Robust Open-Source Solution for Bridge Decrement Estimation for Data with Outliers

Tomasz Owerko, Piotr Owerko, Karolina Tomaszkiewicz


Dynamic tests enable assessment of the structure’s technical condition and provide information necessary for management and maintenance throughout the object’s life cycle. On their basis, the dynamic characteristics of the object are estimated (e.g., the logarithmic decrement). The possible occurrence of atypical features in the obtained signal (e.g. amplitude beat, outliers), as well as the influence of the type of devices and sensors used for measurements, should be considered. If these features are omitted during the analysis, key dynamic characteristics may be evaluated incorrectly. Therefore, this study presents development of a reproducible, universal and robust open-source algorithm for effective estimation of the logarithmic decrement of bridge structures as a reproducible research. Using the presented approach, it is possible to obtain correct results regardless of the signal’s specificity and its atypical features, as well as the type of devices used to collect data in the in-situ conditions. Two approaches based on the use of advanced regression models are considered to estimate the logarithmic decrement. These are direct non-linear approximation (DNAP) and Hilbert non-linear approximation (HNAP). The enriched HNAPsolution was then implemented as a Python module with a "Signal" class and tested on two independent in-situ examples. The presented approach led to effective and correct estimation of the logarithmic decrement, and proved to be insensitive to the type of bridge, its structural characteristics, atypical features of the obtained signal, and the specificity of the data acquisition techniques. In contrast to methods based on deep machine learning, the presented solution does not require a large learning set representative for a given type of design and works independently of the size of the data sample. As demonstrated in the paper, the solution based on the Hilbert transform allows efficient determination of the damping decrement even in the presence of beat frequencies as well as outlier data. The algorithm works independently of the measurement method, with the necessary functions for preprocessing being implemented in the module itself. The solution has been optimized for improved speed, reliability, and reproducibility of results.


Doi: 10.28991/CEJ-2022-08-04-02

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Structural Vibrations; Bridge Load Tests; Amplitude Beat; Logarithmic Decrement; Hilbert Transform; Robust Methods; Non-Linear Approximation; Python Programming; Reproducible Research.


Cantero, D., McGetrick, P., Kim, C. W., & OBrien, E. (2019). Experimental monitoring of bridge frequency evolution during the passage of vehicles with different suspension properties. Engineering Structures, 187, 209–219. doi:10.1016/j.engstruct.2019.02.065.

Lantsoght, E. O. L., van der Veen, C., de Boer, A., & Hordijk, D. A. (2017). State-of-the-art on load testing of concrete bridges. Engineering Structures, 150, 231–241. doi:10.1016/j.engstruct.2017.07.050.

Lantsoght, E. O. L., van der Veen, C., Hordijk, D. A., & de Boer, A. (2017). Development of recommendations for proof load testing of reinforced concrete slab bridges. Engineering Structures, 152, 202–210. doi:10.1016/j.engstruct.2017.09.018.

Owerko, P., & Owerko, T. (2021). Novel Approach to Inspections of As-Built Reinforcement in Incrementally Launched Bridges by Means of Computer Vision-Based Point Cloud Data. IEEE Sensors Journal, 21(10), 11822–11833. doi:10.1109/JSEN.2020.3020132.

Bień, J., & Kuzawa, M. (2020). Dynamic Tests in Bridge Health Monitoring. Studia Geotechnica et Mechanica, 42(4), 291–296. doi:10.2478/sgem-2019-0045.

Hester, D., Brownjohn, J., Bocian, M., & Xu, Y. (2017). Low cost bridge load test: Calculating bridge displacement from acceleration for load assessment calculations. Engineering Structures, 143, 358–374. doi:10.1016/j.engstruct.2017.04.021.

Laura, M., Francesco, C., & Antonio, F. (2020). Static and dynamic testing of highway bridges: A best practice example. Journal of civil structural health monitoring, 10(1), 43-56. doi:10.1007/s13349-019-00368-1.

Owerko, P., & Honkisz, M. (2017). Innovative technique for identification of prestressing tendons layout in post-tensioned bridges using a probe with MEMS accelerometer. Structure and Infrastructure Engineering, 13(7), 869–881. doi:10.1080/15732479.2016.1212905.

Brunetti, M., Ciambella, J., Evangelista, L., Lofrano, E., Paolone, A., & Vittozzi, A. (2017). Experimental results in damping evaluation of a high-speed railway bridge. Procedia Engineering, 199, 3015–3020. doi:10.1016/j.proeng.2017.09.402.

Huang, Q., Wang, Y., Luzi, G., Crosetto, M., Monserrat, O., Jiang, J., Zhao, H., & Ding, Y. (2020). Ground-based radar interferometry for monitoring the dynamic performance of a multitrack steel truss high-speed railway bridge. Remote Sensing, 12(16), 2594. doi:10.3390/RS12162594.

Grimm, D., & Hornung, U. (2015). Leica ATRplus–Leistungssteigerung der automatischen Messung und Verfolgung von Prismen. AVN-allgemeine vermessungs-nachrichten, 8-9. (In German).

Alva, R. E., Pujades, L. G., González-Drigo, R., Luzi, G., Caselles, O., & Pinzón, L. A. (2020). Dynamic monitoring of a mid-rise building by real-aperture radar interferometer: Advantages and limitations. Remote Sensing, 12(6), 1025. doi:10.3390/rs12061025.

Owerko, T., & Kuras, P. (2019). Effective processing of radar data for bridge damage detection. Shock and Vibration, 2019. doi:10.1155/2019/2621092.

Yang, Y. B., Zhang, B., Wang, T., Xu, H., & Wu, Y. (2019). Two-axle test vehicle for bridges: Theory and applications. International Journal of Mechanical Sciences, 152, 51–62. doi:10.1016/j.ijmecsci.2018.12.043.

Nakutis, Ž., & Kaškonas, P. (2011). Bridge vibration logarithmic decrement estimation at the presence of amplitude beat. Measurement, 44(2), 487-492. doi:10.1016/j.measurement.2010.11.012.

Bień, J., Kuzawa, M., & Kamiński, T. (2015). Validation of numerical models of concrete box bridges based on load test results. Archives of Civil and Mechanical Engineering, 15(4), 1046–1060. doi:10.1016/j.acme.2015.05.007.

Kuras, P., Ortyl, Ł., Owerko, T., Salamak, M., & Łaziński, P. (2020). GB-SAR in the Diagnosis of Critical City Infrastructure—A Case Study of a Load Test on the Long Tram Extradosed Bridge. Remote Sensing, 12(20), 3361. doi:10.3390/rs12203361.

Owerko, P., Winkelmann, K., & Górski, J. (2020). Application of probabilistic tools to extend load test design of bridges prior to opening. Structure and Infrastructure Engineering, 16(7), 931–948. doi:10.1080/15732479.2019.1676790.

Owerko, P., & Winkelmann, K. (2020). Improving the procedure of probabilistic load testing design of typical bridges based on structural response similarities. Archives of Civil Engineering, 66(4), 325–342. doi:10.24425/ace.2020.135224.

Sun, C., Zhao, Y., Peng, J., Kang, H., & Zhao, Y. (2018). Multiple internal resonances and modal interaction processes of a cable-stayed bridge physical model subjected to an invariant single-excitation. Engineering Structures, 172, 938–955. doi:10.1016/j.engstruct.2018.06.088.

Zhang, G., Wu, Y., Zhao, W., & Zhang, J. (2020). Radar-based multipoint displacement measurements of a 1200-m-long suspension bridge. ISPRS Journal of Photogrammetry and Remote Sensing, 167, 71–84. doi:10.1016/j.isprsjprs.2020.06.017.

Owerko, T. (2014). Application of ground-based radar interferometry technique to bridge load testing. Pomiary Automatyka Kontrola, 60(12), 1096-1099.

ISO 4866. (2010). Mechanical vibration and shock - Vibration of fixed structures - Guidelines for the measurement of vibrations and evaluation of their effects on structures. International Organization for Standardization, Geneva, Switzerland.

Rao, S. S. (2017). The finite element method in engineering (5th Edition), Butterworth-Heinemann, Oxford, United Kingdom.

Owerko, P., & Ortyl, L. (2013). GPR identification of prestressing tendons in areas with high density of ordinary reinforcement. International Multidisciplinary Scientific GeoConference: SGEM, 2, 771. doi:10.5593/SGEM2013/BA1.V2/S05.012.

Jones Oliphant, T., Peterson, P., SciPy community, E. (2001). SciPy: Open Source Scientific Tools for Python. Available online: (accessed on February 2022).

Owerko, T., Owerko, P., and Tomaszkiewicz, K. (2021). owerko/LDT. Available online: (accessed on January 2022)

Shin, K., & Hammond, J. (2008). Fundamentals of signal processing for sound and vibration engineers. John Wiley & Sons, New jersey, United States.

Kohut, P., Holak, K., Uhl, T., Krupiński, K., Owerko, T., & Kuraś, P. (2012). Structure’s condition monitoring based on optical measurements. Key Engineering Materials, 518, 338–349. doi:10.4028/

Owerko, T. (2013). Variations of Frequency Responses of a Cable-Stayed Bridge and Calculation of the Damping Coefficient of Selected Vibration Modes Based on the Data Recorded with Radar Systems. Geomatics and Environmental Engineering, 7(4), 79. doi:10.7494/geom.2013.7.4.79.

Owerko, T., & Kuras, P. (2019). Effective processing of radar data for bridge damage detection. Shock and Vibration, 2019, 1–13. doi:10.1155/2019/2621092.

Zhang, Y., & Lei, Y. (2021). Data anomaly detection of bridge structures using convolutional neural network based on structural vibration signals. Symmetry, 13(7), 1186. doi:10.3390/sym13071186.

Avci, O., Abdeljaber, O., Kiranyaz, S., Hussein, M., Gabbouj, M., & Inman, D. J. (2021). A review of vibration-based damage detection in civil structures: From traditional methods to Machine Learning and Deep Learning applications. Mechanical Systems and Signal Processing, 147, 107077. doi:10.1016/j.ymssp.2020.107077.

Bao, Y., Tang, Z., Li, H., & Zhang, Y. (2019). Computer vision and deep learning–based data anomaly detection method for structural health monitoring. Structural Health Monitoring, 18(2), 401–421. doi:10.1177/1475921718757405.

Arnold, M., Hoyer, M., & Keller, S. (2021). Convolutional neural networks for detecting bridge crossing events with ground-based interferometric radar data. ISPRS Annals of the Photogrammetry, Remote Sensing and Spatial Information Sciences, 5(1), 31–38. doi:10.5194/isprs-annals-V-1-2021-31-2021.

Mao, J., Wang, H., & Spencer, B. F. (2021). Toward data anomaly detection for automated structural health monitoring: Exploiting generative adversarial nets and autoencoders. Structural Health Monitoring, 20(4), 1609–1626. doi:10.1177/1475921720924601.

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DOI: 10.28991/CEJ-2022-08-04-02


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