Membership-set identification method for structural damage based on measured natural frequencies and static displacements

Based on measured natural frequencies and static displacements, an improved interval analysis technique is proposed for structural damage detection by adopting membership-set identification and two-step model updating procedures. Due to the scarcity of uncertain information, the uncertainties are considered as interval numbers in this article. Via the first-order Taylor series expansion, the interval bounds of the elemental stiffness parameters of undamaged and damaged structures are obtained. The structural damage is detected by the quantitative measure of the possibility of damage existence in elements, which is more reasonable than the probability of damage existence in the condition of less measurement data. In this study, the conversation of the interval analysis method is remarkably reduced by the membership-set identification technique. The present method is applied to a truss structure and a steel cantilever plate for damage identification, and the damage identification results obtained by the interval analysis method and probabilistic method are compared. This article also discusses the effects of damage level and uncertainty level on detection results. The numerical examples show that the wide intervals resulting from the interval operation can be narrowed by the proposed non-probabilistic approach, and the feasibility and applicability of the present method are validated.

[1]  J. Vehí,et al.  Structural assessment under uncertain parameters via interval analysis , 2008 .

[2]  L. D. Peterson,et al.  Health monitoring of aircraft structures using experimental flexibility matrices , 1996 .

[3]  Masoud Sanayei,et al.  STRUCTURAL ELEMENT STIFFNESS IDENTIFICATION FROM STATIC TEST DATA , 1991 .

[4]  Z. Qiu,et al.  Comparison of dynamic response of structures with uncertain-but-bounded parameters using non-probabilistic interval analysis method and probabilistic approach , 2003 .

[5]  S. Caddemi,et al.  The influence of instrumental errors on the static identification of damage parameters for elastic beams , 2006 .

[6]  Jon D. Collins,et al.  Statistical Identification of Structures , 1973 .

[7]  Xiaojun Wang,et al.  Modal analysis of structures with uncertain-but-bounded parameters via interval analysis , 2007 .

[8]  H. Lee,et al.  STATISTICAL DAMAGE ASSESSMENT OF FRAMED STRUCTURES FROM STATIC RESPONSES , 2000 .

[9]  Hong Hao,et al.  Damage identification of structures with uncertain frequency and mode shape data , 2002 .

[10]  Stefano Gabriele,et al.  An Interval Uncertainty Based Method for Damage Identification , 2007 .

[11]  Sergey A. Nazin,et al.  Interval parameter estimation under model uncertainty , 2005 .

[12]  Masoud Sanayei,et al.  Damage assessment of structures using static test data , 1991 .

[13]  Usik Lee,et al.  A structural damage identification method for plate structures , 2002 .

[14]  Masato Abe.  Structural damage detection by natural frequencies , 1996 .

[15]  E. Parloo,et al.  DAMAGE ASSESSMENT USING MODE SHAPE SENSITIVITIES , 2003 .

[16]  Christian Cremona,et al.  Assessment of vibration-based damage identification techniques , 2006 .

[17]  Robert D. Adams,et al.  The location of defects in structures from measurements of natural frequencies , 1979 .

[18]  Isaac Elishakoff,et al.  Three Versions of the Finite Element Method Based on Concepts of Either Stochasticity, Fuzziness, or Anti-Optimization , 1998 .

[19]  Arun Kumar Pandey,et al.  Damage detection from changes in curvature mode shapes , 1991 .

[20]  Asme,et al.  A collection of technical papers : 37th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference, April 15-17, 1996, Salt Lake City, UT , 1996 .

[21]  Hong Hao,et al.  Statistical damage identification of structures with frequency changes , 2003 .

[22]  K. Hjelmstad,et al.  Parameter Estimation of Structures from Static Response. I. Computational Aspects , 1994 .