شناسایی سازه‌ای یک شبکه‌ی دولایه با سیستم پیونده‌ی گویسان به کمک روش‌های خروجی-تنها

نوع مقاله : پژوهشی اصیل (کامل)

نویسندگان
سید رسول نبویان 1
سید امین مصطفویان 2
بهرام نوائی نیا 3
محمد رضا داودی 4
1 استادیار، گروه عمران دانشگاه آیت ا... العظمی بروجردی
2 استادیار، دانشکده ی مهندسی عمران، دانشگاه پیام نور، تهران
3 استاد دانشکده مهندسی عمران دانشگاه صنعتی نوشیروانی بابل
4 دانشیار دانشکده مهندسی عمران دانشگاه صنعتی نوشیروانی بابل
10.22034/25.1.45
چکیده
شبکه‌های دولایه‌ی ساخته‌شده با سیستم پیونده‌ی گویسان که دسته‌ی مهمی از سازه‌های فضاکار هستند، ازجمله سازه‌های رایج و پرکاربرد برای اجرای سقف‌ها می‌باشند. شناسایی مشخصات دینامیکی این سازه‌ها برای تکمیل فرآیند پایش سلامت سازه‌ای، به‌روزرسانی مدل اجزای محدود و تشخیص آسیب ضروری است. محدودیت‌های روش شناسایی ورودی-خروجی باعث شده که در سازه‌های مهندسی از روش خروجی-تنها استفاده شود. در این کار، مدل فیزیکی یک شبکه‌ی دولایه در آزمایشگاه ساخته شد. با انجام آزمایش مودال خروجی-تنها و با استفاده از دو روش حوزه‌ی بسامد تجزیه در حوزه‌ی بسامد تعمیم یافته (EFDD) و تجزیه در حوزه‌ی بسامد با برازش منحنی (CFDD) و نیز دو روش حوزه‌ی زمان شناسایی زیرفضای تصادفی با داده‌ی خام (SSI-DD) و شناسایی زیرفضای تصادفی با کوواریانس داده‌ها (SSI-Cov)، پارامترهای مودال این شبکه‌ی دولایه تعیین شدند. برای تحریک شبکه از دو نوع بارگذاری تحریک مستقیم و تحریک غیرمستقیم استفاده شد. به‌منظور بررسی دقت پارامترهای شناسایی‌شده، یک آزمایش مودال ورودی-خروجی نیز بر روی شبکه انجام و نتایج حاصله به عنوان مبنا گزیده شدند. نتایج نشان داده که دقت پارامترهای شناسایی شده با بارگذاری مستقیم بالاتر از نتایج مشابه با بارگذاری غیرمستقیم بوده است. بیشترین اختلاف نتایج بسامد‌های طبیعی شبکه‌ی دولایه با نتایج مبنا مربوط به مود دوم شبکه و برابر 07/2 % بوده است. میانگین خطای نسبی پارامترهای شناسایی شده نشان داده که روش‌های حوزه‌ی زمان، نسبت میرایی را با خطای کمتری تخمین زدند؛ درحالی‌که روش‌های حوزه‌ی بسامد، بسامد‌های طبیعی و شکل‌های مودی را با دقت بالاتری شناسایی نمودند.

کلیدواژه‌ها

موضوعات

عنوان مقاله English

Output-only Structural Identification of a Double-layer Grid with ball joint system

نویسندگان English

Seyed Rasoul Nabavian 1
Seyedamin Mostafavian 2
B. Navayi Neya 3
Mohammad Reza Davoodi 4
1 Assistant professor, Department of Civil Engineering, Ayatollah Boroujerdi University
2 Assistant professor, Department of Civil Engineering, P‌a‌y‌a‌m‌e N‌o‌o‌r U‌n‌i‌v‌e‌r‌s‌i‌t‌y, T‌e‌h‌r‌a‌n
3 Professor, Department of civil Engineering, Babol Noshirvani University of Technology
4 Associate professor, Department of Civil Engineering, Babol Noshirvani University of Technology
چکیده English

High stiffness to weight ratio, ease and speed of handling, as well as having favorable architectural appearance cause that, double layer grids with ball joint system are widely used to cover large spans. A double-layer grid has a complex behavior due to a large number of elements and a particular type of joints; hence, structural identification of this type of structure is an important issue, which refers to the determination of natural frequencies, mode shapes, and damping ratios. These results are necessary to complete the structural health monitoring, finite element model updating and damage detection. Due to the limitations of input-output methods, modal parameters of civil engineering structures such as bridges, dams, tall buildings, and double layer grids are determined mainly by output-only modal identification. In output-only methods, the vibration parameters are determined based on the information acquired only from the structure’s output. In this work, physical model of a ball jointed double-layer grid with dimensions of 2.8 m at 2.8 m, which is supported on four steel pipes in four corners was made in the laboratory. The grid consists of 32 members connected together with 13 balls, each having ten threaded holes at different angles. each member consists of a middle pipe and connecting parts including conical piece, sleeve and high strength bolt at both ends of the pipe. The middle pipe has the nominal length, diameter and thickness of 120 cm, 7.64 cm and 0.35 cm, respectively. The horizontal center to center distance of adjacent balls in each layer of the grid is 1.414 m and the total height of the structure includes the column length (1.3 m) and the distance between the top and bottom layers (1 m), which is equal to 2.3 m in total. The approximate weight of the structure is 3532 N. All the members and the balls used in the grid are identical. After all the members of the grid have been assembled, the bolt at each joint is tightened in a series of steps by twisting the corresponding sleeve. Exciting the grid, its acceleration response was measured. The modal parameters were obtained using four output-only modal identification techniques; namely enhanced frequency decomposition (EFDD), curve-fit frequency domain decomposition (CFDD), data-driven stochastic subspace identification (SSI-DD) and covariance-driven stochastic subspace identification (SSI-Cov). Two types of excitations were used in output-only modal tests, namely direct and indirect excitations. Since the modal parameters obtained via input-output modal analysis have less uncertainty compared to the output-only modal analysis techniques, an input-output modal test was also performed and the results are considered as reference values. It deduced that parameters identified in the direct excitation, were more accurate compared to indirect excitation. The results showed that the natural frequencies and mode shapes of the double-layer grid were estimated with a high accuracy via the four methods. The greatest relative difference between the natural frequencies belonged to the second mode and equaled 2.07%. The dispersion of estimated damping was much higher compared to natural frequencies and mode shapes. The results indicated that identified damping in the direct excitation was lower than indirect one. Among the 4 methods, SSI-Cov had the least error in damping estimation of the double-layer grid. The values of estimated modal damping ratios were relatively low (fraction of 1%). The mean relative error of the identified parameters showed that the time-domain methods estimated the damping ratios with less error; While the frequency-domain methods identified natural frequencies and mode shapes with higher accuracy.

کلیدواژه‌ها English

Double-layer grid
Structural identification
OMA
Time-domain methods
Frequency-domain methods
[1] H. Fathnejat, P. Torkzadeh, E. Salajegheh, R. Ghiasi, Structural Damage Detection by Model Updating Method Based on Cascade Feed-Forward Neural Network as an Efficient Approximation Mechanism, Int. J. Optim. Civ. Eng. 4 (2014) 451–472
[2] S.R.H. Vaez, N. Fallah, A. Mohammadzadeh, Damage Identification in Large-scale Double-layer Truss Structures Via a Two-stage Approach, Journal of Stress Analysis 3 (2) (2019) 95-107.
[3] Teimouri, H., Davoodi, M.R., Mostafavian, S.A. and Khanmohammadi, L, Damage Detection in Double Layer Grids with Modal Strain Energy Method and Dempster-Shafer Theory, Civil Engineering Infrastructures Journal 2021, 54(2): 253-266.
[4] Teimouri, H., Davoodi, M. R., Mostafavian, S. A. Detecting damage location and severity in a double layer grid using modal strain energy method and data fusion. Journal of Structural and Construction Engineering, 2020; 7(3): 35-54. Doi: 10.22065/jsce.2018.126917.1518.
[5] Tüfekci, Mertol & Tufekci, Ekrem & Dikicioglu, Adnan. (2020). Numerical Investigation of the Collapse of the Steel Truss Roof and a Probable Reason of Failure. 10.20944/preprints 202010.0151.v2.
[6] Fu, F., Parke, G.A.R. Assessment of the Progressive Collapse Resistance of Double-Layer Grid Space Structures Using Implicit and Explicit Methods. Int J Steel Struct 18, 831–842 (2018). https://doi.org/10.1007/s13296-018-0030-1
[7] Y. S. Hamid, P. Disney, and G. a R. Parke, “Progressive Collapse of Double-Layer Space Trusses,” Conference: IABSE-IASS SYMPOSIUM LONDON 2011, At London.
[8] Davoodi MR, Mostafavian SA, Nabavian SR, Jahangiry GH. Determining minimum number of required accelerometers for output-only structural identification of frames. arXiv preprint arXiv:2010.07490. 2020 Oct 15.
[9] A. Cunha, E. Caetano, From input-output to output-only modal identification of civil engineering structures, SAMCO Final Rep. (2005) 1–22.
[10] C. Rainieri, G. Fabbrocino, Operational modal analysis for the characterization of heritage structures, Geofizika. 28 (2011) 109–126.
[11] M. Batel, Operational modal analysis-Another way of doing modal testing, Sound Vib. (2002) 22–27.
[12] D.F. Giraldo, W. Song, S.J. Dyke, J.M. Caicedo, Modal Identification through Ambient Vibration: Comparative Study, J. Eng. Mech. 135 (2009) 759–770. doi:10.1061/(ASCE)0733-9399(2009)135:8(759).
[13] Tarinejad R, Pourgholi M, Yaghmaei-Sabegh S. System Identification of Arch Dams Using Balanced Stochastic Subspace Identification. MCEJ 2017; 17 (1) :53-64
[14] C.E. Ventura, T. Horyna, Measured and calculated modal characteristics of heritage court tower in Vancouver, B.C, Exp. Tech. 24 (2000) 44–47. doi:10.1111/j.1747-1567.2000. tb 02272.x.
[15] F.N. Kudu, Ş. Uçak, G. Osmancikli, T. Türker, A. Bayraktar, Estimation of damping ratios of steel structures by Operational Modal Analysis method, J. Constr. Steel Res. 112 (2015) 61–68.
[16] L. Maliar, D. Kuchárová, Ľ. Daniel, Operational Modal Analysis of the Laboratory Steel Truss Structure, Transp. Res. Procedia. 40 (2019) 800–807.
[17] W. Shi, J. Shan, X. Lu, Modal identification of Shanghai World Financial Center both from free and ambient vibration response, Eng. Struct. 36 (2012) 14–26.
[18] J.M.W. Brownjohn, A. Raby, J. Bassitt, A. Antonini, E. Hudson, P. Dobson, Experimental modal analysis of British rock lighthouses, Mar. Struct. 62 (2018) 1–22.
[19] K.W. Min, J. Kim, S.A. Park, C.S. Park, Ambient vibration testing for story stiffness estimation of a heritage timber building, Sci. World J. (2013).
[20] Shabani, A., Feyzabadi, M., & Kioumarsi, M. (2022). Model updating of a masonry tower based on operational modal analysis: The role of soil-structure interaction. Case Studies in Construction Materials, 16, e00957.‌
[21] Ni, Y. C., Alamdari, M. M., Ye, X. W., & Zhang, F. L. (2021). Fast operational modal analysis of a single-tower cable-stayed bridge by a Bayesian method. Measurement, 174, 109048.‌
[22] Li, J., Bao, T., & Ventura, C. E. (2022). An automated operational modal analysis algorithm and its application to concrete dams. Mechanical Systems and Signal Processing, 168, 108707
[23] Avci, O., Alkhamis, K., Abdeljaber, O., Alsharo, A., & Hussein, M. (2022, March). Operational modal analysis and finite element model updating of a 230 m tall tower. In Structures (Vol. 37, pp. 154-167). Elsevier.‌
[24] Civera, M., Mugnaini, V., & Zanotti Fragonara, L. (2022). Machine learning‐based automatic operational modal analysis: A structural health monitoring application to masonry arch bridges. Structural Control and Health Monitoring, 29(10), e3028.‌
[25] SAIDIN, Siti Shahirah, et al. Operational modal analysis and finite element model updating of ultra-high-performance concrete bridge based on ambient vibration test. Case Studies in Construction Materials, 2022, 16: e01117.‌
[26] Providakis, C. P., Mousteraki, M. G., & Providaki, G. C. (2023). Operational Modal Analysis of Historical Buildings and Finite Element Model Updating Using α Laser Scanning Vibrometer. Infrastructures, 8(2), 37.‌
[27] K.A. Kvåle, O. Øiseth, A. Rønnquist, Operational modal analysis of an end-supported pontoon bridge, Eng. Struct. 148 (2017) 410–423.
[28] A. Cabboi, F. Magalhães, C. Gentile, Á. Cunha, Automated modal identification and tracking: Application to an iron arch bridge, Struct. Control Heal. Monit. 24 (1) (2017) e1854. doi:10.1002/stc.1854.
[29] S. Diord, F. Magalhães, Á. Cunha, E. Caetano, High spatial resolution modal identification of a stadium suspension roof: Assessment of the estimate’s uncertainty and of modal contributions, Eng. Struct. 135 (2017) 117–135. doi:10.1016/j.engstruct.2016.12.060.
[30] M. Diaferio, D. Foti, M. Mongelli, N.I. Giannoccaro, P. Andersen, Operational Modal Analysis of a Historic Tower in Bari, Springer, New York, (2011) 335–342. doi:10.1007/978-1-4419-9316-8_31.
[31] A.C. Altunişik, O.Ş. Karahasan, A.F. Genç, F.Y. Okur, M. Günaydin, E. Kalkan, S. Adanur, Modal parameter identification of RC frame under undamaged, damaged, repaired and strengthened conditions, Meas. J. Int. Meas. Confed. 124 (2018) 260–276. doi:10.1016/j.measurement.2018.04.037.
[32] A. Bajrić, J. Høgsberg, F. Rüdinger, Evaluation of damping estimates by automated Operational Modal Analysis for offshore wind turbine tower vibrations, Renew. Energy. 116 (2018) 153–163. doi:10.1016/j.renene.2017.03.043.
[33] S. Castellanos-Toro, M. Marmolejo, J. Marulanda, A. Cruz, P. Thomson, Frequencies and damping ratios of bridges through Operational Modal Analysis using smartphones, Constr. Build. Mater. 188 (2018) 490–504. doi:10.1016/j.conbuildmat.2018.08.089.
[34] L. Gaul, H. Albrecht, J. Wirnitzer, Semi-active friction damping of large space truss structures, Shock Vib. 11 (2004) 173–186.
[35] S.A. Mostafavian, M.R. Davoodi, J. Vaseghi Amiri, Experimental determination of the natural frequencies of a full-scale double layer grid with ball joint system, 15th World Conf. Earthq. Eng. (2012).
[36] Salehi, S., Davoodi, M. R., Mostafavian, S. Estimation of Damping for a Double-Layer Grid Using Input-Output and Output-Only Modal Identification Techniques. Civil Engineering Infrastructures Journal, 2020; 53(2): 295-311. doi: 10.22059/ceij.2019.284169.1594
[37] Nabavian, S. R., Davoodi, M. R., Navayi Neya, B., Mostafavian, S. A. Damping estimation of a double-layer grid by output-only modal identification. Scientia Iranica, 2021; 28(2): 618-628. doi: 10.24200/sci.2019.51919.2424
[38] Salehi, S., Mostafavian, S., Davoodi, M. Effect of the frequency spacing on modal damping estimation of a double-layer grid. Sharif Journal of Civil Engineering, 2021; 37.2(1.1): 105-115.
[39] M.R. Davoodi, J.V. Amiri, S. Gholampour, S.A. Mostafavian, Determination of nonlinear behavior of a ball joint system by model updating, J. Constr. Steel Res. 71 (2012) 52–62. doi:10.1016/J.JCSR.2011.11.011.
[40] S.A. Mostafavian, M.R. Davoodi, J. Vaseghi Amiri, Ball joint behavior in a double layer grid by dynamic model updating, J. Constr. Steel Res. 76 (2012) 28–38.
[41] Magalhães, F., Cunha, A., Caetano, E. and Brincker, R. (2010). “Damping Estimation Using Free Decays and Ambient Vibration Tests”, Mechanical Systems and Signal Processing 24 (5), 1274–90.
[42] E. Orlowitz, A. Brandt, Comparison of experimental and operational modal analysis on a laboratory test plate, Measurement. 102 (2017) 121–130. doi:10.1016/j.measurement.2017.02.001.
[43] Mostafavian, S., Nabavian, S. R., Davoodi, M. R., Navayi Neya, B. Output-only Modal Analysis of a Beam Via Frequency Domain Decomposition Method Using Noisy Data. International Journal of Engineering, 2019; 32(12): 1753-1761. doi: 10.5829/ije.2019.32.12c.08
[44] R. Brincker, L. Zhang, P. Andersen, “Modal Identification from Ambient Responses Using Frequency Domain Decomposition,” Proc. SPIE - Int. Soc. Opt. Eng. 1 (2000).
[45] R. Brincker, C. Ventura, P.Andersen, Damping estimation by frequency domain decomposition, Proceedings of the 19th international modal analysis conference (IMAC). Vol. 1. 2001.
[46] R. Brincker, L. Zhang, P. Andersen, Modal identification of output-only systems using frequency domain decomposition, Smart Mater. Struct. 10 (2001) 441–445. doi:10.1088/0964-1726/10/3/303.
[47] S. Gade, N. Møller, … H., Frequency domain techniques for operational modal analysis, Testart,Tr H,1st I, (2005).
[48] N. Jacobsen, P. Andersen, R, Applications of frequency domain curve-fitting in the EFDD technique, Core.Ac.Uk.B.-P.I.-X.C.& Expo, (2008).
[49] N.J. Jacobsen, P. Andersen, Operational modal analysis on structures with rotating parts, in: ISMA Conf., 2008.
[50] Tarinejad R, Pourgholi M. Processing of Ambient Vibration Results using Stochastic Subspace Identification based on Canonical Correlation Analysis. Modares Mechanical Engineering 2015; 15 (7) :107-118.
[51] Nabavian, S. R., Davoodi, M. R., Navayi Neya, B., Mostafavian, S. A. Effect of noise on output-only structural identification of beams. Journal of Structural and Construction Engineering, 2020; 7(3): 20-34. doi: 10.22065/jsce.2018.130329.1555
[52] R. Brickner, P. Andersen, understanding stochastic subspace identification, in: Proc. IMAC, Int. Modal Anal. Conf., 2006.
[53] B. Peeters, System identification and damage detection in civil engeneering, (2000).
[54] ARTeMIS Modal 4, Issued by Structural Vibration Solutions AVS. NOVI Science Park, Niles Jernes Vej 10, DK 9220 Aalborg East, Denmark.
[55] A.J. Felber, Development of a hybrid bridge evaluation system, (1994).
[56] R. Brincker, C. Ventura, Introduction to operational modal analysis, John Wiley & Sons, 2015.
[57] M.H. Pashaei, M.R. Davoodi, H. Nooshin, Effects of tightness of bolts on the damping of a mero-type double layer grid, Int. J. Sp. Struct. 21 (2006) 103–110.
[58] A.A. Asoor, M.H. Pashaei, Experimentally study on the effects of type of joint on damping, World Appl. Sci. J. 8 (2010) 608–613.
[59] Y. Park, K. Kim, Semi-active vibration control of space truss structures by friction damper for maximization of modal damping ratio, J. Sound Vib. 332 (2013) 4817–4828.
[60] H. Zhang, Q. Han, Y. Wang, Y. Lu, Explicit modeling of damping of a single-layer latticed dome with an isolation system subjected to earthquake ground motions, Eng. Struct. 106 (2016) 154–165.
[61] L. Gaul, H. Albrecht, J. Wirnitzer, Semi-active friction damping of large space truss structures, Shock Vib. 11 (2004) 173–186.
[62] https://www.dytran.com/Model-5802A-Impulse-Sledge-Hammer-P2578.aspx/
[63] https://www.vibetech.com/mescope
[64] P. Avitabile, Modal Space: Someone Told me that Operating Modal Analysis Produces Better Results and that Damping is Much More Realistic, Exp. Tech. 30 (2006) 25–26. doi:10.1111/j.1747-1567.2006.00102.x.
[65] T. Lauwagie, A Comparison of Experimental, Operational, and Combined Experimental-Operational Parameter Estimation Techniques, Proceedings of Conference on Noise and Vibration Engineering (2006) 2997–3006.
[66] R.J. Allemang, The modal assurance criterion - Twenty years of use and abuse, Sound Vib. 37 (2003) 14–21. doi:10.1016/j.chemgeo.2006.02.014.
مهندسی عمران مدرس
دوره 25، شماره 1 - شماره پیاپی 81
فروردین و اردیبهشت 1404
صفحه 45-58