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Gathering properly labelled, adequately rich, and case-specific data for successfully training a data-driven or hybrid model for structural health monitoring (SHM) applications is a challenging task. We posit that a Transfer Learning (TL) method that utilizes available data in any relevant source domain and directly applies to the target domain through domain adaptation can provide substantial remedies to address this issue. Accordingly, we present a novel TL method that differentiates between the source's no-damage and damage cases and utilizes a domain adaptation (DA) technique. The DA module transfers the accumulated knowledge in contrasting no-damage and damage cases in the source domain to the target domain, given only the target's no-damage case. High-dimensional features allow employing signal processing domain knowledge to devise a generalizable DA approach. The Generative Adversarial Network (GAN) architecture is adopted for learning since its optimization process accommodates high-dimensional inputs in a zero-shot setting. At the same time, its training objective conforms seamlessly with the case of no-damage and damage data in SHM since its discriminator network differentiates between real (no damage) and fake (possibly unseen damage) data. An extensive set of experimental results demonstrates the method's success in transferring knowledge on differences between no-damage and damage cases across three strongly heterogeneous independent target structures. The area under the Receiver Operating Characteristics curves (Area Under the Curve - AUC) is used to evaluate the differentiation between no-damage and damage cases in the target domain, reaching values as high as 0.95. With no-damage and damage cases discerned from each other, zero-shot structural damage detection is carried out. The mean F1 scores for all damages in the three independent datasets are 0.978, 0.992, and 0.975.