This paper addresses the problem of active learning for time-series modeling while considering safety constraints. The authors propose a method that dynamically explores the input space to generate informative input and output trajectories for learning a Gaussian Process (GP) model. The input trajectories are parametrized as consecutive sections, and the next section is determined stepwise based on maximizing information gain while ensuring safety. The safety aspect is incorporated into the exploration mechanism through a separate GP model that predicts safe input regions. The algorithm is evaluated on both synthetic and real-world technical applications, demonstrating its effectiveness in learning accurate time-series models while adhering to safety requirements. The main contributions include formulating an active learning setting for time-series modeling, integrating safety into the exploration mechanism, and providing theoretical analysis and empirical evaluations.This paper addresses the problem of active learning for time-series modeling while considering safety constraints. The authors propose a method that dynamically explores the input space to generate informative input and output trajectories for learning a Gaussian Process (GP) model. The input trajectories are parametrized as consecutive sections, and the next section is determined stepwise based on maximizing information gain while ensuring safety. The safety aspect is incorporated into the exploration mechanism through a separate GP model that predicts safe input regions. The algorithm is evaluated on both synthetic and real-world technical applications, demonstrating its effectiveness in learning accurate time-series models while adhering to safety requirements. The main contributions include formulating an active learning setting for time-series modeling, integrating safety into the exploration mechanism, and providing theoretical analysis and empirical evaluations.