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Deep learning models have been widely used in data-driven bridge structural damage diagnosis methods in recent years. However, these methods require training and test datasets to satisfy the same distribution, which is difficult to satisfy in practice. Domain adaptation transfer learning is an efficient method to solve this problem. Most of the current domain adaptation methods focus on close-set scenarios with the same classes in the source and target domains. However, in practical applications, new damage caused by long-term degradation often makes the target and source domains dissimilar in the class space. For such challenging open-set scenarios, existing domain adaptation methods will be powerless. To effectively solve the above problems, an adversarial auxiliary weighted subdomain adaptation algorithm is proposed for open-set scenarios. Adversarial learning is introduced to proposed an adversarial auxiliary weighting scheme to reflect the similarity of target samples with source classes. It effectively distinguishes unknown damage from known states. This paper further proposes a multi-channel multi-kernel weighted local maximum mean discrepancy metric (MCMK-WLMMD) to capture the fine-grained transferable information for conditional distribution alignment (sub-domain alignment). Extensive experiments on transfer tasks between three bridges verify the effectiveness of the algorithm in open-set scenarios.