Damage detection of civil engineering structures needs to consider the effect of normal environmental variations on structural dynamic properties. This study develops a novel structural damage detection method using factor analysis in the sparse Bayesian learning framework. The unknown changing environmental factors that affect the structural dynamic properties are treated as latent variables in the model. The automatic relevance determination prior is adopted for the factor loading matrix for model selection. All variables and parameters, including the factor loading matrix, error vector and latent variables, are solved using the iterative expectation-maximization technique. The variables are then used to reconstruct structural responses. The Euclidean norm of the error vector is calculated as the damage indicator to detect possible damage when limited vibration data are available. Two laboratory-tested examples are utilized to verify the effectiveness of the proposed method. Results demonstrate that the number of underlying environmental factors and structural damage can be accurately identified, even though the changing environmental data are unavailable. The proposed method has the advantages of online monitoring and automatic identification of underlying environmental factors.

土木工程结构的损伤检测需要考虑正常环境变化对结构动力特性的影响。本研究开发了一种在稀疏贝叶斯学习框架中使用因子分析的新型结构损伤检测方法。影响结构动力学特性的未知变化的环境因素在模型中被视为潜在变量。自动相关性确定先验被用作模型选择的因子加载矩阵。所有变量和参数，包括因子加载矩阵，误差向量和潜在变量，都使用迭代期望最大化技术求解。然后将变量用于重构结构响应。计算误差向量的欧几里得范数作为损坏指标，以在有限的振动数据可用时检测可能的损坏。利用两个实验室测试的例子来验证所提出方法的有效性。结果表明，即使没有变化的环境数据，也可以准确识别潜在的环境因素和结构破坏的数量。该方法具有在线监测和自动识别潜在环境因素的优点。即使没有变化的环境数据。该方法具有在线监测和自动识别潜在环境因素的优点。即使没有变化的环境数据。该方法具有在线监测和自动识别潜在环境因素的优点。