For safely applying reinforcement learning algorithms on high-dimensional nonlinear dynamical systems, a simplified system model is used to formulate a safe reinforcement learning framework. Based on the simplified system model, a low-dimensional representation of the safe region is identified and is used to provide safety estimates for learning algorithms. However, finding a satisfying simplified system model for complex dynamical systems usually requires a considerable amount of effort. To overcome this limitation, we propose in this work a general data-driven approach that is able to efficiently learn a low-dimensional representation of the safe region. Through an online adaptation method, the low-dimensional representation is updated by using the feedback data such that more accurate safety estimates are obtained. The performance of the proposed approach for identifying the low-dimensional representation of the safe region is demonstrated with a quadcopter example. The results show that, compared to previous work, a more reliable and representative low-dimensional representation of the safe region is derived, which then extends the applicability of the safe reinforcement learning framework.