## 1 Introduction
developed a distribution-to-warping function regression model of the distributions of various channels based on the functional transformation technique [38]. DL-based methods, on the other hand, rely on a black-box model of the spatiotemporal correlation among multiple channels in the monitoring time series to reconstruct missing values and minimize reconstruction error. These methods include recurrent neural networks (RNN), denoising autoencoders, convolutional neural networks (CNN), and generative adversarial neural networks (GAN). For example, [PERSON] et al. developed a group sparsity-aware CNN model for continuous missing data imputation, where CNN is employed to generate the base matrix and optimize the group-sparsity reconstruction [36]. Although missing data imputation has been extensively studied for types (a) and (b) of missing data, type (c)--continuous missing of whole channels--has received little attention. Furthermore, current methods for missing data imputation are generally used solely for data pre-processing and normalization, providing no additional information for downstream tasks. Consequently, these methods are considered \"redundant\" in the context of downstream tasks [24]. To address this, there is a need to unify missing data imputation and downstream tasks within a single deep learning (DL) framework. This will enable the development of more effective and efficient approaches for handling missing data and can help improve the overall performance of downstream tasks. Therefore, in this paper, we propose a robust DL-based damage identification approach for SHM that considers missing data. We employ an autoencoder framework to learn the underlying relationship among monitoring data from different channels, extract hidden representations, and construct an encoder and decoder module using long short-term memory (LSTM). The data reconstruction error is utilized as the loss function and the damage indicator. During the training process, we randomly drop channels of the inputs to simulate missing data, and the LSTM-structured autoencoder model tries to reconstruct the data of all channels. We validated our proposed method using the SHM dataset for cable tension data, which was released in the 1 st IPC-SHM (International Project Competition for Structural Health Monitoring) [39]. This paper is organized as follows: Section 2 first introduces the basic modules, i.e., the dropout mechanism, the LSTM cell, and the autoencoder framework; thereafter, it proposes the model used in this paper that combines the basic modules. Section 3 then introduces the open-source dataset, the preprocessing procedure, and the implementation details of the proposed method. Section 4 discusses the results, including the proposed method and the conventional DNN model. Figure 1: Three types of missing data. This paper is organized as follows: Section 2 introduces the basic modules, including the dropout mechanism, LSTM cell, and autoencoder framework, and then proposes the combined model used in this study. In Section 3, we introduce the open-source dataset, the preprocessing procedure, implementation details, and the results of the proposed method. Section 4 is the conclusion. Section 5 contains the discussion and future directions.