This work proposes a novel supervised learning approach to identify damage in operating bridge structures. We propose a method to introduce the effect of environmental and operational conditions into the synthetic damage scenarios employed for training a Deep Neural Network, which is applicable to large-scale complex structures. We apply a clustering technique based on Gaussian Mixtures to effectively select Q representative measurements from a long-term monitoring dataset. We employ these measurements as the target response to solve various Finite Element Model Updating problems before generating different damage scenarios. The synthetic and experimental measurements feed two Deep Neural Networks that assess the structural health condition in terms of damage severity and location. We demonstrate the applicability of the proposed method with a real full-scale case study: the Infante Dom Henrique bridge in Porto. A comparative study reveals that neglecting different environmental and operational conditions during training detracts the damage identification task. By contrast, our method provides successful results during a synthetic validation.