Abstract: In general, operational environment changes will result in corresponding changes of structural dynamic characteristics, which thereby masks changes caused by damages. In practical engineering, it is crucial to eliminate the influence of changing operational environments for structural damage identification. At present, principal-component analysis is frequently employed to achieve this purpose. However, only when data is approximately Gaussian distributed and linearly correlated, traditional principal-component analysis is very effective. When there are non-Gaussian distribution and nonlinear correlation in the data, the effect is poor. Therefore, a structural damage identification method based on mixed principal-component analysis was proposed. At first, Gaussian mixed model was applied to fit the joint probability density function of multi-dimensional (non-Gaussian distributed and nonlinearly correlated) data, resulting in a linear combination of multiple local Gaussian components. Next, corresponding principal-component analysis models were established respectively for all Gaussian components. Finally, the Mahalanobis square distance and Euclidean square distance were calculated respectively for the residuals of all principal component analysis models, which were weighted and standardized as the comprehensive damage index of the structure. The mass-spring system simulation data and the wood truss bridge test data were used to verify the proposed method. The results show that the proposed method can effectively deal with non-Gaussian distribution and nonlinear correlation among damage characteristic data, and thus eliminate the influence of changing operational environments to significantly improve the ability of structural damage identification.

Key words: bridge engineering; structural damage identification; operational environment changes; non-Gaussian distribution; nonlinear correlation; mixed principal-component analysis

摘要： 运营环境变化通常会引起结构动力特性随之变化，进而掩盖损伤引起的变化。在工程实际中，剔除运营环境变化的影响对结构损伤识别至关重要，当前较多采用主成分分析实现该目的。然而，传统的主成分分析仅当数据近似满足高斯分布且线性相关时非常有效，当数据中存在非高斯分布和非线性相关等情形时则效果较差。为此，提出一种基于混合主成分分析的结构损伤识别方法，首先，利用高斯混合模型将多维(非高斯分布且非线性相关)数据的联合概率密度函数拟合为多个局部高斯分量的线性组合；其次，对所有高斯分量分别建立相应的主成分分析模型；最后，对所有主成分分析模型的残差部分分别计算马氏平方距离和欧氏平方距离，经加权标准化后作为结构的综合损伤指标。采用质量弹簧系统仿真数据和木桁架桥试验数据对所提方法进行验证，结果表明：该方法可有效处理损伤特征数据中的非高斯分布和非线性相关等问题，从而剔除运营环境变化的影响以显著提升结构损伤识别的能力。

关键词: 桥梁工程；结构损伤识别；运营环境变化；非高斯分布；非线性相关；混合主成分分析