while the second stage utilizes a Multi-Criteria Decision Making (MCDM) framework based on the Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) algorithm to assign optimized weights to the structural metrics and rank the candidate windows accordingly. As a result, the ideal frequency window is identified based on its TOPSIS score and subsequently validated using the MAC, confirming that the selected window corresponds to reliable structural modes. The framework is validated using long-term in situ measurements from a Roller Compacted Concrete (RCC) dam operating under significant environmental and operational noise. The dataset comprises continuous, high-resolution (200 Hz) vibration recordings collected between 1 July 2023 and 30 October 2024. While the calendar duration is limited to several weeks, the uninterrupted 24 h measurements yield a high-density time-series dataset with substantial information content, enabling a statistically meaningful and robust evaluation of modal identification performance under real-world and noisy conditions. The results reveal that relying solely on traditional selection criteria such as pole density and the MAC can often lead to the identification of spurious modes, particularly in noisy environments. In contrast, the proposed TOPSIS-based multi-criteria decision-making framework incorporates a broader range of structural indicators, balancing frequency, damping, spatial, and energy-related metrics to enhance the consistency and reliability of mode selection. This approach proved effective even under high-noise conditions, successfully distinguishing true structural modes from artificial ones. Application of the TOPSIS method to RCC dam data revealed consistent fundamental frequencies at approximately 5–10 Hz, 10 Hz, and 15 Hz, confirming its robustness and suitability for complex structural monitoring tasks.
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