Missing time series data in a structural health monitoring system remains a problem in some real-time applications, such as the calculation of cable force. To solve this problem, several algorithms have been proposed to impute missing data. However, studies on extracting temporal correlations from different dimensions to improve imputation have rarely been conducted. In this study, a matrix containing correlations between days and within one day is constructed, and an amputation method based on principal component analysis (PCA) is extended to reconstruct the matrix. We extend PCA in the form of probability—that is, probabilistic principal component analysis (PPCA) to avoid overfitting. The performance of the proposed method is systematically evaluated in two different scenarios: random missing data scenario and continuous missing data scenario. The results indicate that fully extracting temporal correlations from measured values can improve the estimation of missing values. PPCA also outperforms PCA in two scenarios, particularly the continuous missing data scenario, suggesting that the probability framework can enhance the accuracy of imputation. Thus, the imputation errors can be markedly improved if temporal correlations from different dimensions are appropriately considered.

在某些实时应用中，例如缆索力的计算，结构健康监控系统中缺少时间序列数据仍然是一个问题。为了解决这个问题，已经提出了几种算法来估算丢失的数据。但是，很少进行从不同维度提取时间相关性以改善归因的研究。在这项研究中，构建了一个包含天与一天之内的相关性的矩阵，并扩展了基于主成分分析（PCA）的截肢方法以重建该矩阵。我们以概率形式（即概率主成分分析（PPCA））扩展PCA，以避免过度拟合。在两种不同的情况下，系统地评估了所提出方法的性能：随机丢失数据场景和连续丢失数据场景。结果表明，从测量值中完全提取时间相关性可以改善对缺失值的估计。PPCA在两种情况下也优于PCA，尤其是连续丢失数据的情况，这表明概率框架可以提高估算的准确性。因此，如果适当考虑来自不同维度的时间相关性，则可以显着改善插补误差。