In this paper, a robust wireless sensor network configuration design method is proposed to develop the optimal configuration under the consideration of sensor failure and energy consumption. A malfunctioned sensor in a wireless sensor network may lead to data transmission failure of the entire sensing cluster, inducing severe deterioration in system identification performance. The proposed method determines a wireless sensor network configuration that is robust against sensor failure. By utilizing Bayesian inference, we introduce a robust indicator to evaluate the impact on estimation accuracy of sensor configurations with various malfunctioned sensors. Moreover, a network formation strategy is proposed to optimize the energy efficiency of the wireless sensor network configuration. Therefore, the resultant robust wireless sensor network configuration can operate with the minimum energy consumption while the measurement information of the sensor network with malfunctioned sensors can be guaranteed. The proposed method is illustrated by designing the robust wireless sensor network configurations of a truss model and a bridge model.