The voltage crossing limit problem is gradually highlighted and the stable operation of the system is becoming increasingly complex in the context of building a new distribution system. In this paper,based on the holomorphic embedding method,the offset characteristics of node voltage indicator trajectories under topology changes are studied,and a weak node identification method considering fault reconfiguration in distribution networks is proposed. Firstly,the node voltage index and distribution network voltage visible safety region are derived and constructed based on the idea of decoupling power system. Then,the node voltage index trajectory is solved based on the holomorphic embedding method. The concept of voltage index offset distance characterizing the trajectory characteristics is defined,and the probabilistic voltage index trajectory solution method is proposed taking into account the topology changes after the fault in distribution network. Finally,the weak node evaluation index system and identification method are proposed according to the relative position relationship between the voltage visible security region of distribution network and the node voltage index trajectory by considering the normal state and N-1+1 fault state operation conditions of the distribution network. Using the IEEE 33-node distribution system as an example for arithmetic analysis,the results show that the proposed method can realize the visual monitoring of the node voltage status and accurately identify the weak nodes.