استفاده از روش تجزیه متعامد بهینه جهت استخراج اطلاعات مودال سازه‌ها تحت اثر بارهای ضربه‌ای

نوع مقاله : Articles

نویسندگان

گروه سازه، دانشکده مهندسی عمران، دانشگاه تربیت دبیر شهید رجایی، تهران، ایران

چکیده

تعیین مشخصات مودال سازه‌ها نظیر فرکانس‌های طبیعی و نسبت‌های میرایی، از جمله موضوعات پر اهمیت در مهندسی سازه به شمار می‌رود. در این راستا ارائه یک روش آزمایشگاهی کم‌هزینه و پایدار در برابر انواع نویزها همواره حائز اهمیت است. در مقاله حاضر روش جدیدی جهت تعیین فرکانس‌های طبیعی و نسبت‌های میرایی سازه‌ها با استفاده از تکنیک ریاضی تجزیه متعامد بهینه ارائه شده است. در این روش از پاسخ ارتعاشی سازه به بارهای ضربه‌ای، بدون نیاز به محاسبه اندازه ضربه استفاده می‌شود. یکی از نقاط قوت روش پیشنهادی، تجمیع نویز آزمایشگاهی در مودهای بی‌اهمیت بالا می‌باشد. به‌عبارت‌دیگر در فرایند محاسبه فرکانس‌های مربوط به چند مود اول، نویز آزمایشگاهی وارد محاسبات نمی‌شود و در مودهای بالاتر که از اهمیت کمتری برخوردارند، تجمیع خواهد شد. کارایی روش جدید با استفاده از شبیه‌سازی عددی و نیز صحت‌سنجی آزمایشگاهی مورد ارزیابی قرار گرفت. روش پیشنهادی به دلیل سادگی، کم‌هزینه بودن و عدم نیاز به تجهیزات پیشرفته آزمایشگاهی می‌تواند به‌عنوان ابزاری مفید جهت تعیین اطلاعات مودال یک سازه و همچنین کنترل نتایج به‌دست‌آمده از روش‌های آزمایشگاهی دیگر به‌کار رود.

کلیدواژه‌ها


عنوان مقاله [English]

Determination of the Modal Information of Structures under Impact Loads Using Proper Orthogonal Decomposition

نویسندگان [English]

  • Amir Zayeri Baghlani Nejad
  • Mussa Mahmoudi Sahebi
Department of Civil Engineering, Shahid Rajaee Teacher Training University, Tehran, Iran
چکیده [English]

Determining the modal characteristics of structures such as natural frequencies and damping ratios is one of the most important issues in structural engineering. In this regard, providing a low-cost and robust experimental method against all types of noises is very important. In the present paper, a new algorithm for determining the natural frequencies and damping ratios of structures under impact loads using the proper orthogonal decomposition technique is presented. This method uses the vibrational response of the structure to impact loads, without the need to calculate the impact magnitude. One of the strength points of the proposed methodology is the accumulation of laboratory noises in the latest modes. In other words, in the process of calculating the frequencies related to the first few modes, laboratory noise does not enter the calculations and will be aggregated in higher modes that are less important. The feasibility and efficiency of the new method was evaluated using numerical simulations as well as laboratory validation. In this research, four pure numerical models were used to evaluate and validate the accuracy of the proposed algorithm. These models include a simply supported beam, a two-dimensional portal frame, a three-dimensional truss and a clambed-clambed beam. The natural frequencies and damping ratios of the mentioned models were calculated using the new method, then the results were compared with those that obtained from the finite element method. Very good agreement was observed between the results of the two methods. For further investigation, various states such as the effect of the noise on the results, the effect of multiple impact loads and the effect of the number of sensors were also studied. The results of these numerical studies showed that the proposed method is very stable and robust against laboratory noises and has small errors. Acceptable results can be obtained in using a few numbers of sensors (even one sensor) and repetition of the test. Also, the results for multiple impact loads are almost similar to the results obtained from the excited state with a simple impulse load. In this study, in order to further investigate the efficiency of the POD based method, a small-scale laboratory model developed at Shahid Rajaee Teacher Training University and whose modal information has already been calculated using the closed image processing method, was studied. Good agreement was observed between the results of the two methods, so it can be another reason for the efficiency and capability of the new method.
Based on various studies, it was concluded that for structures with low damping, the proposed method has acceptable accuracy and with increasing damping, the accuracy of the results gradually decreases. Since conventional structures have a relatively low attenuation, the proposed algorithm is very suitable for determining their modal information. The proposed method due to the availability, cheapness and no need for complex experimental tools can be used as a useful algorithm to determine the modal information of a structure as well as control the results obtained from other experimental methods.

کلیدواژه‌ها [English]

  • Dynamic Experiment
  • Impulse Load
  • Modal Information
  • Proper orthogonal decomposition
1.    Ewins, D.J. (2000) Modal Testing: Theory, Practice and Application. Research Studies Press LTD, Baldock, Hertfordshire, England.
2.    Ewins, D.J. (2000) Basics and state-of-the-art of modal testing. Sadhana, 25(3), 207-220.
3.    Yin, H.P. and Duhamel, D. (2000) Finite difference formulation for modal parameter estimation. Journal of sound and vibration, 231(2), 259-275.
4.    Lardies, J. and Gouttebroze, S. (2002) Identification of modal parameters using the wavelet transform. International Journal of Mechanical Sciences, 44(11), 2263-2283.
5.    Le, T.P. and Argoul, P. (2004) Continuous wavelet transform for modal identification using free     decay response. Journal of Sound and Vibration,        277(1-2), 73-100.
6.    Yang, K., Yu, K., and Li, Q. (2013) Modal parameter extraction based on Hilbert transform   and complex independent component analysis     with reference. Mechanical Systems and Signal Processing, 40(1), 257-268.
7.    Yan, W.J. and Katafygiotis, L.S. (2015) A two-stage fast Bayesian spectral density approach for ambient modal analysis. Part I: posterior most probable value and uncertainty. Mechanical Systems and Signal Processing, 54, 139-155.
8.    Yan, W.J. and 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.
9.    Amezquita-Sanchez, J.P. and Adeli, H. (2016) Signal processing techniques for vibration-based health monitoring of smart structures. Archives of Computational Methods in Engineering, 23(1), 1-15.
10.    Perez-Ramirez, C.A., Amezquita-Sanchez, J.P., Adeli, H., Valtierra-Rodriguez, M., Romero-Troncoso, R.D.J., Dominguez-Gonzalez, A., and Osornio-Rios, R.A. (2016) Time-frequency techniques for modal parameters identification of civil structures from acquired dynamic signals. Journal of Vibroengineering, 18(5), 3164-3185.
11.    Sirca Jr, G.F. and Adeli, H. (2012) System identification in structural engineering. Scientia Iranica, 19(6), 1355-1364.
12.    Rathinam, M. and Petzold, L.R. (2003) A new   look at proper orthogonal decomposition. SIAM Journal on Numerical Analysis, 41(5), 1893-1925.
13.    Feeny, B.F. and Liang, Y. (2003) Interpreting proper orthogonal modes of randomly excited vibration systems. Journal of Sound and Vibration, 265(5), 953-966.
14.    Han, S. and Feeny, B. (2003) Application of proper orthogonal decomposition to structural vibration analysis. Mechanical Systems and Signal Processing, 17(5), 989-1001.
15.    Allison, T.C. (2007) System Identification via the Proper Orthogonal Decomposition. Ph.D. Dissertation Virginia Polytechnic Institute and State University, Blacksburg, Virginia.
16.    Kallinikidou, E., Yun, H.B., Masri, S.F., Caffrey, J.P., and Sheng, L.H. (2013) Application of orthogonal decomposition approaches to long-term monitoring of infrastructure systems. Journal of Engineering Mechanics, 139(6), 678-690.
17.    Napolitano, K.L. (2016) ‘Using singular value decomposition to estimate frequency response functions’. In: Topics in Modal Analysis & Testing, 10, Springer, Cham, 27-43.
18.    Liang, Y.C., Lee, H.P., Lim, S.P., Lin, W.Z., Lee, K.H., and Wu, C.G. (2002) Proper orthogonal decomposition and its applications-Part I: Theory. Journal of Sound and vibration, 252(3), 527-544.
19.    Lumley, J.L. (1970) Stochastic Tools in Turbulence. New York: Academic press.
20.    Kosambi, D. (1943) Statistics in function space. Journal of Indian Mathematical Society, 7, 76-88.
21.    Karhunen, K. (1946) Uber Lineare Methoden in der Wahrscheinlichkeitsrechnung. Annals of Academic Science Fennicae, Series A1 Mathematics and Physics, 37, 3-79.
22.    Loeve, M. (1948) Fonctions Al´eatoires du Second Ordre. In: Processus Stochastiques et Mouvement Brownien, P. Levy (ed.), Gauthier-Villars.
23.    Pougachev, V.S. (1953) General theory of the correlations of random functions. Izvestiya Akademii Nauk USSR, 17, 1401-1402.
24.    Obukhov, M. A. (1954) Statistical description of continuous fields. Transactions of the Geophysical International Academy Nauk USSR 24, 3-42.
25.    Sirovich, L. (1987) Turbulence and the dynamics of coherent structures. II. Symmetries and trans-formations. Quarterly of Applied Mathematics, 45(3), 573-582.
26.    Fitzsimons, P.M. and Rui, C. (1993) Determining low dimensional models of distributed systems. Advances in Robust and Nonlinear Control Systems, 53, 9-15.
27.    Eftekhar Azam, S. (2014) Online Damage Detection in Structural Systems: Applications of Proper Orthogonal Decomposition, and Kalman and Particle Filters. Springer Science & Business Media.
28.    Chopra, A.K. (2016) Dynamics of Structures: Theory and Applications to Earthquake Engineering. 5th Ed., Prentice Hall.
29.    Ebrahimian, H., Astroza, R., Conte, J.P., and de Callafon, R.A. (2017) Nonlinear finite element model updating for damage identification of civil structures using batch Bayesian estimation. Mechanical Systems and Signal Processing, 84, 194-222.
30.    Havaran, A. and Mahmoudi Sahebi, M. (2020) Extracting structural dynamic properties utilizing close photogrammetry method. Measurement, 150, 107092.