This study focuses on vibration-based damage detection for a structure that has nonlinear behavior even in the undamaged state. Based on the vibration responses of a single sensor, a non-Gaussian multivariate probability density function (PDF) is developed and used as a feature. The change between the PDF of the undamaged state and that of a potentially damaged state is used to indicate the damage. Since what of interest is the change of the PDF, instead of estimating the two PDFs separately, the ratio of them is estimated directly using a density ratio estimation method. In addition, principal component analysis is applied to reduce the dimensionality of the PDFs. The effectiveness and advantages of the proposed method are demonstrated in two case studies: an experimental nonlinear beam and simulations of an offshore wind turbine subjected to nonlinear pile-soil interaction. Compared with a second-order statistical method, the proposed method shows better damage detection performance due to the integration of higher order statistical information.

中文翻译：

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使用概率密度比估计的非线性结构损伤检测

本研究的重点是针对即使在未损坏状态下也具有非线性行为的结构的基于振动的损伤检测。基于单个传感器的振动响应，非高斯多元概率密度函数 (PDF) 被开发并用作特征。未损坏状态的 PDF 与潜在损坏状态的 PDF 之间的变化用于指示损坏。由于感兴趣的是PDF的变化，而不是单独估计两个PDF，而是直接使用密度比估计方法估计它们的比率。此外，应用主成分分析来降低 PDF 的维数。在两个案例研究中证明了所提出方法的有效性和优势：实验非线性梁和海上风力涡轮机受到非线性桩土相互作用的模拟。与二阶统计方法相比，由于融合了高阶统计信息，该方法显示出更好的损伤检测性能。