The objective of this study is to improve the survivability and reliability of the FBG sensor network in the structural health monitoring (SHM) system. Therefore, a model reconstruction soft computing recognition algorithm based on support vector regression (SVR) is proposed to achieve the high reliability of the FBG sensor network, and the grid search algorithm is used to optimize the parameters of SVR model. Furthermore, in order to demonstrate the effectiveness of the proposed model reconstruction algorithm, a SHM system based on an eight-point fiber Bragg grating (FBG) sensor network is designed to monitor the foreign-object low velocity impact of a CFRP composite plate. Simultaneously, some sensors data are neglected to simulate different kinds of FBG sensor network failure modes, the predicting results are compared with non-reconstruction for the same failure mode. The comparative results indicate that the performance of the model reconstruction recognition algorithm based on SVR has more excellence than that of non-reconstruction, and the model reconstruction algorithm almost keeps the consistent predicting accuracy when no sensor, one sensor and two sensors are invalid in the FBG sensor network, thus the reliability is improved when there are FBG sensors are invalid in the structural health monitoring system.