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

Abstract 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.

[1]  Jean-Louis Guyader,et al.  Reconstruction of a distributed force applied on a thin cylindrical shell by an inverse method and spatial filtering , 2007 .

[2]  Chaodong Zhang,et al.  A hybrid method coupling empirical mode decomposition and a long short-term memory network to predict missing measured signal data of SHM systems , 2020 .

[3]  Hui Li,et al.  The State of the Art of Data Science and Engineering in Structural Health Monitoring , 2019, Engineering.

[4]  Gang Liu,et al.  Damage assessment with state–space embedding strategy and singular value decomposition under stochastic excitation , 2014 .

[5]  Bin Ran,et al.  Robust and flexible strategy for missing data imputation in intelligent transportation system , 2017 .

[6]  Luis Eduardo Mujica,et al.  Damage classification in structural health monitoring using principal component analysis and self‐organizing maps , 2013 .

[7]  James H. Garrett,et al.  Exploration and evaluation of AR, MPCA and KL anomaly detection techniques to embankment dam piezometer data , 2015, Adv. Eng. Informatics.

[8]  Jingjing He,et al.  Structural response reconstruction based on empirical mode decomposition in time domain , 2012 .

[9]  Yuequan Bao,et al.  Analyzing and modeling inter-sensor relationships for strain monitoring data and missing data imputation: a copula and functional data-analytic approach , 2018, Structural Health Monitoring.

[10]  Junjie Li,et al.  Prediction of long-term temperature effect in structural health monitoring of concrete dams using support vector machines with Jaya optimizer and salp swarm algorithms , 2019, Adv. Eng. Softw..

[11]  Kay Smarsly,et al.  Decentralized fault detection and isolation in wireless structural health monitoring systems using analytical redundancy , 2014, Adv. Eng. Softw..

[12]  Paul Geladi,et al.  Principal Component Analysis , 1987, Comprehensive Chemometrics.

[13]  Luis Eduardo Mujica,et al.  A study of two unsupervised data driven statistical methodologies for detecting and classifying damages in structural health monitoring , 2013 .

[14]  Yang Shen,et al.  A new distributed time series evolution prediction model for dam deformation based on constituent elements , 2019, Adv. Eng. Informatics.

[15]  Tapani Raiko,et al.  Tkk Reports in Information and Computer Science Practical Approaches to Principal Component Analysis in the Presence of Missing Values Tkk Reports in Information and Computer Science Practical Approaches to Principal Component Analysis in the Presence of Missing Values , 2022 .

[16]  Feng Zhu,et al.  A novel principal components analysis (PCA) method for energy absorbing structural design enhanced by data mining , 2019, Adv. Eng. Softw..

[17]  Ian F. C. Smith,et al.  Model-free data interpretation for continuous monitoring of complex structures , 2008, Adv. Eng. Informatics.

[18]  Ho-Kyung Kim,et al.  Reconstruction of dynamic displacement and velocity from measured accelerations using the variational statement of an inverse problem , 2010 .

[19]  Yi-Qing Ni,et al.  Experimental investigation of seismic damage identification using PCA-compressed frequency response functions and neural networks , 2006 .

[20]  Yi-Qing Ni,et al.  Bayesian multi-task learning methodology for reconstruction of structural health monitoring data , 2018, Structural Health Monitoring.

[21]  Luis Eduardo Mujica,et al.  Q-statistic and T2-statistic PCA-based measures for damage assessment in structures , 2011 .

[22]  Yuequan Bao,et al.  A novel distribution regression approach for data loss compensation in structural health monitoring , 2018 .