Damage location and estimation in large space structures

Abstract

This thesis presents a unique method of damage detection in large space structures. The goal is to develop an efficient algorithm which can be automated in an on-line format, and can asses damage in many elements. Theses are goals not realized by current methods. Damage incurred in a structural member is modeled as a linear reduction in that member's modulus of elasticity. The damaged structure's global stiffness matrix is expressed as the healthy global stiffness matrix minus some perturbation matrix. A vector expression of the perturbation matrix allows the percent reduction in damage to be solved for exactly in an equation involving the healthy truss model and a mode identified from the damaged structure. An algorithm for locating and estimating single-element damage is built around this equation. Simulations of the algorithm are performed on two planar truss models. The vector expression of the damage perturbation is shown to lead to a mode shape - strain energy relationship. From this, it is shown that a smaller truss model can be computed from element stiffness vectors. Damage can then be detected as existing among a small group of elements. Simulations show detection in one group to be independent from damage in other groups. From this information, a dimensionally expanded version of the single-element detection method can be used to exactly locate and estimate damage in many elements simultaneously. This process is presented as a sequential algorithm which meets all of the desired criteria.