## 5 Conclusions  
With their ability to automatically identify patterns and detect anomalies without requiring an explicit physical model of the structure, machine learning tools are instrumental in exploiting the full potential of SHM. Unsupervised approaches, which do not require labeled training data from various damage scenarios, are particularly crucial for civil engineering systems where collecting diverse damage data is difficult, if not impossible. With training data that can adequately capture variations in operational and environmental conditions at the baseline state, these methods allow for distinguishing damage-induced changes in sensor readings from those caused by such variations. Building on this machine-learning perspective, this paper presents a damage identification methodology implementing an AE trained on measured data from the baseline state of the structural system. As a highly suitable feature for output-only SHM applications, transmissibility calculated directly from the acceleration measurements is used as input to the AE to capture the healthy-system response and effectively characterize the structural  
Figure 13: Latent space features for transmissibility functions T\({}_{34}\) and T\({}_{56}\): (**a,c**) Low noise level (2–5%); (**b,d**) high noise level (10%). system's dynamic properties. The reconstruction errors generated by the trained model from the transmissibility input serve explicitly as the damage-sensitive feature in training the OC-SVM for damage classification. The trained AE processes input data from different structural states, producing reconstruction errors that are subsequently evaluated by the OC-SVM to determine whether there is damage. For the state detected as 'damaged', the proposed damage index is used to determine the location of the damage within the provided sensor resolution. The numerical investigations demonstrated the advantages of incorporating nonlinear encoding into dimensionality reduction by the improved reconstruction accuracy and robustness of the AE compared to a classical method of PCA. More specifically, while PCA provides a closed-form solution for projecting data onto a lower-dimensional subspace, preserving maximum variance, the AE introduces nonlinear transformations and learns the components indirectly through optimization that may be instrumental in enhancing the data representation. Experimental data from a masonry arch bridge model validated the proposed approach to detect and locate damage in an unsupervised manner using only a small set of training data to track the health state of the system. Since the proposed methodology does not require a finite element model but operates in a fully data-driven fashion, the localization performance is clearly limited with the resolution of sensor locations. The damage detection aspect of the proposed methodology is proven to be robust, even in the presence of noisy data. However, the accuracy of damage localization is highly dependent/more sensitive on precise sensor data. The reconstruction error, as a damage-sensitive feature, proves to be more consistent and reliable compared to the latent space features, which exhibit greater variability. Incorporating a one-class classification algorithm eliminates the need for a pre-determined threshold and offers flexibility and adaptability in detecting damage. More specifically, OC-SVM has been shown to handle varying data characteristics and noise levels effectively. In conclusion, the proposed unsupervised methodology requires only measured acceleration response signals from the structure. The only limitation of the technique is that it requires impact testing across multiple locations to generate a comprehensive set of TFs. However, with a model-free approach that can be employed in an unsupervised manner, this is a manageable trade-off. Recent advances in impact testing methodologies and mobile sensing systems that can navigate throughout the structure may help mitigate this limitation.