Closed-form modal flexibility sensitivity and its application to structural damage detection without modal truncation error

The closed form of the sensitivity of modal flexibility for a real undamped system is derived based on the algebraic eigen sensitivity method. The formula is then adopted to detect the damage location and severity. The merit of the proposed approach over many other exiting modal flexibility sensitivity-based schemes is that it eliminates the adverse effect of the truncating higher-order modes. Moreover, the proposed approach could identify results with sufficient accuracy by employing one mode or multiple modes. To tackle the operational mode shape normalization problem ascribed to the unknown ambient excitation, the scaling factors are employed. A number of assumed damage scenarios in beams has been used to demonstrate the applicability of the proposed damage detection method. It is demonstrated that the proposed method is not sensitive to noise, and it can effectively identify single and multiple damage.

[1]  S. S. Law,et al.  Model error correction from truncated modal flexibility sensitivity and generic parameters. II: experimental verification , 2004 .

[2]  Guido De Roeck,et al.  STRUCTURAL DAMAGE IDENTIFICATION USING MODAL DATA. I: SIMULATION VERIFICATION , 2002 .

[3]  C. Lim,et al.  A generalized flexibility matrix based approach for structural damage detection , 2010 .

[4]  A. Tomaszewska.  Influence of statistical errors on damage detection based on structural flexibility and mode shape curvature , 2010 .

[5]  A. Emin Aktan,et al.  CONDITION AND DAMAGE ASSESSMENT: ISSUES AND SOME PROMISING INDICES , 2002 .

[6]  In-Won Lee,et al.  An efficient algebraic method for the computation of natural frequency and mode shape sensitivities—Part I. Distinct natural frequencies , 1997 .

[7]  Dionisio Bernal,et al.  Flexibility-Based Approach for Damage Characterization: Benchmark Application , 2004 .

[8]  Jun Zhao,et al.  Sensitivity Study for Vibrational Parameters Used in Damage Detection , 1999 .

[9]  Guirong Yan,et al.  Damage localization in ambient vibration by constructing proportional flexibility matrix , 2003 .

[10]  Norris Stubbs,et al.  Flexural damage index equations of a plate , 2005 .

[11]  D. Bernal.  Flexibility-Based Damage Localization from Stochastic Realization Results , 2006 .

[12]  S. S. Law,et al.  Model error correction from truncated modal flexibility sensitivity and generic parameters: Part I—simulation , 2004 .

[13]  Ahmet E. Aktan,et al.  Bridge-condition assessment by modal flexibility , 1994 .

[14]  Qiuhai Lu,et al.  MULTIPLE DAMAGE LOCATION WITH FLEXIBILITY CURVATURE AND RELATIVE FREQUENCY CHANGE FOR BEAM STRUCTURES , 2002 .

[15]  Ahmet E. Aktan,et al.  Application of Modal Flexibility and Its Derivatives in Structural Identification , 1998 .

[16]  Guido De Roeck,et al.  The Local Flexibility method for Vibration-based damage localization and quantification , 2008 .

[17]  Antonio Ruiz,et al.  An evolutionary multiobjective framework for structural damage localization and quantification , 2007 .

[18]  A. Emin Aktan,et al.  Use of Modal Flexibility for Damage Detection and Condition Assessment: Case Studies and Demonstrations on Large Structures , 2006 .

[19]  D. Bernal.  Load Vectors for Damage Localization , 2002 .

[20]  S. Law,et al.  Structural Damage Detection from Modal Strain Energy Change , 2000 .

[21]  A. K. Pandey,et al.  Damage Detection in Structures Using Changes in Flexibility , 1994 .

[22]  E. Peter Carden,et al.  Vibration Based Condition Monitoring: A Review , 2004 .

[23]  Mustafa Gul,et al.  Damage assessment using flexibility and flexibility-based curvature for structural health monitoring , 2008 .

[24]  Wei-Xin Ren,et al.  Damage detection by finite element model updating using modal flexibility residual , 2006 .

[25]  Charles R. Farrar,et al.  Damage identification and health monitoring of structural and mechanical systems from changes in their vibration characteristics: A literature review , 1996 .

[26]  Dionisio Bernal,et al.  Damage localization in output-only systems: A flexibility based approach , 2002 .

[27]  E. Parloo,et al.  SENSITIVITY-BASED OPERATIONAL MODE SHAPE NORMALISATION , 2002 .

[28]  Wang-Ji Yan,et al.  Statistic structural damage detection based on the closed-form of element modal strain energy sensitivity , 2012 .

[29]  Guido De Roeck,et al.  STRUCTURAL DAMAGE IDENTIFICATION USING MODAL DATA. II: TEST VERIFICATION , 2002 .

[30]  Q. W. Yang.  A mixed sensitivity method for structural damage detection , 2009 .

[31]  C. M. Mota Soares,et al.  Structural Damage Identification: A Survey , 2008 .

[32]  Billie F. Spencer,et al.  Experimental Verification of the Flexibility-Based Damage Locating Vector Method , 2007 .