STATISTICAL DAMAGE ASSESSMENT OF FRAMED STRUCTURES FROM STATIC RESPONSES

This paper presents a damage assessment algorithm for framed structures based on a system identification scheme with a regularization technique. The regularization technique is introduced to alleviate the ill-posedness of the system identification problems. A new regularization function based on the Frobenius norm of the difference between the estimated and the baseline stiffness matrix is proposed. A parameter grouping technique is adopted to locate damaged members and to overcome sparseness of measured data. A data perturbation method is employed to obtain statistical distributions of system parameters with a set of noise-polluted measured data. A statistical approach by a hypothesis test is presented to assess damage. The validity of the proposed method is demonstrated through numerical examples.

[1]  Lawrence L. Kupper,et al.  Probability, statistics, and decision for civil engineers , 1970 .

[2]  S. P. Neuman,et al.  A statistical approach to the inverse problem of aquifer hydrology: 1. Theory , 1979 .

[3]  J. V. Beck,et al.  Combined function specification-regularization procedure for solution of inverse heat conduction problem , 1984 .

[4]  C. W. Groetsch,et al.  The theory of Tikhonov regularization for Fredholm equations of the first kind , 1984 .

[5]  Wilson H. Tang,et al.  Probability concepts in engineering planning and design , 1984 .

[6]  D. Schnur,et al.  Finite element solution of two‐dimensional inverse elastic problems using spatial smoothing , 1990 .

[7]  F. J. Soeiro,et al.  Structural damage detection based on static and modal analysis , 1989 .

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

[9]  Per Christian Hansen,et al.  Analysis of Discrete Ill-Posed Problems by Means of the L-Curve , 1992, SIAM Rev..

[10]  K. Hjelmstad,et al.  Parameter Estimation of Structures from Static Response. II: Numerical Simulation Studies , 1994 .

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

[12]  Huy Duong Bui,et al.  Inverse Problems in the Mechanics of Materials: An Introduction , 1994 .

[13]  Keith Hjelmstad,et al.  ON THE UNIQUENESS OF MODAL PARAMETER ESTIMATION , 1996 .

[14]  Keith D. Hjelmstad,et al.  Damage detection and assessment of structures from static response , 1997 .

[15]  H. Lee,et al.  A new spatial regularization scheme for the identification of the geometric shape of an inclusion in a finite body , 1999 .