Skip to main content
SpringerLink
Log in

A novel Tikhonov regularization-based iterative method for structural damage identification of offshore platforms

  • Original article
  • Published:
Journal of Marine Science and Technology Aims and scope Submit manuscript

Abstract

The structural damage identification, which entails finding a best approximate solution to an over-determined system of linear equations, is actually one of the practical problems encountered in structural health monitoring. A major challenge to structural damage identification is the ill-conditioned problem caused by noise contamination and spatially incomplete measurements. A novel Tikhonov regularization iterative method (TRIM) is proposed to solve the ill-conditioned system of linear equations. This method iteratively reconstructs the regularization matrix by gradually updating the regularized solution. A merit is that the false-positive indicators of damage are greatly reduced; and as a result this approach would be able to detect smaller damages that could not be detected by  using traditional approaches. Another development embedded in TRIM is that a procedure, called singular value dichotomy, is developed to determine the regularization parameters. Several problems, such as the tremendous prior trials, due to the application of L-curve, are avoided. A numerical study is conducted on an offshore platform structure to demonstrate the effectiveness of the proposed method. The result shows that the new method outperforms the traditional Tikhonov regularization method in damage identification.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17
Fig. 18
Fig. 19
Fig. 20

Similar content being viewed by others

References

  1. Mojtahedi A, Yaghin M, Hassanzadeh Y et al (2011) Developing a robust SHM method for offshore jacket platform using model updating and fuzzy logic system. Appl Ocean Res 33:398–411

    Article  Google Scholar 

  2. Doebling S, Farrar C, Prime M (1998) A summary review of vibration-based damage identification methods. Shock Vib Dig 30:91–105

    Article  Google Scholar 

  3. Li YY (2010) Hypersensitivity of strain-based indicators for structural damage identification: a review. Mech Syst Signal Pr 24:653–664

    Article  Google Scholar 

  4. Fan W, Qiao PZ (2011) Vibration-based damage identification methods: a review and comparative study. Struct Health Monit 10:83–111

    Article  Google Scholar 

  5. Shi ZY, Law SS, Zhang LM (2000) Structural damage identification from modal strain energy change. J Eng Mech 126:1216–1223

    Article  Google Scholar 

  6. Hu SLJ, Li HJ, Wang SQ (2006) Cross-modal strain energy method for estimating damage severity. J Eng Mech 132(4):429–437

    Article  Google Scholar 

  7. Li HJ, Fang H, Hu SLJ (2007) Damage localization and severity estimate for three-dimensional frame structures. J Sound Vib 301:481–494

    Article  Google Scholar 

  8. Wang SQ, Li HJ, Hu SLJ (2007) Cross modal strain energy method for damage localization and severity estimation. In: International conference on offshore mechanics and arctic engineering. San Diego, California, USA, pp 245–249

  9. Xu MQ, Wang SQ (2017) Cross modal strain energy-based structural damage identification in the presence of noise effects. Adv Mech Eng 9:1–14

    Google Scholar 

  10. Faddeev DK, Faddeeva VN (1962) On ill-conditioned systems of linear equations. Ussr Comput Math Math Phys 1(3):447–454

    Article  Google Scholar 

  11. Stutz LT, Tenenbaum RA, Corrêa RAP (2015) The differential evolution method applied to continuum damage identification via flexibility matrix. J Sound Vib 345:86–102

    Article  Google Scholar 

  12. Entezami A, Shariatmadar H, Sarmadi H (2017) Structural damage identification by a new iterative regularization method and an improved sensitivity function. J Sound Vib 399:285–307

    Article  Google Scholar 

  13. Riley JD (1955) Solving systems of linear equations with a positive definite, symmetric, but possibly ill-conditioned matrix. Math Tables Other Aids Comput 9(51):96–101

    Article  MathSciNet  MATH  Google Scholar 

  14. Golub GH, Hansen PC, O’Leary DP (1999) Tikhonov regularization and total least squares. Siam J Matrix Anal Appl 21:185–194

    Article  MathSciNet  MATH  Google Scholar 

  15. Engl HW, Ramlau R (2000) Regularization of inverse problems. Kluwer Academic, Norwell, pp 347–366

    Google Scholar 

  16. Hansen PC (2007) Regularization tools version 4.0 for Matlab 7.3. Numer Algorithms 4:189–194

    Article  MathSciNet  MATH  Google Scholar 

  17. Calvetti D, Reichel L (2003) Tikhonov regularization of large linear problems. Bit Numer Math 43:263–283

    Article  MathSciNet  MATH  Google Scholar 

  18. Weber B, Paultre P, Proulx J (2009) Consistent regularization of nonlinear model updating for damage identification. Mech Syst Signal Pr 23:1965–1985

    Article  Google Scholar 

  19. Zhang C, Song GQ, Wu GY (2012) Structure damage identification by finite element model updated with improved Tikhonov regularization. Eng Mech 29:29–30

    Article  Google Scholar 

  20. Tian FZ, Hong ZJ, Zhang C et al (2016) The application of model updating with L1/2-in structural damage identification. J Nanchang Univ (Natural Science) 40:131–136

    Google Scholar 

  21. Guyan RJ (1965) Reduction of stiffness and mass matrices. AIAA J 3:380–380

    Article  Google Scholar 

  22. Hansen PC, O’Leary DP (1993) The use of the L-curve in the regularization of discrete ill-posed problems. Siam J Sci Comput 14:1487–1503

    Article  MathSciNet  MATH  Google Scholar 

  23. Wang SQ (2013) Damage identification in offshore platform structures from limited modal data. Appl Ocean Res 41:48–56

    Article  Google Scholar 

  24. Mottershead JE, Friswell MI (1993) Model updating in structural dynamics: a survey. J Sound Vib 167:347–375

    Article  MATH  Google Scholar 

  25. Messina A, Williams EJ, Contursi T (1998) Structural damage detection by a sensitivity and statistical-based method. J Sound Vib 216(5):791–808

    Article  Google Scholar 

  26. Wang SQ, Liu FS (2010) New accuracy indicator to quantify the true and false modes for eigensystem realization algorithm. Struct Eng Mech 34:625–634

    Article  Google Scholar 

Download references

Acknowledgements

The authors acknowledge the support by the National Science Fund for Distinguished Young Scholars (51625902), the National Natural Science Foundation of China (51379196), and the Taishan Scholars Program of Shandong Province (TS201511016). And the valuable comments from three anonymous reviewers are highly appreciated.

Author information

Authors and Affiliations

  1. Shandong Provincial Key Laboratory of Ocean Engineering, Ocean University of China, Qingdao, 266100, China

    Shuqing Wang, Mingqiang Xu & Zhipeng Xia

  2. College of Civil Engineering, Ludong University, Yantai, 264025, China

    Yingchao Li

Authors
  1. Shuqing Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Mingqiang Xu
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Zhipeng Xia
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Yingchao Li
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Shuqing Wang.

Ethics declarations

Conflict of interest

The authors declare that there is no conflict of interest.

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Wang, S., Xu, M., Xia, Z. et al. A novel Tikhonov regularization-based iterative method for structural damage identification of offshore platforms. J Mar Sci Technol 24, 575–592 (2019). https://doi.org/10.1007/s00773-018-0579-6

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00773-018-0579-6

Keywords

Search

Navigation