A new model as a damage index in an eigen value problem with application in health monitoring of offshore jacket platform

Subject Areas : Statistics

Mehdi  Alavinejhad ¹ (Department of marine industries- Science and Research branch- Islamic Azad universit)
Madjid  Ghodsi Hassanabad ² (Department of Marine Industries-Science and Research branch-Islamic Azad University)
Mohammadjavad  Ketabdari ³ (Department of Maritime Engineering- Amirkabir University of Technology)
Masoud  Nekooei ⁴ (Department of Civil Engineering- Science and Research Branch- Islamic Azad University)

Received: 2021-04-16 Accepted : 2021-06-22 Published : 2021-07-23

Keywords: ماتریس سختی, مسئله مقدار ویژه, سکوی شابلونی فراساحلی, انرژی کرنش مودال, تشخیص آسیب,

Abstract :

A set of second-order differential equations (the initial value problem) is used to analyze the vibrations of structures. This method is based on changing the second-order differential equations to the eigenvalue problem, which is usually used for modal analysis of structures. This problem involves a matrix equation with mass and stiffness as coefficient matrices. Changes in some stiffness matrix arrays change eigenvalues ​​and eigenvectors, and changes in stiffness matrices indicate damage to one or more structural members. Therefore, identifying modified arrays is very useful for monitoring the health of structures. Modified stiffness array arrays can be obtained by comparing new eigenvalues ​​and eigenvectors with old ones. The Stubbs Index (Modal Strain Energy) Stubbs (MSE) uses only special vectors to identify injuries. In the improved modal strain energy method (IMSE) proposed by Lee et al., In addition to special vectors, special values ​​are also entered in relation to the damage index. In this research, a new injury index is presented with the development of the above two indicators, which show more accurate results than them. In this study, the health monitoring of a template platform structure of Forouzan Persian Gulf oil field is compared to compare the accuracy of these three indicators. The results show that the new method is more accurate than the Stubbs and IMSE indices, especially in the presence of multiple injuries.

References:

[1] Chopra AK (2020) Dynamics of structures: Theory and applications to earthquake engineering. Fifth edition, Pearson education limited, United Kingdom.

 

[2] Qu ZQ (2004) Model Order Reduction Techniques with application in finite element analysis. Springer-Verlag London Ltd.

 

]3[ علی‌زاده نظر کندی، ح. (1395). خواص تابع مقدار ویژه. پژوهش‌های نوین در ریاضی. سال دوم. شماره 7.

 

]4[ آل‌هوز، ع. باغی‌پور، م. هاشمی، ا. (1398). کران‌هایی برای مقادیر ویژه ماتریس فاصله تعمیم‌یافته در گراف‌ها. پژوهش‌های نوین در ریاضی. سال پنجم. شماره 21.

 

]5[ عبودی، م. (1399). گراف‌هایی که دارای تعداد کمی مقدار ویژه مثبت هستند. پژوهش‌های نوین در ریاضی. سال ششم. شماره 27. صفحه 60-53.

 

[6] Lai HY, Hsu JC, Chen CK (2008) An innovative eigenvalue problem solver for free vibration of Euler_Bernoulli beam by using the Adomian decomposition method. Computers and Mathematics with Applications 56:3204-3220.

 

[7] Hsu JC, Lai HY, Chen CK (2009) An innovative eigenvalue problem solver for free vibration of uniform Timoshenko beams by using the Adomian modified decomposition method. J of Sound and Vibration 325:451–470.

 

[8] Farooq U, Feeny BF (2008) Smooth orthogonal decomposition for modal analysis of randomly excited systems. J of Sound and Vibration 316:137–146.

 

[9] Hansen MH (2004) Aeroelastic stability analysis of wind turbines using an eigenvalue approach. Wind Energy 7:133–143.

 

[10] Maurini C, Porfiri M, Pouget J (2006) Numerical methods for modal analysis of stepped piezoelectric beams. J of Sound and Vibration 298:918–933.

 

[11] Agudo A, Agapito L, Calvo B, Montiel JMM (2014) Good Vibrations: a modal analysis approach for sequential non-rigid structure from motion. IEEE conference on computer vision and pattern recognition. .https://doi.org/ 10.1109/CVPR.2014.202.

 

[12] Datta BN (2002) Finite-element model updating, eigenstructure assignment and eigenvalue embedding techniques for vibration systems. Mechanical systems and signal processing 16(1):83–96.

 

[13] Yan WJ, Ren WX (2011) A direct algebraic method to calculate the sensitivity of element modal strain energy. Int J Numer Meth Biomed. Engng 27:694–710.

 

[14] Kim JT, Stubbs N (2002) Improved damage identification method based on modal information. J of Sound and Vibration 252:223-238.

 

[15] Li YY, Cheng L, Yam LH, Wong WO (2002) Identification of damage locations for plate-like structures using damage sensitive indices: strain modal approach. Computers & Structures 80:1881-1894.

 

[16] Yang HZ, Li HJ, Wang S (2003) Damage localization of offshore platforms under ambient excitation. China Ocean Engineering 17(4): 495-504.

 

[17] Ge M, Lui EM (2005) Structural damage identification using system dynamic properties. Computers & Structures 83(2185-2196).

 

[18] Shih HW, Thambiratnam D, Chan T (2009) Vibration based structural damage detection in flexural members using multi-criteria approach. J of Sound and Vibration, 323(3-5):645-661.

 

[19] Hu H, Wu C (2009) Development of scanning damage index for the damage detection of plate structures using modal strain energy method. Mechanical Systems and Signal Processing 23:274-287.

 

[20] Seyedpoor SM (2012) A two stage method for structural damage detection using a modal strain energy based index and particle swarm optimization. Int J of Non-Linear Mechanics 47:1-8.

 

[21] Liu F, Li H, Li W, Wang B (2014) Experimental study of improved modal strain energy method for damage localisation in jecket-type offshore wind turbines. Renewable Energy 72:174-181.

 

[22] Seyedpoor SM, Yazdanpanah O (2014) An efficient indicator for structural damage localization using the change of strain energy based on static noisy data. Applied Mathematical Modeling 38:2661-2672.

 

[23] Wang S, Liu F, Zhang M (2014) Modal strain energy based structural damage localization for offshore platform using simulated and measured data. J of Ocean University of China 13:397-406.

 

[24] Li Y, Wang S, Zhang M, Zheng C (2016) An improved modal strain energy method for damage detection in offshore platform structures. J Marine Sci Appl 15:182-192.

 

[25] Ghasemi MR, Nobahari M, Shabakhty N (2018) Enhanced optimization-based structural damage detection method using modal strain energy and modal frequencies. Engineering with Computers 34:637-647.

 

[26] Kim JT, Stubbs N (1995) Damage detection in offshore jacket structures from limited modal information. Int J of Offshore and Polar Engineering 5:58-66.

 

[27] Stubbs N, Kim JT, Farrar CR (1995) Field verification of a non-destructive damage localization and severity estimation algorithm. Proc of the 13th Int Modal Analysis Conference 210.

 

[28] Roy R, Craig JR, Kurdila AJ (2006) Fundamentals of Structural Dynamics. 2nd Edition, John wiley & sons.

 

[29] Copyright (2018) 3D Frame Analysis Library Technical Notes & Examples. ENGISSOL Ltd. https:// www.engissol.com/ Downloads/ Technical% 20Notes% 20and% 20examples. pdf.