Local damages to a structure will cause disproportional collapse if the system is lack of robustness.This structural safety cannot be guaranteed by traditional ways, such as reliability analysis tools and construction management approaches. Therefore, it is very important to develop related theories for structural robustness.This paper presents a methodology to quantitatively assess the structural robustness from the topological point of view. In the proposed method, the structural failure is viewed as a feedback process. The transformations between the damage input and failure output form a closed-loop. The decisive factor of the operation of such a closed-loop is thought as the structural topology. Furthermore, the damage input and the failure output of the structure are measured by the uncertain disturbance and the change of the topology, respectively. After the sensitivity of the structural topology to the uncertain disturbance is studied, the transfer matrix is discovered to indicate the rationality of the topological relationship. The importance of each loading path, the structural robustness and the most vulnerable part of the system can be found concisely in accordance with this matrix.
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