There has been increased interest in missing sensor data imputation, which is ubiquitous in the field of structural health monitoring (SHM) due to discontinuous sensing caused by sensor malfunction. To address this fundamental issue, this paper presents an incremental Bayesian tensor learning method for reconstruction of spatiotemporal missing data in SHM and forecasting of structural response. In particular, a spatiotemporal tensor is first constructed followed by Bayesian tensor factorization that extracts latent features for missing data imputation. To enable structural response forecasting based on incomplete sensing data, the tensor decomposition is further integrated with vector autoregression in an incremental learning scheme. The performance of the proposed approach is validated on continuous field-sensing data (including strain and temperature records) of a concrete bridge, based on the assumption that strain time histories are highly correlated to temperature recordings. The results indicate that the proposed probabilistic tensor learning approach is accurate and robust even in the presence of large rates of random missing, structured missing and their combination. The effect of rank selection on the imputation and prediction performance is also investigated. The results show that a better estimation accuracy can be achieved with a higher rank for random missing whereas a lower rank for structured missing.

中文翻译：

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用于结构监测数据插补和响应预测的增量贝叶斯张量学习

人们对缺失传感器数据插补的兴趣越来越大，由于传感器故障引起的不连续传感，这在结构健康监测 (SHM) 领域无处不在。为了解决这个基本问题，本文提出了一种增量贝叶斯张量学习方法，用于重建 SHM 中的时空缺失数据和预测结构响应。特别是，首先构建时空张量，然后是贝叶斯张量分解，提取潜在特征以进行缺失数据插补。为了实现基于不完整传感数据的结构响应预测，张量分解进一步与矢量自回归集成在增量学习方案中。基于应变时间历程与温度记录高度相关的假设，所提出方法的性能在混凝土桥梁的连续现场传感数据（包括应变和温度记录）上得到验证。结果表明，即使在存在大量随机缺失、结构化缺失及其组合的情况下，所提出的概率张量学习方法也是准确且稳健的。还研究了秩选择对插补和预测性能的影响。结果表明，较高的随机缺失秩和较低的结构化缺失秩可以获得更好的估计精度。结果表明，即使在存在大量随机缺失、结构化缺失及其组合的情况下，所提出的概率张量学习方法也是准确且稳健的。还研究了秩选择对插补和预测性能的影响。结果表明，较高的随机缺失秩和较低的结构化缺失秩可以获得更好的估计精度。结果表明，即使在存在大量随机缺失、结构化缺失及其组合的情况下，所提出的概率张量学习方法也是准确且稳健的。还研究了秩选择对插补和预测性能的影响。结果表明，较高的随机缺失秩和较低的结构化缺失秩可以获得更好的估计精度。