Enhanced Structural Damage Detection Using Alternating Projection Methods

Alternating projection algorithms are examined for the solution of damage detection problems in structures. The damage detection problem is formulated as a feasibility problem to find a damaged stiffness matrix that is close to the refined stiffness matrix of the undamaged structure and that satisfies the necessary symmetry, sparsity, positive definiteness, eigenequation, and damage localization constraints. Alternating projection methods are proposed to utilize the orthogonal projections onto these constraint sets in an iterative fashion to find a solution that best satisfies these constraints. In addition, directional alternating projections that exploit the geometry of the damage detection feasibility problem are introduced to improve the computational efficiency of the approach. The techniques are applied to detect damage in a simulated cantilever beam model and in the NASA eight-bay truss damage detection experimental test bed.