## 1 Introduction  
Structural health monitoring (SHM) is a practical and essential process for assessing the structural integrity of structures to prevent damage from ageing, material deterioration, environmental behavior, poor construction, and natural disasters. The essential technique of structural health monitoring is structural damage detection. Many approaches for detecting damage have been proposed and implemented in recent years. Vibration-based damage detection is among the most productive approaches to detect structural deterioration in general [1]. Vibration-based damage detection approaches can be divided into physical model-based and data-based methods [2]. The measurement data obtained by sensors positioned on the monitored structure is the sole data source for data-based approaches. Data-based methods are more commonly used as structural monitoring tools because they account for the impacts of uncertainty on structural damage [3] and are computationally affordable. Recent advances in computation technology facilitate the development of more complex models for data-based methods by means of so-called deep learning [4], which is characterized by artificial neural networks with high numbers of layers. This allows learning complex non-linear mappings between inputs and outputs from data. These data-based methods can be trained through supervised or unsupervised learning. In recent years, supervised learning has been widely used in SHM. For example, [PERSON] et al. [5] applied the supervised learning method based on one-dimensional convolutional neural network (1D-CNN) to successfully verify the recognition performance of 1D-CNN under nine damage conditions. [PERSON] et al. [6] used the trained 1D-CNN to diagnose the damage status of structures. [PERSON] et al. [7] proposed a new analysis method of building a vulnerability framework based on machine learning and tested and verified the reliability of the established module through the rapid visual scanning support model. Although supervised learning has been found to improve damage detection accuracy, it requires a substantial amount of complete and diverse damage case data for training. Furthermore, manually labelling the enormous amount of data obtained is impractical. Certain researchers have employed finite element models to generate sufficient training data from various decision support systems [8]. However, it is difficult to simulate the environment's uncertainty and boundary conditions and the nonlinear relationship between the damage level and the variation level of the model properties. Therefore, unsupervised learning is the preferred method for damage detection [9]. Unsupervised learning has been popular in recent years for damage detection. [PERSON] et al. [10] suggested an unsupervised damage detection model for detecting damage in scenarios with environmental variables. This model uses Mahalanobis distance to distinguish different damage states, and performance is validated on laboratory-scale bridges exposed to various damage states. [PERSON] et al. [11] adopted an unsupervised clustering method based on Fuzzy c-means (FCM) and Gustafson-Kessel (GK) clustering algorithms to build a model using only data obtained from the entire structure. Damage to a three-layer bookshelf structure is detected using these well-trained models. The damage detection results reveal that all intact cases are classified better than damage cases. The GK algorithm's performance is superior to that of the FCM method in specific damage circumstances. [PERSON] et al. [12] extracted characteristics from pre-processed signals of whole states and another set of pre-processed signals of unknown states using Restricted Boltzmann Machines. The raw acceleration signal is processed using a simultaneous compressive wavelet transform and a Fast-Fourier transform. The collected features are then performed to analyze data states. The one-class support vector machine (OC-SVM) has been frequently employed in damage detection as an unsupervised machine learning method.