مهندسی مکانیک مدرس

مهندسی مکانیک مدرس

شناسایی مودال سیستم‌های سازه‌ای با استفاده از یک روش مؤثر مبتنی بر ترکیب انتقال‌پذیری و تبدیل موجک

نویسندگان
دانشکده مهندسی عمران، دانشگاه تبریز
چکیده
اخیراً به منظور شناسایی مشخصات دینامیکی سیستم‌های سازه‌ای، رویکرد جدیدی تحت عنوان تحلیل مودال عملیاتی مبتنی بر انتقال‌پذیری (TOMA) ارائه شده است که پارامترهای مودال سازه‌ها را با استفاده از مفهوم انتقال‌پذیری تعیین می‌کند. در رویکرد TOMA، بر خلاف روش‌های OMA که از فرض ورودی نویز سفید بهره می‌برند، هیچ فرض محدودکننده‌ای برای تحریکات ورودی در نظر گرفته نمی‌شود و پارامترهای مودال سیستم‌های سازه‌ای مبتنی بر ویژگی‌های ماتریس انتقال‌پذیری استخراج می‌گردند. روش‌های انتقال‌پذیری نیز همانند سایر روش‌های حوزه فرکانس، در شناسایی مقادیر میرایی سیستم نتایج چندان قابل قبولی ارائه نمی‌دهند. از این رو در مقاله حاضر یک روش ترکیبی جدید تحت عنوان انتقال‌پذیری طیف فوریه-تبدیل موجک (FST-WT) پیشنهاد شده است که علاوه بر تعیین فرکانس‌های طبیعی و اشکال مودی سیستم، به شناسایی دقیق مقادیر میرایی مبتنی بر ویژگی‌های تبدیل موجک نیز می‌پردازد. در این تحقیق، قابلیت روش FST-WT در شناسایی و استخراج پارامترهای مودال یک سیستم 5 درجه آزادی تحت ارتعاش آزاد، با استفاده از پاسخ‌های بدست آمده از مدل سیمولینک متلب مورد بررسی قرار گرفته است. برای این منظور فرکانس‌ها و اشکال مودی به ترتیب از عکس مقدار تکین دوم و اولین بردار تکین چپ ماتریس انتقال‌پذیری استخراج شده و مقادیر میرایی نیز با استفاده از سیگنال‌های تک فرکانسی (ضرایب موجک) بدست آمده از تبدیل موجک، مبتنی بر معیار آنتروپی حداقل شانون تعیین گردیده‌اند. مقایسه نتایج شناسایی تطابق خوبی را با مقادیر دقیق نشان می‌دهد.
کلیدواژه‌ها

موضوعات


عنوان مقاله English

Modal identification of structural systems using an effective method based on combining the transmissibility and wavelet transform

نویسندگان English

Majid Damadipour
Reza Tarinejad
Mohammad Hossein Aminfar
Faculty of Civil Engineering
چکیده English

Recently, a new approach called Transmissibility based Operational Modal Analysis (TOMA) has been presented in order to identify the dynamic characteristics of structural systems that determines the modal parameters of structures using the concept of transmissibility. In the TOMA approach, unlike OMA methods that use the assumption of white noise input, no limiting assumption is considered for the input excitations, and the modal parameters of structural systems are extracted based on the features of transmissibility matrix. The transmissibility methods, like other frequency domain methods, do not present very satisfactory results in identifying the damping values. Therefore, in the present paper, a new combined method called Fourier Spectral Transmissibility-Wavelet Transform (FST-WT) is proposed which, in addition to determining the natural frequencies and mode shapes of the system, also addresses the exact detection of damping values based on the features of wavelet transform. In this research, the capability of the FST-WT method in identifying and extracting the modal parameters of a 5-DOF system under free vibration is investigated using the responses obtained from the MATLAB Simulink model. For this purpose, the frequencies and mode shapes are respectively extracted from the inverse of the second singular value and the first left singular vector of transmissibility matrix, and the damping values are also determined using the single frequency signals (wavelet coefficients) obtained from wavelet transform based on the minimal Shannon entropy criterion. The comparison of the identification results shows a good agreement with the exact values.

کلیدواژه‌ها English

Transmissibility based Operational Modal Analysis (TOMA)
Fourier Spectral Transmissibility-Wavelet Transform (FST-WT) method
Inverse of second singular value
Single frequency signals
Minimal Shannon entropy criterion
[1] J. Yadegari, 0. Bahar, Modal parameter identification using ambient vibration testing with introducing a new software, Civil Engineering Infrastructures Journal. Vol. 44, No. 1, pp. 121-130, 2010. (In Persian
[2] B. Peeters, G. De Roeck, Reference based stochastic subspace identification in civil engineering, Inverse Problems in Engineering, Vol. 8, No. 1, pp. 47-74, 2000.
[3] J. N. Juang, R. S. Pappa, An eigensystem realization algorithm for modal parameter identification and model reduction, Journal of Guidance, Control, and Dynamics, Vol. 8, No. 5, pp. 620-627, 1985.
[4] M. D. Hill, An experimental verification of the eigensystem realization algorithm for vibration parameter identification. Student Research Accomplishments: Multidisciplinary Center for Earthquale Engineering Research University at Bufalo, pp. 29-37, 2004.
[5] A. J. Felber, Development of Hybrid Bridge Evaluation System, PhD thesis, University of British Columbia, Vancouver, Canada, 1993.
[6] R. Brincker, L. Zhang, P. Andersen, Modal identification from ambient responses using frequency domain decomposition, Proceedings of the 18th International Modal Analysis Conference (IMAC), San Antonio, Texas, February 7-10, 2000.
[7] R. Brincker, C. E. Ventura, P. Andersen, Damping estimation by frequency domain decomposition, Proceedings of the 19th International Modal Analysis Conference (IMAC), Kissimmee, Florida, February 5-8, 2001.
[8] L. Zhang, R. Brincker, P. Andersen, An overview of operational modal analysis: Major development and issues, Proceedings of the 1St International Operational Modal Analysis Conference (IOMAC), Copenhagen, Denmark, April 26-27, 2005.
[9] C. E. Ventura, B. Laverick, R. Brincker, P. Andersen, Comparison of dynamic characteristics of two instrumented tall buildings, Proceedings of the 21st International Modal Analysis Conference (IMAC), Kissimmee, Florida, February 3-6, 2003.
[10] R. Brincker, L. Zhang, P. Andersen, Modal identification of output only systems using frequency domain decomposition, Journal of Smart Materials and Structures, Vol. 10, No. 3, pp. 441-445, 2001.
[11] J. Lardies, M. N. Ta, M. Berthillier, Modal parameter estimation based on the wavelet transform of output data, Archive of Applied Mechanics, Vol. 73, No. 9, pp. 718-733, 2004.
[12] T. Kijewski, A. Kareem, Wavelet transforms for system identification in civil engineering, Computer-Aided Civil and Infrastructure Engineering, Vol. 18, No. 5, pp. 339-355, 2003.
[13) M. Damadipour, System Identification of a Concrete Arch Dam and Calibration ofits Finite Element Model with Emphasis on Nonuniform Ground Motion, Master of Science Thesis, Faculty of Civil Engineering, University of Tabriz, Tabriz, Iran, 2012. (In Persian
[14] R. Tarinejad, M. Damadipour, Modal identification of structures by a novel approach based on FDD-wavelet method, Journal ofSound and Vibration, Vol. 333. No. 3. pp. 1024-1045.2014.
[15] R. Tarinejad, M. Damadipour, Operational modal analysis of structures using a new time-frequency domain approach. Proceedings of the 6th International Operational Modal Analysis Conference (IOMAC), Gijon, Spain, May 12-14, 2015.
[16] R. Tarinejad, M. Damadipour, Extended FDD-WT method based on correcting the errors due to non-synchronous sensing of sensors, Mechanical Systems and Signal Processing. Vol. 72, No. 1, pp. 547-566, 2016.
[17] W. X. Ren, Z. H. Zong, Output-only modal parameter identification of civil engineering structures. Structural Engineering and Mechanics, Vol. 17, No. 3-4, pp. 429-444, 2004.
[18] C. Devriendt, P. Guillaume, The use of transmissibility measurements in output-only modal analysis, Mechanical Systems and Signal Processing, Vol. 21, No. 7, pp. 2689-2696, 2007.
[19] C. Devriendt, P. Guillaume, Identification of modal parameters from transmissibility measurements. Journal of Sound and Vibration, Vol. 314, No. I, pp. 343-356, 2008.
[20] G. H. Golub, C. F. VanLoan, Matrix Computations, Fourth Edition, pp. 76-80, Baltimore: Johns Hopkins University Press, 2013.
[21] W. J. Yan, W. X. Ren, Operational modal parameter identification from power spectrum density transmissibility, Computer-Aided Civil and Infrastructure Engineering, Vol. 27, No. 3, pp. 202-217, 2012.
[22] I. G. AraOjo, J. E. Laier, Operational modal analysis using SVD of power spectral density transmissibility matrices. Mechanical Systems and Signal Processing, Vol. 46, No. 1, pp. 129-145, 2014.
[23] W. J. Yan, W. X. Ren, An Enhanced Power Spectral Density Transmissibility (EPSDT) approach for operational modal analysis: theoretical and experimental investigation, Engineering Structures, Vol. 102, No. 1, pp. 108-119, 2015.
[24] J. Lin, L. S. Qu, Feature extraction based on Morlet wavelet and its application for mechanical fault diagnosis, Journal of Sound and Vibration, Vol. 234, No. 1, pp. 135-148, 2000.
[25] R. Polikar, The story of wavelets, Physics and Modern Topics in Mechanical and Electrical Engineering, pp. 192-197, Wisconsin: World Scientific and Engineering Society Press, 1999.
[26) G. Jinghuai, L. Youming, C. Wenchao, On the instantaneous attributes analysis of seismic data via wavelet transform, 68th Annual International Meeting of the Society of Exploration Geophysicists, New Orleans. USA, September 13-18, 1998.
[27) J. Lardies, S. Gouttebroze, Identification of modal parameters using the wavelet transform. International Journal of Mechanical Science, Vol. 44, No. 11, pp. 2263-2283, 2002.
[28] B. Yan, A. Miyamoto, A comparative study of modal parameter identification based on wavelet and Hilbert-Huang transforms, Computer-Aided Civil and Infrastructure Engineering, Vol. 21, No. 1, pp. 9-23, 2006.
[29] J. Butterworth, J. H. Lee, B. Davidson. Experimental determination of modal damping from full scale testing, 13th World Conference on Earthquake Engineering, Vancouver, Canada, August 1-6, 2004. [30] R. Brinker, C. Ventura, Introduction to Operational Modal Analysis, First Edition, pp. 151-185. Chichester: John Wiley & Sons, 2015.