{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,27]],"date-time":"2026-03-27T20:28:46Z","timestamp":1774643326637,"version":"3.50.1"},"reference-count":33,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2023,5,2]],"date-time":"2023-05-02T00:00:00Z","timestamp":1682985600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["51829801"],"award-info":[{"award-number":["51829801"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["CYXC2207"],"award-info":[{"award-number":["CYXC2207"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Collaborative Innovation Project of Chaoyang District, Beijing","award":["51829801"],"award-info":[{"award-number":["51829801"]}]},{"name":"Collaborative Innovation Project of Chaoyang District, Beijing","award":["CYXC2207"],"award-info":[{"award-number":["CYXC2207"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Remote Sensing"],"abstract":"<jats:p>Structural health monitoring (SHM) is vital for ensuring the service safety of aging bridges. As one of the most advanced sensing techniques, Global Navigation Satellite Systems (GNSS) could capture massive spatiotemporal information for effective bridge structural health monitoring (BSHM). Unfortunately, GNSS measurements often contain outliers due to various factors (e.g., severe weather conditions, multipath effects, etc.). All such outliers could jeopardize the accuracy and reliability of BSHM significantly. Previous studies have examined the feasibility of integrating the conventional multi-rate Kalman filter (MKF) with an adaptive algorithm in the data processing processes to ensure BSHM accuracy. However, frequent parameter adjustments are still needed in tedious data processing processes. This study proposed an outlier detection method using a Nelder-Mead simplex robust multi-rate Kalman filter (RMKF) for supporting trustworthy BSHM using GNSS and accelerometer. In the end, the authors have validated the proposed method using the monitoring data collected at the Wilford Bridge in the UK. Results showed that the accuracy of the total dynamic vibration displacement time series has been improved by 21% compared with the results using the conventional MKF approach. The authors envision that the proposed method will shed light on reliable and explainable data processing policy and trustworthy BSHM.<\/jats:p>","DOI":"10.3390\/rs15092385","type":"journal-article","created":{"date-parts":[[2023,5,3]],"date-time":"2023-05-03T01:36:38Z","timestamp":1683077798000},"page":"2385","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":20,"title":["Outlier Detection Based on Nelder-Mead Simplex Robust Kalman Filtering for Trustworthy Bridge Structural Health Monitoring"],"prefix":"10.3390","volume":"15","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-2472-4201","authenticated-orcid":false,"given":"Liangliang","family":"Hu","sequence":"first","affiliation":[{"name":"The Key Laboratory of Urban Security and Disaster Engineering of the Ministry of Education, Beijing University of Technology, Beijing 100124, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yan","family":"Bao","sequence":"additional","affiliation":[{"name":"The Key Laboratory of Urban Security and Disaster Engineering of the Ministry of Education, Beijing University of Technology, Beijing 100124, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zhe","family":"Sun","sequence":"additional","affiliation":[{"name":"The Key Laboratory of Urban Security and Disaster Engineering of the Ministry of Education, Beijing University of Technology, Beijing 100124, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2440-8054","authenticated-orcid":false,"given":"Xiaolin","family":"Meng","sequence":"additional","affiliation":[{"name":"The Key Laboratory of Urban Security and Disaster Engineering of the Ministry of Education, Beijing University of Technology, Beijing 100124, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Chao","family":"Tang","sequence":"additional","affiliation":[{"name":"Beijing Urban Construction Exploration & Surveying Design Research Institute Co., Ltd., Beijing 100101, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Dongliang","family":"Zhang","sequence":"additional","affiliation":[{"name":"The Key Laboratory of Urban Security and Disaster Engineering of the Ministry of Education, Beijing University of Technology, Beijing 100124, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2023,5,2]]},"reference":[{"key":"ref_1","unstructured":"(2023, April 01). Report Card For America\u2019s Infrastructure. Available online: https:\/\/infrastructurereportcard.org\/cat-item\/bridges-infrastructure\/."},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Haldar, A. (2012). Health Assessment of Engineered Structures, World Scientific.","DOI":"10.1142\/8628"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"12","DOI":"10.1088\/1755-1315\/109\/1\/012024","article-title":"The effect of load position to the accuracy of deflection measured with LVDT sensor in I-girder bridge","volume":"109","author":"Hidayat","year":"2017","journal-title":"IOP Conf. Ser. Earth Environ. Sci."},{"key":"ref_4","first-page":"e2467","article-title":"Global Navigation Satellite System-based positioning technology for structural health monitoring: A review","volume":"27","author":"Yu","year":"2019","journal-title":"Struct. Control Health Monit."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"61","DOI":"10.1007\/s10291-023-01402-y","article-title":"An investigation of PPP time transfer via BDS-3 PPP-B2b service","volume":"27","author":"Ge","year":"2023","journal-title":"GPS Solut."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"109658","DOI":"10.1016\/j.measurement.2021.109658","article-title":"Two flexible vision-based methods for remote deflection monitoring of a long-span bridge","volume":"181","author":"Yu","year":"2021","journal-title":"Measurement"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"1063","DOI":"10.1016\/j.istruc.2022.03.064","article-title":"Reliability analysis of bridge girders based on regular vine Gaussian copula model and monitored data","volume":"39","author":"Xiao","year":"2022","journal-title":"Structures"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"647","DOI":"10.1520\/JTE20140321","article-title":"Wavelet Analysis with Different Frequency GPR Antennas for Bridge Health Assessment","volume":"44","author":"Kilic","year":"2016","journal-title":"J. Test. Eval."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"102440","DOI":"10.1016\/j.yofte.2020.102440","article-title":"Study on bridge weigh in motion (BWIM) system for measuring the vehicle parameters based on strain measurement using FBG sensors","volume":"61","author":"Alamandala","year":"2021","journal-title":"Opt. Fiber Technol."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"05019011","DOI":"10.1061\/(ASCE)BE.1943-5592.0001470","article-title":"Fiber Bragg Grating\u2014Differential Settlement Measurement System for Bridge Displacement Monitoring: Case Study","volume":"24","author":"Bonopera","year":"2019","journal-title":"J. Bridge Eng."},{"key":"ref_11","first-page":"e2308","article-title":"Vibration-based structural condition assessment using convolution neural networks","volume":"26","author":"Khodabandehlou","year":"2019","journal-title":"Struct. Control Health Monit."},{"key":"ref_12","unstructured":"Sohn, H., Kim, K., Choi, J., Koo, G., and Chung, J. (2018). Experimental Vibration Analysis for Civil Structures, Springer International Publishing."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"1201","DOI":"10.1785\/BSSA0610051201","article-title":"Zero baseline correction of strong-motion accelerograms","volume":"61","author":"Trifunac","year":"1971","journal-title":"Bull. Seismol. Soc. Am."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"932","DOI":"10.1785\/BSSA0870040932","article-title":"Stable baseline correction of digital strong-motion data","volume":"87","author":"Chiu","year":"1997","journal-title":"Bull. Seismol. Soc. Am."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"281","DOI":"10.1111\/j.1467-8667.2007.00536.x","article-title":"A State-Space Approach for Deriving Bridge Displacement from Acceleration","volume":"23","author":"Gindy","year":"2008","journal-title":"Comput.-Aided Civ. Infrastruct. Eng."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"371","DOI":"10.1016\/j.engstruct.2004.10.013","article-title":"The determination of bridge displacement using measured acceleration","volume":"27","author":"Park","year":"2005","journal-title":"Eng. Struct."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"1700","DOI":"10.1029\/2003GL017302","article-title":"Recovering permanent displacements from seismic records of the June 9, 1994 Bolivia deep earthquake","volume":"30","author":"Zhu","year":"2003","journal-title":"Geophys. Res. Lett."},{"key":"ref_18","first-page":"177","article-title":"Experimental monitoring of the Humber Bridge using GPS","volume":"120","author":"Ashkenazi","year":"1997","journal-title":"ICE Proc. Civ. Eng."},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Meng, X., Nguyen, D.T., Xie, Y., Owen, J., Psimoulis, P., Ince, S., Chen, Q., Ye, J., and Bhatia, P. (2018). Design and Implementation of a New System for Large Bridge Monitoring\u2014GeoSHM. Sensors, 18.","DOI":"10.3390\/s18030775"},{"key":"ref_20","unstructured":"Xiaolin, M. (2002). Real-Time Deformation Monitoring of Bridges Using GPS Accelerometers. [Ph.D. Thesis, University of Nottingham]."},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"Xiong, C., Lu, H., and Zhu, J. (2017). Operational Modal Analysis of Bridge Structures with Data from GNSS\/Accelerometer Measurements. Sensors, 17.","DOI":"10.3390\/s17030436"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"706","DOI":"10.1016\/j.ymssp.2006.03.005","article-title":"Multi-rate Kalman filtering for the data fusion of displacement and acceleration response measurements in dynamic system monitoring","volume":"21","author":"Smyth","year":"2007","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"2904","DOI":"10.1785\/0120110007","article-title":"Real-Time Strong-Motion Broadband Displacements from Collocated GPS and Accelerometers","volume":"101","author":"Bock","year":"2011","journal-title":"Bull. Seismol. Soc. Am."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"46","DOI":"10.1016\/j.advengsoft.2017.06.010","article-title":"Real-time monitoring system for local storage and data transmission by remote control","volume":"112","author":"Casciati","year":"2017","journal-title":"Adv. Eng. Softw."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"12","DOI":"10.1785\/gssrl.79.1.12","article-title":"Load Response on a Large Suspension Bridge during the NYC Marathon Revealed by GPS and Accelerometers","volume":"79","author":"Kogan","year":"2008","journal-title":"Seismol. Res. Lett."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"639","DOI":"10.1016\/j.engstruct.2017.06.018","article-title":"Long-span bridges: Enhanced data fusion of GPS displacement and deck accelerations","volume":"147","author":"Yan","year":"2017","journal-title":"Eng. Struct."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"3791856","DOI":"10.1155\/2016\/3791856","article-title":"Reference-Free Displacement Estimation of Bridges Using Kalman Filter-Based Multimetric Data Fusion","volume":"2016","author":"Cho","year":"2016","journal-title":"J. Sens."},{"key":"ref_28","first-page":"265","article-title":"Optimal GPS\/accelerometer integration algorithm for monitoring the vertical structural dynamics","volume":"8","author":"Meng","year":"2014","journal-title":"J. Appl. Geod."},{"key":"ref_29","doi-asserted-by":"crossref","unstructured":"Sun, A., Zhang, Q., Yu, Z., Meng, X., Liu, X., Zhang, Y., and Xie, Y. (2022). A Novel Slow-Growing Gross Error Detection Method for GNSS\/Accelerometer Integrated Deformation Monitoring Based on State Domain Consistency Theory. Remote Sens., 14.","DOI":"10.3390\/rs14194758"},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"24359","DOI":"10.1109\/JSEN.2021.3112177","article-title":"Bridge Dynamic Displacement Monitoring Using Adaptive Data Fusion of GNSS and Accelerometer Measurements","volume":"21","author":"Yang","year":"2021","journal-title":"IEEE Sens. J."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"836","DOI":"10.1785\/0220130178","article-title":"Real-Time Assessment of the Broadband Coseismic Deformation of the 2011 Tohoku-Oki Earthquake Using an Adaptive Kalman Filter","volume":"85","author":"Niu","year":"2014","journal-title":"Seismol. Res. Lett."},{"key":"ref_32","doi-asserted-by":"crossref","unstructured":"Jing, C., Huang, G., Zhang, Q., Li, X., Bai, Z., and Du, Y. (2022). GNSS\/Accelerometer Adaptive Coupled Landslide Deformation Monitoring Technology. Remote Sens., 14.","DOI":"10.3390\/rs14153537"},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"259","DOI":"10.1007\/s10589-010-9329-3","article-title":"Implementing the Nelder-Mead simplex algorithm with adaptive parameters","volume":"51","author":"Gao","year":"2010","journal-title":"Comput. Optim. 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