Damage detection and localization in tower structures using strain fractional-order statistical moments and linear programming models

Vibration-based damage identification methods have been widely applied in structural health monitoring. However, the complex geometry and multiple components of tower structures often reduce the accuracy and efficiency of damage localization. To address this issue, this study presents a novel damage detection and localization approach for tower structures based on the theory of strain fractional-order statistical moments ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mrow> <mml:msub> <mml:mrow> <mml:mi>S</mml:mi> </mml:mrow> <mml:mrow> <mml:mi mathvariant="normal">FSM</mml:mi> </mml:mrow> </mml:msub> </mml:mrow> </mml:math> ). The main contribution lies in the novel introduction of the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mrow> <mml:msub> <mml:mrow> <mml:mi>S</mml:mi> </mml:mrow> <mml:mrow> <mml:mi mathvariant="normal">FSM</mml:mi> </mml:mrow> </mml:msub> </mml:mrow> </mml:math> theory and the development of a linear programming model for sensor optimization. By leveraging the high sensitivity of strain responses to localized damage, the study proposes the change rate of strain fractional-order statistical moments ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mrow> <mml:msub> <mml:mrow> <mml:mi mathvariant="normal">CRS</mml:mi> </mml:mrow> <mml:mrow> <mml:mi mathvariant="normal">FSM</mml:mi> </mml:mrow> </mml:msub> </mml:mrow> </mml:math> ) as a reliable and sensitive damage index. A positive correlation between the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mrow> <mml:msub> <mml:mrow> <mml:mi>S</mml:mi> </mml:mrow> <mml:mrow> <mml:mi mathvariant="normal">FSM</mml:mi> </mml:mrow> </mml:msub> </mml:mrow> </mml:math> index and modal strain energy is demonstrated, and a linear programming-based sensor optimization model is introduced to reduce sensor requirements, divide detection regions, and improve localization accuracy. The proposed method is validated through numerical simulations and field experiments on a representative tower structure. The results show that the method enables accurate identification and localization of multiple damage sites under various excitation conditions and noise levels, while requiring fewer sensors than comparative methods.