Vertical and Horizontal Combined Algorithm for Missing Data Imputation in Bridge Health Monitoring System
Publication: Journal of Bridge Engineering
Volume 28, Issue 6
Abstract
Structural health monitoring (SHM) provides strong support for bridge safety evaluation by tracking the real-time structural performance. An accurate and efficient imputation method for missing data in the SHM system is of vital importance for bridge management. In this paper, an innovative vertical–horizontal combined (VHC) algorithm is proposed to estimate the missing SHM data by a more comprehensive consideration of different types of information reflected in different time dimensions of the monitoring data. In the vertical time dimension, the variation trends and changing ranges for the missing data are analyzed by the relational analysis from the global view of data. In the horizontal time dimension, the exact value of the missing data is estimated based on the adjacent data inside the missing data set from the local view of data. The proposed VHC algorithm is validated and compared with the current methods in the data imputation for the missing deflection values in the SHM system of an example tie-arch bridge. The results show that the proposed algorithm demonstrates the best imputation performance among all methods for both missing types with the highest imputation accuracy/similarity and satisfying the 95% confidence bound. The application of reward coefficient significantly increases the imputation accuracy for the continuous missing situation and the improvement grows with the missing step number. Loss ratio and sample size also have significant influences on the imputation performance with the proposed method.
Practical Applications
Data missing in the structural health monitoring (SHM) system affects the continuity of monitoring data and the structural conditions reflected by them. This paper proposed an innovative data imputation algorithm combining information from both vertical and horizontal time dimensions of the monitored data in the bridge SHM system. The proposed vertical–horizontal combined (VHC) algorithm shows better imputation performance when compared with the current methods widely used in engineering practice and shows a higher applicability in a small sample size situation. Thus the proposed algorithm provides an accurate and efficient tool for dealing with the data missing phenomenon in the SHM system and is of great importance to the safety evaluation and further management decision process for bridge structure. Moreover, the methodologies and approaches proposed in this paper are quite general and can be applied to the missing data imputation problems in many research fields with time series data.
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Acknowledgments
The research work was supported in part by the National Nature Science Foundation of China (Grant Nos. 52278226 and 51908503). Opinions and findings presented are those of the authors and do not necessarily reflect the views of the sponsors.
References
Al-khateeb, H. T. 2016. Bridge evaluation utilizing structural health monitoring data. Newark, DE: Univ. of Delaware.
Babazadeh, R. 2017. “A hybrid ARIMA-ANN approach for optimum estimation and forecasting of gasoline consumption.” RAIRO-Oper. Res. 51 (3): 719–728. https://doi.org/10.1051/ro/2016059.
Bao, Y., Z. Tang, H. Li, and Y. Zhang. 2019. “Computer vision and deep learning-based data anomaly detection method for structural health monitoring.” Struct. Health Monit. 18 (2019): 401–421. https://doi.org/10.1177/1475921718757405.
Dan, L., J. Deogun, W. Spaulding, and B. Shuart. 2004. “Towards missing data imputation: A study of fuzzy k-means clustering method.” Rough Sets Curr. Trends Comput. 3066: 573–579. https://doi.org/10.1007/978-3-540-25929-9-70.
Dan, L., G. Hong, and L. Zhang. 2013. “A hybrid genetic algorithm-fuzzy c-means approach for incomplete data clustering based on nearest-neighbor intervals.” Soft Comput. 17 (10): 1787–1796. https://doi.org/10.1007/s00500-013-0997-7.
Dharmalingam, M., and R. Amalraj. 2014. “Back-propagation neural network architecture for solving the double dummy bridge problem in contract bridge.” Int. Conf. Intell. Comput. Appl. 2014: 454–461. https://doi.org/10.1109/ICICA.2014.99.
Fan, G., J. Li, and H. Hao. 2019. “Lost data recovery for structural health monitoring based on convolutional neural networks.” Struct. Control Health Monit. 26 (10): e2433. https://doi.org/10.1002/stc.2433.
Fathalla, E., Y. Tanaka, and K. Maekawa. 2018. “Remaining fatigue life assessment of in-service road bridge decks based upon artificial neural networks.” Eng. Struct. 171 (15): 602–616. https://doi.org/10.1016/j.engstruct.2018.05.122.
Hong, Y., Y. H. Zhang, L. Zhang, and T. Xu. 2017. “Research on floating car speed short-time prediction with wavelet–ARIMA under data missing.” Green Intell. Transp. Syst. 503: 289–298. https://doi.org/10.1007/978-981-13-0302-9_29.
Hu, S. R., W. M. Chen, and P. Zhang. 2009. “Correlation analysis for multiple sensors of bridge structural health monitoring systems.” [In Chinese.] China Civ. Eng. J. 42 (3): 81–86. https://doi.org/10.3321/j.issn:1000-131X.2009.03.014.
Huang, J., and H. Sun. 2016. “Grey relational analysis based k nearest neighbor missing data imputation for software quality datasets.” In Proc., IEEE Int. Conf. on Software Quality, Reliability and Security, 86–91. New York: IEEE.
Irawan, N. D., W. Wijono, and O. Setyawati. 2017. “Perbaikan missing value menggunakan pendekatan korelasi pada metode k-nearest neighbor.” Jurnal Infotel 9 (3): 305–311. https://doi.org/10.20895/infotel.v9i3.286.
Kuo, Y., T. Yang, and W. G. Huang. 2008. “The use of grey relational analysis in solving multiple attribute decision-making problems.” Comput. Ind. Eng. 55 (1): 80–93. https://doi.org/10.1016/j.cie.2007.12.002.
Lin, Q., and C. Li. 2021. “Nonstationary wind speed data reconstruction based on secondary correction of statistical characteristics.” Struct. Control Health Monit. 28 (9): e2783. https://doi.org/10.1002/stc.2783.
Maillo, J., S. Ramírez, I. Triguero, and F. Herrera. 2016. “KNN-IS: An iterative spark-based design of the k-nearest neighbors classifier for big data.” Knowledge-Based Syst. 117 (3): 3–15. https://doi.org/10.1016/j.knosys.2016.06.012.
MOT (Ministry of Transport). 2021. “Transportation development report in 2020.” [In Chinese.] Jilin Sci. Technol. Commun. 2: 40–46.
Murti, D. M. P., U. Pujianto, A. P. Wibawa, and M. I. Akbar. 2019. “K-nearest neighbor (K-NN) based missing data imputation.” In Proc., 5th Int. Conf. on Science in Information Technology, 83–88. https://doi.org/10.1109/ICSITech46713.2019.8987530.
Nassir, S. T., A. B. Khamees, and W. T. Mousa. 2018. “Estimation the missing data of meteorological variables in different Iraqi cities by using ARIMA model.” Iraqi J. Sci. 59 (2A): 792–801. https://doi.org/10.24996/ijs.2018.59.2a.17.
Phan, T. T. H., E. P. Caillault, A. Lefebvre, and A. Bigand. 2020. “Dynamic time warping-based imputation for univariate time series data.” Pattern Recognit. Lett. 139 (11): 139–147. https://doi.org/10.1016/j.patrec.2017.08.019.
Poloczek, J., N. A. Treiber, and O. Kramer. 2014. “KNN regression as geo-imputation method for spatio-temporal wind data.” Adv. Intell. Syst. Comput. 299 (27): 185–193. https://doi.org/10.1007/978-3-319-07995-0_19.
Ravi, V., and M. Krishna. 2014. “A new online data imputation method based on general regression auto associative neural network.” Neurocomputing 138 (11): 106–113. https://doi.org/10.1016/j.neucom.2014.02.037.
Sumitro, S., Y. Matsui, M. Kono, T. Okamoto, and K. Fujii. 2001. “Long span bridge health monitoring system in Japan.” Health Monit. Manage. Civ. Infrastruct. Syst. 4337: 517–524. https://doi.org/10.1117/12.435628.
Sun, B., H. K. Zhou, F. H. Dong, W. D. Ruan, and X. J. Zhang. 2022. “Risk assessment of bridge construction safety considering multi-information fusion.” ASCE-ASME J. Risk Uncertainty Eng. Syst. Part A: Civ. Eng. 8 (4): 04022045. https://doi.org/10.1061/AJRUA6.0001267.
Sun, B., S. H. Ye, T. F. Qiu, C. Q. Fu, D. Wu, and X. Y. Jin. 2023. “Cracking mechanism of corroded reinforced concrete column based on acoustic emission technique.” J. Mater. Civ. Eng. 35 (4): 04023034. https://doi.org/ 10.1061/(ASCE)MT.1943-5533.0004705.
Sun, L. M., Z. Q. Shang, and Y. Xia. 2019. “Development and prospect of bridge structure health monitoring in the context of big data.” [In Chinese.] China J. Highway Transp. 32 (11): 1–20. https://doi.org/10.19721/j.cnki.1001-7372.2019.11.001.
Tang, J., G. Zhang, Y. Wang, H. Wang, and F. Liu. 2015. “A hybrid approach to integrate fuzzy c-means based imputation method with genetic algorithm for missing traffic volume data estimation.” Transp. Res. Part C Emerging Technol. 51 (2): 29–40. https://doi.org/10.1016/j.trc.2014.11.003.
Tang, X., H. Yao, Y. Sun, C. Aggarwal, P. Mitra, and S. Wang. 2020a. “Joint modeling of local and global temporal dynamics for multivariate time series forecasting with missing values.” Proc. AAAI Conf. Artif. Intell. 34 (4): 5956–5963. https://doi.org/10.48550/arXiv.1911.10273.
Tang, Z. Y., Y. Q. Bao, and H. Li. 2020b. “Group sparsity-aware convolutional neural network for continuous missing data recovery of structural health monitoring.” Struct. Health Monit. 20 (4): 1738–1759. https://doi.org/10.1177/1475921720931745.
Wan, K., S. Ahmad, and A. Sabri. 2013. “Arima model and exponential smoothing method: A comparison.” AIP Conf. Proc. 1522 (13): 1312–1321. https://doi.org/10.1063/1.4801282.
Winter, B. D., and R. A. Swartz. 2017. “Wireless structural control using multi-step TDMA communication patterning bandwidth allocation.” Struct. Control Health Monit. 24 (12): e2025. https://doi.org/10.1002/stc.2025.
Yang, Y., and S. Nagarajaiah. 2016. “Harnessing data structure for recovery of randomly missing structural vibration responses time history: Sparse representation versus low-rank structure.” Mech. Syst. Sig. Process. 74 (2016): 165–182. https://doi.org/10.1016/j.ymssp.2015.11.009.
Zhang, Z., and Y. Luo. 2017. “Restoring method for missing data of spatial structural stress monitoring based on correlation.” Mech. Syst. Sig. Process. 91 (2017): 266–277. https://doi.org/10.1016/j.ymssp.2017.01.018.
Zhao, L., Z. Chen, Z. Yang, Y. Hu, and M. S. Obaidat. 2018. “Local similarity imputation based on fast clustering for incomplete data in cyber-physical systems.” IEEE Syst. J. 12 (2): 1610–1620. https://doi.org/10.1109/JSYST.2016.2576026.
Information & Authors
Information
Published In
Journal of Bridge Engineering
Volume 28 • Issue 6 • June 2023
Copyright
© 2023 American Society of Civil Engineers.
History
Received: Aug 16, 2022
Accepted: Feb 18, 2023
Published online: Apr 13, 2023
Published in print: Jun 1, 2023
Discussion open until: Sep 13, 2023
ASCE Technical Topics:
- Algorithms
- Bridge engineering
- Bridge management
- Bridge tests
- Business management
- Data analysis
- Design (by type)
- Engineering fundamentals
- Field tests
- Information management
- Management methods
- Mathematics
- Methodology (by type)
- Practice and Profession
- Research methods (by type)
- Structural design
- Structural engineering
- Structural health monitoring
- Structural safety
- Tests (by type)
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