American Society of Civil Engineers


Damage Identification of Euler–Bernoulli Beams Using Static Responses


by Faouzi Ghrib, Ph.D., P.Eng., (corresponding author), (Associate Professor, Dept. of Civil and Environmental Engineering, Univ. of Windsor, 401 Sunset Ave., ON N9B 3P4, Canada. E-mail: fghrib@uwindsor.ca), Li Li, (Ph.D. Candidate, Dept. of Civil and Environmental Engineering, Univ. of Windsor, 401 Sunset Ave., ON N9B 3P4, Canada.), and Patricia Wilbur, (Dept. of Civil and Environmental Engineering, Univ. of Windsor, 401 Sunset Ave., ON N9B 3P4, Canada.)

Journal of Engineering Mechanics, Vol. 138, No. 5, May 2012, pp. 405-415, (doi:  http://dx.doi.org/10.1061/(ASCE)EM.1943-7889.0000345)

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Document type: Journal Paper
Abstract: The paper presents two computational procedures to reconstruct the stiffness distribution and to detect damage in Euler–Bernoulli beams. A novel methodology of damage identification is developed using static deflection measurements. The first formulation is based on the principle of the equilibrium gap along with a finite-element discretization, and leads to an overdeterminate linear system. The solution is obtained by minimizing a regularized functional using a Tikhonov total variation (TTV) scheme. The second proposed formulation is a minimization of a data-discrepancy functional between measured and model-based deflections. The optimal solution is obtained using a gradient-based minimization algorithm and the adjoint method to calculate the Jacobian. Also discussed is a simple procedure to measure the deflection of beams using a close-range photogrammetry technique. An edge detection-based algorithm is devised for quasi-continuous deflection measurement. The proposed identification methodology is validated using experimental data. Four beams with predefined damage scenarios are tested. In each case, the location and damage levels are reconstructed with good accuracy. However, results show that, in general, the equilibrium gap-based formulation has greater success than the data-discrepancy method. The proposed methodology has the potential to be used for long-term health monitoring and damage assessment of civil engineering structures.


ASCE Subject Headings:
Optimization
Damage
Beams
Stiffness
Finite element method

Author Keywords:
Equilibrium gap method
Adjoint optimization
Inverse problem
Damage identification
Finite-element model updating
Beam stiffness