Baseline-free damage localization of wind turbine towers using optimal fractional-order curvature ratio curve: A two-step validation approach

Wind turbine towers play a vital role in supporting turbines and ensuring the stability and efficiency of power generation. However, long-term exposure to complex environmental and operational loads makes them vulnerable to local stiffness degradation. This study proposes a baseline-free damage localization method based on an optimal fractional-order curvature ratio curve (OFCRC), which enables the identification of damage locations using a single measurement without requiring reference data from the intact state. In the first stage, the OFCRC is derived and employed as a sensitive curvature-based indicator to detect abrupt stiffness variations, enabling rapid and accurate localization of potential damage. The OFCRC is constructed directly from the ratios of relative displacement statistical moments between adjacent measuring points, without solving any eigenvalue problem or extracting mode shapes, and thus constitutes a fully self-contained baseline-free localization indicator. In the second stage, to verify and quantify the detected damage, the identified mode shapes—obtained through the team’s existing optimal fractional statistical moment (FSM) approach—are incorporated into an improved direct stiffness method (IDSM) for evaluating the extent of stiffness loss. Numerical simulations, scaled-model tower experiments, and field measurements of a 2-MW wind turbine tower validate the method’s effectiveness. The proposed OFCRC method represents the novel contribution of this study, enabling rapid and baseline-free localization, while the subsequent integration with established FSM–IDSM methods provides a complete two-step framework for both localization and quantification. The proposed approach provides a robust, baseline-free, and single-measurement solution for the rapid structural health screening of wind turbine tower groups.