## 1 Introduction  
Civil infrastructures, including roads and bridges [1; 2; 3], buildings [4; 5; 6], dams [7; 8; 9], etc., are suffering from performance deterioration due to harsh environments, loadings, and even natural or man-made disasters. Structural health monitoring (SHM) is a critical technique that emerged in the past decades to detect and evaluate the condition of a structure in real-time [10; 11; 12]. The technique involves two critical aspects, namely'sensing' and 'data' [13]. While sensing techniques, including smart materials, sensor developments, and computer vision-based sensing techniques, have been greatly developed in these years [14; 15], data analysis and data mining for condition assessment remain bottleneck problems in SHM [13]. The use of SHM systems on in-service bridges results in the collection of big data, posing a significant challenge for efficient data analysis within the SHM community. This challenge has prompted research in the areas of pattern recognition (PR) and machine learning (ML). In 1999, [PERSON] first pointed out that vibration-based damage identification in SHM is a special issue of statistical pattern recognition (SPR), outlining four steps in the SPR paradigm: operational evaluation, data acquisition and cleansing, feature selection and data compression, and statistical model development [16]. Originating from the field of artificial intelligence (AI), ML has demonstrated significant potential in various fields and has become the most commonly used statistical model. Its primary goal is to recognize patterns hidden within vast amounts of data for high-dimensional, complex problems or systems. ML encompasses a wide range of algorithms, including random forests, support vector machines, heuristic and generic algorithms, and artificial neural networks. For instance, the recently developed heuristic algorithm, the beetle antennae search (BAS) algorithm, has emerged and has been utilized in many real-world optimization problems [17; 18; 19]. ML-based paradigms have become the most effective tool for tackling the big data challenge due to their ability to mine inherent patterns in data. Long-term ML practices have shown that the quality of feature selection directly affects the effectiveness of machine learning algorithms. Since deep learning (DL) was proposed in 2006 [20; 21; 22], the SHM community has progressed from developing sophisticated handcrafted features to using self-learning features with DL in an end-to-end approach [23; 24; 25; 26; 27]. DL can be seen as an unsupervised feature-learning method with deep layers [28]. Compared to manually handcrafted features, DL-based features can usually approximate more complex nonlinear correlation relationships and be more efficient. Despite the great successes achieved by data-driven methods in SHM, these approaches often assume ideal datasets and rarely consider the problem of missing data. Unfortunately, missing data is a frequently encountered problem in SHM and other real-world applications [29; 30; 31; 32; 33; 34; 35] due to the sensor fault, making the well-trained model highly unrobust. Generally, missing data in SHM can be divided into 3 types [36]: discrete missing at random time points, the continuous missing of continuous time points, and the continuous missing of the whole channel, as illustrated in Figure 1. Missing data introduces incomplete and non-standard data formats, thus affecting the data-driven methods for SHM. Missing data imputation is thus developed to estimate the missing values from the available data and impute the missing data to form the standard inputs of the data-driven model [37]. There are two main categories of methods: model-based and DL-based. Model-based methods typically utilize a regression or statistical model to reconstruct missing data by considering relationships among the available datasets. These methods include compressed sensing (CS), singular value decomposition (SVD), likelihood-based approaches, and k-nearest neighbor-based techniques. For instance, [PERSON] et al.