Missing data estimation method for time series data in structure health monitoring systems by probability principal component analysis

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.