# A Comparison of Deep Learning Algorithms for Anomaly Detection in Discrete Mechanical Systems  
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detection are based on supervised learning strategies, where data from both healthy and damaged conditions of the structure are used as training sets to compute a function able to map new data fed as input. However, the acquisition of the input exciting the structure is often prohibitive, leading to a lack of robustness and a failure to guarantee the convergence of the machine learning technique [13]. In addition, data from a damaged structure are challenging to obtain. For this reason, to overcome these limitations, convolutional autoencoders (CAEs) can be used to detect damage based only on raw vibrational data of the healthy structure [14; 15; 16]. [PERSON] et al. [17] showed that a one-dimensional CNN was useful for detecting anomalies in bridge vibration signals. [PERSON] et al. [18] demonstrated the capability of autoencoders based on a long short-term memory structure for detecting anomaly vibrations in a Vertical Carousel Storage and Retrieval System for industrial applications. [PERSON] et al. [19] assessed the structural condition of a viaduct by means of a sparse autoencoder that learned important data features (to characterize the vibration signals) and a support vector machine that classified the corresponding damage based on the extracted features. [PERSON] et al. improved fatigue life prediction through a combination of synthetic data and an ANN without requiring additional tests or new parameters by overcoming the limit of [PERSON]'s damage rule when taking into account different factors such as temperature, environment, sequence loads, and mean stress [20].  
Moreover, through the adoption of physics-informed neural networks (PINNs), it is possible to restrict the space of admissible solutions by considering the physical laws that govern the time-dependent dynamics of the structure [13; 21; 22]. [PERSON] et al. [23] introduced a novel approach to modeling the bearing fatigue life of wind turbines by incorporating both physics-based and data-driven components into the model. The authors proposed a recurrent neural network (RNN) that included a physics-informed layer to account for known factors affecting the bearing fatigue and a data-driven layer to describe more complex components, leading to a hybrid model that offered improved accuracy and predictive capabilities for assessing bearing fatigue in real-world applications.  
The primary motivation behind PINNs in anomaly detection is to overcome the high cost of acquiring abnormal data in physical systems and the substantial amount of data required for training NNs. With PINNs, the approach combines first principles (physical laws and equations) with neural networks, thereby reducing the search space for network parameters and lowering the need for vast amounts of training data. This compression of the parameter space gives PINNs a significant advantage over traditional NN approaches, making them an attractive option for anomaly detection and location [24].  
This paper presents a comparison of the results obtained from an unsupervised deep learning algorithm and a PINN for structural monitoring using only vibrational data acquired in the healthy state as the training set. Both the NNs are tested on a four-storey building using acceleration data from accelerometers placed on each floor. The aim of the paper is to demonstrate the improved capability of PINNs in detecting damage over conventional unsupervised neural networks. The paper is organized as follows: a description of the structure and the mathematical model are presented in Section 2, the experimental campaign is discussed in Section 3, the algorithm is described in Section 4, the results are presented in Section 5, and the conclusion and future research trends are discussed in the Section 6.