Analytical discussion on applicability of frequency domain decomposition method to systems excited by an impulse force
Abstract
This paper focuses on the use of vibration measurements for the purpose of cost-effective performance evaluation for the safety management and maintenance of Japan’s social infrastructure like bridges. Since modal properties are often used to diagnose damage of structures by analysing their changes, various modal identification methods have been developed in the past few decades. Among these, the FDD method has still attractive attention because of its simplicity and practicality. It is also highly applicable to simultaneous observation at multiple points and even complex modes can be identified instantly. On the other hand, the applicability of this method to impact tests applied to evaluate the condition of structures has not been sufficiently discussed to date. In this study, we will clarify the applicability to impact tests by reconstructing the theoretical background of the FDD method. Furthermore, we will show from theory that when there is a correlation between inputs, higher-order singular values, which should be noted when applied to impact tests, will be affected. The conclusions obtained from the reconstruction of the theoretical background will be verified based on numerical experiments and actual observation records.
Keyword : frequency domain decomposition, modal identification, ambient vibration observation, impact force, cross-correlation inputs, bridge structure, numerical experiment
How to Cite
Iiyama, K., Morikawa, H., Chen, P.-Y., & Sakai, K. (2024). Analytical discussion on applicability of frequency domain decomposition method to systems excited by an impulse force. Journal of Civil Engineering and Management, 30(5), 452–464. https://doi.org/10.3846/jcem.2024.21347
This work is licensed under a Creative Commons Attribution 4.0 International License.
References
Au, S. K. (2011). Fast Bayesian FFT method for ambient modal identification with separated modes. Journal of Engineering Mechanics, 137, 214–226. https://doi.org/10.1061/(ASCE)EM.1943-7889.0000213
Bendat, J. S., & Piersol, A. G. (1993). Engineering applications of correlation and spectral analysis. John Wiley & Sons.
Brincker, R., Zhang, L., & Andersen, P. (2000). Output-only modal analysis by frequency domain decomposition. In Proceedings of ISMA25: 2000 International Conference on Noise and Vibration Engineering (pp. 717–723), Katholieke Universiteit, Leuven.
Brincker, R., Zhang, L., & Andersen, P. (2001). Modal identification of output-only systems using frequency domain decomposition, Smart Materials and Structures, 10(3), 441–445. https://doi.org/10.1088/0964-1726/10/3/303
Brincker, R., Andersen, P., & Jacobsen, N.-J. (2007). Automated frequency domain decomposition for operational modal analysis. In Proceedings of IMAC-XXIV: A Conference & Exposition on Structural Dynamics Society for Experimental Mechanics.
Chen, T., Chen, G., Chen, W., Hou, S., Zheng, Y., & He, H. (2021). Application of decoupled ARMA model to modal identification of linear time-varying system based on the ICA and assumption of “short-time linearly varying”. Journal of Sound and Vibration, 499(12), Article 115997. https://doi.org/10.1016/j.jsv.2021.115997
Danial, M., Hasan, A., Ahmad, Z. A. B., Salman, L. M., & Hee, L. M. (2018). Enhanced frequency domain decomposition algorithm: a review of a recent development for unbiased damping ratio estimates. Journal of Vibroengineering, 20(5), 1919–1936. https://doi.org/10.21595/jve.2018.19058
Ermert, L., Poggi, V., Burja’nek, J., & F ̈ah, D. (2014): Fundamental and higher two-dimensional resonance modes of an Alpine valley. Geophysical Journal International, 198(2), 795–811. https://doi.org/10.1093/gji/ggu072
Ghannadi, P., & Kourehli, S. S. (2022). Efficiency of the slime mold algorithm for damage detection of large-scale structures. The Structural Design of Tall and Special Buildings, 31(14), Article e1967. https://doi.org/10.1002/tal.1967
Ghannadi, P., Khatir, S., Kourehli, S. S., Nguyen, A., Boutchicha, D., & Wahab, M. A. (2023). Finite element model updating and damage identification using semi-rigidly connected frame element and optimization procedure: An experimental validation. Structures, 50, 1173–1190. https://doi.org/10.1016/j.istruc.2023.02.008
Gul, M., & Catbas, F.N. (2011). Structural health monitoring and damage assessment using a novel time series analysis methodology with sensor clustering. Journal of Sound and Vibration, 330, 1196–1210. https://doi.org/10.1016/j.jsv.2010.09.024
Hızal, Ç. (2020). Modified frequency and spatial domain decomposition method based on maximum likelihood estimation. Engineering Structures, 224, Article 111007. https://doi.org/10.1016/j.engstruct.2020.111007
Hızal, Ç. (2023a). FDD based modal identification of structures using least squares approach. Structures, 55, 1071–1083. https://doi.org/10.1016/j.istruc.2023.06.092
Hızal, Ç. (2023b). FRF-based probabilistic modal parameter identification of structures with known seismic input. Mechanical Systems and Signal Processing, 189, Article 110092. https://doi.org/10.1016/j.ymssp.2022.110092
Hızal, Ç., & Aktaş, E. (2021). Probabilistic investigation of error propagation in frequency domain decomposition-based operational modal analysis. Structural Control and Health Monitoring, 28, Article e2759. https://doi.org/10.1002/stc.2759
Hizal, Ç., & Turan, G. (2020). A two-stage Bayesian algorithm for finite element model updating by using ambient response data from multiple measurement setups. Journal of Sound and Vibration, 469, Article 115139. https://doi.org/10.1016/j.jsv.2019.115139
Kang, J., Liu, L., Shao, Y., & Ma, Q. (2021). Non-stationary signal decomposition approach for harmonic responses detection in operational modal analysis. Computers and Structures, 242, Article 106377. https://doi.org/10.1016/j.compstruc.2020.106377
Lee, J. J., & Yun, C. B. (2006). Damage diagnosis of steel girder bridges using ambient vibration data. Engineering Structures, 28, 912–925. https://doi.org/10.1016/j.engstruct.2005.10.017
Mosavi, A. A., Dickey, D., Seracino, R., & Rizkalla, S. (2012). Identifying damage locations under ambient vibrations utilizing vector autoregressive models and Mahalanobis distances. Mechanical Systems and Signal Processing, 26, 254–267. https://doi.org/10.1016/j.ymssp.2011.06.009
Mostafavian, S., Nabavian, S. R., Davoodi, M., & Neya, B. N. (2019). Output-only modal analysis of a beam via frequency domain decomposition method using noisy data. International Journal of Engineering, 32(12), 1753–1761. https://doi.org/10.5829/ije.2019.32.12c.08
Nagamatsu, A. (1993). Modo kaiseki nyumon [Introduction to modal analysis]. Corona Publishing Co., Ltd. (in Japanese).
Naira, K. K., Kiremidjianb, A. S., & Law, K. H. (2006). Time series-based damage detection and localization algorithm with application to the ASCE benchmark structure. Journal of Sound and Vibration, 291, 349–368. https://doi.org/10.1016/j.jsv.2005.06.016
Ng, C. T., Wang, P., Au, S. K., & Li, B. (2023). Uncertainty laws of experimental modal analysis with known broadband input. Mechanical Systems and Signal Processing, 204, Article 110624. https://doi.org/10.1016/j.ymssp.2023.110624
Ni, Y. C., & Zhang, F. L. (2019). Fast Bayesian frequency domain modal identification from seismic response data. Computers and Structures, 212, 225–235. https://doi.org/10.1016/j.compstruc.2018.08.018
Noori, M., Rainieri, C., Domaneschi, M., & Sarhosis, V. (Eds.). (2024). Data driven methods for civil structural health monitoring and resilience. Latest developments and applications. CRC Press. https://doi.org/10.1201/9781003306924
Pioldi, F., Ferrari R., & Rizzi, E. (2015). Output-only modal dynamic identification of frames by a refined FDD algorithm at seismic input and high damping. Mechanical Systems and Signal Processing, 68–69, 265–291. https://doi.org/10.1016/j.ymssp.2015.07.004
Pioldi, F., Ferrari R., & Rizzi, E. (2017a). Earthquake structural modal estimates of multi-storey frames by a refined frequency domain decomposition algorithm. Journal of Vibration and Control, 23(13), 2037–2063. https://doi.org/10.1177/1077546315608557
Pioldi, F., Salvi, J., & Rizzi, E. (2017b). Refined FDD modal dynamic identification from earthquake responses with soil-structure interaction. International Journal of Mechanical Science, 127, 47–61. https://doi.org/10.1016/j.ijmecsci.2016.10.032
Poggi, V., Ermert, L., Burja’nek, J., Michel, C., & F ̈ah, D. (2014). Modal analysis of 2-D sedimentary basin from frequency domain decomposition of ambient vibration array recordings. Geophysical Journal International, 200(1), 615–626. https://doi.org/10.1093/gji/ggu420
Qin, S., Feng, J., Tang, J., Huo, X., Zhou, Y., Yang, F., & Wahab, M. A. (2024). Condition assessment of a concrete filled steel tube arch bridge using in-situ vibration measurements and an Improved Artificial Fish Swarm Algorithm. Computers & Structures, 291, Article 107213. https://doi.org/10.1016/j.compstruc.2023.107213
Qu, C. X., Yi, T. H., Li, H. N., & Chen, B. (2018). Closely spaced modes identification through modified frequency domain decomposition. Measurement: Journal of the International Measurement Confederation, 128, 388–392. https://doi.org/10.1016/j.measurement.2018.07.006
Qu, C.-X., Liu, Y.-F., Yi, T.-H., & Li, H.-N. (2023). Structural damping ratio identification through iterative frequency domain decomposition. Journal of Structural Engineering, 149(5), Article 04023042. https://doi.org/10.1061/JSENDH.STENG-11837
Rodrigues, J., Brincker, R., & Andersen, P. (2004). Improvement of frequency domain output-only modal identification from the application of the random decrement technique. In Proceedings of the 23rd International Modal Analysis Conference, Dearborn, Michigan.
Rodriguez-Suesca, A. E., Gutierrez-Junco, O. J., & Hernandez-Montes, E. (2022). Vibration performance assessment of deteriorating footbridges: A study of Tunja’s public footbridges. Engineering Structures, 256, Article 113997. https://doi.org/10.1016/j.engstruct.2022.113997
Suzuki, Y., Iiyama, K., Morikawa, H., Sakai, K., & Araki, G. (2022). New method to estimate bedrock shape of small-scale basin using modal properties of sediment. Soil Dynamics and Earthquake Engineering, 149, Article 106882. https://doi.org/10.1016/j.soildyn.2021.106882
Van, P. N. (2016). Building structure parameter identification using the frequency domain decomposition (FDD) method. In AETA 2015: Recent Advances in Electrical Engineering and Related Sciences (pp. 869–880). https://doi.org/10.1007/978-3-319-27247-4_72
Yan, W. J., & Katafygiotis, L. S. (2015). A two-stage fast Bayesian spectral density approach for ambient modal analysis. Part II: Mode shape assembly and case studies. Mechanical Systems and Signal Processing, 54, 156–171. https://doi.org/10.1016/j.ymssp.2014.08.016
Zhang, L., Wang, T., & Tamura, Y. (2005). A Frequency-spatial decomposition (FSDD) technique for operational modal analysis. In Proceedings of the 1st International Operational Modal Analysis Conference (IOMAC), Copenhagen, Denmark.
Zhang, L., Wang, T., & Tamura, Y. (2010). A frequency–spatial domain decomposition (FSDD) method for operational modal analysis. Mechanical Systems and Signal Processing, 24, 1227–1239. https://doi.org/10.1016/j.ymssp.2009.10.024
Bendat, J. S., & Piersol, A. G. (1993). Engineering applications of correlation and spectral analysis. John Wiley & Sons.
Brincker, R., Zhang, L., & Andersen, P. (2000). Output-only modal analysis by frequency domain decomposition. In Proceedings of ISMA25: 2000 International Conference on Noise and Vibration Engineering (pp. 717–723), Katholieke Universiteit, Leuven.
Brincker, R., Zhang, L., & Andersen, P. (2001). Modal identification of output-only systems using frequency domain decomposition, Smart Materials and Structures, 10(3), 441–445. https://doi.org/10.1088/0964-1726/10/3/303
Brincker, R., Andersen, P., & Jacobsen, N.-J. (2007). Automated frequency domain decomposition for operational modal analysis. In Proceedings of IMAC-XXIV: A Conference & Exposition on Structural Dynamics Society for Experimental Mechanics.
Chen, T., Chen, G., Chen, W., Hou, S., Zheng, Y., & He, H. (2021). Application of decoupled ARMA model to modal identification of linear time-varying system based on the ICA and assumption of “short-time linearly varying”. Journal of Sound and Vibration, 499(12), Article 115997. https://doi.org/10.1016/j.jsv.2021.115997
Danial, M., Hasan, A., Ahmad, Z. A. B., Salman, L. M., & Hee, L. M. (2018). Enhanced frequency domain decomposition algorithm: a review of a recent development for unbiased damping ratio estimates. Journal of Vibroengineering, 20(5), 1919–1936. https://doi.org/10.21595/jve.2018.19058
Ermert, L., Poggi, V., Burja’nek, J., & F ̈ah, D. (2014): Fundamental and higher two-dimensional resonance modes of an Alpine valley. Geophysical Journal International, 198(2), 795–811. https://doi.org/10.1093/gji/ggu072
Ghannadi, P., & Kourehli, S. S. (2022). Efficiency of the slime mold algorithm for damage detection of large-scale structures. The Structural Design of Tall and Special Buildings, 31(14), Article e1967. https://doi.org/10.1002/tal.1967
Ghannadi, P., Khatir, S., Kourehli, S. S., Nguyen, A., Boutchicha, D., & Wahab, M. A. (2023). Finite element model updating and damage identification using semi-rigidly connected frame element and optimization procedure: An experimental validation. Structures, 50, 1173–1190. https://doi.org/10.1016/j.istruc.2023.02.008
Gul, M., & Catbas, F.N. (2011). Structural health monitoring and damage assessment using a novel time series analysis methodology with sensor clustering. Journal of Sound and Vibration, 330, 1196–1210. https://doi.org/10.1016/j.jsv.2010.09.024
Hızal, Ç. (2020). Modified frequency and spatial domain decomposition method based on maximum likelihood estimation. Engineering Structures, 224, Article 111007. https://doi.org/10.1016/j.engstruct.2020.111007
Hızal, Ç. (2023a). FDD based modal identification of structures using least squares approach. Structures, 55, 1071–1083. https://doi.org/10.1016/j.istruc.2023.06.092
Hızal, Ç. (2023b). FRF-based probabilistic modal parameter identification of structures with known seismic input. Mechanical Systems and Signal Processing, 189, Article 110092. https://doi.org/10.1016/j.ymssp.2022.110092
Hızal, Ç., & Aktaş, E. (2021). Probabilistic investigation of error propagation in frequency domain decomposition-based operational modal analysis. Structural Control and Health Monitoring, 28, Article e2759. https://doi.org/10.1002/stc.2759
Hizal, Ç., & Turan, G. (2020). A two-stage Bayesian algorithm for finite element model updating by using ambient response data from multiple measurement setups. Journal of Sound and Vibration, 469, Article 115139. https://doi.org/10.1016/j.jsv.2019.115139
Kang, J., Liu, L., Shao, Y., & Ma, Q. (2021). Non-stationary signal decomposition approach for harmonic responses detection in operational modal analysis. Computers and Structures, 242, Article 106377. https://doi.org/10.1016/j.compstruc.2020.106377
Lee, J. J., & Yun, C. B. (2006). Damage diagnosis of steel girder bridges using ambient vibration data. Engineering Structures, 28, 912–925. https://doi.org/10.1016/j.engstruct.2005.10.017
Mosavi, A. A., Dickey, D., Seracino, R., & Rizkalla, S. (2012). Identifying damage locations under ambient vibrations utilizing vector autoregressive models and Mahalanobis distances. Mechanical Systems and Signal Processing, 26, 254–267. https://doi.org/10.1016/j.ymssp.2011.06.009
Mostafavian, S., Nabavian, S. R., Davoodi, M., & Neya, B. N. (2019). Output-only modal analysis of a beam via frequency domain decomposition method using noisy data. International Journal of Engineering, 32(12), 1753–1761. https://doi.org/10.5829/ije.2019.32.12c.08
Nagamatsu, A. (1993). Modo kaiseki nyumon [Introduction to modal analysis]. Corona Publishing Co., Ltd. (in Japanese).
Naira, K. K., Kiremidjianb, A. S., & Law, K. H. (2006). Time series-based damage detection and localization algorithm with application to the ASCE benchmark structure. Journal of Sound and Vibration, 291, 349–368. https://doi.org/10.1016/j.jsv.2005.06.016
Ng, C. T., Wang, P., Au, S. K., & Li, B. (2023). Uncertainty laws of experimental modal analysis with known broadband input. Mechanical Systems and Signal Processing, 204, Article 110624. https://doi.org/10.1016/j.ymssp.2023.110624
Ni, Y. C., & Zhang, F. L. (2019). Fast Bayesian frequency domain modal identification from seismic response data. Computers and Structures, 212, 225–235. https://doi.org/10.1016/j.compstruc.2018.08.018
Noori, M., Rainieri, C., Domaneschi, M., & Sarhosis, V. (Eds.). (2024). Data driven methods for civil structural health monitoring and resilience. Latest developments and applications. CRC Press. https://doi.org/10.1201/9781003306924
Pioldi, F., Ferrari R., & Rizzi, E. (2015). Output-only modal dynamic identification of frames by a refined FDD algorithm at seismic input and high damping. Mechanical Systems and Signal Processing, 68–69, 265–291. https://doi.org/10.1016/j.ymssp.2015.07.004
Pioldi, F., Ferrari R., & Rizzi, E. (2017a). Earthquake structural modal estimates of multi-storey frames by a refined frequency domain decomposition algorithm. Journal of Vibration and Control, 23(13), 2037–2063. https://doi.org/10.1177/1077546315608557
Pioldi, F., Salvi, J., & Rizzi, E. (2017b). Refined FDD modal dynamic identification from earthquake responses with soil-structure interaction. International Journal of Mechanical Science, 127, 47–61. https://doi.org/10.1016/j.ijmecsci.2016.10.032
Poggi, V., Ermert, L., Burja’nek, J., Michel, C., & F ̈ah, D. (2014). Modal analysis of 2-D sedimentary basin from frequency domain decomposition of ambient vibration array recordings. Geophysical Journal International, 200(1), 615–626. https://doi.org/10.1093/gji/ggu420
Qin, S., Feng, J., Tang, J., Huo, X., Zhou, Y., Yang, F., & Wahab, M. A. (2024). Condition assessment of a concrete filled steel tube arch bridge using in-situ vibration measurements and an Improved Artificial Fish Swarm Algorithm. Computers & Structures, 291, Article 107213. https://doi.org/10.1016/j.compstruc.2023.107213
Qu, C. X., Yi, T. H., Li, H. N., & Chen, B. (2018). Closely spaced modes identification through modified frequency domain decomposition. Measurement: Journal of the International Measurement Confederation, 128, 388–392. https://doi.org/10.1016/j.measurement.2018.07.006
Qu, C.-X., Liu, Y.-F., Yi, T.-H., & Li, H.-N. (2023). Structural damping ratio identification through iterative frequency domain decomposition. Journal of Structural Engineering, 149(5), Article 04023042. https://doi.org/10.1061/JSENDH.STENG-11837
Rodrigues, J., Brincker, R., & Andersen, P. (2004). Improvement of frequency domain output-only modal identification from the application of the random decrement technique. In Proceedings of the 23rd International Modal Analysis Conference, Dearborn, Michigan.
Rodriguez-Suesca, A. E., Gutierrez-Junco, O. J., & Hernandez-Montes, E. (2022). Vibration performance assessment of deteriorating footbridges: A study of Tunja’s public footbridges. Engineering Structures, 256, Article 113997. https://doi.org/10.1016/j.engstruct.2022.113997
Suzuki, Y., Iiyama, K., Morikawa, H., Sakai, K., & Araki, G. (2022). New method to estimate bedrock shape of small-scale basin using modal properties of sediment. Soil Dynamics and Earthquake Engineering, 149, Article 106882. https://doi.org/10.1016/j.soildyn.2021.106882
Van, P. N. (2016). Building structure parameter identification using the frequency domain decomposition (FDD) method. In AETA 2015: Recent Advances in Electrical Engineering and Related Sciences (pp. 869–880). https://doi.org/10.1007/978-3-319-27247-4_72
Yan, W. J., & Katafygiotis, L. S. (2015). A two-stage fast Bayesian spectral density approach for ambient modal analysis. Part II: Mode shape assembly and case studies. Mechanical Systems and Signal Processing, 54, 156–171. https://doi.org/10.1016/j.ymssp.2014.08.016
Zhang, L., Wang, T., & Tamura, Y. (2005). A Frequency-spatial decomposition (FSDD) technique for operational modal analysis. In Proceedings of the 1st International Operational Modal Analysis Conference (IOMAC), Copenhagen, Denmark.
Zhang, L., Wang, T., & Tamura, Y. (2010). A frequency–spatial domain decomposition (FSDD) method for operational modal analysis. Mechanical Systems and Signal Processing, 24, 1227–1239. https://doi.org/10.1016/j.ymssp.2009.10.024