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A multi-fidelity (MF) active learning method is presented for design optimization problems characterized by noisy evaluations of the performance metrics. Namely, a generalized MF surrogate model is used for design-space exploration, exploiting an arbitrary number of hierarchical fidelity levels, i.e., performance evaluations coming from different models, solvers, or discretizations, characterized by different accuracy. The method is intended to accurately predict the design performance while reducing the computational effort required by simulation-driven design (SDD) to achieve the global optimum. The overall MF prediction is evaluated as a low-fidelity trained surrogate corrected with the surrogates of the errors between consecutive fidelity levels. Surrogates are based on stochastic radial basis functions (SRBF) with least squares regression and in-the-loop optimization of hyperparameters to deal with noisy training data. The method adaptively queries new training data, selecting both the design points and the required fidelity level via an active learning approach. This is based on the lower confidence bounding method, which combines performance prediction and associated uncertainty to select the most promising design regions. The fidelity levels are selected considering the benefit-cost ratio associated with their use in the training. The method's performance is assessed and discussed using four analytical tests and three SDD problems based on computational fluid dynamics simulations, namely the shape optimization of a NACA hydrofoil, the DTMB 5415 destroyer, and a roll-on/roll-off passenger ferry. Fidelity levels are provided by both adaptive grid refinement and multi-grid resolution approaches. Under the assumption of a limited budget of function evaluations, the proposed MF method shows better performance in comparison with the model trained by high-fidelity evaluations only.