DAMAGE AND MATERIAL IDENTIFICATION USING INVERSE ANALYSIS
In this thesis, we formulate novel solutions to two inverse problems using optical measurements as input data: i) local level damage identification of beams, and ii) material constitutive parameter identification using digital image correlation measurement of surface strain/displacements. A novel photogrammetric procedure based on edge-detection was devised to measure the quasi-continuous deflection of beams under given loading. This method is based on the close-range photogrammetry technique made possible through recent developments of image processing algorithms and modern digital cameras. Two computational procedures to reconstruct the stiffness distribution and to detect damage in Euler-Bernoulli beams are developed in this thesis. The first formulation is based on the principle of the equilibrium gap along with a finite element discretization. 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. The proposed identification methodology is validated using experimental data. The proposed methodology has the potential to be used for long term health monitoring and damage assessment of civil engineering structures. The identification of material plasticity parameters is carried out by minimizing a least-square functional measuring the gap between inhomogeneous displacement fields obtained from measurements and finite element simulations. The material parameters are identified simultaneously by means of direct, derivative-free optimization methods where the finite element simulation is treated as a black-box procedure. Methods verifying and validating the identified results are given. Particular interest is given to the identifiability issue in deterministic and statistical sense. The validation procedure intends to detect false positive results (type-II errors). The performance of the computational procedures is illustrated by numerical and experimental examples. The proposed approach avoids using the gradient of the cost function in the identification process; it has the benefit of allowing the use of any finite element code as a black box to solve the direct problem.