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Civil structures, infrastructures and lifelines are constantly threatened by natural hazards and climate change. Structural Health Monitoring (SHM) has therefore become an active field of research in view of online structural damage detection and long term maintenance planning. In this work, we propose a new SHM approach leveraging a deep Generative Adversarial Network (GAN), trained on synthetic time histories representing the structural responses of both damaged and undamaged multistory building to earthquake ground motion. In the prediction phase, the GAN generates plausible signals for different damage states, based only on undamaged recorded or simulated structural responses, thus without the need to rely upon real recordings linked to damaged conditions.